US 20080221711 A1 Abstract An instrument for measuring the size distribution of a particle sample by counting and classifying particles into selected size ranges. The particle concentration is reduced to the level where the probability of measuring scattering from multiple particles at one time is reduced to an acceptable level. A light beam is focused or collimated through a sample cell, through which the particles flow. As each particle passes through the beam, it scatters, absorbs, and transmits different amounts of the light, depending upon the particle size. So both the decrease in the beam intensity, due to light removal by the particle, and increase of light, scattered by the particle, may be used to determine the particle size, to classify the particle and count it in a certain size range. If all of the particles pass through a single beam, then many small particles must be counted for each large one because typical distributions are uniform on a particle volume basis, and the number distribution is related to the volume distribution by the particle diameter cubed.
Claims(14) 1. Apparatus for optimizing path length of a light beam through a particle dispersion to improve accuracy of measurement of light scattered from particles, comprising:
a) an optical system for illuminating a particle dispersion, b) a detection system comprising at least one detector for quantifying light scattered by at least one of said particles, c) a sample cell, comprising two optical windows, which confine said particle dispersion and pass light, from a light source, through said particle dispersion to produce light scattered by said particle dispersion, and d) means for adjusting a separation between said optical windows to change a path length of light, from said light source, through said sample cell. 2. The apparatus of 3. The apparatus of 4. The apparatus of 5. The apparatus of 6. The apparatus of 7. The apparatus of 8. A method for determining an optimum path length of a light beam passing through a particle dispersion, so as to reduce inaccuracies in particle analysis caused by multiple scattering of light from particles, the method comprising the steps of:
a) determining a specified value of a path length which produces excessive multiple scattering, b) adjusting said path length to a specified value, c) measuring first scattered light values at said specified value of path length, d) reducing said path length to a second value, e) measuring second scattered light values at said second value of said path length, f) determining a difference between said second scattered light values and said first scattered light values, g) if said difference is greater than a specified limit, repeating steps (b) through (f), while setting said specified value of path length, in step (b), to said second value of said path length, h) if said difference is less than a specified limit, using said second scattered light values to determine particle characteristics. 9. The method of 10. The method of 11. A method for determining an optimum path length of a light beam passing through a particle dispersion, so as to reduce inaccuracies in particle analysis caused by scattering measurement errors, the method comprising the steps of:
a) adjusting a path length to a specified value, b) measuring scattered light values at said specified value of said path length, c) calculating an optimum value of path length based upon said specified value of said path length and said scattered light values, d) adjusting said path length to said optimum value of path length, e) measuring scattered light values at said optimum value of path length and using scattered light values to determine particle characteristics. 12. The method of 13. Apparatus for measuring scattered light from individual particles which are nearly confined to a plane on a surface or in a thin layer of a dispersant, comprising:
a) an optical system for illuminating said particles, b) a detection system comprising at least one detector for quantifying light scattered from a specific region on said plane, and c) mechanical means for moving an interaction volume of said optical system and detection system to various locations on said plane to measure separately light scattered at each location. 14. Apparatus for removing angular drift in a system for analyzing particles, comprising:
a) an optical system for illuminating a particle dispersion, b) a detection system comprising at least one detector for quantifying light scattered by at least one particle, and c) a sample cell, comprising two optical windows, wherein the windows confine the particle dispersion and pass light, from a light source, through said particle dispersion to produce light scattered by said particle dispersion, wherein said optical system and detection system are attached to a first side of said sample cell, and wherein the apparatus includes a retroreflector positioned in a vicinity of a second side of said sample cell, wherein the retroreflector comprises means for removing angular drift of a light beam caused by drift in position, or drift in optical properties, of said optical system, said sample cell, and/or said detection system. Description This is a continuation of U.S. patent application Ser. No. 11/538,669, filed Oct. 4, 2006, which is a continuation-in-part of U.S. patent application Ser. No. 10/598,443, filed Aug. 30, 2006, which is a U.S. national phase of PCT/US2005/07308, which claims the priority of U.S. provisional application Ser. No. 60/550,591, filed Mar. 6, 2004. Priority is also claimed from U.S. provisional application Ser. No. 60/723,639, filed Oct. 5, 2005. This invention relates to systems and methods for analyzing particles in a sample using laser light diffraction. More particularly, the present invention relates to systems and methods that analyze laser light diffraction patterns to determine the size of particles in a sample. The present invention comprises apparatus for optimizing path length of a light beam through a particle dispersion to improve accuracy of measurement of light scattered from particles, comprising: a) an optical system for illuminating a particle dispersion, b) a detection system comprising at least one detector for quantifying light scattered by at least one of said particles, c) a sample cell, comprising two optical windows, which confine said particle dispersion and pass light, from a light source, through said particle dispersion to produce light scattered by said particle dispersion, and d) means for adjusting a separation between said optical windows to change a path length of light, from said light source, through said sample cell. The invention also comprises a method for determining an optimum path length of a light beam passing through a particle dispersion, so as to reduce inaccuracies in particle analysis caused by multiple scattering of light from particles, the method comprising the steps of: a) determining a specified value of a path length which produces excessive multiple scattering, b) adjusting said path length to a specified value, c) measuring first scattered light values at said specified value of path length, d) reducing said path length to a second value, e) measuring second scattered light values at said second value of said path length, f) determining a difference between said second scattered light values and said first scattered light values, g) if said difference is greater than a specified limit, repeating steps (b) through (f), while setting said specified value of path length, in step (b), to said second value of said path length, h) if said difference is less than a specified limit, using said second scattered light values to determine particle characteristics. The invention also comprises a method for determining an optimum path length of a light beam passing through a particle dispersion, so as to reduce inaccuracies in particle analysis caused by scattering measurement errors, the method comprising the steps of: a) adjusting a path length to a specified value, b) measuring scattered light values at said specified value of said path length, c) calculating an optimum value of path length based upon said specified value of said path length and said scattered light values, d) adjusting said path length to said optimum value of path length, e) measuring scattered light values at said optimum value of path length and using scattered light values to determine particle characteristics. The invention also comprises apparatus for measuring scattered light from individual particles which are nearly confined to a plane on a surface or in a thin layer of a dispersant, comprising: a) an optical system for illuminating said particles, b) a detection system comprising at least one detector for quantifying light scattered from a specific region on said plane, and c) mechanical means for moving an interaction volume of said optical system and detection system to various locations on said plane to measure separately light scattered at each location. The invention also comprises apparatus for removing angular drift in a system for analyzing particles, comprising: a) an optical system for illuminating a particle dispersion, b) a detection system comprising at least one detector for quantifying light scattered by at least one particle, and c) a sample cell, comprising two optical windows, wherein the windows confine the particle dispersion and pass light, from a light source, through said particle dispersion to produce light scattered by said particle dispersion, wherein said optical system and detection system are attached to a first side of said sample cell, and wherein the apparatus includes a retroreflector positioned in a vicinity of a second side of said sample cell, wherein the retroreflector comprises means for removing angular drift of a light beam caused by drift in position, or drift in optical properties, of said optical system, said sample cell, and/or said detection system. This application describes an instrument for measuring the size distribution of a particle sample by counting and classifying particles into selected size ranges. The particle concentration is reduced to the level where the probability of measuring scattering from multiple particles at one time is reduced to an acceptable level. A light beam is focused or collimated through a sample cell, through which the particles flow. As each particle passes through the beam, it scatters, absorbs, and transmits different amounts of the light, depending upon the particle size. So both the decrease in the beam intensity, due to light removal by the particle, and increase of light, scattered by the particle, may be used to determine the particle size, to classify the particle and count it in a certain size range. If all of the particles pass through a single beam, then many small particles must be counted for each large one because typical distributions are uniform on a particle volume basis, and the number distribution is related to the volume distribution by the particle diameter cubed. This large range of counts and the Poisson statistics of the counting process limit the size dynamic range for a single measurement. For example, a uniform particle volume vs. size distribution between 1 and 10 microns requires that one thousand 1 micron particles be measured for each 10 micron particle. The Poisson counting statistics require 10000 particles to be counted to obtain 1% reproducibility in the count. Hence one needs to measure more than 10 million particles. At the typical rate of 10,000 particles per second, this would require more than 1000 seconds for the measurement. In order to reduce the statistical count uncertainties, large counts of small particles must be measured for each large particle. This problem may be eliminated by flowing portions of the sample flow through light beams of various diameters, so that larger beams can count large count levels of large particles while small diameter beams count smaller particles without the small particle coincidence counts of the large beam. Accurate particle size distributions are obtained by using multiple beams of ever decreasing spot size to improve the dynamic range of the count. The count vs. size distributions from each beam are scaled to each other using overlapping size ranges between different pairs of beams in the group, and the count distributions from all of the beams are then combined. Light scattered from the large diameter beam should be measured at low scattering angles to sense large particles. The optical pathlength of this beam in the particle sample must be large enough to pass the largest particle of interest for that beam. For small particles, the interaction volume in the beam must be reduced along all three spatial directions. The beam crossection is reduced by an aperture or by focusing the beam into the interaction volume. The interaction volume is the intersection of the particle dispersion volume, the incident light beam, and viewing volume of the detector system. When the particle dispersion volume is much larger than the light beam and detector viewing volume, the interaction volume is the intersection of the incident light beam and the field of view for the detector which measures scattered light from the particle. However, for very small particles, reduction of the optical path along the beam propagation direction is limited by the gap thickness through which the sample must flow. This could be accomplished by using a cell with various pathlengths or a cell with a wedge shaped window spacing (see Three problems associated with measuring very small particles are scattering signal dynamic range, particle composition dependence, and Mie resonances. The low angle scattered intensity per particle changes by almost 6 orders of magnitude between 0.1 and 1 micron particle diameter. Below approximately 0.4 micron, photon multiplier tubes (PMT) are needed to measure the minute scattered light signals. Also the scattered intensity can change by a factor of 10 between particles of refractive index 1.5 to 1.7. However, the shape of the scattering function (as opposed to the amplitude) vs. scattering angle is a clear indicator of particle size, with very little refractive index sensitivity. This invention proposes measurement of multiple scattering angles to determine the size of each individual particle, with low sensitivity to particle composition and scattering intensity. Since multiple angle detection is difficult to accomplish with bulky PMT's, this invention also proposes the use of silicon photodiodes and heterodyne detection, in some cases, to measure low scattered signals from particles below 1 micron. However, the use of any type of detector and coherent or non-coherent detection are claimed. Spherical particles with low absorption will produce a transmitted light component which interferes with light diffracted by the particle. This interference causes oscillations in the scattering intensity as a function of particle size. The best method of reducing these oscillations is to measure scattering from a white light or broad band source, such as an LED. The interference resonances at multiple wavelengths are out of phase with each other, washing out the resonance effects. But for small particles, one needs a high intensity source, eliminating broad band sources from consideration. The resonances primarily occur above 1.5 micron particle diameter, where the scattering crossection is sufficient for the lower intensity of broadband sources. So the overall concept may use laser sources and multiple scattering angles for particles below approximately 1 micron, and broad band sources with low angle scattering or total scattering for particle size from approximately 1 micron up to thousands of microns. We will start with the small particle detection system. Lens For particles above approximately 0.4 microns, signals from all 4 detectors will have sufficient signal to noise to provide accurate particle size determination. The theoretical values for these 4 detectors vs. particle size may be placed in a lookup table. The 4 detector values from a measured unknown particle are compared against this table to find the two closest where S The true size is then determined by interpolation between these two best data sets based upon interpolation in 4 dimensional space. The size could also be determined by using search algorithms, which would find the particle size which minimizes the least square error while searching over the 4 dimensional space of the 4 detector signals. For particles of size below some empirically determined size (possibly around 0.4 micron), detector By tracing rays back from slits The data for each particle would be compared to a group of theoretical data sets. Using some selection routine, such as total RMS difference, the two nearest size successive theoretical sets which bracket either side of the measured set would be chosen. Then the measured set would be used to interpolate the particle size between the two chosen theoretical sets to determine the size. The size determination is made very quickly (unlike an iterative algorithm) so as to keep up with the large number of data sets produced by thousands of particles passing through the sample cell. In this way each particle could be individually sized and counted according to its size to produce a number-vs.-size distribution which can be converted to any other distribution form. These theoretical data sets could be generated for various particle refractive indices and particle shapes. In general, a set of design rules may be created for the intersection of fields of view from multiple scattering detectors at various angles. Let us define a coordinate system for the incident light beam with the z axis along the direction of propagation and the x axis and y axis are both perpendicular to the z axis, with the x axis in the scattering plane and the y axis perpendicular to the scattering plane. The scattering plane is the plane which includes the source beam axis and the axis of the scattered light ray. In most cases the detector slits are oriented parallel to the y direction. Many configurations are possible, including three different configurations which are listed below: - 1) The incident beam is smaller than the high scattering angle detector field crossection, which is smaller than the low scattering angle detector field crossection. Only particle pulses that are coincident with the high angle detector pulses are accepted. The incident beam may be spatially filtered (
FIG. 1A ) in the y direction, with the filter aperture imaged into the interaction volume. This aperture will cut off the Gaussian wings of the intensity profile in the y direction, providing a more abrupt drop in intensity. Then fewer small particles, which pass through the tail of the intensity distribution, will be lost in the detection noise and both large and small particles will see the same effective interaction volume. - 2) The incident beam is larger than the low scattering angle detector field crossection, which is larger than the high scattering angle detector field crossection. Only particle pulses that are coincident with the high angle detector pulses are accepted. The correlation coefficient of the pulses or the delay (determined by cross correlation) between pulses is used to insure that only pulses from particles seen by every detector are counted.
- 3) The incident beam width and all fields from individual detectors progress from small to large size. Then particles counted by the entity with the smallest interaction volume will be sensed by all of the rest of the detectors. Only particles sensed by the smallest interaction volume entity will be counted, because this smallest interaction volume will be contained in all of the interaction volumes for the other detectors, which will also see this particle. For example, if the progression from smallest to largest interaction volume is low angle to high angle, then only events with a low angle scattering pulse will be accepted.
- 4) In all cases, the slits could be replaced by rectangular apertures, which would remove spurious scattering and source light components which are far from the interaction volume.
When the beam is larger than the detector fields of view, good intensity uniformity is obtained in the interaction volume. However, then many signal pulses, which are not common to all detector fields of view, will be detected and must be eliminated from the count by the methods described in this application. When the beam is smaller than the fields of view, the intensity uniformity is poor, but fewer signal pulses are detected outside of the common volume of the detector fields. Also the higher source intensity of the smaller beam provides higher signal to noise for the scattered light pulses. In this case, the detector intensity variation can be corrected for by deconvolution methods described later or reduced by aperture ( In most cases the divergence of the laser beam should be minimized in the scatter plane to allow detection of particle scatter at low scattering angles. Then the laser spot should be wider in the x direction, and the major axis of the source rectangular aperture ( The two detector pairs, 1+2 and 3+4, could also be used independently to measure count vs. size distributions. The lower angle pair could only measure down to the size where the ratio of their angles is no longer sensitive to size and the scattering crossections are too small to maintain signal to noise. Likewise for the high angle detectors, they can only measure up to sizes where their ratio is no longer monotonic with particle size. However, absolute scattered signal levels could be used to determine the particle size outside of this size region. Since extremes of these operational ranges overlap on the size scale, the two pairs could be aligned and operated independently. The small angle detectors would miss some small particles and the high angle detectors would miss some large particles. But the two independently acquired particle size distributions could be combined using their particle size distributions in the size region where they overlap. Scale one distribution to match the other in the overlap region and then use the distribution below the overlap from the high angle detectors for below the overlap region and the distribution from the low angle detectors for the distribution above the overlap region. In the overlap region, the distribution starts with the high angle result and blends towards the low angle result as you increase particle size. Detector triplets could also be used, where the largest angle of the low angle set and the lowest angle of the high angle set overlap so as to scale the scattering measurements to each other. In some cases, the angular range of each of the heterodyne detectors must be limited by the considerations described later (see The flat window surfaces could be replaced by spherical surfaces (see The detector currents from the low angle system and the high angle system must be processed differently. Every particle passing through the interaction volume will produce a pulse in the detector current. Detectors For small particles the heterodyne signals will be buried in laser source noise. where: K is a constant which includes the product of the reflectivities of the beamsplitter R Io(t) is the source beam intensity as function of time t
where S is the scattering efficiency or scattering crossection for the particle The light source intensity will consist of a constant portion Ioc and noise n(t): We may then rewrite equations for I The heterodyne beat from a particle traveling with nearly constant velocity down the sample cell will cover a very narrow spectral range with high frequency F. For example, at 1 meter per second flow rate, the beat frequency would be in the megahertz range. If we use narrow band filters to only accept the narrow range of beat frequencies we obtain the narrow band components for I where we have assumed that n(t) is much smaller than Ioc. And also n(t) is the portion of the laser noise that is within the electronic narrowband filter bandwidth (see below). The laser noise can be removed to produce the pure heterodyne signal, Idiff, through the following relationship: This relationship is realized by narrowband filtering of each of the I The particle dispersion flow rate could also be adjusted to maximize the heterodyne signal, through the electronic narrowband filter, by matching the Doppler frequency from flowing particle scattered light with the center of the filter bandpass. This entire correction could also be accomplished in the computer by using a separate A/D for each filtered signal and generating the difference signal by digital computation inside the computer. The phase and gain adjustments mentioned above, without particles in the beam, could be adjusted digitally. Also these gain adjustments could also be determined from measurement of the signal offsets I Where I If both signals were digitized separately, other correlation techniques could be used to reduce the effects of source intensity noise. Beamsplitter The noise correction techniques described on the prior pages (and In this case, the heterodyne signal is the sum of many COS functions with various frequencies and phases. The noise, common to both the heterodyne signal and incident light source intensity, will still be completely removed in Idiff. In the case of fiber optic heterodyning systems, the laser monitor current, I One other aspect of this invention is a means for auto-alignment of the optics. Auto alignment is needed to correct for changes in beam direction and focus due to changes of dispersant refractive index and mechanical drift of optical components. Auto-alignment could be done periodically by the computer or whenever a new particle sample or new dispersing fluid is introduced to the system. These techniques can be used to auto-align any of the apertures, in this application, which are in an image plane of the particle, such as apertures - 1) With low concentration of particles in the flow stream, adjust the position of slit
**611**to maximize the correlation (using an analog multiplier and RMS circuit) between the signals from detectors**603**and**604**. At this point the intersection of the fields of views of both detectors cross at the incident beam and the signals are maximum. - 2) Then adjust the position of slit
**610**until the correlation of detectors**601**and**602**with detectors**603**and**604**is a maximum. After this adjustment both detectors**601**and**602**view the intersection defined by step 1.
During particle counting and measurement, only particles seen by both detectors The pulses shown in The particle counting rate can also be increased by digitizing the peak scattered signal (directly from detectors Another variation of this concept triggers on the actual signal instead of the derivative, as shown in In most cases, the detector signals are either digitized directly, peak detected with the circuit in where I This analysis is usually done for the detector with the smallest interaction volume, the heterodyne system in the case of The shape and width of the S(a The method described above handles the variations caused by the particle passing through various random paths in the interaction volume. This method can also correct for the variations due to random positions along the path where the digitization occurs. Therefore the peak detectors or integrators could be eliminated. The signal from the envelope detector (detectors Also all the signals could be digitized directly after the high pass (or narrow band) filter on the detectors (detectors All of the optical design and algorithm techniques described in this disclosure may leave some residual size response broadening which may be particle size dependent. This instrument response broadening is determined by measuring a nearly mono-sized particle sample (such as polystyrene spheres). For example, due to noise or position dependence in the beam, a certain size particle will produce a range of S(a
Where Nm is the vector of values of the measured (broadened) number-vs.-measured parameter distribution and N is the vector of values of the actual particle number-vs.-size distribution which would have been measured if the broadening mechanisms were not present. “*” is a matrix vector multiply. The number distribution is the number of particles counted with parameter amplitudes within certain ranges. It is a differential distribution which describes counts in different channels or bins, each bin with a different range of parameter, which may be size, scattering ratio, etc. M is a matrix of column vectors with values of the broadened number-vs.-measured parameter function for each particle size in N. For example, the nth column of M is a vector of values of the entire measured number-.vs.-measured parameter distribution obtained from a large ensemble of particles of the size which is represented by the nth element of vector N. This matrix equation can be solved for the particle number-vs.-size distribution, N, by matrix inversion of M or by iterative inversion of the matrix equation. This particle number-vs.-size distribution can be determined by using this matrix equation in many different forms. The term “measured parameter” in this paragraph can refer to many size dependent parameters including: scattering signal amplitude (pulse peak or integral, etc.), the ratio (or other appropriate mathematical relationship) between scattered signals at two or more different angles, or even particle diameter (a broadened particle size distribution determined directly from a broadened process can also be “unbroadened” by using broadened particle size distributions for each monosized sample column in matrix M). So we solve for N, given Nm and M. If each column of M is simply a shifted version of the prior column, then the instrument response is shift invariant and the relationship is a convolution of N with the system impulse response IMP:
where ** is the convolution operator For this case, deconvolution algorithms may be used to solve for N, given Nm and IMP. The generalized matrix equation above may also include the effects of coincidence counting. As discussed earlier, over one million particles should be counted for a uniform volume distribution to be accurately determined in the large particle region. In order to insure low coincidence counts, the source spot size in the interaction region might be reduced to approximately 20 microns in width so that the particle concentration can be raised to count 1 million particles at flow rates of 1 meter per second in a reasonable time. For example, the worst case is slit The correction for coincidences may also be accomplished by an iterative procedure, which solves for N, given Nm, and then corrects each scattered signal for coincidences. Each scattered signal, S where SUMj means summation over the j index. Ai is the “particle signal” for a particle of the ith size bin in the particle size distribution. Particle signals can include S In the case of signals S(a - 1) Use the surface plot of
FIGS. 10 and 10 *a*to determine the raw number distribution Nm. - 2) Solve the matrix equation Nm=M*N for the true number distribution N.
- 3) Recalculate S(a
**1**) and S(a**2**) using the equation above and the distribution N:
- 4) Do steps 1 through 3 again
- 5) repeat iteration loop of step 4 until the change in number distribution N between successive loops is below some threshold.
For particles between approximately 1 and 10 microns, the ratio of scattered intensities at two angles below approximately 3 degrees scattering angle is optimal to provide highest size sensitivity and accuracy. A white light source or broad band LED should be used to reduce the Mie resonances for spherical particles. Above 10 microns, the measurement of total scatter from a white light source provides the best size sensitivity and depth of focus for a spatially filtered imaging system as shown in The 2-dimensional detector array is imaged into the center of the sample cell with magnification corresponding to approximately 10×10 micron per array pixel in the sample cell plane. A 10 micron particle will produce a single dark pixel if it is centered on one pixel or otherwise partially darkened adjacent pixels. By summing the total light lost in these adjacent pixels, the total light absorbed or scattered outside of pinhole This detector array system has an enormous particle size dynamic range. The particle will remove approximately the light captured by twice its crossectional area. So a 2 micron particle will reduce the total light flux on a 10×10 micron pixel by 8 percent. But the entire array of 1000×1000 pixels can cover a crossection of 10×10 millimeters. So the size range can cover 2 microns to 10000 microns. The size dynamic range is almost 4 orders of magnitude. The smallest particles are detected by their total light scattering and absorption. For very large particles, the angular extent of the scattering pattern may fall within the aperture of pinhole In order to avoid smeared images, the detector array must integrate the current from each pixel over a short time to reduce the distance traveled by the particle dispersion flow during the exposure. This may also be accomplished by pulsing the light source to reduce the exposure time. Smearing in the image can be corrected for using deconvolution techniques. But the scattering extinction measurements will be accurate as long as each contiguous pixel group does not smear into another contiguous pixel group. Add up all of contiguous pixel signals (from the smeared image of the particle) after presence of the particle to determine the particle scattering attenuation and size. If the particle image is smaller than one pixel, then the attenuation of that pixel is the scattering extinction for that particle. Essentially, you are measuring nearly the total amount of light scattered or absorbed by the particle during the exposure. Using this total lost optical flux divided by the incident intensity provides the scattering crossection for the particle, even if the particle is not resolved by the optical system or if that loss is distributed over more pixels than expected from perfect imaging of the particle. This is the power of this technique. The size accuracy is not limited by the image resolution. A 10 mm by 10 mm detector array, with 10×10 micron pixels, can measure particle diameters from a few microns up to 10 mm, with thousands of particles in the source beam at one time. The 10 mm particles will be sized directly by adding up pixels and multiplying the interior pixels by 1 and the edge pixels by their fractional attenuation and adding all of the pixels up to get the total crossectional area and size. A 5 micron particle, centered on one 10×10 micron pixel, will attenuate that pixel by 50% (the total scattering extinction crossection is approximately twice the actual particle area, outside of the Mie resonance region). In both cases the particles are easily measured. You are adding up all of the signal differences (signal without particle—signal with particle) of contiguous changed pixels to get the total light lost due the particle. Pinhole Image smearing could also be reduced by using pulsed flow. The particle sample flow would stop during the period when the light source is pulsed or when the detector array is integrating. Then a flow pulse would push the next slug of sample into the detector array field of view before the next signal collection period. The sample would be approximately stationary during the signal collection on the detector array. This pulsing could be accomplished by pressurizing the particle dispersion chamber and using a pulsed valve to leave short segments of the sample dispersion through the source beam interaction volume. The nearly parallel window cell could also be replaced by a wedge shaped cell which would control the particle count in different size regions, as discussed above (see Non-spherical particles present another problem for single particle sizing: non-symmetrical scattering patterns. Assume that the incident light beam is propagating along the Z direction and the XY plane is perpendicular to the Z direction, with origin at the particle. The XZ plane is the center scattering plane of the group of scattering planes which are intercepted by detectors The particle concentration must be optimized to provide the largest count levels while still insuring single particle counting. The concentration may be optimized by computer control of particle injection into the flow loop which contains the sample cell, as shown in Another consideration for The system shown in The optical source used with the detector arrays in One problem with the techniques described above is coincidence counting. The cell path must be large to pass the largest anticipated particle (except for the wedge cell shown in The signal frequency for each particle signal pulse could also be determined individually by either the timing of zero crossings or by using a phase locked loop, avoiding the power spectrum calculation. Each particle pulse will consist of a train of oscillations which are modulated by the intensity profile through that particular mask region. The oscillation amplitude and frequency provide the scattering amplitude and settling velocity, respectively, for that particle. The size can be determined from the settling velocity, if the particle density and fluid viscosity are known, or the size can be determined from the ratio of amplitudes from two different scattering angles (or angular ranges), or the amplitude at one scattering angle (or angular range) (but with possible higher sensitivity to particle composition). The particle density or fluid viscosity can be determined by combination of the scattering amplitudes and the signal oscillation frequency. Mask All slit apertures in this disclosure (for example, slit If the signal to noise is sufficient for non-coherent detection with any detector in The progression of crossectional size, in the interaction volume, from smallest to largest is: light source, fields of view from detectors The particles being measured by system in - 1) scattered light amplitude normalized to the maximum scattered light amplitude measured over all the particles of the same size at that scattering angle.
- 2) Pulse width at certain fraction of pulse peak level
- 3) delay between pulses from two different detectors
- 4) correlation between pulses from two different detectors
Any of these parameters can be used to define a threshold for counting particles as shown in In the sample cell with flat windows, many of the incident source beams and scattered light rays are at high angles of incidence on the sample cell windows. The interior surface of the window is in contact with a liquid which reduces the Fresnel reflection at that surface. However, the exterior surface is in air which can cause an enormous Fresnel reflection at these high incident angles. This reflection can be reduced by anti-reflection coating the exterior surface, but with high cost. A better solution is to attach prisms (see Another configuration for the sample cell is a cylindrical tube. The particle dispersion would flow through the tube and the scattering plane would be nearly perpendicular to the tube axis and flow direction. In this case, the beam focus and detector fields of view would remain coincident in the scattering plane for various dispersant refractive indices and only inexpensive antireflection coatings are needed. However, since the flow is perpendicular to the scattering plane, the heterodyne oscillations cannot be produced by the particle motion. The optical phase modulation mirror in the local oscillator arm (called “mirror”) in Any of the measurement techniques described can be used individually or in combination to cover various particle size ranges. Examples of possible combinations are listed below: For particle diameter 0.05-0.5 microns use Use heterodyne detection (if needed). Take ratio of the detector signals. For particle diameter 0.4-1.2 microns use Use heterodyne detection (if needed). Take ratio of the detector signals. All 4 signals can also be used together for the range 0.05 to 1.2 microns, using a 4 parameter function or lookup tables. Many choices for scattering angles will provide high sensitivity to size in certain size ranges. These include the following examples of ratios of signals for various particle size ranges: 75 degree/10 degree for 0.05 to 0.5 micron particles, 10 degree/1 degree for 2 to 15 micron particles, 2 degree/1 degree for 0.5 to 4 micron particles, 10 degree/2 degree for 1 to 5 micron particles, 25 degree/15 degree for 0.4 to 1.4 micron particles, 10 to 20 degrees/5 to 8 degrees for 0.05 to 1.6 micron particles, 25 to 50 degrees/5 to 8 degrees for 0.3 to 0.7 micron particles. Any single angle specification assumes that scattered light is collected in some angular range which is centered on that angle and does not have extensive overlap with the angular range of the other angle in the ratio. These angle pairs could also be used separately to determine particle size, based upon absolute amplitude (instead of ratio) and using look up tables, simultaneous equations, or the 2-dimensional analysis shown later (see Use the detector with the smallest interaction volume to trigger data collection. These angles are only representative of general ranges. Almost any combination of angles will provide sensitivity to size over a certain size range. But some combinations will provide greater size sensitivity and larger size range. For example, instead of 10, 20, 30, 80 degree angles, any group of angles with one widely spaced pair below approximately 30 degrees and another widely spaced pair above approximately 30 degrees would work. Each detector sees an angular range centered about the average angle specified above. But each detector angular range could be somewhat less than the angular spacing between members of a detector pair. In some cases, without optical phase modulation, the angular ranges of each heterodyne detector should be limited to prevent heterodyne spectral broadening as described later (see For particle diameter 1-10 microns use detectors For particle diameter greater than 1 microns, use the 2 dimensional array in Another configuration is to use the scattering flux ratio of scattering at 4 degrees and 1 degree, in white light, for 0.5 to 3.5 microns. And use absolute flux at 1 degree (white light, same system) for 3 to 15 microns. And use the 2 dimensional array in In all of these systems, the white light source can be replaced by a laser. However, the particle size response will become more sensitive to particle and dispersant composition. And also the response vs. size may not be monotonic due to interference effects between the particle scattered light and light transmitted by the particle (Mie resonances), producing large size errors. If lasers or LEDs are required for collimation or cost requirements, scattering measurements can be made at more than one wavelength, using multiple sources, to reduce the composition dependence. Particle size of each object would be determined from all of these multi-wavelength measurements by using a multi-parameter function (size=function of multiple parameters), by interpolation in a lookup table as described above, or by a search algorithm. And in all cases the angles are nominal. Many different combinations of average angles, and ranges of angles about those average angles, can be used. Each combination has a different useable particle size range based upon size sensitivity, composition sensitivity, and monotonicity. All of these different possible combinations are claimed in this application. Also note that the ratio of S(a These cases are only examples of combinations of systems, described in this application, which could be combined to provide a larger particle size range. Many other combinations are possible and claimed by this inventor. One problem associated with measuring large particles is settling. The system flow should be maintained at a sufficiently high level such that the larger particles remain entrained in the dispersant. This is required so that the scattered light measurements represent the original size distribution of the sample. For dense large particles, impracticable flow speeds may be required. This problem may be avoided by measuring all of the particles in one single pass, so that the total sample is counted even though the larger particles may pass through the light beam as a group (due to their higher settling velocities) before the smaller particles. A small open tank is placed above the sample cell region, connected to the cell through a tube. The tube contains a valve which can be shut during introduction of the particle sample into the tank to prevent the sample from passing through the cell until the appropriate time. The liquid in the tank is continuously stirred during the introduction of sample to maximize the homogeneity in the tank. A light beam may be passed through the mixing vessel via two windows to measure scattered light or extinction to assist in determining the optimum amount of sample to add to obtain the largest counts without a high coincidence count level. The optical detectors are turned on and the valve is opened to allow the particle mixture to pass through the cell with gravitational force. This can also be accomplished by a valve below the sample cell or by tilting the tank up to allow the mixture to flow over a lip and down through the cell, as shown in The system in The systems based upon One other remaining problem with absolute scattering intensity measurements is the sensitivity of pulse intensity to the position where the particle passes through the beam. Measuring the distribution of pulse amplitudes from a nearly mono-sized calibration particle dispersion (with a low coefficient of variation for the size distribution) provides the response of the counter for a group of particles of nearly identical size. This count distribution, which is the same for any particle whose size is much smaller than the light beam crossection, provides the impulse response for a deconvolution procedure like the one described previously. The scattering pulses can be selected based upon their pulse length by only choosing pulses with intensity normalized lengths above some threshold or by using the various pulse selection criteria listed below. This selection process will help to narrow the impulse response and improve the accuracy of the deconvolution. This process is also improved by controlling the intensity profile to be nearly “flat top” as described previously. The scattered signal from any particle is proportional to the intensity of the light incident on the particle. Hence as the particle passes through different portions of the incident light beam, each scattered signal will vary, but the ratio of any two signals (at two different scattering angles) will theoretically be constant as long as the field of view of each detector can see the particle at the same time. This can be insured by eliminating the signals from long intensity tails, of the Gaussian intensity profile of the laser beam, which may not be seen by all detectors. This is accomplished by placing an aperture, which cuts off the tails (which may be Gaussian) of the incident light intensity distribution, in an image plane which is conjugate to the interaction volume. This aperture will produce a tail-less illumination distribution in the interaction volume, providing a narrower size range response to mono-sized particle samples (the impulse response). In the case of an elliptical Gaussian from a laser diode, the aperture size could be chosen to cut the distribution at approximately the 50% points in both the x and y directions (which are perpendicular to the propagation direction). Such an aperture would cause higher angle diffractive lobes in the far field of the interaction volume, which could cause large scatter background for low scattering angle detectors. Since this aperture should only be used for measurements at high scattering angles where the background scatter can be avoided, the low angle detector set and high angle detector set may need to view separate light beams. The apertured beam size should be much larger than the particles which are being measured in that beam. Hence, to cover a large size range, apertured beams of various sizes could be implemented. The particle size distributions from these independent systems (different source beams or different detector groups) could be combined to produce one continuous distribution. These apertures could also have soft edges to apodize the beam, using known methods to flatten the beam intensity profile while controlling the scattering by the aperture. This could also be accomplished by using diffractive optics for producing flat top distributions from Gaussian beam profiles as mentioned earlier. Also apertures can be oriented to only cut into the beam in the appropriate direction such that the diffracted light from that beam obstruction will be in the plane other than the scattering plane of the detectors. This is accomplished by orienting the aperture edges so that they are not perpendicular to the scattering plane. The aperture edges which cut into the beam at higher levels of the intensity profile should be nearly parallel to the scattering plane to avoid high scattering background. The apertured beams will help to reduce the size width of the system response to a mono-sized particle ensemble, because the intensity variation of the portion of the beam which is passed by the aperture is reduced. Other analysis methods are also effective to reduce the mono-sized response width for absolute scattering and scattering ratio measurements. Methods which accept only scattering signal pulses, or portion of pulses, which meet certain criteria can be very effective in narrowing the size width of the system response to mono-sized particles. Some examples of these acceptance criteria are listed below. Any of these criteria can be used to determine which peaks or which portion of the peaks to be used for either using the scattering signal ratios or absolute values to determine the particle size. - 1. Choose only the time portion of both pulses where the pulse from the detector which sees the smaller interaction volume, or has the shorter duration, is above some threshold. The threshold could be chosen to be just above the noise level or at some higher level to eliminate any possibility of measuring one signal while the second signal is not present. Then either take the ratio of the signals (or ratio the peaks of the signals with peak detector) over that time portion or the ratio of the integrals of the signals over that time portion. The absolute integrals or peak values during this time portion could also be used to determine size, as described before.
- 2. Only accept pulses where the separation (or time delay between peaks or rising edges) between pulses from the multiple detectors is below some limit
- 3. Only accept pulses where the width of a normalized pulse or width of a pulse at some threshold level is within a certain range as determined by the shortest and longest particle travel paths through the accepted portion of the interaction volume.
- 4. Only accept the portion of the pulses where the running product S
**1**.*S**2**(a vector containing the products of S**1**and S**2**for every point during the pulses) of the two signals is above some limit. Then either take the ratio of the signals over that portion or the ratio of the integrals of the signals over that portion. - 5. Only use the portion of pulses where sum(S
**1**.*S**2**)/(sum(S**1**)*sum(S**2**)) is greater than some limit (sum(x)=summation of the data points in vector x) - 6. Use only the portion of the pulses where (S
**1**.*S**2**)/(S**1**+S**2**) is greater than some limit - 7. integrate each pulse and normalize each integral to the pulse length or sample length
- 8. Use only the portion of the pulses where the value of S
**1***S**2**is be greater than some fraction of the peak value of the running product S**1**.*S**2** - 9. Integrate both signals S
**1**and S**2**only while the signal from the smaller interaction volume is above a threshold or while any of the above criteria are met. - 10. fit a function to the selected portion (based upon various criteria described above) of each pulse. The fitting function form can be measured from the signal of a particle passing through the center of the beam or can be based upon the beam intensity profile
- 11. When both S
**1**and S**2**have risen above some threshold, start integrating (or sample the integrators from) both signals. If the integrators for S**1**and S**2**are integrating continually (with resets whenever they approach saturation) then these integrators could be sampled at various times and the differences would be used to determine the integrals in between two sample times. Otherwise the integrators could be started and stopped over the period of interest. These sampled integrals are IT**10**and IT**20**for S**1**and S**2**respectively, when each of them rises above the threshold. When the first signal to drop falls back down below the threshold, sample the integrator on each of S**1**and S**2**(integrals IT**1***a*and IT**2***a*). When the second signal (signal number *) to drop falls below the threshold, sample the integral IT*b for that signal. Use the ratio of the integral differences, (IT**1***a*−IT**10**)/(IT**2***a*−IT**20**), during the period when both signals are above the threshold to determine size. Accept and count only pulses where a second ratio (IT*a−IT***0**)/(IT*b−IT***0**) is above some limit. This second ratio indicates the fraction of the longer pulse which occurs during the shorter pulse. As the particle passes through the light beam further away from the center of the interaction volume, this ratio will decrease. Only particles which pass through the beam close to the center of the interaction volume will be chosen by only accepting pulses where the shorter pulse length is a large fraction of the longer pulse length. These pulse lengths could also be determined by measuring the difference in the length of time between the above trigger points for each pulse. Pulses with a shorter difference in time length are accepted into the count by ratioing their integrals during the period when both of them are above the threshold.
These criteria can be easily implemented by digitizing S All of these variations will not be perfect. Many of them rely upon approximations which can lead to variation in calculated size for a particle that passes through different portions of the beam. The important advantage is that the broadening of the mono-sized particle response is the same for all size particles which are much smaller than the source beam. Therefore this broadened response, which is calculated by measuring the count distribution from a mono-sized distribution or by theoretical modeling, can be used as the impulse response to deconvolve the count distribution of any size distribution. The intensity ratio is sensitive to size and mildly sensitive to particle and dispersant refractive index. Size accuracy is improved by using scattering theory (such as Mie theory for spherical particles), for the actual refractive index values, to calculate the scattering ratio vs. particle diameter function. However, sometimes these refractive indices are not easily determined. Three scattering angles could be measured to generate a function which has reduced sensitivity to refractive index. D=particle diameter
Solve the set of equations: where -
- i=diameter index
- j=index of refraction index
and S**1***ij*=theoretical scattering signal over scattering angular range #**1**, for particle diameter D=Di and the jth index of refraction S**2***ij*=theoretical scattering signal over scattering angular range #**2**, for particle diameter D=Di and the jth index of refraction ( . . . )ij indicates that all the variables inside the parentheses have index ij.
A set of simultaneous equations are created for various diameters Di using signal ratios calculated from the appropriate scattering theory (Mie theory or non-spherical scattering theory) for various particle and dispersant refractive indices. These equations are then solved for the constants A Particles which are two small for single particle counting may be measured by stopping the flow and using the heterodyne signal of the scattered light to measure the size distribution from the Brownian motion of the particles. This Brownian measurement should be done at higher particle concentration, before the particle dispersion is auto-diluted to the lower counting concentration by the system shown in Other methods of generating the heterodyne local oscillator are also claimed in this disclosure for systems like in In By powering the source at various intensity levels, the scattered light from particles which span a large range of scattering intensities can be measured with one analog to digital converter. Even though the dynamic range of the scattered light may be larger than the range of the A/D, particles in different size ranges can be digitized at different source intensity levels. The resulting signals can be normalized to their corresponding source intensity and then used to determine the size of each particle. In Also it is recognized that many of the ideas in this disclosure have application outside of particle counting applications. Any other applications for these ideas are also claimed. In particular, the ideas put forth in Many drawings of optical systems in this disclosure show small sources with high divergence which are spatially filtered by a lens and pinhole and then collimated by a second lens. In all cases, a low divergence laser beam could replace this collimated source, as long as the spectral properties of the laser are appropriate for smoothing of Mie resonances if needed. Another issue is interferometric visibility in the heterodyne signals described before. Misalignment of beamsplitter or lenses For particles which are much smaller than the size of the laser spot, the scattered signal for particles passing through various portions of the laser spot will be distributed over a range of peak amplitudes. For a group of monosized particles, the probability that a peak amplitude will be between value S-deltaS/2 and S+deltaS/2 is Pn(S)deltaS, where Pn(S) is the probability density function for scattering amplitude in linear S space. “deltaQ” means the difference in Q between the end points of the interval in Q, where Q may be S or Log(S) for example. For a group of monosized particles of a second size (diameter D If we switch to logarithmic space for S, we find that the probability density becomes shift invariant to a change in particle size. (Pg(Log(S)) only shifts along the Log(s) axes as R or particle size changes. Where Pg(Log(S)) is the probability density function in Log(S) space. This shift invariance means that the differential count-vs.-Log(S) distribution, Cg, in logarithmic space is a convolution of the probability function Pg shown in Cg=NgΘPg in convolution form where Pg is the response (impulse response) from a monosized particle ensemble Cg=Ng*Pgm in matrix form, where each column in matrix Pgm is the probability function for the size corresponding to the element of Ng which multiplies it. This more general equation can also be used for any case, including when Pg is not a convolution form. These equations can be inverted to solve for Ng, given Cg and Pg, by using deconvolution techniques or matrix equation solutions. Pg is determined theoretically from the laser beam intensity profile or empirically from the Cg measured for one or more monosized particle samples. If the shape of Pg has some sensitivity to particle size, the matrix equation is preferable. These relationships also hold for the above functions, when they are functions of more than one variable. For example, consider the case where Cg is a function of scattering values S A group of monosized particles will produce a differential count distribution in S If all of the particles in a particular sample are in a size region where the signal ratio is not sensitive to particle size, such as the Rayleigh size regime, the scattering model could be determined empirically from dynamic scattering measurements. If the particle flow is stopped, the heterodyning detection system can measure the Doppler spectral broadening due to Brownian motion (dynamic light scattering). The particle size distribution from this measurement may be used directly, or the optical scattering model may be determined from the dynamic scattering size distribution and the static angular scattering to invert the absolute scattering signal amplitudes from the count-vs.-scattering signal distribution. In this way, the low size resolution distribution from dynamic light scattering will provide scattering model selection for the higher size resolution counting method. This technique can be used over the entire size range of the dynamic light scattering to select the scattering model for counting particles inside or outside of the size range of dynamic light scattering. The scattering model may also be determined by inverting the count distribution in S This multi-parameter analysis also provides for separation of mixtures of particles of different compositions such as polymer particles mixed with metal particles or polymer particles mixed with air bubbles. Hence, the count of air bubbles could be eliminated from the count distribution. This process could also be used by replacing signals, in these multiple parameter plots, with ratios of signals. Any of these multiple angle configurations may be extended to many more angles simply by adding more scatter detectors which view the same interaction volume. For example, consider The accuracy of the process described above improves as more scattering angles are measured. For example, the measured values of the scattered light for each of three scattering angles could be measured for each particle. These data points are then analyzed in a three dimensional scatter or dot plot. A line could be generated in 3 dimensional space by determining the path where the maximum concentration of particles (or dots in the plot) reside. In any one axis, this line may be multi-valued vs. particle diameter, especially in the region of Mie resonances. However, the line will not be multi-valued in 3 dimensional space. The spread of points about this line will be determined by the intensity distribution of the source beam in the interaction region. This group of points could be deconvolved in 3 dimensional space to produce a more sharply defined set of points, with less spread from the line, providing better size resolution along the line. But a better solution is to measure 4 scattering values at 4 different scattering angles for each particle. And then take ratio of each of any 3 values with the fourth value (or any other value) to remove the effect of intensity variation for particles which pass through different portions of the beam. Produce a scatter plot of these 3 ratios in three dimensions, where each point in 3 dimensional space is placed in Xm, Ym, and Zm values corresponding to the three ratios for each particle. Since the intensity distribution broadening is reduced, most of the points will tightly follow a line in three dimensional space. Outliers which are not close to the line passing through the highest concentration of data points may be eliminated as not being real single particles. The remaining data points (Xm,Ym,Zm) are then compared to different theoretical models to determine the composition and/or shape of the particles. The 3 dimensional function which describes the theoretical scattering is Zt where Zt is a function of Xt and Yt Let (Xm,Ym,Zm) be the set of data points measured from the counted particles. Where the values in the X,Y,Z coordinates represent the absolute scattering signals S Where Yt(Xm) is the theoretical value of Yt at Xm and Zt(Xm) is the theoretical value of Zt at Xm. Then find the theoretical model which produces the minimum sum of Esum over all values of Xm in the data set. Where Ny is the number of points in region Xmy and Nz is the number of points in Xmz. And SUM is the sum of Et over its valid region of Xmy or Zmy. Esum is calculated for various theoretical scattering models, for spherical and non-spherical particles, and the model with the lowest Esum is chosen as the model for the sample. The sum of Esum values from multiple particle samples can also be compared for different theoretical models. The model with the lowest sum of Esum values is used to analyze all of those samples of that type. This calculation may be computationally intensive, but it only needs to be done once for each type of sample. Once the optimal theoretical model is determined for each particle sample type, the appropriate stored model can be retrieved whenever that sample type is measured. The chosen theoretical model will provide the particle diameter as a function of Xm, Ym, and Zm for each detected object. Signal ratios show reduced sensitivity to the position of the particle in the source beam because each scattering signal is proportional to the optical irradiance on the particle. Usually to obtain optimal signal to noise, a laser source will be used to provide high irradiance but with lower irradiance uniformity due to the Gaussian intensity profile. The broadening in the monosized response, as shown in The measurement of particle shape has become more important in many processes. Usually the shape can be described by length and width dimensions of the particle. If the length and width of each particle were measured, a scatter plot of the counted particles may be plotted on the length and width space to provide useful information to particle manufacturers and users, and this type scatter plot is claimed in this invention. If the particles are oriented in a flow stream, the angular scattering could be measured in two nearly orthogonal scattering planes, one parallel and one perpendicular to the flow direction. Each of these scatter detection systems would measure the corresponding dimension of the particle in the scattering plane for that detection system. If the flow of particle dispersion flows through a restriction, so as to create an accelerating flow field, elongated particles will orient themselves in the flow direction. When measuring larger particles, which require smaller scattering angles, the scatter collection lens may be centered on the Z axis, with scattering detectors in the back focal plane of the collection lens, as shown in The accuracy of the methods outlined above is improved by solving another type of problem. The sizes calculated from angular scattering data in each of two or more directions are not usually independent. In order to accurately determine the shape parameters of a particle, the simultaneous equations must be formed in all of the scattering signals. The form of the equations is shown below: Where Si is the scattering signal from the ith detector. In the case of three directions (or scattering planes) and three detectors per direction, we have 9 total detectors and i=1, 2, . . . 9) W is the “width” parameter and L is the “length” parameter of the particle. In the case of a rectangular shape model, W is width and L is length. In the case of an ellipsoidal model, W is the minor axis and L is the major axis, etc. O is the orientation of the particle which could be the angle of the particle's major axis relative to Ys, for example. The functions Fi are calculated from non-spherical scattering algorithms and the form of Fi changes for different particle shapes (rectangles, ellipsoids, etc.). These equations, Si=Fi, form a set of simultaneous equations which are solved for W, L and O for each particle. If the Fi functions do not have a closed form, iterative methods may be employed where the Jacobian or Hessian are determined by numerical, rather than symbolic, derivatives. Also the closed form functions for Fi could be provided by fitting functions to Fi(W,L,O) calculated from the non-spherical scattering algorithms. If we had two detection angles per each of three scattering planes, we would have 6 equations with 3 unknowns. With three detectors per scattering plane the size range may be extended and we will have 9 equations with 3 unknowns. For particles with more complicated shapes, such as polygonal, more scattering planes may be required to determine the particle shape parameters. In any case, a shape model is assumed for the particles and the set of equations Si=Fi are created for that model where Fi is a function of the unknown size parameters and Si is the scattered signal on detector i. This method can be applied to any of the shape measuring configurations shown before. This technique can also be applied to ensemble size measuring systems when the particles all have the same orientation as in accelerating flow. This invention claims scattering measurements from any number of angular ranges, in any number of scattering planes. Low scattering signals from small particles may be difficult to detect. As shown before, ratios of scattering signals can be analyzed as a multi-dimensional function. Another method is to look at the individual signal ratios vs. particle diameter as shown in The ratio of scattering signals from different scattering angles reduces the dependence of the particle size determination on the particle path through the light beam. Particles with signals below some threshold are eliminated from the count to prevent counting objects with low signal to noise. The accuracy of counts in each size bin will depend upon how uniform this elimination criteria is over the entire size range. Many methods have been described in this application for reducing this problem. These methods are improved by having a source beam with a “flat top” intensity distribution and very sharply defined edges. This flat top intensity distribution can be provided by placing an aperture in an optical plane which is conjugate to the interaction volume or by using diffractive optic or absorption mask beam shapers. Another technique which will accurately define an interaction volume is shown in Many figures ( The matching of light wavefronts between the source beam and scattered light at the heterodyne detectors is important to maintain optimum interferometric visibility and maximum modulation of the heterodyne signal on each detector. Since perfect wavefront matching is not achievable, the interferometric visibility must be determined for each detector to correct the signals for deviation from theoretical heterodyne modulation amplitude. The visibility is determined by measuring particles of known size and comparing the heterodyne signals to the signals expected from theory. To first order, the interferometric visibility should be independent of particle size for particles much smaller than the source beam in the interaction volume. The visibility could be measured for particles of various sizes to measure any second order effects which would create visibility dependence on particle size. If only signal ratios are used for determining size determination, only the ratios of interferometric visibility need to be calibrated by measuring scattering from particles of known size. The number of cycles in the heterodyne modulated pulse is determined by the length of the trajectory of the particle through the source beam. The frequency of the heterodyne modulation is determined by the velocity of the particle through the beam. In general the power spectrum of the signal will consist of the spectrum of the pulse (which may be 10 KHz wide) centered on the heterodyne frequency (which may be 1 MHz). Both of these frequencies are proportional to the particle velocity. Actually the best frequency region for the signal will be determined by the power spectral density of the detector system noise and/or the gain-bandwidth product of the detector electronics. For this reason, in some cases the particle flow velocity should be lowered to shift the signal spectrum to lower frequencies. The particle concentration is then adjusted to minimize the time required to count a sufficient number of particles to reduce Poisson statistic errors. This is easily accomplished for small particles which usually have higher count per unit volume and require lower noise to maintain high signal to noise. In cases where optical heterodyne detection is not used, the signal to noise may be improved by phase sensitive detection of the scattered light. Modulation of the optical source may provide for phase sensitive detection of the scattering signal. The source is modulated at a frequency which is much larger than the bandwidth of the signal. For example, consider a source modulated at 1 megahertz with a scattering pulse length of 0.1 millisecond. Then the Fourier spectrum of scattered signal pulse would cover a region of approximately 10 KHz width centered at 1 megahertz. If this signal is multiplied by the source drive signal at 1 megahertz, the product of these two signals will contain a high frequency component at approximately 2 megahertz and a difference frequency component which spans 0 to approximately 10 KHz. In order to eliminate the most noise but preserve the signal, this product signal could be filtered to transmit only the frequencies contained in the scattering pulse, without modulation (perhaps between 5000 and 15000 Hz). This filtered signal product will have higher signal to noise than the raw signal of scattered pulses. This signal product can be provided by an analog multiplier or by digital multiplication after both of these signals (the scattering signal and the source drive signal) are digitized. This product is more easily realized with a photon multiplier tube (PMT) whose gain can be modulated by modulating the anode voltage of the PMT. Since the PMT gain is a nonlinear function of the anode voltage, an arbitrary function generator may be used to create PMT gain modulation which follows the modulation of the source. The voltage amplitude will be a nonlinear function of the source modulation amplitude, such that the gain modulation amplitude is a linear function of the source modulation amplitude. An arbitrary function generator can generate such a nonlinear modulation which is phase locked to the source modulator. As described at the beginning of this disclosure, multiple sized beams can also be used to control the effects of seeing more than one particle in the viewing volume at one time. The key is to choose the proper scattering configuration to provide a very strong decrease of scattering signal with decreasing particle size. Then the scattering signals from smaller particles do not affect the pulses from larger ones, because the smaller particle signals are much smaller than those from the larger particles. For example, by measuring scattered light at very small scattering angles, the scattered light will drop off as the fourth power of the diameter in the Fraunhofer regime and as the sixth power of diameter in the Rayleigh regime. In addition, for typically uniform particle volume vs. size distributions, there are many more smaller particles than larger ones. The Poisson statistics of the counting process will reduce the signal fluctuations for the smaller particles because individual particles pulses will overlap each other producing a uniform baseline for the larger particles which pass through as individual pulses. This baseline can be subtracted from the larger particle pulse signals to produce accurate large particle pulses. This method can be used in many of the systems in this application, where a large increase in scatter signal level occurs between large and small particles. One example of this method is shown by the optical configuration in This configuration allows each detector element to see scatter from only a certain aperture in the mask and over a certain scattering angle range determined by it's spatial mask. If the spatial mask defines a range of low scattering angles, the total scatter for the detectors viewing through that spatial mask will show a strong decrease with decreasing particle size. The signal will decrease at least at a rate of the fourth power of the particle diameter or up to greater than the sixth power of the diameter. Assuming the weakest case of fourth power, we can obtain a drop by a factor of 16 in signal for a factor of 2 change in diameter. This means that you need to control the particle concentration such that no multiple particles are measured for the smallest particle size measured in each aperture. The largest particle size which has significant probability of multiple particles in the aperture at one time should produce scattering signals which are small compared to the scattering from lower size measurement limit set for that aperture. However, this particle concentration constraint is relaxed if multiple pulses are separated by deconvolution within a signal segment, as shown in One annular filter aperture could also be replaced by a pinhole, which only passes the light from the source (the dashed line rays). Then the signals on each detector element would decrease as a particle passes through it's corresponding aperture at the sample cell. This signal drop pulse amplitude would directly indicate the particle size, or it could be used in conjunction with the other annular signals. No limits on the number of apertures in the sample cell mask or of annular filter/detector sets are assumed. More annular filter/detector sets can be added by using more beamsplitters. Also lens Each detector element has a shape which determines how much of the scattered light at each scattering angle is collected by the detector element. For example detector for the bth element in the ath assembly Here d is the dimension of the particle in the direction of the corresponding scattering plane. The scattered intensity at radius r from the center of the detector assembly (corresponding to zero scattering angle) for dimension of d is f(r,d). And wa(r) is the angular width (or weighting function) of the detector element at radius r in assembly “a”, in other words the angle which would be subtended by rotating the r vector from one side of the element to the other side at radius r. For the simple 3 element assemblies shown in S The signal on each detector element will consist of pulses as each particle passes through the beam. The Sab values above can be the peak value of the pulse or the integral of the pulse or other signal values mentioned in this disclosure. For example, one possible case would be: For this case S These S values can also be analyzed using methods shown in The actual particle size system may consist of systems, each which is similar to the one shown in For smaller particles, the source beam will be more focused (higher divergence and smaller spot size in the sample cell region) into the sample cell. This will help to define a smaller interaction volume, with higher intensity, for the smaller particles which usually have higher number concentration than the larger particles. Another feature of this design is the ability to use correlation or pulse alignment to determine which particle pulses are accurately measured and which pulses may be vignetted in the optical system. When R The delay between any two pulses from separate detector elements can also be used to select valid pulses for counting. As the particle passes through the beam farther from best focus of the source beam, the delay between the pulses will increase. Some threshold can be defined for the delay. All pulse pairs with delays greater than the threshold are not included in the count. One example is shown in Another criteria for pulse rejection is pulse width. As shown in The pulse rejection criteria described above is used to reduce the number of coincidence counts by using apertures to limit the volume which is seen by the detectors. The interaction volume can also be limited by providing a short path where the particles have access to the beam as shown in The beam focus may shift with different dispersant refractive indices due to refraction at the flat surface on the end of each cone. This shift in focus and angular refraction of scattered light at a surface can be corrected for in software by calculating the actual refracted rays which intercept the ends of each detector element to define the scattering angular range of that element for the particular dispersant refractive index in use. This correction is not needed for concave surfaces, on each cone tip, whose centers of curvature are coincident with the best focal plane of the source between the two tips. Then all of the beam rays and scattered rays pass through the concave surface nearly normal to the surface with very little refraction and low sensitivity to dispersant refractive index. Another problem that can be solved by particle counting is the problem of background drift in ensemble scattering systems which measure large particles at low scattering angles. An ensemble scattering system measures the angular distribution of scattered light from a group of particles instead of a single particle at one time. This angular scattering distribution is inverted by an algorithm to produce the particle size distribution. The optical system measures scattered light in certain angular ranges which are defined by a set of detector elements in the back focal plane of lens The detector elements which measure the low angle scatter usually see a very large scattering background when particles are not in the sample cell. This background is due to debris on optical surfaces or poor laser beam quality. Mechanical drift of the optics can cause this background light to vary with time. Usually the detector array is scanned with only clean dispersant in the sample cell to produce background scatter signals which are then subtracted from the scatter signals from the actual particle dispersion. So first the detector integrators are scanned without any particles in the sample cell and then particles are added to the dispersion and the detector integrators are scanned a second time. The background scan data is subtracted from this second scan for each detector element in the array. However, if the background drifts between the two scans, a true particle scattering distribution will not be produced by the difference between these two scans. A third scan could be made after the second scan to use for interpolation of the background during the second scan, but this would require the sample cell to be flushed out with clean dispersant after the particles are present. A much better solution, shown in As mentioned before in this disclosure, the particle shape can be determined by measuring the angular distribution of scattered light in multiple scattering planes, including any number of scattering planes. The particle shape and size is more accurately determined by measuring the angular scattering distribution in a large number of scattering planes, requiring many detector elements in the arrays shown in The detector array could be scanned at a frame rate, where during the period between successive frame downloads (and digitizations) each pixel will integrate the scattered light flux on its surface during an entire passage of only one particle through the source beam. Each pixel current is electronically integrated for a certain period and then its accumulated charge is digitized and stored; and then this cycle is repeated many times. During each integration period the pixel detector current from scattered light from any particle, which passes through the beam, will be integrated during the particle's total passage through the light source beam. Therefore the angular scattering distribution for that particle will be recorded over a large number of scattering planes by all of the detector elements in the array. This 2-dimensional scattering distribution could be analyzed as described previously, using a large number of simultaneous equations and more shape parameters, by assuming a certain model for the particle shape (ellipsoidal, rectangular, hexagonal, etc.). As shown before, the particle shape and random orientation can be determined from these equations. Also, conventional image processing algorithms for shape and orientation can be used on the digitized scattering pattern to find the orientation (major and minor axes, etc.) and dimensions of the scatter pattern. The particle size and shape can be determined from these dimensions. Also the particle size and shape can be determined from the inverse 2-dimensional Fourier transform of the scattering distribution for particles in the Fraunhofer size range, but with a large computation time for each particle. The inverse Fourier transform of the 2-dimensional scattering distribution, which is measured by the 2 dimensional detector array, will produce an image, of the particle, from which various dimensions can be determined directly, using available image processing algorithms. For example, consider an absorbing rectangular particle of width and length dimensions A and B, with both dimensions in the Fraunhofer size range and minor and major axes along the X and Y directions. If the particle is not absorbing or is outside of the size range for the Fraunhofer approximation, then the theoretical 2-dimensional scattered intensity distribution is calculated using known methods, such as T-matrix and Discrete Dipole Approximation, (see “Light Scattering by Nonspherical Particles”, M. Mishchenko, et al.). In the Fraunhofer approximation, the irradiance in the scattering pattern on the 2-dimensional detector array will be given by: is the irradiance in the forward direction at zero scattering angle relative to the incident light beam direction where:
The corresponding x and y coordinates on the 2 dimensional detector array will be: The scattering pattern crossections in the major and minor axes consist of two SIN C functions with first zeros located at: where F is the focal length of the lens These equations describe the process for determining particle shape for a randomly oriented rectangular particle where we have assumed that the particle is much smaller than the uniform intensity portion of the source beam. Other equations, which model scatter from non-uniform illumination, must be used when these conditions are not satisfied. Other parameters (such as the point in the scatter distribution which is 50% down from the peak) which describe the width and length of the scattering pattern can be used instead of xo and yo, but with different equations for A and B. In general, the corresponding particle dimensions can be determined from these parameters, using appropriate scattering models which describe the scattering pattern based upon the effects of particle size, shape, particle composition and the fact that the scattering pattern was integrated while the particle passed through a light source spot of varying intensity and phase. This analysis for rectangular particles is one example for rectangular particles. The model for each particle shape (polygon, ellipsoid, cube, etc.) must be computed from scattering theory for nonspherical particles using algorithms such as T-matrix method. The hardware concept is shown in A second similar optical system (system B which contains lenses Lens If the upstream system B is not used, the CCD array scans of each scatter pattern should be made over multiple long periods (many individual particles counted per period with one array scan per particle) where the light source intensity or detector pixel gain is chosen to be different during each period. In this way particles in different size and scattering efficiency ranges will be counted at the appropriate source irradiance or detector pixel gain to provide optimal signal to noise. So during each period, some particles may saturate the detectors and other particles may not be measured due to low scattering signals. Only particles whose scattering efficiency can produce signals within the dynamic range of the array for that chosen light source level or gain will be measured during that period. So by using a different source level or gain during each period, different size ranges are measured separately, but with optimal signal to noise for each size range. The counting distributions from each period are then combined to create the entire size and shape distribution. This method will require longer total measurement time to accumulate sufficient particle counts to obtain good accuracy because some particles will be passed without counting. The use of system B to predict the optimal light source level or pixel gain provides the optimum result and highest counts per second. These methods can also be used to mitigate detector array dynamic range problems in any other system in this application. The main system counting capability, as shown in Linear CCD arrays do not have sufficient dynamic spatial range to accurately measure scatter pattern profiles from particles over a large range of particle size. For example, for a million pixel array, the dimensions are 1000 by 1000 pixels. If at least 10 pixel values are needed to be measured across the scatter profile to determine the dimension in each direction, then 1000 pixels will only cover 2 orders of magnitude in size. This size range can be increased to 4 orders of magnitude by using two arrays with different angular scales. One note must be made about diagrams in this application. The size of the scatter collection lens, (i.e. lens This application also describes concepts for combining three different particle size measurement modalities: particle counting, ensemble scattering measurements, and dynamic light scattering. In this case, particle counting is used for the largest particles (>100 microns) which have the largest scattering signals and lowest particle concentration and least coincidence counts. The angular scatter distribution from a particle ensemble is used to determine particle size in the mid-sized range (0.5 to 100 microns). And dynamic light scattering is used to measure particles below 0.5 micron diameter. These defined size range break points, 0.5 and 100 microns, are approximate. These methods will work over a large range of particle size break points because the useful size ranges of these three techniques have substantial overlap: Single beam large particle counting (depends on the source beam size) 10 to 3000 microns
One problem that can be solved by particle counting is the problem of background drift in ensemble scattering systems which measure large particles at low scattering angles. An ensemble scattering system measures the angular distribution of scattered light from a group of particles instead of a single particle at one time. The detector elements which measure the low angle scatter (for example D A much better solution is to connect each of the detector elements, for the lowest angle scatter, to individual analog to digital converters, or peak detectors as disclosed before by this inventor. Then these signals could be analyzed by many of the counting methods which were disclosed by this inventor. This would essentially produce an ensemble/counting hybrid instrument which would produce counting distributions for the large particles at low scattering angles and deconvolved particle size distributions from the long time integrated detector elements (ensemble measurement) at higher scattering angles for the smaller particles. These distributions can be converted to a common format (such as particle volume vs. size or particle count vs. size) and combined into one distribution. The advantage is that the frequency range for the particle pulses is much higher than the frequencies of the background drift. And so these pulses can be measured accurately by subtracting the local signal baseline (under the pulse), determined from interpolation of the signals on the leading and trailing edge of each pulse, using the digitized signal samples. At very low scattering angles, the scattering signal drops off by at least the fourth power of particle diameter. Therefore larger particle pulses will stand out from the signals from many smaller particles which may be in the beam at any instant of time. Also the number concentration of larger particle will be low and provide for true single particle counting. The smallest particles are measured using dynamic light scattering as shown in The particle counting uses the lowest angle zones (D Another method for eliminating this intensity distribution effect is to use ratios of detector signals. This works particularly well when many of the detectors have scatter signals. However, for very large particles, only scattering detector D The signal ratio technique is needed when the “region passed by aperture” in This equation is easily inverted by using iterative deconvolution to determine Nd(d) by using H(log(S)) to deconvolve Ns(log(S)). In some cases, for example when S=A Where H is the matrix and Nd(d) is a vector of the actual counts per unit size interval. Each column of matrix H is the measured count per unit log(S) interval vs. log(S) response to a particle of size corresponding to the element in Nd(d) which multiplies times it in the matrix multiply ‘*’. This matrix equation can be solved for Nd(d), given Ns(log(S)) and H(log(S)). This equation will also hold for the case where the functions of log(S) are replaced by other functions of S. These multi-dimensional views and the previously described methods apply to all combinations of signals (S The previous concept for ensemble particle systems uses particle counting to eliminate the particle size errors caused by background drift in the angular scattering signals, because the frequency content of the counted pulses is much higher than the background drift, and so the pulses can be detected by methods described previously by this inventor, without being effected by background drift. The local baseline is easily subtracted from each pulse because the background drift is negligible during the period of the pulse. However, this advantage can also be used with the integrators as shown in These methods do not assume any particular number of lower angle zones. For example, D Normally all of the ADC scans of the multiplexer output are summed together and this sum is then inverted to produce the particle size distribution. But due to the large difference in scattering efficiency between large and small particles, smaller particles can be lost in the scatter signal of larger ones in this sum. This problem can be mitigated by shortening the integration time for each multiplexer scan and ADC cycle to be shorter than the period between pulses from the large particles. Then each multiplexer scan and subsequent digitization can be stored in memory and compared to each other for scattering angle distribution. ADC scans of similar scattering angular distribution shape are summed together and inverted separately to produce multiple particle size distributions. Then these resulting particle size distributions are summed together, each weighted by the amount of total integration time of its summed ADC scans. In this way, scans which contain larger particles will be summed together and inverted to produce the large particle size portion of the size distribution and scans which contain only smaller particles will be summed together and inverted to produce the small particle size portion of the size distribution, without errors caused by the presence of higher angle scatter from larger particles. Another method to measure larger particles is to place a sinusoidal target in an image plane of the sample cell on front of a scatter detector as described previously by this inventor. The dispersant flow could be turned off and then the particle settling velocity could be measured by the modulation frequency of the scatter signal from individual particles settling through the source beam. The hydrodynamic diameter of each particle can then be determined from the particle density, and dispersant density and viscosity. Finally the three size distributions from dynamic light scattering, ensemble scattering and counting are combined to produce one single distribution over entire size range of the instrument by scaling each size distribution to the adjacent distribution, using overlapping portions of the distribution. Then segments of each distribution can be concatenated together to produce the complete size distribution, with blending between adjacent distributions in a portion of each overlap region. This method works well but it does not make most effective use of the information contained in the data from the three sizing methods. Each inversion process for each of the three techniques would benefit from size information produced by other techniques which produce size information in its size range. This problem may be better solved by inverting all three data sets together so that each of the three methods can benefit from information generated by the others at each step during the iterative inversion process. For example, the logarithmic power spectrum (dynamic light scattering), logarithmic angular scattering distribution and logarithmic count distribution could be concatenated into a single data vector and deconvolved using an impulse response of likewise concatenated theoretical data. However, in order to produce a single shift invariant function, the scale of the counting data must be changed to produce a scale which is linear with particle size. For example, the pulse heights on an angular detector array will scale nearly as a power function of particle size, but the power spectrum and ensemble angular scattering distributions shift along the log frequency and log angle axes linearly with particle size. So a function of the pulse heights must be used from the count data to provide a count function which shifts by the same amount (linear with particle size) as the dynamic light scattering and ensemble distributions. This function may vary depending upon the particle size range, but for low scattering angles the pulse height would scale as the fourth power of the particle diameter, so that the log of the quarter power of the pulse heights should be concatenated into the data vector. This technique will work even though the concatenated vectors are measured verses different parameters (logarithm of frequency for dynamic light scattering, logarithm of scattering angle for ensemble scattering, and logarithm of pulse height or integral for counting), simply because each function will shift by the same amount, in its own space, with change in particle diameter. And so the concatenation of the three vectors will produce a single shift invariant function which can be inverted by powerful deconvolution techniques to determine the particle size distribution. This technique can also be used with any two of the measurement methods (for example: ensemble scattering and dynamic light scattering) to provide particle size over smaller size ranges than the three measurement process. In the concatenated problem where this convolution form is not realized, the problem can also be formulated as a matrix equation, where the function variables can be Log(x) or x (where x is the variable frequency (dynamic light scattering), scattering angle (ensemble angular scattering) or S (the counting parameter)). Again these functions can be concatenated into vectors and a matrix of theoretical concatenated vectors. And this single matrix equation, which contains the dynamic light scatter, the ensemble scatter and the count data, can be solved for the differential particle volume vs. size distribution, Vd, without being restricted to convolution relationships or the need for matching function shifts with particle size.
Where Fm is the vector of measured values which consist of three concatenated data sets (dynamic, angular, and counting). Ht is the theoretical matrix, whose columns are the theoretical vectors which each represent the theoretical Fm of the size corresponding to the value Vd which multiplies that column. This matrix equation can be solved for Vd, given Fm and Ht. If the convolution form holds, then the equation becomes: Where Him is the Fm response at a single particle size and Θ is the convolution operator. This equation can be solved for Vd, given Fm and Him. Another way to accomplish this is to constrain the inversion process for each technique (dynamic light scattering, ensemble scattering and counting), to agree with size distribution results from the other two techniques in size regions where those other techniques are more accurate. This can be accomplished by concatenating the constrained portion of the distribution, Vc, onto the portion (Vk) which is being solved for by the inversion process during each iteration of the inversion. The concatenated portion is scaled relative to the solved portion (AVc), at each iteration, by a parameter A which is also solved for in the inversion process during the previous iteration. This can be done with different types of inversion methods (global search, Newton's method, Levenburg-Marquart, etc.) where the scaling parameter A is solved for as one additional unknown, along with the unknown values of the particle size distribution. This technique will work for any processes where data is inverted and multiple techniques are combined to produce a single result. Solve for k values of Vk and constant A Another hybrid combination is particle settling, ensemble scattering, and dynamic light scattering as shown in The following list describes the various options for using scattered light to measure size. In each case, the following matrix equation must be solved to determine V from measurement of F:
This equation can be solved by many different methods. However, because this equation is usually ill-conditioned, the use of constraints on the values of V is recommended, using apriori knowledge. For example, constraining the particle count or particle volume vs. size distributions to be positive is very effective. In some cases, as shown previously by this inventor, changing the abscissa scale (for example from linear to logarithmic) of F can produce a convolution relationship between F and V, which can be inverted by very powerful deconvolution techniques. 1) Angular scatter or attenuation due to scatter:
Response broadening mechanisms in the H matrix: A) source intensity variation in x and y directions where particles can pass (broadening reduced by aperturing of the intensity distribution at an image plane of the sample cell or using diffractive or absorptive optic beam shapers and apodizers to provide a “flat top” intensity distribution in the interaction volume)
Response broadening mechanisms in the H matrix: Finite length of modulated signal segment from each particle
1) Angular scatter or attenuation due to scatter
Response broadening mechanisms in the H matrix: The broad angular range of scatter from a single particle described by scattering theory
Response broadening mechanisms in the H matrix: Finite length of modulated signal segment from each particle
In some cases, the matrix equation must be replaced by a set of non-linear equations which are solved to determine the particle size distribution from a count distribution which contains broadening due to a mechanism listed above. A more generalized form for this equation is to use operator notation Q=O[W], where O is an operator which operates on W to produce Q. For example in the case of counting: Depending upon the type of broadening mechanism, O may include operations such as matrix operation, set of non-linear equations, or convolution operator. The count distribution N(S) is the number of events with signal characteristic S between S-deltaS and S+deltaS as a function of S. S can be any of the signal characteristics (such as scatter signal peak or integral) or functions (such as logarithm) of these signal characteristics. Let Nm(S) be the measured count distribution which contains the broadening. And let Nt(S) be the count distribution without broadening. In each case, the operator describes the contribution to Nm(S) from an event of signal characteristic S. This operator is produced by calculating the broadened N(s) response to a large group of particles, with identical size and shape characteristics. This response is calculated for many values of particle characteristics to produce a set of equations. The response can also be determined empirically by measurement of a large number of particles with a narrow size distribution. Multiple narrow sized samples are measured at various mean sizes to produce the count response functions Nm(S) for those sizes. Then the response functions at other sizes are produced by interpolation between these measured cases, using theoretical behavior to solve for the interpolated values. The operator Another system for counting and sizing particles, using imaging, is shown in The source As shown in Also, the hollow cone source in Another problem associated with counting techniques is the coincidence counting error. In some cases, pulses from individual particles will overlap as shown in Σ=sum over variable i
So the original pulses can be recovered from S(t) by inverting the above equation, using H(t) as the impulse response in a Fourier transform deconvolution or in iterative deconvolution algorithms. As shown by Another concept for measuring the shape and size of small particles is shown in In order to increase the range of dimensions which can be measured, more scattering angular ranges must be measured. For example, To demonstrate this concept, consider the elements with optical axes marked with “x”, in the front view ( The same technique can be used for aperture This lens array idea is most effective for large numbers of detection elements. For smaller numbers of elements, each element could have a separate wedge prism behind it to divert the light to a lens which would focus it onto a particular fiber optic or detector element. But still the point is to eliminate the need for a custom detector array, to reduce the detector element size to reduce noise, and to allow use of highly sensitive detectors such as photomultipliers, which have limited customization. Quadrant detectors are commercially available for most detector types, including silicon photodiodes and photomultipliers. The shape of detector array or optic array elements is not limited to wedge shape. Other shapes such as linear shapes shown in This method can also be used to measure “equivalent particle diameter” without any shape determination. In this case, a diffractive optic as shown in Any of the masks or detector structures, including those in When using a photomultiplier (PMT), one must prevent the detector from producing large current levels which will damage the detector. This damage could be avoided by using a feedback loop which reduces the anode voltage of the PMT when the anode current reaches damaging levels. In order to avoid non-linear behavior over the useful range of the detector, the change of anode voltage should be relatively sharp at the current damage threshold level, with very little change below that level. The response time of the feedback loop should be sufficiently short to prevent damage. The feedback signal could also be provided by a premeasuring system as shown in Another important point is that any of the scattering techniques described in this disclosure can be applied to particles which are prepared on a microscope slide (or other particle container), which is scanned through the interaction volume instead of flowing a particle dispersion through the interaction volume. This provides some advantages: the particles are confined to a thin layer reducing the number of coincidence counts and the detection system could integrate scattered light signal for a longer time from smaller particles, to improve signal to noise, by stopping the scan stage or reducing the scan speed when smaller particles are detected (this can also be accomplished by slowing the flow rate in the dispersion case). However, preparing a slide of the particles for analysis, greatly increases the sample preparation time and the potential for sample inhomogeneity. When a cover slip is placed onto the dispersion, the smaller particles are forced farther from their original positions, distorting the homogeneity of the sample. This method can also be used in dynamic scattering cases (heterodyne detection with flow) by moving the microscope slide with a known velocity through the source beam. The scattering signal currents from elements on these detector arrays are digitized to produce scattered signal vs. time for each detector element. All detectors could be digitally sampled simultaneously (using a sample and hold or fast analog to digital converter) or each detector could be integrated over the same time period, so that signal ratios represent ratios of signals at the same point in time or over the same period of time and same portion of the source beam intensity profile. The data from each detector element is analyzed to produce a single value from that element per particle. This analysis may involve determining the time of maximum peak of the detection element with largest scatter signal and then using the same time sample for all of the other detection elements. Also the peak can be integrated for all detection elements to produce a single value for each element. Also the methods described previously for pulse analysis can be employed, including the methods ( The integral of F(x) between x=x1 and x=x2 is given by: The sum of terms of Fi(x) over index i from i=n to i=m is given by: Where Fi(x) is the ith term Each scattering angle corresponds to a radius, measured from the center of the source beam, in the detection plane. For the case shown in where M is the angular magnification of the optical system (angular magnification of lens Consider the case of rectangular particles, with dimensions da and db and rotational orientation α, as shown in I is the scattered intensity. Øi is the bisecting angle of the intersection of the ith scattering plane with the detector plane in the detector plane, as illustrated in where INT is now a 2-dimensional integral over Ø and r. -
- for a conventional detector array (such as a CCD array) with pixels on a rectangular coordinate system in x and y, where INT is a 2-dimensional integral in x and y space. In this case the r and Ø (or Øi) coordinates are replaced by x and y using the conversion relationships:
Let F
[X]m is the measured value of X (derived from signals measured by the optical system detectors) and [X]t is the theoretical function which describes X as a function of the particle characteristics. Some of these particle characteristics are unknowns (da, db, and a for example) to be solved from the equation set. Recognize that i indicates the ith scattering plane and ij indicates the jth detector in the ith scattering plane. FijA and FijB are the corresponding detector elements from two different detector arrays (A and B), each with a different Wij (r), as shown in detector pairs A and B in 8701 and 8702 in Where x̂p=x to the pth power and x*y=product of x and y. Then the previously listed sets of simultaneous equations can be formed from these equations for Fij. Where Bq are coefficients which are products of values of Cm and Qp, which are all known functions of da, db, α, and Øi. This concept can easily be extended to other particle types (just assume da and db to be the major and minor axes for an elliptical particle) and particles with more dimensions, such as pentagons, etc. In each case, the model must expand to account for the added dimensions dc, dd, de, etc. In order to solve for particle types with larger number of dimensions (i.e. octagons, etc.), sufficient scattering planes and detectors must be used to provide a fully determined set of simultaneous equations. In other words, the number of equations should be greater than or equal to the number of unknowns, which include the dimensions, da,db,dc, . . . etc. and the particle orientation, α. However, as indicated before, the solution of these equations can be computationally time consuming. The measurement of scattered light in many scattering planes can reduce the computational time, because the extrema of the dimension function can be found quickly. For example, take the case of the rectangular particle, where da, db, and a could be solved for with only measurements in 3 scattering planes. The solution of these 3 equations may require iterative search and much computer time per particle. However, if scattering is measured in many more scattering planes, the major and minor axes of the rectangle can be determined immediately, eliminating the requirement for determining the particle orientation a or reducing the range of a for the search solution. For example, if we interpolate a plot of Ri vs. Øi (or Rijk vs. i), we will obtain a function (or functions) with a maximum at Ømax and a minimum at Ømin, as shown in Many applications will require only particle characteristics which correlate to some quality of the manufactured product. Examples of these characteristics include: 1) equivalent spherical diameter and aspect ratio, 2) maximum and minimum equivalent dimensions as determined from the scattering planes with minimum and maximum Rijk, respectively, 3) dimension in the minimum Rijk scattering plane and the dimension in the plane perpendicular to that plane, 4) dimension in the maximum Rijk scattering plane and the dimension in the plane perpendicular to that plane. The equivalent dimension is the dimension calculated for that plane as though the plane were a major or minor axis plane using the scattering theory for a rectangle. All of the detector, mask, and diffractive optic configurations shown in this disclosure are only examples. This disclosure claims the measurement of any number of scattering angular ranges in each of any number of scattering planes, as required to determine the shape and size of each particle. All segmented detector arrays or lens arrays could be replaced by 2-dimensional detector arrays. In this case the inverse 2-dimensional Fourier Transform of the spatial distribution of detector element flux values would produce a direct 2-dimensional function of the particle shape, in the Fraunhofer approximation. The dimensions of the contour plot (perhaps by choosing the 50% contour of the peak contour) of this 2-dimensional inverse Fourier Transform function will provide the outline of the particle directly, for particles which are modeled by the Fraunhofer approximation. However, the size range of this type of array (per number of detector elements) is not as efficient as the wedge shaped scattering plane arrays described previously, because the detector elements in the commercially available 2-dimensional arrays are all the same size. When the particles become large enough to produce scattered light in only the lowest scattering angle detector element, the size determination becomes difficult, because two reliable scattering values are not available to determine the size in that scatter plane and absolute scatter signals must be used without signal ratios. This problem could be solved by using a custom array, where low scattering angle elements are smaller than larger scattering angle elements. This progression of element size with increasing scattering angle can also be accomplished with a equal pixel 2-D array which follows a lens, holographic optic, binary optic, or diffractive optic with non-linear distortion. The lens or diffractive optic distorts the scattering pattern so that the pattern is spread out near the center and compressed more at higher radii (larger scattering angles) in the pattern. In this way, detector elements closer to the center of the pattern will subtend a smaller scattering angular width than elements farther from the center. This would increase the size range of the detector array and still allow use of standard CCD type linear arrays. However, due to the limited dynamic range of most CCD arrays, a single PMT or other large dynamic range pre-sensor, placed upstream of the CCD array, could provide some indication of scattering signal level before the particle arrives in the view of the CCD array, similar to the systems shown in This wider size range can also be obtained by using different weighting functions (Wij) for two different detector elements which view the same range of scattering angle (or different ranges of scattering angle) in the same scattering plane, as described previously. As long as the Wij functions are different for the two measurements, the ratio of those scattered flux values will be size dependent over a large range of particle size and will be relatively insensitive to position of the particle in the beam. The Wij function can be implemented in the detector element shape, as shown in where r is the radius in the scattering plane from the center of the lens array. Each value of r corresponds to a different scattering angle. Then the effective weighting functions are the product of the transmission functions and the weighting function, Wijs, of the segment or element shape in the detector array or optic array. For wedge shaped segments the shape weighting function is: Hence the effective weighting functions are: Where F In some cases, wedge shaped detector elements are easily implemented because they include the same group of scattering planes throughout the range of scattering angle. When the same wedged shaped elements are used in both arrays, the transmission functions could provide the difference in Wij. For example one combination could consist of these functions:
Many combinations of transmission functions will work. This invention disclosure claims the use of any two different W The radial weighting function Wij can also be used with a single position sensitive detector, which uses multiple electrodes to determine the position of the centroid of the pattern on the detector. As the particle size decreases, the centroid, as measured through the Wij mask, will move towards larger radial value r, indicating the particle size. In general, we have two cases for measuring 2 dimensional scattering distributions. The detector array can be a set of radial extensions in various scattering planes (as in In general, the values Fij values as a function of size may be multi-valued in some size regions. Consider the simple case of 3 flux measurements, in each of 3 different scattering angle ranges. The first case, shown in These concepts can be combined with imaging systems to record the image of selected particles after they have passed through the interaction volume. An imaging system could be placed downstream of the interaction volume, with a pulsed light source which is triggered to fire at the correct delay, relative to the scatter pulse time, so that the particle has flowed into the center of the imaging beam during image capture. The pulsed light source has a very short pulse period so that the moving particle has very little motion during the illumination and image capture on a CCD array. The particle is imaged onto the CCD array at high magnification with a lens (microscope objective would be a good choice). In this way, particles which meet certain criteria, can be imaged to determine their morphology. The alignment of aperture Most of the concepts in this application can accommodate aerosol particle samples, by removing the sample cell and by flowing the aerosol through the interaction volume of the incident beam. The effective scattering angles may change due to the change in refractive index of the dispersant. Many methods in this application have used the heterodyne detection of scattered light to detect a particle. This is particularly useful for silicon detectors, which have lower sensitivity than PMTs. The beat frequency, Fb, depends upon the angle, θm, between the direction of motion and the direction of the incident light beam, and upon the scattering angle, θs. Where v is the particle velocity and w1 is the light wavelength in the dispersant. In some cases, the dynamic range of detectors will not be sufficient to cover the entire range of scatter signals from the particles. In particular, particles in the Rayleigh scattering range will produce scatter signals proportional to the 6 Idiff only contains the heterodyne signal. The common mode noise in the local oscillator and the heterodyne signal is removed by this differential measurement (see the previous description of the method). Heterodyne detection provides very high signal to noise, if the laser noise is removed by this equation and method. However, if the heterodyne frequency is only due to Doppler shift of the scattered light from particle motion, then the frequency of the heterodyne beat frequency will depend upon scattering angle and scattering plane (for example, the scattering plane, which is perpendicular to the particle flow, will show zero Doppler frequency shift of the scattered light). The addition of the optical phase or frequency shifter provides a much higher heterodyne frequency which is nearly equal for all scattering angles and scattering planes, allowing heterodyne detection of particle size and shape. The only problem presented by the frequency shifter is that all light that hits the detector, by scatter or reflection, will be frequency shifted. Without the frequency shifter, only scatter from moving particles will contribute to the heterodyne signal at the beat frequency, so background light can be distinguished from particle scatter based upon signal frequency. So when the frequency shifter is used, a background scatter heterodyne signal should be recorded without particles and this background signal should be subtracted from the scatter heterodyne signal with particles present. Addition of an optical frequency shifter also provides a higher beat frequency and phase sensitive detection capability. The signals due to the particle motion and the Doppler effect have random phase for each particle. So the other advantage of the frequency shifter is that the heterodyne signal will have a known phase (same as the frequency shifter), which could allow for phase sensitive detection (lock in amplifier). As shown before, the signals from this system will consist of a sinusoidal signal with an envelope function from a particle's passage through the intensity profile of the source beam. So all of the techniques described previously for processing these signals can be applied to this case. For the heterodyne systems, as shown in The system in The method shown in In both Where S In both Consider two optical systems, AA and BB. Any detector system in system AA using an aperture, which is in the image plane of the particle, can be used in any other system BB by placing that aperture at an appropriate image plane of the particles in system BB, along with the detection system from system AA. For example, the detector subsystem of pinhole In many cases, the light intensity, illuminating the particles, must be increased by focusing the source light beam to provide sufficient scatter signals. In all scattering systems with a collimated light source, the collimated light beam may be replaced by a focused light beam. However, the scatter detectors must not receive light from this focused beam in order to avoid large background signals which must be subtracted from the detector signals to produce the scatter portion of the signal. The source light beam should be blocked between the particle sample and the scatter detector. The most effective location for this light block is in the back focal plane of the lens which collects the scattered light. Examples of this plane are the planes of annular spatial filters in All drawings of optical systems in this disclosure are for illustrative purposes and do not necessarily describe the actual size of lens apertures, lens surface shapes, lens designs, lens numerical apertures, and beam divergences. All lens and mirror designs should be optimized for their optical conjugates and design requirements of that optical system using known lens and mirror design methods. Any single lens can be replaced by an equivalent multi-lens system which may provide lower aberrations. The drawings are designed to describe the concept; and so some beam divergences are exaggerated in order to clearly show beam focal planes and image planes within the optical system. If these drawings were made to scale, certain aspects of the invention could not be illustrated. And in particular, the source beam divergence half angle must be smaller than the lowest scattering angle which will be measured from particles in that beam. For low scattering angles (larger particles) the source beam would have a very small divergence angle, which could not be seen on the drawing. Also in this disclosure, where ever an aperture is used to pass scattered light and that aperture is in an image plane of the scattering particle, a lens can be placed between the detector(s) (or optic array) and that aperture to reduce smearing of the scattering pattern due to the finite size of the aperture. The detectors could be placed in the back focal plane of said lens, where each point in the focal plane corresponds to the same scattering angle from any point in the interaction volume. The detector(s) (or optic array) would be placed in the back focal plane of said lens to effectively place the detector at infinity, where the angular smearing is negligible, as shown and discussed in Where r is the radius on the scattering detector or optic array and L is the distance between the array and the aperture which is conjugate to the particle. When the detector is in the back focal plane of a lens, then L is the lens focal length. Also in this document, any use of the term “scattering angle” will refer to a range of scattering angles about some mean scattering angle. The angular range is chosen to optimize the performance of the measurement in each case. For example the use of the terms “low scattering angle” or “high scattering angle” refer to two different ranges of scattering angles, because each detector measures scattered light over a certain range of scattering angles Note that all optic arrays described in this disclosure can be constructed from segments of conventional spherical and aspherical lenses, diffractive optics, binary optics, and Fresnel lenses. Also the local signal baseline (local or close to the pulse in time) should be subtracted from most of the signals described in this application because very small amounts of background scattered light will be detected from multiple scattering of particles outside of the interaction volume. This background light will usually change over a time period which is longer than the pulse length from a particle passing through the interaction volume, due to larger particles, which pass outside of the interaction volume. As these larger particles pass through any portion of the beam they create primary scatter which is rescattered from particles in the field of view of the detectors, but which are outside of the interaction volume. Since large numbers of particles may be involved, their scatter into the detectors may be equal to or larger than the scatter from the single particle in the interaction volume. Therefore, both fluctuating and static background scatter should be removed from the single particle scatter signal by baseline subtraction. This subtraction could be accomplished by fitting a curve to the scattering signal, using only points before and after the single particle pulse. The values of this fitted curve in the region of the pulse would be subtracted from the signal to correct the pulse signal for the added background. In most cases a linear fit will be sufficient. Particle scatter signal pulses with large baseline levels or large changes in baseline across the pulse, can be eliminated from the particle count due to inaccurate baseline correction. This problem of multiple scattering is also mitigated by the concept, shown in Ensemble particle size measuring systems gather data from a large group of particles and then invert the scattering information from the large particle group to determine the particle size distribution. This scatter data usually consists of a scatter signal vs. time (dynamic scattering) or scatter signal vs. scattering angle (static scattering). The data is collected in data sets, which are then combined into a single larger data record for processing and inversion to produce the particle size distribution. Inversion techniques such as deconvolution and search routines have been used. The data set for dynamic light scattering consists of a digital record of the detector signal over a certain time, perhaps 1 second. The power spectra or autocorrelation functions of the data sets are usually combined to produce the combined input to the inversion algorithm for dynamic light scattering to invert the power spectrum or autocorrelation function into a particle size distribution. Also the data sets can be combined by concatenation, or by windowing and concatenation, to produce longer data sets prior to power spectrum estimation or autocorrelation. Then these power spectra or autocorrelation functions are averaged (the values at each frequency or delay are averaged over the data sets) to produce a single function for inversion to particle size. Like wise for angular scattering, the angular scatter signals from multiple detectors are integrated over a short interval. These angular scattering data sets are combined by simply averaging data values at each scattering angle over multiple data sets. Since the inverse problem for these systems is usually ill-conditioned, detecting small amounts of large particles mixed in a sample of smaller particles may be difficult because all of the particle signals from the particle sample are inverted as one signal set. If the signals, from only a few larger particles, is mixed with the signals from all of the other smaller particles, the total large particle scatter signal may be less than 0.01 percent of the total and be lost in the inversion process. However, in the single short data set which contained the larger particle's scattered light, the larger particle scatter may make up 50% to 90% of the total signal. The larger particle will easily be detected during inversion of these individual data sets. Users of these systems usually want to detect small numbers of large particles in a much larger number of smaller particles, because these larger particles cause problems in the use of the particle sample. For example, in lens polishing slurries, only a few larger particles can damage the optical surface during the polishing process. In most cases these larger particles represent a very small fraction of the sample on a number basis. Therefore, if many signal sets (a digitized signal vs. time for dynamic scattering or digitized signal vs. scattering angle for static scattering) are collected, only a few sets will include any scattered signals from larger particles. An algorithm could sort out all of the data sets which contain signals from larger particles and invert them separately, in groups, to produce multiple size distributions, which are then weighted by their total signal time and then combined to form the total particle size distribution. The data sets may also be sorted into groups of similar characteristics, and then each group is inverted separately to produce multiple size distributions, which are then weighted by their total signal time and then summed over each size channel to form the total particle size distribution. In this way, the larger particles are found easily and the smaller particle data sets are not distorted by scatter signals from the larger particles. Even if all of the signals for large particles over the full data collection time is less than 1% of the total signal, including large and small particles, this small amount would be inverted separately and the resulting distribution would be added to the rest of the size distribution with the proper relative particle volume percentage. This technique works better when many short pieces of data are analyzed separately, because then the best discrimination and detection of particles is obtained. However, this also requires much pre-inversion analysis of a large number of data sets. The key is that these data sets can be categorized with very little analysis. In the case of angular light scattering, comparison of signal values from a few scattering angles from each signal set is sufficient to determine which signal sets include signals from larger particles or have specific characteristics. In the case of dynamic light scattering, the spectral power in certain frequency bands, as measured by fast Fourier transform of the data set or by analog electronic bandpass filters could be used to categorize data sets. Consider a dynamic scattering system where the scattering signal from the detector (in heterodyne or homodyne mode) is digitized by an analog to digital converter for presentation to a computer inversion algorithm. In addition, the signal is connected to multiple analog filters and RMS circuits, which are sequentially sampled by the analog to digital converter to append each digitized data set with values of total power in certain appropriate frequency bands which provide optimal discrimination for larger particles. The use of analog filters may shorten the characterization process when compared to the computation of the Fourier transform. These frequency band power values are then used to sort the data sets into groups of similar characteristics. Since larger particles will usually produce a large signal pulse, both signal amplitude and/or frequency characteristics can be used to sort the data sets. The total data from each formed group is then processed and inverted separately from each of the other groups to produce an individual particle size distribution. These particle size distributions are summed together after each distribution is weighted by the total time of the data collected for the corresponding group. The use of analog filters is only critical when the computer speed is not sufficient to calculate the power spectrum of each data set. Otherwise the power spectra could be calculated from each data set first, and then the power values in appropriate frequency bands, as determined from the computed power spectrum, could be used to sort the spectra into groups before the total data from each group is then processed and inverted separately to produce an individual particle size distribution. For example the ratio of the power in two different frequency bands can indicate the presence of large particles. The resulting particle size distributions are summed together after each distribution is weighted by the total time of the data collected for the corresponding group. This process could also be accomplished using the autocorrelation function instead of the power spectrum of the scatter signal. Then the frequency would be replaced by time delay of the autocorrelation function and different bands of time delay would be analyzed to sort the data sets before creating data groups. In angular scattering, a group of detectors measure scattered light from the particles over a different angular range for each detector. These detector signals are integrated over a certain measurement interval and then the integrals are sampled by multiplexer and an analog to digital converter. In this case, the angular scattering values at appropriate angles, which show optimal discrimination for larger particles, could be used to sort the angular scattering data sets into groups before the total data from each group is then processed and inverted separately to produce an individual particle size distribution for that group. These resulting particle size distributions are summed together after each distribution is weighted by the total time of the data collected for the corresponding group. These sorting techniques can also be used to eliminate certain data sets from any data set group which is inverted to produce the particle size distribution. For example, in dynamic scattering, very large particles may occasionally pass through the interaction volume of the optical system and produce a large signal with non-Brownian characteristics which would distort the results for the data set group to which this defective data set would be added. Large particles, which are outside of the instrument size range, may also cause errors in the inverted size distribution for smaller particles when their data sets are combined. Also vibration or external noise sources may be present only during small portions of the data collection. These contaminated data sets could be identified and discarded, before being combined with the rest of the data. Therefore, such defective data sets should be rejected and not added to any group. This method would also be useful in conventional dynamic light scattering systems, where multiple groups are not used, to remove bad data sets from the final grouped data which is inverted. By breaking the entire data record into small segments and sorting each segment, the bad data segments can be found and discarded prior to combination of the data into power spectra or autocorrelation functions and final data inversion. This method would also be useful in static angular scattering to eliminate data sets from particles which are outside of the instrument size range. In some cases, a large number of categories for sorted groups are appropriate to obtain optimal separation and characterization of the particle sample. The number of categories is only limited by the cumulated inversion time for all of the sorted groups. The total inversion time may become too long for a large number of groups, because a separate inversion must be done for each group. However, after the information is sorted, abbreviated inversion techniques may be used because the high accuracy of size distribution tails would not be required to obtain high accuracy in the final combined particle size distribution. In many cases, only two groups are necessary to separate out the largest particles or to eliminate defective data sets. This disclosure claims sorting of data sets for any characteristics of interest (not only large particles) and for any applications where large data sets can be broken up into smaller segments and sorted prior to individual analysis or inversion of each individual set. Then the resulting distributions are combined to create the final result. This includes applications outside of particle size measurement. Another application is Zeta potential measurement. Low scattering angles are desirable in measurement of mobility of particles to reduce the Doppler broadening due to Brownian motion. However, large particles scatter much more at small angles than small particles do; and so the scatter from any debris in the sample will swamp the Doppler signal from the motion of the smaller charged particles in the electric field. This inventor has disclosed methods of measuring Dynamic light scattering from small interaction volumes created by restricting the size of the illuminating beam and the effective viewing volume. When only scattered light from a very small sample volume is measured, the scatter from large dust particles will be very intermittent, due to their small count per unit volume. So the techniques outlined above can be used to eliminate the portions of the signal vs. time record which contain large signal bursts due to passage of a large particle. In this way, Zeta potential measurements can be made at low scattering angles without the scattering interference from dust contaminants. In optical systems which need to count very small particles, light sources with shorter wavelengths may be preferred due to the higher scattering efficiencies (or scattering crossections) at shorter wavelengths. The alignment of angular scattering systems can drift due to drift of the source beam position or changes in the wedge between the sample cell windows. In most of the optical systems described in this application, certain ranges of angular scattered light are measured separately. Usually two angular ranges will only provide high particle dimension sensitivity over a limited size range. The following methods can be used to extend the size range of the detection systems: 1) many detectors in each scattering plane
In cases where a 2-dimensional detector array is in the image plane of the particles, that 2-dimensional array can be replaced by a 1-dimensional array which repeatedly scans across the interaction volume as the particles flow through that volume in a direction perpendicular to the long dimension of that array (the direction between adjacent pixels). Essentially the same information as obtained with the 2-dimensional array can be obtained sequentially on the 1-dimensional array because the other perpendicular dimension is provided by the particle motion. The two dimensional “virtual pixel” distribution of scattered signals is reconstructed by combining these sequential 1-dimensional scans, based upon the flow velocity. And as before, contiguous particle pixels (virtual pixels with signals indicative of a particle) are combined to produce scattering signals for each particle, as described previously for In all cases shown in this application, all possible polarizations and wavelengths of the source and all polarization and wavelength selections of the detection system can be employed. Each Fij in the previous analysis can have a specific light polarization and wavelength which optimizes the accuracy of the particle characterization. Any combination will provide size and shape information. However, the theoretical scattering model must accurately describe the wavelength and polarization state of the source and the polarization and wavelength selection of the detector. Polarization and wavelength effects can be used to determine particle size and shape using the search or optimization methods described previously. Below is a list of the best configurations for detection of size and shape using polarization effects in the optical systems described in this application: Any source can be polarized in a particular direction. Any detection system can select any polarization, including the polarizations parallel and perpendicular to that source polarization direction. For example two orthogonal polarizations can be selected by a polarizing beamsplitter which splits the scattered light into two separated scattering detection systems. Each of these detectors can consist of any detection system described previously in this application. Also each scattering plane segment in a detection array, such as shown in The set of signal values S (flux signal peak, integral, etc.), other functions of S (f(S)), and ratios, R, of signal values are a function M of the particle parameters, P, (dimensions, size, shape, etc.). M is also a function of the descriptors, O, of the optical system such as scattering plane orientations, scattering angles, polarization states and wavelengths of the sources, and polarization selections of the detectors. M may include a set of simultaneous equations (linear or nonlinear), an integral equation such as a convolution, or a single equation. M is determined from known scattering theory based upon the optical system O and the range of parameters P. M should be simplified by the methods described above to reduce computation time. In some cases, M can be directly inverted to Minv to produce P as a function of S, f(S), and R. In other cases, where explicit inversion of M is not possible, search, function minimization, or optimization methods should be employed to minimize an error function, such as E: These may include iterative methods. Where Smeasi is the value measured for the ith signal and Sti is the theoretical value for the ith signal based on the estimate for P; and where Rmeasi is the signal ratio value measured for the ith signal ratio and Rti is the theoretical ratio value for the ith signal ratio based on the estimate for P; and where f(S)measi is the signal function value measured for the ith signal function and f(S)ti is the theoretical signal function value for the ith signal function based on the estimate for P. The algorithms are designed to refine this P estimate using iterative procedures to find the estimated P values which minimize the error E. These algorithms include Newton's method, Levenburg Marquardt method, Davidon-Fletcher-Powell, constrained and unconstrained optimization methods, global search algorithms, etc. All of these methods will minimize E, by using M to calculate Sti, f(S)ti, and Rti for each new estimate of P. This minimization is performed individually for each particle to determine the size and shape parameters for that particle. In some cases, this inversion process will use a certain conceptual form for the properties of M, such as the 2-dimensional structure in In general we can define a Sv vector which consists of all of the measured quantities and a Pv vector which consists of all of the particle characteristics, which are to be determined from Sv: Where Si are scatter signals (flux signal peak, integral, etc.), Ri are ratios of different Si values, and fi are other functions of the Si values. The Pv vector consists of particle characteristic values, such as particle major axis length, particle aspect ratio, and particle orientation, for example. Then the optical model M is the transform operator between these two vectors: M is a function of the optical configuration descriptor, O, which includes the scattering plane orientations, scattering angles, polarization states and wavelengths of the sources, and polarization selections of the detectors. The M function is determined from theoretical scattering calculations such as Mie theory or T-matrix and Discrete Dipole Approximation, (see “Light Scattering by Nonspherical Particles”, M. Mishchenko, et al.). This M function can be approximated by regression analysis of the scattering value results from these scattering calculations. An example of this regression is shown below for 2 Pv parameters for polynomial regression: Where Oj is the optical system descriptor for signal Svj and A is the power operator. The regression analysis of scattering results from the theoretical scattering calculations produces the coefficients, Aij and Bijk. This technique can be extended to more than 2 elements in Pv, by providing more layers of coefficients. These equations, or the more general solution equations for M(Pv) shown above, are solved iteratively by finding the values in Pv which minimize the error Err: Where Svmj are the measured values of Svj; and Svej are the calculated values, in vector Sve, for the current iteration estimate for Pve (Sve=M(Pve)). The optimization methods, described above, are used to iteratively change the values in Pve to lower and minimize Err. Then the best Pv is equal to Pve, when Err(Pve) is minimum. This iterative process may consume excessive time, when required for each counted particle. Depending upon the available computer resources, direct inversion of M may be preferred. In some cases, the operator M can be inverted directly. For example, the regression analysis could switch the variables in the regression approximation equations to solve for Pv: The regression analysis of scattering results from the theoretical scattering calculations produces the coefficients, Cij and Dijk and creates the inverse operator Minv. Then Pv is directly calculated from Sv: The use of polynomial regression is just one example of reducing scatter results from very computationally intensive algorithms (such as Mie, T-matrix, or Discrete Dipole Approximation) to simple equations which can be computed in a fraction of a second instead of minutes. In general, other types of regression functions, such as Bessel functions, may be more appropriate. The optical system, O, must be designed to produce Sv which has large sensitivity to Pv. The scattering plane orientations, scattering angles, polarization states and wavelengths of the sources, and polarization selections of the detectors must be chosen to maximize this sensitivity to avoid ill-conditioning of the equation set Pv=Minv(Sv). Also in some cases, the discrete values in the data sets (Svd and Pvd) from the theoretical scattering calculations can be used to create a discrete multi-dimensional function set which can be searched in multi-dimensional space: Find the discrete values Pvd, by search and interpolation of the multi-dimensional data set, which produce Svd values which agree with Svm values to minimize Errd. The same analysis, as described for polarization properties, can be used for different source or detection wavelengths, which also determine the system response to particle characteristics. Optical filters in the detection system and various source wavelengths are used. And appropriate scattering models are used to describe the effects of wavelength on the scattering pattern. In many cases, the angular scale of the scattering distribution scales approximately inversely with wavelength. Any point in the angular scattering distribution moves toward higher scattering angle as the wavelength is decreased. Therefore, use of different wavelengths for Fij, can provide additional information for particle characteristics. For example, the Mie resonances respond to wavelength changes differently than the non-resonating portion of the scattering distribution, providing a means for better correction of Mie resonance induced errors. Also in any system described previously, the flow velocity could be lowered for smaller particles to increase their residence time in the interaction volume, providing longer signal period and better signal to noise. Also most of these techniques do not require the dispersant to be a liquid. These techniques are also claimed for measuring the size and shape of particles dispersed in a gas or aerosol. The same flowing conditions can be produced by pumping the gas aerosol in a closed loop through the optical system, or by pumping or settling the aerosol in a single pass through the optical system. If absolute signal values are used instead of signal ratios, the single size response will be broader in the multi-dimensional space and the deconvolution problem will be more ill-conditioned. However, this can be the best choice for very small particles where the absolute signals will have much higher particle size sensitivity than the signal ratios. This application claims any combination of the apparatus and methods described in this application to extend the size range of the total system. These methods may also be combined with conventional direct imaging systems to size larger particles. When more than one particle is present in the interaction volume, particle size errors can occur. Many of the systems and methods described in this application reduce the probability of counting coincident particles by providing interaction volumes of various sizes, such as shown in In many cases described above, coincidence counts cannot be avoided and the measured count distribution must be corrected for coincidence counts. The count distribution N(S) is the number of events with signal characteristic S between S-deltaS and S+deltaS as a function of S. As before, S can be any of the signal characteristics (such as scatter signal peak or integral) or some functions of these signal characteristics. Let Nm(S) be the measured count distribution which contains count errors due to coincidence counts. And let Nt be the true count distribution without coincidence count errors. Then the following relationship can be formed: Where Pk(S) is the probability that k particles, with characteristic S, will be present coincidentally in the interaction volume used to measure characteristic S. This probability is derived from the Poisson probability distribution using the average number (Na) of particles of signal characteristic S present in the interaction volume during a single data collection or at the point of data sampling (signal peak or integral measurement for example). where EXP is the exponential function and * is multiply operation The equations for Nm(Si) form a set of Nsi simultaneous equations which can be solved for Nt(Si), given Nm(Si) and Pk(Si). The value nns is the total number of counting channels, each with a different center Sj value. The value nnk is the maximum number of coincident particles in the interaction volume for a particle which produces signal Sj. The value of nnk depends upon the particle concentration for each value of Sj. The value nnk may be limited to the point where Pk(S) (for k=nnk) becomes negligible or to the point where baseline correction effectively removes the signal due to the coincident particles of signal Sj. These equations are solved by many different types of algorithms including iterative processes such as function minimization or optimization algorithms (global search, Newton's method, Levenburg-Marquardt method, etc.). The values of Nt can be constrained to be positive, using constrained optimization methods to improve accuracy. The iterative process could start with an estimate for Nt(S), called Nte(S). Then, using iterative optimization methods, the values in Nte(S) are changed, during each iteration, to produce a new estimated Nm(S) function, called Nme(S), (calculated from the equation below) which fits better to the actual measured values of Nm(S). This iterative process is continued until the error, Em, is minimized. The values of Nte(S) at minimum Em are the final values for the count distribution without coincidence counts. Nm(S) are the actual measured values. In general, the coincidence counts are best removed from the count data using the methods described for Application PCT/US2005/007308 (Application 1) is a basis document for this application. The term Application 1 also includes updates made to PCT/US2005/007308, which are included in this application. The particle counting optical systems, including those described previously by this inventor, can measure and count particles on microscope slides or other substrates (windows for example), without flowing particles through the interaction volume. The interaction volume is the volume of particle dispersion from which scatter detectors can receive scattered light from the particles. The interaction volume is the intersection of the particle dispersion volume, the incident light beam, and viewing volume of the detector system. These substrates can include particles dispersed on microscope slides (with and without cover slips) or a particle dispersion sandwiched in a thin layer between two optical windows. Using this method, the thickness of the sample volume is reduced, reducing the background scatter from other particles, in the sample, which are illuminated by the source beam or scattered light from other particles. The counting process is accomplished by moving the substrate, upon which the particles are dispersed, so that the optical system can view various spots or interaction volumes on that substrate and measure any particles that are present at each location. Essentially the moving substrate provides the particle motion which is provided by the dispersion flow in the flowing systems described previously by this inventor. This motion can also provide the Doppler shift required for some of the heterodyne detection systems described previously by this inventor. Either the optical system or the substrate (or both) can be moved so that the interaction volume of the optical system is scanned across the substrate to sample continuous scatter signals during the motion or to interrogate individual sites for particles. This scan can consist of any profile (zig-zag, serpentine, spiral etc.) which will efficiently interrogate a large portion of the substrate surface. The scan could also be stopped at various locations to collect scattering signal over a longer period with improved signal to noise. The flow system shown in In order to optimize the counting efficiency, the particle concentration should be increased to the maximum level, which will still allow a high probability of single particle counting, without coincidences. In this way, the largest number of particles will be counted in a given time period, with very few coincidence counts. This is difficult to accomplish on a substrate, such as a microscope slide, without using trial and error. Microscope slides and other substrates are difficult to populate with particles in a repeatable manner, with predictable particle concentration per unit area. The system, in The flowing system in This adjustable sample cell concept can be used in any particle counter (including those described previously by this inventor) by replacing the sample cell in said system with this adjustable sample cell and providing the hardware and software which will generate the information from which the cell window spacing adjustment will be determined. Since, during the particle counting scan, movement of either the optical system or sample cell (or both) may be provided by motor driven stages, the weight of these systems should be limited to avoid heavy acceleration loads on the stages. The optical system weight could be lowered by using laser diode or LED sources. Also the sample cell could be connected to the flow system through long flexible tubes to allow motion of only the light weight cell. If the velocity of the motor driven stage is too low to obtain high particle count rates, the effective speed of the source spot in the thin particle layer can be increased by mounting the optics (or sample cell) on piezoelectric actuators and using linear motion of the stage. The piezoelectric actuators would quickly scan the source spot and collection optics in a short oscillating pattern perpendicular to the linear motion of the stage to produce a serpentine pattern across the window with very high surface velocity. A single serpentine sweep across the window covers a rectangular region with length equal to the total linear motion and width equal to the perpendicular oscillating pattern motion. After each full single serpentine sweep, the stage is moved so that the rectangular region of the next sweep is placed adjacent to the prior sweep region, by jumping over one sweep rectangular width in the direction perpendicular to the linear motion. The stage would travel back and forth across the entire window (stepping forward with each cycle) to move the fast oscillating source spot across the entire area of window. The flow system in This concept can also be used in other types of scattering systems. For example, in ensemble angular scattering instruments (measuring scattered light from a group of particles), low particle concentration is required to avoid multiple scattering. But some users prefer to measure the particle size of dispersions at higher particle concentration when the particle size distribution is dependent upon the particle concentration. Multiple scattering occurs when the scattered light from a particle is scattered again by other particles, before being received by the detector. Since the optical scatter model usually assumes only primary scattered light, inversion of this multiple scattered light angular distribution will produce errors in the calculated particle size distribution. Multiple scattering depends upon the total number of particles in the beam. Therefore, by reducing the pathlength of the incident light beam in the particle dispersion, multiple scattering can be reduced to optimal levels, even at very high particle concentration. This pathlength adjustment could be accomplished under computer control using the sample cell shown in Where SUM=sum over the index i and F In any system, particle counting or ensemble scattering, the concentration can also be adjusted by adding clean dispersant to the flow loop Also the distribution shape difference method could also be used between successive particle concentration changes (by sample injection in The design in In either case, counting or ensemble measurement, the dispersion flow must be stopped if the window spacing becomes too small to allow flow in the small gap between the windows. Otherwise, the particles could be counted as they flow through the cell in position B, without the serpentine scan if the particles can flow at sufficient velocity to provide a high count rate for a fixed detector system. Ensemble scattering measurements could also be made during dispersion flow through the cell in Position B. The windows could also extend into the sample cell volume, with regions for passage of particles around both sides of the windows. Then when the windows are close together, the dispersion flow can continue around the windows, while the flow between the windows is restricted. This inventor has also disclosed and filed applications which describe methods and apparatus which can determine the shape of particles by measuring scattered light in various scattering planes, as described in FIGS. 79, 80, 81, 83, 84, 86, and 88 of Application 1, for example. Mask A in This rotating mask method can also be used in any system which measures a single interaction volume (FIG. 78 in Application 1 for example). The rotating mask, lens, and a single detector would replace the detector array in Also notice that most counting systems, including these counting systems and other systems described in Application 1, can be combined with an ensemble scattering system by using a beam splitter to split off a portion of the scattered light from the ensemble system to the counting system (or visa versa). In some cases, where scattered light at very high scattering angles must be measured to determine the size of very small particles, the sample cell can be modified as shown in Referenced by
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