US 3609356 A
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Description (OCR text may contain errors)
Unitedv States Patent Guenther ll. Schwuttke Poughlteepsie;
Leo J. Van Mellaert, Flshklll, both of N.Y. 784,052
Dec. 16, 1968 7 Sept. 28, 1971 International Business Machines Corporation Armonk, N.Y.
 inventors [21 Appl. No.  Filed  Patented  Assignee FEEDBACK CONTROLLED SCANNING MICROSCOPY APPARATUS FOR x-nAv DIFFRACTION TOPOGRAPIIY 14 Claims, 16 Drawing Figs.
 US. Cl. 250/515  lot. (I .....G0ln 23/10  Field of Search 250/415 Primary Examiner-Walter Stolwein Assistant Examiner-A. L. Birch Attorney- Hanifin and Jancin ABSTRACT: Disclosed is apparatus for forming topographs of large crystalline areas using X-ray diffraction microscopy techniques. The apparatus includes an X-ray source which directs an X-ray beam at a crystal which is mounted on a position control unit. The position control unit includes a scanning goniometer for translating the crystal and a low friction device for rotating the crystal both with respect to the incident X-ray beam. A beam detector is positioned to detect a diffracted beam as it leaves the crystal. The X-ray detector is connected to the position control-unit through a feedback control unit. The feedback control unit operates by introducing a small input perturbation signal into the position control unit thereby causing the crystal to rotate back and forth and causing the diffracted X-ray beam to have an X-ray component which results from the input perturbation signal. The feedback control unit operates to monitor the intensity of the dill'racted X- ray beam and the perturbation component thereof so as to adjustautomatically the angular position of the position control unit toward an angle (the Bragg angle) which causes the X-ray detector to detect a maximum intensity.
st- FEEDBACK a 55 CONTROL J TOPOGRAPH COMPARATOR SYSTEM UNIT POSITION CONTROL um'r P'ATENIED3EP2819Y:
sum 10F 5 FIG. 1
TOPOGRAPH COMPARATOR SYSTEM X'RAY DETECTOR POSITION CONTROL UNIT FEEDBACK UNIT 54 -b CONTROL FIG. 2
LOW-PASS FILTER MULTIPLIER 5? RATE CONVERTER a FILTER PERTUBATION GENERATOR T R [L A L L GUENTER H. SCHWUTTKE PATENTED SEP28 lsn SHEET 2 [IF 5 FIG. 5
9 MAX FIG; 6
= SCAN POSITION PATENTEUSEP28|97| FIG. 9
MULTIV SHEET 3 [IF 5 FIG. 70
f0 70Hz 2o MONOST PULSE LOW-PASS AMPLIT F ER CONTROL \AMPL CTL PULSE/ f WIDTH comm COMPARE LOW-PASS AMP FILTER 12A 11 REFERENCE AMPL A f 2H2 fo= 30Hz NARROW 5 BAND PASS sin(wr+)% FILTER 9 9 l FEEDBACK CONTROLLED SCANNING mcnoscorv APPARATUS FOR X-R'AY Bil-FRACTION TOPOGRAPHY The invention herein described was made in the course of or under a contract or subcontract thereunder, with the Air Force Systems Command, United States Air Force.
BACKGROUND OF THE INVENTION beam which is directed at the material under investigation.
The X-ray beam impinging upon the material excites the atomic electrons and causes X-ray radiation from all of the uniformly located atoms of the material. The resultant waves are either enhanced (constructive interference) or attenuated (destructive interference) to form a diffracted beam depend ing upon the lattice spacing of the material and the wavelength .of the X-ray beam. The intensity of the diffracted X-ray beam is dependent upon the angle, 0, which the incident X-ray beam forms with the crystal lattice planes of the material. The diffracted beam is at its highest intensity when the incident beam forms exactly the Bragg angle with the crystal lattice planes, the Bragg angle being the angle determined by the well-known Bragg equation of X-ray diffraction.
At the Bragg angle, an incident X-ray beam forms a dif fracted beam which is detected by X-ray photograph techniques to form a topograph of the material. The diffracted X-ray beam leaves the material at the Bragg angle and contains information relating to lattice parameters, presence of strains, degree of alloying, and other atomic phenomena. lmperfections and other condition affecting the crystalline structure of the material cause a diffracted X-ray beam to vary in intensity because of the destructive interference (generally a small quantity of interference when compared with the destructive interference occurring when the X-ray beam is not incident at the Bragg angle) which those imperfections or conditions create. By recording the variations in intensity of the diffracted beam, the imperfections and other conditions of the crystal are identifiable as variations in contrast in the recorded X-ray photographs.
Although the general principle of obtaining an X-ray topograph of a single crystal material having a small cross-sectional area is known, large area topographs present problems because of Bragg angle variations which often exist between different parts of a large crystal, particularly when that crystal has been subjected to various steps in a semiconductor-manufacturing process.
Those variations in the Bragg angle from location to location on a crystal are particularly troublesome when a scanning goniometer is employed. In a scanning goniometer, a narrow cross section X-ray beam is projected at one small area of a crystal and the crystal is translated back and forth without changing its angle with respect to the incident X-ray beam. With this scanning (i.e., translation), the full area of the crystal receives, a small area at a time, the incident X-ray beam. If the crystal is near perfect, the instantaneous Bragg angle, Omax, (the local Bragg angle for any given point during a scan) remains the same and a recording made using X-ray photograph techniques is fully and uniformly exposed. If the crystal is not perfect and the instantaneous Bragg angle changes during the scan (e.g. such as occurs when a crystal is stressed) then large areas of the crystal are not positioned at the Bragg angle when the X-ray is incident thereon and accordingly large areas do not transmit a diffracted X-ray with intensity variations indicative of the imperfections or other structural conditions. Those areas which do not transmit, of
course, leave large undeveloped areas in the X-ray photograph which yield little or no useful information about the material under investigation.
In order to overcome the problem presented by variations in the instantaneous Bragg angles in crystals, one prior art approach employs the scanning oscillator technique (SOT). In the scanning oscillator technique, the crystal sample is mounted on a scanning goniometer where the sample is scanned back and forth, in the same manner previously mentioned, with a photographic plate positioned to record the diffracted beam. Simultaneously with the scanning (translation) of the crystal, the goniometer is oscillated (rotated) so that the crystal is moved back and forth through an arc which is large enough to insure that the Bragg angle will be contained within the are. The extreme positions of rotation in each oscillation are necessarily, therefore, sufficient to form those instantaneous Bragg angles which have the maximum deviation from the average Bragg angle. Since the crystal is slowly scanned back and forth across the X-ray beam many times, the oscillation (during that scanning) of the sample around the average Bragg angle insures that all areas of the crystal are positioned, at least during some periods for some of the scans, with an X- ray beam incident at the instantaneous Bragg angle. With all areas thus receiving radiation at the instantaneous Bragg angle, the scanning oscillator technique insures that no unexposed areas appear in the topograph which is recorded on the photographic plate.
While the scanning oscillation technique has achieved improved results that were previously impossible, that is, has achieved, good quality large area topographs for the first time, that scanning oscillator technique still has its drawbacks. First, the time required to complete an X-ray photograph with oscillation is longer than without oscillation. The longer time results because the oscillation around the average Bragg 'a'ngle causes the X-ray beam to be incident at other than the Bragg angle for a large percentage of the time. A second drawback of the scanning oscillator technique can be the background scattering which is caused because the Bragg angle is approached and departed from during each oscillation. As the Bragg angle is approached and departed from during each oscillation, the intensity of the diffracted beam increases up to a peak at the instantaneous Bragg angle and thereafter decreases. This variation in intensity caused by large angle oscillations around the instantaneous Bragg angle may result in an undesirable cloudy appearance in the X-ray photographs.
Because of the time problem and the background scattering problem, the scanning oscillator technique is not as efficient as is desired particularly in a process control environment where rapid availability is important. With these problems in mind, an objective of the present invention is to provide an apparatus which is capable of producing topographs of large area crystals with minimum exposure time and which is usable during different stages of a semiconductor manufacturing process. The invention has a further objective of overcoming the background scattering problem (and resultant lack of contrast in topographs) which can arise when the prior art scanning oscillator technique is employed.
SUMMARY OF THE lNVENTlON The invention is an apparatus for forming topographs of large crystalline areas using X-ray diffracted microscopy techniques. The apparatus includes an X-ray source which directs a high-intensity, well-collimated X-ray beam at a crystalline sample such as a semiconductor wafer. The crystal is mounted on a position control unit which functions to adjust the position of the crystal with respect to the X-ray beam such that the X-ray beam always tends to be incident at the instantaneous Bragg angle. An X-ray beam detector is positioned to detect a diffracted X-ray beam as it leaves the crystal. The X- ray detector is connected to the position control unit through a feedback control unit. That feedback control unit operates to monitor the intensity of the diffracted X-ray beam and to adjust automatically the angular position of the position control unit toward an angle (the instantaneous Bragg angle) which causes the X-ray detector to detect a maximum intensi- The position control unit includes a scanning goniometer including a crystal mount which is supported on springs, a needle point or by other similar low friction devices. Those low friction devices allow the crystal mount (and of course any attached crystal) to be rotated without the rotation generating any significant frictional forces. Rotation of the mount is caused by electromagnetic coils, or other electrical means, which are positioned on either side of the axis of rotation which passes through the crystal sample held in the mount. Increasing the current in the electromagnetic coils causes the mount to rotate in one direction and decreasing the current causes the mount to rotate in the other direction. The mount is positioned so that the rotation is about the Bragg angle of the crystal sample.
A feedback control unit is connected between the X-ray detector and the position control unit and operates to sense variations in intensity detected by the detector and uses those variations to energize the position control unit causing the position control unit to be rotated toward that direction which maximizes the intensity of the diffracted beam, that is, toward the instantaneous Bragg angle.
The feedback control unit operates by introducing a small AC input perturbation signal into the electromagnetic elements of the position control unit. That input perturbation signal causes the crystal mount and crystal sample to rotate back and forth as a function of that signal. The X-ray detector senses in the difiracted X-ray beam an X-ray component which results from the input perturbation signal. The detector generates an output electrical signal which includes the received perturbation signal component. The feedback control unit filters the received perturbation signal from the X-ray detector output signal. The received perturbation signal is then normalized and cross-correlated with the input perturbation signal to obtain a correlation signal which is a measure of the detected X-ray beam intensity variation as a function of the crystal angular variation around the instantaneous Bragg angle. The correlation signal is integrated to obtain a position control signal which is connected to the electromagnetic coils (along with the input perturbation signal) to continually adjust the position control unit toward a position which maximizes the intensity of the diffracted X-ray beam as measured by the X-ray detector output.
The above described feedback controlled X-ray microscopy system can be connected directly to a topograph comparator system. By employing an X-ray vidicon tube as the X-ray detector, the output of that vidicon tube is fed directly to a data processing system which stores and compares empirically derived topographs with the topograph detected by the vidicon. Failure of the topograph of the crystal under X-ray test to appear like the empirically derived topograph causes that sample to be rejected or to be further processed to correct the deficiencies.
It is apparent from the above summary of the invention that the object of providing an X-ray microscopy apparatus which is capable of providing higher quality, large-area topographs than heretofore possible and in a manner which is faster than the prior art scanning oscillator technique is achieved. Because the feedback controlled position control unit of the present invention maintains the crystal at the instantaneous Bragg angle throughout the scanning of the test sample, the X- ray beam is virtually never incident at other than the instantaneous Bragg angle. The present invention, by maintaining the X-ray beam incident at the instantaneous Bragg angle, overcomes the time problem in the prior art scanning oscillator technique created because in that prior art technique the X-ray source is not incident at the instantaneous Bragg angle for a large percentage of the time. The present invention is also superior in that it holds the crystal at the instantaneous Bragg angle without large angle oscillations thereabout thereby reducing the background scattering attendant the prior art scanning oscillator technique.
' The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of the preferred embodiments of the invention as illustrated in the accompanying drawings.
FIG. 1 depicts in block diagram form the apparatus of the present invention.
FIG. 2 depicts a preferred embodiment of the feedback control unit 18 of FIG. 1.
FIG. 3 depicts curves representing, with respect to the FIG. I apparatus, the intensity, I, of the diffracted beam 5 as a function of the angle 0 which the crystal 4 makes with the incident X-ray beam 2.
FIG. 4 depicts a representation of crystal 4 in FIG. I drawn to show the lattice planes and the angles formed by incident and diffracted X-ray beams.
FIG. 5 depicts the apparatus by which the X-ray source I of FIG. 1 forms a narrow X-ray beam.
FIG. 6 depicts a curve representing the variation in Omax as a function of the crystal translation, as indicated in FIG. 5 from L1 to L2.
FIG. 7a depicts a schematic representation of the position control unit 15 of FIG. 1. FIG. 7b depicts a further schematic representation of the FIG. 7a device when a control current, i, is applied to the coils 38 in FIG. 7a.
FIG. 8a depicts a top view of position control unit 15 in FIG. 1. FIG. 8b depicts a front view of the device of FIG. 80.
FIG. 9 depicts one preferred embodiment of the rate converter and filter 57 of FIG. 2.
FIG. 10a depicts one preferred embodiment of the perturbation generator 67 of FIG. 2. FIG. [0b depicts waveforms representative of the signals generated in connection with the circuit of FIG. 10a.
FIG. 11 depicts, in schematic form, one alternate embodiment of the position control unit 15 of FIG. I.
FIG. 12 depicts another alternate embodiment of the position control unit l5.
FIG. 13 depicts still another alternate embodiment of the position control unit 15.
DESCRIPTION OF PREFERRED EMBODIMENTS GENERAL The general arrangement of the X-ray diffraction microscopy apparatus of the present invention is shown in FIG. I. That general arrangement is similar to that shown and described in the article New X-ray Diffraction Microscopy Technique For The Study Of Imperfections In Semiconductor Crystals, by G. H. Schwuttke, appearing in The Journal Of Applied Physics, Volume 36, No. 9, Pages 2,7l22,72l (Sept. 1965). That article describes the prior art a scanning oscillator technique discussed above. The orientation of the X-ray source and the crystal is generally the same in that prior art technique as in the present invention so that the article is here by incorporated by reference into this specification for the purpose of completing the disclosure as to the general details of an X-ray defraction microscopy system.
With reference to FIG. I, an X-ray source I directs an X-ray beam 2 toward the single crystal 4. The X-ray beam 2 is incident upon the crystal 4 at an angle, 0, formed with the axis AA' parallel to the diffracting plane of the crystal 4. A diffracted beam 5 is transmitted from the crystal 4 and is detected by the X-ray detector 6. The diffracted beam 5 passes through an opening 8 in an X-ray stop II). The difiracted beam 5 also impinges upon the photographic plate 12 which records the diffracted beam. The diffracted beam also continues on to the X-ray detector 6. The crystal 4 and the photographic plate l2 are connected to a position control unit 15 which, as schematically shown by dotted lines, is operative to translate both the crystal 4 and the photographic plate 12 in planes parallel to the axis B-B. The stop 10 is stationary.
The position control unitoperates to translate both the crystal 4 and the photographic plate 12 in a direction perpendicular to the axis A-A' so that the incident X-ray beam 2 effectively transverses the full face 3 of the crystal 4 while the photographic plate 12 simultaneously records the diffracted beam 5. The crystal 4 and the photographic plate 12 are locked together in their translating motion and accordingly, each different position of incidence of the face 3 causes the defracted beam 5 to be incident at a different corresponding place on the plate 12.
In addition to the translation in the direction of the axis B- B, the position control unit 15 causes the crystal 4 to continuously adjust the angle toward the instantaneous Bragg angle, Omax, such that the diffracted X-ray beam is of maximum intensity.
In accordance with the present invention, the intensity of the diffracted X-ray beam 5 is detected by detector 6 which develops an electrical signal, I, which is fed to the feedback control unit 18. The feedback control unit 18, as described in more detail in connection with FIG. 2, develops a position control signal, which continuously feeds the position control unit and causes that control unit 15 to adjust the angle 0 toward the instantaneous Bragg angle.
CRYSTAL ORIENTATION Wlth reference to FIG. 4, a crystal wafer 4a representative of the crystal 4 in FIG. I is shown. In FIG. 4, the crystal is oriented with the uniformly positioned atoms lying in low index planes parallel to the plane defined by the axes AA' and C-C. The incident X-ray beam 2, denoted by the vector S0, is kept in the plane formed by A-A and B-B'. With SO incident at the angle 0 as shown a diffracted beam 5, denoted by the vector S, also forms an angle 6 with the axis A-A'. The diffraction vector (5-80) is formed along the axis B-B'. With the vectors described, in the angle between the diffraction vector (5-80) and the axis CC' is denoted a and between (8-80) and the axis AA is denoted b. In aligning the apparatus of the present invention, the planes including C-C' and (S-SO), AA' and (8-80), respectively, are generally kept orthogonal to each other. FIG. 4 is drawn with a and b equal to 90. The apparatus is such that the angle 0 can be controlled with an accuracy of one second of are or greater and the angle a with an accuracy of one minute of arc or greater.
X-RAY SOURCE AND DETECTOR Wlth reference to FIG. 5, the X-ray source 1 in FIG. 1 is shown in expanded detail. The source 1 consists of the X-ray tube focus 26 directing an X-ray beam through a soller slit 27, through a collimating tube consisting of slit 1 and slit 2 and finally forming a line focus 7 (i.e., a relatively narrow high beam) on the crystal 4. Any X-ray source which provides a line focus or point focus may be employed. An example of such a system is the Norelco diffraction unit with horizontal tube mount (Norelco conversion kit number 5 I070 fitted with a standard X-ray tube number 32113 having a North American Phillips molybdenum target).
The X-ray diffraction camera containing the photographic plate 12 is mounted on the position control unit, to be described in detail hereinafter. The crystal 4 and the photo graphic plate 12 translate synchronously in planes parallel to the B-B axis. The translation unit and camera portion of the position control unit are similar to that described in the final report under Air Force Contract AF19(604)73 l 3, Project No. 4608, entitled X-ray Diffraction Microscopy of Imperfections In Semiconductor Crystals" by G. H. Schwuttke as shown therein in FIG. 4 on Page 8 and as described in connection therewith.
The X-ray detector 6 of FIG. 1 is preferably a conventional scintillation counter which operates to detect the intensity of the diffracted X-ray beam 5 yielding an electrical output signal at its output terminal 29. The output signal, I, at 29 is in the form of a series of spike pulses where the frequency of the pulses varies as a function of the intensity of the diffracted beam 5. Since the intensity of the beam 5 is highly sensitive to the angle 0 which the crystal forms where the incident X-ray beam 2, the signal I is a function of 0 and can be expressed as I ==l (6).
BRAGG ANGLE VARIATIONS In FIG. 3, I is plotted, for two different measurements represented by curves A and B, as a function of 6 over a small variation in 0. At some angle of 6, the output intensity, lmax A, of the defracted beam 5 is a maximum as denoted by Omax. The angle Omax is, of course, the instantaneous Bragg angle and it is desired that the X-ray beam be incident at Omax. The angles 01 and 02 on either side of 0max are the angles at which the intensity, Imax A, falls to the half power level. The difference 02 01 is typically within an order of magnitude of 10 are seconds.
Although it is desirable to operate the apparatus of the present invention so that the angle 0 is maintained as close as possible to ()max, Omax varies as a function of the translation position. Stated in another way, the instantaneous Bragg angle, Omax, varies as the crystal is translated from one position L1, in FIG. 5, to the position L2. A typical example of the variation of Omax, that is, the instantaneous Bragg angle as a function of translation position for a silicon wafer is shown in FIG. 6.
In FIG. 6, the Omax varies from one extreme instantaneous Bragg angle, On, to the other extreme, 0h. FIG. 6 demonstrates that if the crystal 4 is positioned at Ll with the X-ray beam incident near its edge, the crystal must be rotated so that 9 equals 0; in order for the crystal to be positioned at the Bragg angle," that is, positioned at Omax. 0| is, therefore, the instantaneous Bragg angle for position Ll. Similarly, when the crystal 4 is translated with an edge halfway between LI and L2 so that the X-ray beam is incident near the center of the crystal, 0 must equal 6h in order for 0 to equal Bmax. For semiconductor crystals 6h-0z is typically of the order of one or two are degrees. For the prior art scanning oscillator technique, therefore, each oscillation necessarily includes an are which exceeds both 01 and 6h as measured from the average Bragg angle someplace between 6!: and 0:.
Of course, variations from the Omax value at any point on the curve of FIG. 6 will cause a variation in the intensity of the diffracted beam in the manner described in connection with FIG. 3. In view of the variations of Omax, it is the purpose of the position control unit 15 of FIG. I to adjust the crystal sample so that 0=0max during the translations between LI and L2.
POSITION CONTROL UNIT FIGS. 7a and 7b depict schematic representations of the position control unit 15 of FIG. 1. In FIG. 7a, the crystal 4 of FIG. 1 is rigidly mounted (frictionally, mechanically, magnetically or by any convenient manner) in a crystal holder 32 which holder in turn is freely suspended on the leaf springs 34. The holder 32 has mounted thereon permanent magnets 36 which are each positioned to be magnetically coupled to different ones of the electromagnetic coils 38. An increase of the control current 1' through the coils 38 causes the holder 32 and of course the sample 4 to be rotated in the counterclockwise direction clue to the forces that the coils 38 exert on the permanent magnets 36. As shown schematically in FIG. 7b an increase in currenti causes the sample 4 to displace the springs 34 and to increase the angle 0 (the angle that the incident radiation 2 forms with the diffracting plane parallel to A-A' A decrease in i, of course, decreases the angle 0.
FIGS. 8 a and 8 b depict the detailed structure of one preferred embodiment of a position control unit. In FIGS. and 8b, the magnetic coils 38, the permanent magnets 36, the leaf springs 34, and the crystal sample 4 are numbered the same as in the FIGS. 7a and 7b. The coils 38 include cores 39 and are conventional units. The permanent magnets 36 are also conventional and are mounted on the extreme ends of the holder 32 closely positioned to the cores 39. The leaf springs 34 are mounted at one end to the rigid frame 41 of the position control unit. The other ends of the springs are connected to the movable holder 32 so that the holder is free to float when the current i is applied through the coils 38 as discussed in connection with FIGS. 7a and 7b.
The holder 32 is provided with a hand operated vernier 43 which aids in rotating the sample 4 (via wonn gear 45 and rotatable engaged member 47) during an initial positioning of the crystal. The rigid frame and table 41 are mounted on a translating table 44 for translating the holder and frame 41 from L1 to L2 and from L2 to L1 in order to scan the crystal across the incident X-ray beam. The table 44 slides along the tracks 46 as driven by a scan motor 48 and a screw gear 49. The scan motor, screw gear and tracks are conventional and operate to translate the table 41 at a constant velocity in both directions. The scan motor is controlled by limit switches S1 and S2 which function to reverse the direction of translation in a conventional manner as indicated in FIG. 8b. The table 44, of course, can be mounted on conventional tables (not shown) for rotating the whole apparatus of FIG. 8 a and FIG 8 b in any plane for initial alignment (in cooperation with the vernier 43) of the crystal 4.
FEEDBACK CONTROL UNIT While the position control unit 15 of FIG. 1 functions to actually rotate the crystal 4, in accord with the current i, it is the function of the feedback control unit 18 of FIG. I to supply the appropriate current i which maintains the angle at the instantaneous value of Omax. The details of the feedback control unit 18 are shown and described in connection with FIG. 2. Before describing the circuit of FIG. 2, however, a description of its theory of operation will first be given.
Theory of Feedback Control Unit Operation The desired result is to operate the diffraction system of FIG. I such that the output intensity, I, from the X-ray detector 6 is a maximum. In order that l is a maximum, the diffracted beam must be a maximum and this condition is achieved when the angle 0=6max.
In order to continuously adjust 0 toward Omax, conventional automatic control systems cannot be used. In conventional control systems, a sensor device or detector will measure directly the deviation of the controlled system from the desired operating point and the output signal of that detector is usually a monotonic function of that deviation. In contrast with conventional systems, the angular dependence of the measured X-ray intensity I is not monotonic as shown, for example, in the FIG. 3 curve ofl versus 0. In FIG. 3, two values of 0, one left and one right of the abscissa value of Omax, can always be found giving the same value for l Because of this diatonic nature ofl around Hmax, it is not possible to decide from a simple observation of the intensity I in which direction the angle 0 should be adjusted to make the apparatus operate at the peak of the FIG. 3 diffraction curve.
Although I is not a monotonic function of 0, the angular derivative of the intensity, dI/dk, is a monotonic function of 9 and the apparatus will operate such that 0=0max when (dl/dk )=0. The feedback control unit 18 of FIG. 1 operates, therefore, to detect and form the value (dl/dk) and thereafter to integrate that value to obtain the current i which is the signal which drives the coils 38 of the position control unit and which causes a particular value of 6 to be formed.
Mathematical Development Of Theory The theory will be explained with reference to FIG. I where I is the output of detector 6, where the feedback control unit 18 includes means for first obtaining dI/dk and includes means for thereafter integrating dI/d k with an integrator gain constant, K, to form the control current i and where the position control unit 15 has the transfer characteristics to convert i to an output value of 0, that is, to adjust the crystal to a value of 6.
The relationship between d l/dk and 6 for the described system of FIG. I is given by:
where t represents the variable time. Taking the derivative of expression l with respect to time yields the following:
From expression (2), it is clear that the angle 0 is adjusted in the direction of the maximum of I. For 0=0max, expression (3) shows that dk/dlxO indicating that the value of 0 will remain at the peak value Omax. The control scheme is mathematically straightforward and all that remains to be described is suitable means for generating the angular derivative signal dI/dkon a continuous basis.
In designing the circuit to obtain dl/dk on a continuous basis, it must be remembered that the derivative of a function is not a property of a single point of that function but only expresses the behavior of that function in the vicinity of the point at which the derivative is defined. Accordingly, one requirement of the feedback control unit of the present invention is that it continuously explore the response I in the immediate vicinity of that value of 0 at which the system is operating. The value of 0 at which the system is operating is called the operating point, 9", and is shown on the operating curve of FIG. 3. In contrast to mathematical limiting procedures for defining a derivative, it is not possible to operate with arbitrary small excursions about the operating point since instrumentation errors and noise set a lower limit for the magnitude of the perturbation below which it becomes impractical to operate.
Assuming that the system operates at the point 0=0 on the response curve I of FIG. 3, the practical measurement of dl/dk requires a perturbation around this operating point given by:
wherein p(t) is a suitable perturbation signal. One of the prime requirements for the perturbation signal p(!) is that the error which p(t) introduces into the control system should not disrupt satisfactory system operation. This requirement means that for X-ray diffraction applications, the steady state excursions from the peak of the FIG. 3 diffraction curve due to p(t) should be limited such that the average intensity of the diffracted beam does not excessively fluctuate. Further criteria for selecting a suitable p(t) depend upon the simplicity and accuracy with which it is desired to recover dI/dk from I. In general, any arbitrary signal p(l), deterministic or stochastic, may be chosen although the accuracy of the system is dependent upon that choice.
Since the output, I, of the X-ray detector is a function of 0 l=l(6). From expression (4), therefore,
*+P( or in shortened form I=I(l). Assuming that the function I is well behaved, I can be written in a Taylor expansion about 0" as follows:
Error 6* [p1,] Error,
thenthen the transform of atypical term of expression (6) as given by the convolution integral is of the form:
l 11"] 1 m 1 d"I For all practical cases, the excursions 0 about 0* are small and the control value of 0* is slowly varying. It follows, therefore, that the signals I(0*), dl/d0,...,d"I/d0" can be considered to be stationary so that their respective Fourier transforms can be approximated by Dirac functions. This simplifies the expression (10) to the following:
The criterion for selection of a suitable perturbation signal can now be stated simply. The spectra of the successive powers of p(t) in expression (6) should be nonoverlapping to a degree such that the term p(t)(dI/d0) can be easily extracted with sufficient accuracy from the other terms of I in expression (6). That extraction can be accomplished with classical signal processing an filtering techniques.
A class of signals for which the spectra of powers of these signals are overlapping minimally are the signals having point spectra. The simplest in this class are the harmonic signals. For p(t)=sin0.t the spectrum of p, p p and p have a minimum of overlap in the frequency domain. Therefore, one method for recovering dI/d0 from the signal I is to pass I through a band-pass filter centered at (1 0: and having a bandwidth such that only the frequency component sinat is maintained in the output signal. The filtered output signal i would then be expressed as follows:
The most severe error term in expression (12) would be the component:
which would be derived from the sin3wt term derived from expression (6) when p(t) equals sinwt. It can be easily shown, however, that the magnitude of expression (13) is sufficiently small so that it can be ignored for all practical purposes. Similarly, for sufficiently smooth [(0) functions, the higher order harmonic error terms will vanish rapidly and hence the total error term may be ignored for the present invention.
If the perturbation signal p(t) contains more harmonics than a single sinusoidal frequency, it can be shown that the accuracy with which dI/d0 can be recovered decreases. Even though 75 the accuracy decreases, that decrease does not necessarily mean that no satisfactory control system can be built with a nonsinusoidal perturbation signal. In conclusion, many perturbation signals may be employed within the scope of the present invention. In view of the above treatment, however, sinwt is a preferred signal.
Circuit Details In FIG. 2, one preferred embodiment of a feedback control unit which implements the above mathematical operations is shown. lts input terminal 54 and output terminal 55 are connected between like numbered terminals in HO. 1. The input terminal 54 receives the signal I from the X-ray detector 6 of FIG. 1. Since the signal 1 from the detector 6 is inconveniently in the form of spike pulses and is in an environment of noise, the rate converter and filter circuit 57 is employed to precondition the signal before the correlation in the multiplier 59. The output of circuit 57 at terminal 58 is in the form of [sinmt] [dI/d0 at 0* The rate converter and filter circuit 57 is shown and will be described in more detail in connection with FIG. 9.
The multiplier 59 functions to carry out the correlation of the detected signal at 58 with a signal r(t) derived from the perturbation signal p(t) both generated in the perturbation generator 67. Further details as to a preferred multiplier 59 are shown and described in connection with FIG. 10 below.
A conventional low pass filter 61 operates to select the value dl/d0 at 0* from the output of the multiplier 59. With the perturbation signal p(t)=sinmt with w=a as assumed, the eutoff frequency of the filter 61 is below a. In a preferred embodiment a=30 Hz.
The output of the low pass filter 61 is fed to a conventional integrator 63, the output of the integrator 63 is a current i( 0*) which is fed as one component of the current'i to the coils 38 of the position control unit shown schematically in FIG. 7a. The component i( 0*) operates to hold the crystal 4 such that the angle 0 equals 0*. 1f 0* is less than 0max, dI/d0 at 0* from the low pass filter is positive and the integrator therefore increases the value of i(0*). lf dI/d0 is negative from the low pass filter 61, the integrator functions to decrease the value of i(0*) so as to tend to make 0* equal to 0max. lf 0* equals 0max, then dI/d0 from the low pass filter 61 is zero and the output of the integrator remains constant.
Added to the component current i(0*) from the integrator 63 is the perturbation signal p(t) from the perturbation generator 67. The adder 65 is conventional and the current i fed to the position control unit 15 of FIG. 1 is i(0*+p(t)). The perturbation generator 67 in a preferred embodiment includes a conventional sine wave generator for generating the signal p(t)=sin at. For simplicity. the amplitude of the sin at perturbationsignal has been ignored but, of course, the amplitude is selected such that the variation of 0 about 0* caused by p(!) is not excessive. As a general rule and with reference to FIG. 3, variations of 0 about 0* should not exceed 01 or 02, the half power angles. Appropriate means, therefore, for adjusting the amplitude of i(p(t)) with respect to i(0*) to achieve that not excessive variation of 0 may be included within the perturbation generator 67. Usually, p(t) caused variations of 0 will be much less than 01 and 02 on the order of magnitude of l or 2 are seconds (compared with a typical (020l)=l0 are seconds). The manner of deriving the multiplication signal r(t) from the perturbation signal p(t) will be described in connection with FIG. 10 hereinafter.
Rate Converter and Filter In FIG. 9, the rate converter and filter 57 of FIG. 2 is shown in detail. The converter has input terminal 54 and output terminal 58. lo a preferred embodiment, the rate converter includes a monostable multivibrator 68 which converts the spiked waveform (shown above terminal 54 in FIG. 9) to a rectangular waveform at the output 68. The multivibrator has an input from the amplifier 72 for changing the width x of the multivibrator output pulses. The multivibrator 68 is connected to a pulse amplitude control circuit 69 which functions to adjust the height y of the pulses received from the multivibrator 68 under control ofa signal from the comparator amplifier 72. The output of the control circuit 69 is connected to the conventional low pass filter 70 which has a cutoff frequency of about 70 Hz. when a=30 Hz. The filter 70, in effect, averages the rectangular pulses from control circuitry 69 and the output of that filter 70 includes, in the frequency spectrum, both signals in the 30 Hz. range and DC signals.
The feedback loop for adjusting the pulse width (at the output from the monostable multivibrator 68) and the pulse amplitude (at the output from the control circuitry 69) is achieved by sensing the DC component of the output of the filter 70 by means of the low pass filter 71 which has a cutoff frequency much lower than 30 Hz. so as to essentially detect only the DC component of that signal. The DC component is compared with a reference amplitude in a conventional comparator amplifier 72. The signals from the comparative amplifier 72 adjust the pulse width and pulse height from the output of circuits 68 and 69, respectively, so as to insure that the average power to the low pass filter 70 is a constant. The need for the feedback control of the average power arises because of extreme variations in the intensity of the diffracted beam of FIG. 1 which variations are independent of the angle 0.
These .variations in intensity not a function of 6 arise principally because of the difference in transmittance from one crystal to another due to the difference in structure and the degree of imperfections which occur from crystal to crystal. Additionally, variations in structure from local point to local point during the translation of the crystal also give rise to variations in intensity in the diffracted beam. The ratio of observed maximum to minimum intensities is of the order of It should be stressed that these variations in intensity are variations which exist over and above variations arising because 0 differs from Omax. With reference to FIG. 3, the difference in intensity is a difference between curve A and curve B where both curves have Omax equal to the same value of 0 but which have grossly different values in maximum intensity, lmax. The function of the feedback loop including the circuit 71, 72 as controlling the circuits 68 and 69 is to normalize the detected value of I such that its average value is the same whether the operating curve A or B or any other curve is presently at any given instant descriptive of the diffracted beam intensity.
After having converted the spiked pulses at terminal 54 to a DC-normalized signal having frequency components less than 70 Hz. at terminal 73, that signal at 73 is passed through a conventional narrow band-pass filter 74 having a center frequency of 30 Hz. and a bandwidth of 2 Hz. to derive the signal at output terminal 58 which is applied to the multiplier of 59 of FIG. 2. The output signal at 58 is in the form of sinwt dl/dO at 0* [ignoring the error term in expression (I2) per the above discussion of error] where w=d=30 Hz. in the embodiment discussed. Of course, if the value of a were arbitrarily chosen as some other value, the values of the filters would be appropriately adjusted. The narrow band-pass filter 74 is principally used to eliminate as much as noise as possible from the signal at 58.
Multiplier and Perturbation Generator In FIG. 10a, the multiplier circuit 59 includes a conventional phase inverter 78 which functions to shift the phase of the input signal on terminal 58 180 on output terminal 79 from the output on output terminal 80. The output at 80 is the same as the input at 58. The signal at 58 is then effectively multiplied by a shift of 180 depending on which output, either 79 or 80 is selected by the switch 82. The switch 82 is any conventional double pole signal throw switch preferably electronically implemented. The switch 82 is switched between terminal 80 and 79 by means of the signal r(t) generated by the perturbation generator 67. The signal r(t) is derived from the signal sin (wt+ l as shown in FIG. 10b. The sin(mt+ l signal is derived from the sinwt signal generated in signal generator 84 and phase sifted through a conventional variable phase shifter 85. The direct output of the signal generator 84 is the signal p(t) connected to the adder 65 shown in FIG. 2. The phase shifter q is necessary to adjust for the phase angle of the response of the electromechanical position control unit 15 to the perturbation signal p(t). This phase shift 1 appears via the diffracted X-ray beam 5 in the X-ray detector 6 and some minor additional phase shift (all lumped into 1 is added in the feedback control unit 18 (all shown in FIG. 1).
Although not previously discussed and omitted for notational convenience, the angle 1 should appear in the signal at terminal 58 where I represents all of the phase shifts accumulated from terminal 55 through the position control unit, the X-ray detector and the rate converter and filter. Accordingly, the signal at 58 is actually sin(wt+ l dl/dl) at 0". The variable phase shifter 85 is adjusted to match the phase shift to the angle I in the signal at 58.
Although the mathematical development of the theory of operation of the present invention employed p(t) for the correlation, the present invention in the preferred embodiment employs r( t) which is a square wave signal with its zero crossing coincident with the zero crossings of the p(t) signal. With p(t)=sinwt, a square wave r(t) having the same zero crossing is given by:
i C, sin [(2/r+1)at] When r(t) is multiplied by the signal, I at terminal 58 in multiplier 59 the product becomes:
sin at i c sin [(2k+ Dal].
d! r( 01;, E
Expression (16), however, may be expressed as follows:
when expression (17) is integrated in the conventional integrator 63, the output becomes the desired i(0* OPERATION Since many of the details of operation have been previously discussed in connection with the above description, the operation will be described under this heading only in a summary fashion and generally with reference to FIG. I. To begin operation, a crystal 4 is placed in the position control unit as shown in detail in FIG. 8a. Thereafter, the crystal and the position control unit are rotated such that the X-ray source is incident with 0 approximately equal to Omax. With the position control unit thus situated, the scan motor 48 in FIG. 8 is initiated to scan the crystal back and forth between the extreme translation positions Ll andLZ. With the crystal thus positioned, the X-ray source 1 is energized and the resultant diffracted beam 5 is detected by the X-ray detector 6.
Thereafter, the perturbation generator 67 generates the signal p(t)=sinat where a=30 Hz. That perturbation signal is addedjn adder 65 with some initialization value K0) from the integrator 63 to form the current i which is supplied to the coils 38 (shown schematically in FIG. 7a) of the position control unit 15. This current i equals i(0*+p(l)) where the component i(0*) holds the crystal 4 at the operating point 0* and the component i(p(t)) causes the crystal to oscillate about 0* at the frequency of sinat. The magnitude of the oscillation about is such that the variation in the diffracted beam 5 average intensity is insignificant. For example, a variation in I not greater than l0 percent of the difference in intensity between l(0max) and KM), as discussed in connection with curve A of FIG. 3, would not be significant.
The X-ray detector 6 forms a signal I at its output 29 which is converted and filtered in the circuitry 57 of FIG. 2 to form at terminal 58 the signal sin(at-HI dl/dt) at 0*. The multiplier 59 multiplies that signal at terminal 58 with the signal r(t) as defined in expression (14) and as derived from the perturbation generator 67. That multiplication provides a signal of the form of expression (16) which is passed through low pass filter 61 having a cutoff frequency of 2a to form the derivative 9&0, dl/df) at 0* as indicated in expression (17,). That signal from the filter 61 is integrated in integrator 63 to form the component signal i(0*) which is again added with the signal p(t) in adder 65 to form the current i. The output from the integrator 63 continually changes such that the component current i(0*) continually adjusts the angle 0 such that 0* tends to equal Omax.
ALTERNATE AND FURTHER EMBODIMENTS The position control unit of FIG. 1 has many equivalent variations. In FIG. 11, for example, a cantilever embodiment is shown where springs 34 only appear on one side of the crystal 4 with the magnetic elements 36 and 38 appearing on the other side. Of course, the permanent magnet 36 in FIG. 11 or any of the other permanent magnets 36 in the other views in this specification could be electromagncts having a suitable coil and holding current. While electromagnetic coupling has been preferred, of course, other nonfrictional forces such as electrostatic devices could be employed. For example, in FIG. 11 the magnet 36 and the coil 38 would be replaced by electrostatic plates. As previously indicated, springs, pin or jewel bearings, pneumatic floating and other low friction devices may be used to support the crystal mount.
In FIG. 12, a further equivalent variation of the position control unit is shown where the sample holder 2 is mounted on a flexible rod 88 which is free to resiliently bend and rotate. The coils 38 are positioned in perpendicular planes so as to coact with the magnets 36 and move the crystal 4 and holder 32 in two dimensions. Energizing the coils 38a with a signal including a perturbation component p(t) causes the holder 32 to be perturbed in the plane of the paper. Similarly, energizing the coils 38b with a perturbation component q(t) causes the holder 32 to be perturbed such that rotation occurs around the axis going through the rod 88 in a plane which comes out of the paper. Although in the embodiment described above in connection with FIG. 7 only one signal p(t) was employed. A second feedback control unit (not shown) can be employed in parallel with feedback control unit 18 of FIG. 1. The second control unit would be responsive to the perturbation signal q(t). If p(t)=sinat, then q(t) could equal sinBt. The second feedback control unit in parallel with the first control unit 18 would be analogous to that first unit but would be tuned to select 5 frequencies and exclude at frequencies. An appropriate control signal i(0*+q(t)) would be obtained as the output of the second feedback control unit and would feed coil 38b in FIG. 12. Of course, suspending the holder 32 from a hanging spring would allow the holder in crystal 4 to be perturbed in three dimensions rather than two of FIG. 12 if an appropriate third feedback control unit (not shown) were employed.
In FIG. 13, the perturbation p(t) and the angular position component i( 0") are not fully added together but are supplied to different positioning control units. With the switch 92 open, the p(t) signal is passed directly to the coils 38 which coils function to perturb the holder 32 in the manner previously discussed in connection with FIGS. 7a and 7b. The i(0*) component is not passed to the coils 38 as before but is passed to a rotational actuator 90 which separately functions to rotate the whole frame 41 in the same plane that the coils 38 rotate the holder 32. Actuator may be any conventional motor and gear combination, synchroqesolver or any other conventional positioning device. With the switch 92 open, both the adder 65 and threshold circuit 91 may be eliminated as serving no function.
Alternatively, the switch 92 may be closed in which a portion of the i(0*) input is added via adder 65 with the perturbation signal p(t) in order to give a fine adjustment of the angular position of the actuator 32. major portion of the i( 0*) input is transmitted to the actuator 90 for grossadjustments of the actuator 32 angle. The gross adjustment, of course, rotates the whole frame 41. The threshold circuit 91 may be any conventional device splitting the gross signal from the fine. The design of such a device would be obvious to those skilled in the art. I
While the feedback control unit 18 (as shown in detail in FIG. 2) included a normalizing DC gain feedback loop comprising the filter 71 and the comparative amplifier 72 for controlling the multivibrator 68 and the amplitude control 69, the apparatus, of course, can be operated without this feedback DC control while still retaining satisfactory perfonnance. The feedback gain control is particularly useful when many samples of varying conditions of structure are to be tested. The essential function of the feedback control unit is to provide a signal such as sin(wt+1 dI/dO in such a form that dl/dO can be recovered in a convenient manner such as by the multiplier 59 and the low pass filter 61.
While one preferred embodiment employs a scintillation counter for the X-ray detector 6, other equivalent detectors such as Geiger counters or X-ray vidicon tubes may be employed.
Although the photographic plate 12 is used in a preferred embodiment for recording the diffracted X-ray beam, electronic means may be used to record the topograph. For example, with the Xray detector 6, a vidicon tube, conventional means for converting the output of the vidicon tube to electronically storable signals may be employed to record topographs in system 20 when connected by switch 95. Having made an electronic recording of the topograph, conventional data processing techniques may be employed to compare that recorded topograph with empirically derived standard topographs to determine if the particular crystal 4 under test conforms to the desired standard. If the topograph from the crystal 4 varies significantly, the comparator system may render a signal via some signalling device such as a light, a typewriter output, or other similar means indicating the nature of the variation and whether or not the crystal should be rejected, reprocessed or accepted.
While the invention has been particularly shown and described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that the foregoing and other changes in form and detail may be made therein without departing from the spirit and scope of the invention.
What is claimed is:
1. A microscopy apparatus for examining a crystalline material comprising:
a radiation source for directing an incident radiation beam at the crystalline material and for thereby forming a diffracted radiation beam;
detector means for detecting the intensity of the diffracted beam;
position control means for supporting the crystalline material and for adjusting the angular position of the material with respect to the incident radiation beam; and
feedback control means connecting said detector means to said position control means, said feedback control means being operative to adjust said position control means toward an angular position which causes said detector means to detect a maximum intensity.
2. The apparatus of claim 1 wherein said position control means includes means for translating and means for rotating the crystalline material with respect to the incident radiation beam.
3. The apparatus of claim 2 wherein said feedback control means generates a control current as a function of the intensity detected by said detector means;
wherein said position control means includes support means angularly fixed with respect to the incident radiation beam;
wherein said means for rotating includes mount means rotatably mounted on said support means; and
wherein said mount and said support means include electrical means connected to receive the control current and to generate an electrical field which is operative, as a function of the control current, to rotate said mount means with respect to said support means.
4. An X-ray microscopy apparatus for examining a crystal comprising:
an X-ray source for directing an incident X-ray beam at the crystal and for thereby forming a diffracted X-ray beam which varies in intensity as a function of the angle formed between the crystal and the incident X-ray beam;
detector means, positioned to receive the diffracted beam, for detecting the intensity of the diffracted beam and for generating a detector signal as a function of that intensity;
feedback control means connected to said detector means and operative to generate a control signal as a function of the detector signal;
position control means including support means angularly fixed with respect to the incident X-ray beam, including a mount for holding the crystal in the path of the incident X-ray beam, including low friction means for rotatably fastening said mount to said support means so as to allow the crystal to be rotated with respect to the incident X-ray beam, including an electromagnetic field generator attached to said support means and connected to said feedback control means so as to generate an electromagnetic field as a function of the control signal, and including field responsive means, attached to said mount, operative to coact with the electromagnetic field so as to rotate said mount and the crystal and thereby tend to make the intensity detected by said detector means a maximum.
5. The apparatus of claim 4 wherein said low friction means includes one or more leaf springs connected between said mount and said support means.
6. The apparatus of claim 4 further including an X-ray photograph positioned between the crystal and the X-ray detector so as to record the diffracted X-ray beam.
7. The apparatus of claim 4 wherein said feedback control means includes,
integrator means for forming an integrator component of the control signal which establishes the crystal at a variable but relatively fixed operating angle with respect to the incident X-ray beam,
a perturbation generator for introducing a perturbation component into the control signal so as to angularly perturb the crystal about the operating angle,
and correlation means connected to said integrator means for recovering, from the detector signal, variations in detected intensity as a function of variations in the angle which the crystal forms with the incident X-ray beam.
8. The apparatus of claim 6 wherein said correlation means includes,
multiplier means for multiplying a signal derived from the detector signal by a perturbation signal derived from said perturbation generator to form a multiplied signal,
and includes a filter, connected between said multiplier means and said integrator, for recovering from said multiplied signal a filtered signal which varies as a function of the first derivative of the diffracted beam intensity with respect to the angle formed between the crystal and the incident X-ray beam.
9. The apparatus of claim 8 wherein said perturbation component is of the form sincut.
10. The apparatus of claim 9 wherein the perturbation signal is a square wave having axis crossings corresponding with the axis crossings of sinwt.
11. An X-ray microscopy apparatus for forming an X-ray topograph comprising:
an X-ray source for generating an incident X-ray beam and for directing the incident beam at said crystal thereby forming a difiracted X-ray beam, said incident beam forming an incident angle with said crystal and said diffracted beam varying in intensity as a diatonic function of said incident angle,
a scintillation counter for detecting the intensity of the diffracted beam and for generating a detector signal as a function of that intensity,
feedback control means including rate converter and filter means connected to said scintillation counter and operative to precondition said detector signal to form a preconditioned signal, including a perturbation generator for generating first and second perturbation signals, including multiplier means connected to said rate converter and filter means and to said perturbation generator for multiplying the preconditioned signal by the first perturbation signal to form a multiplied signal, including a low pass filter connected to said multiplier and operative to filter from the multiplied signal a filtered signal which varies as a function of the first derivative of the diffracted beam intensity with respect to the incident angle including an integrator connected to said low pass filter and operative to integrate the filtered signal to form an integrator signal, including an adder connected to said integrator and to said perturbation generator for adding the integrator signal to the second perturbation signal to form a control signal, and
position control means including support means angularly fixed with respect to the incident X-ray beam, including a mount for holding said crystal in the path of the incident beam, including one or more leaf springs for rotatably fastening said mount to said support means so as to allow the crystal to e rotated with respect to the incident X-ray beam, including an electromagnetic field generator attached to said support means and connected to said adder so as to generate an electromagnetic field as a function of the control signal, and including one or more permanent magnets attached to said mount within the electromagnetic field whereby said magnets coact with the electromagnetic field so as to rotate said mount and said crystal and thereby tend to make the intensity detected by said detector means a maximum.
12. The apparatus of claim 11 wherein said position control means further includes translating means connected to said support means for translating said crystal with respect to said incident beam.
13. A process control apparatus for comparing a sample crystal topograph with a standard crystal topograph comprising:
a radiation source for directing an incident radiation beam at a sample crystal and for thereby forming a diffracted radiation beam;
detector means for detecting the intensity of the diffracted beam and thereby forming topograph signals representing the sample crystal topograph;
position control means for supporting the sample crystal and for adjusting the angular position of the crystal with respect to the incident radiation beam;
feedback control means connecting said detector means to said position control means, said feedback control means being operative to adjust said position control means toward an angular position which causes said detector means to detect a maximum intensity; and
a topograph comparator system means, connected to said detector means, operative in response to the topograph signals to compare the sample crystal topograph with a standard crystal topograph.
14. The apparatus of claim 13 wherein said position control means includes means for translating and means for rotating the sample crystal with respect to the incident radiation beam.