CN103630336B - The dynamic interferometry method of array is postponed based on random phase retardation - Google Patents

Abstract

The invention discloses a kind of dynamic interferometry method postponing array based on random phase retardation.Step is as follows: adopt and postpone the phase shifting device of array as dynamic interference system, described delay array comprises 4 sub-wave plates and each wavelet sheet is respectively λ/4 slice, λ/2 slice, 3 λ/4 slice, λ sheet, postpones array rear and arranges the polaroid that shake direction and horizontal direction angle are 45 °; In dynamic interferometer test arm, place standard flat mirror, collect 4 linear carrier frequency phase-shift interferences by CCD; Fourier transform is carried out to each linear carrier frequency phase-shift interference, demarcates and postpone array each wavelet sheet phase retardation; In the test arm of dynamic interferometer, put into be measured, regulate inclination pitching and the axial defocusing of to be measured, obtain simultaneous phase-shifting interferogram; According to each wavelet sheet phase retardation demarcated and simultaneous phase-shifting interferogram, process obtains the PHASE DISTRIBUTION of to be measured.The method is quick and easy, is applicable to the dynamic interferometer adopting light splitting scheme.

Description

The dynamic interferometry method of array is postponed based on random phase retardation

Technical field

The invention belongs to interference of light metering field, particularly a kind of dynamic interferometry method postponing array based on random phase retardation.

Background technology

The interference of light detects one of high-precision optical element and the most effective means of system, and along with the progress of the technology such as detecting technique, precision optical machinery, computer technology, modern age, optical interferometry technology obtained significant progress.Along with the proposition of shift-phase interferometry, achieve high precision, real-time, multiparameter, automatic test, greatly improve the measuring accuracy of interferometer, facilitate the raising of contemporary optics manufacture level.But movable phase interfere is responsive especially to environment, ambient vibration and air turbulence can have a strong impact on measurement result, and therefore, most of interference testing work is all carry out on the optics vibration-isolating platform of laboratory.But increasing occasion needs on-line checkingi, calibrates big-and-middle-sized optical element or optical system at present.In this case, tradition phase-shifting interferometry precision will be subject to the impact of the factor such as ambient vibration, air turbulence, even causes measuring unsuccessfully time serious.

Dynamic interference system can obtain several phase-shift interferences in synchronization, different locus, effectively can avoid the impact becoming error component when vibration, air turbulence etc.The spatial Phase-shifting Method scheme that current dynamic interference system adopts mainly contains quarter wave plate and polarizer group and forms spacing phase shifter, quarter wave plate and micro-polarization arrays and form spacing phase shifter, micro-delay array and polaroid and form spacing phase shifter.The phase retardation accuracy requirement of existing scheme to the light transmission shaft of polaroid and wave plate is higher, and therefore most of simultaneous phase-shifting interference system all needs to carry out accurate calibration to the Axis Azimuth angle of this two classes polarizer.Existing polarizer calibration steps is all rely on other assistant experiment condition to calibrate Axis Azimuth angle before measuring, realizes than being easier to single polaroid and wave plate.Due to higher to the integrated requirement of polarizer in dynamic interference system, the difficulty of simultaneously calibrating multiple polarization components and parts is in a system comparatively large, and in addition, the manufacture difficulty of micro-polarization arrays and micro-delay array is comparatively large, and cost is very high.

Summary of the invention

The object of the present invention is to provide a kind of dynamic interferometry method postponing array based on random phase retardation, utilize random phase retardation to postpone array as spacing phase shifter, in dynamic interference system, accurate calibration is carried out to polarizer.

The technical solution realizing the object of the invention is: a kind of dynamic interferometry method postponing array based on random phase retardation, comprises the following steps:

Step 1, adopt and postpone the phase shifting device of array as dynamic interference system, described delay array comprises 4 sub-wave plates and each wavelet sheet is respectively λ/4 slice, λ/2 slice, 3 λ/4 slice, λ sheet, postpones array rear and arranges polaroid, and thoroughly shake direction and the horizontal direction angle of this polaroid are 45 °;

Step 2, places standard flat mirror in dynamic interferometer test arm, and the inclination pitching of adjustment standard flat mirror makes the fringe number in interferogram be greater than 20, collects 4 linear carrier frequency phase-shift interferences by CCD;

Step 3, carries out Fourier transform to each linear carrier frequency phase-shift interference, demarcates and postpones array each wavelet sheet phase retardation;

Step 4, puts into be measured in the test arm of dynamic interferometer, regulates inclination pitching and the axial defocusing of to be measured, obtains simultaneous phase-shifting interferogram;

Step 5, the simultaneous phase-shifting interferogram in each wavelet sheet phase retardation demarcated according to step 3 and step 4, process obtains the PHASE DISTRIBUTION of to be measured.

Compared with prior art, remarkable advantage of the present invention is: (1) does not need to carry out manual calibration to the phase retardation postponing each wavelet sheet of array before measuring, and method is quick and easy; (2) without any additional assistant experiment hardware, the dynamic interferometry system that great majority adopt light splitting scheme is applicable to; (3) there is accurate, reliable advantage.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the dynamic interferometry method that the present invention is based on random phase retardation delay array.

Fig. 2 is the linear carrier frequency simultaneous phase-shifting interferogram that the present invention is collected by CCD.

Fig. 3 is the spectrogram that Fig. 2 neutral line carrier frequency interferogram is corresponding, wherein corresponds respectively to (a) λ/4 wave plate, (b) λ/2 wave plate, (c) 3 λ/4 wave plate, (d) λ wave plate.

Fig. 4 is that the present invention tests gained simultaneous phase-shifting interferogram.

Fig. 5 is the PHASE DISTRIBUTION figure that measuring method of the present invention obtains.

The PHASE DISTRIBUTION figure that Fig. 6 tradition four step phase-shifting methods obtain.

Embodiment

Below in conjunction with drawings and the specific embodiments, further description is made to the present invention.

Composition graphs 1, the present invention is based on the dynamic interferometry system that random phase retardation postpones array, adopt and postpone the phase shifting device of array as dynamic interference system, reference light and test light are respectively through 4 quadrants postponing array, again through polaroid, produce simultaneous phase-shifting interferogram, the amount of phase shift of each sub-interferogram is followed successively by pi/2, π, 3 pi/2s, 2 π.In the present invention, thoroughly shake direction and horizontal direction angle of polaroid is calibrated to 45 ° (existing method can be calibrated), and postponing each wavelet sheet phase retardation in array is γ ₁, γ ₂, γ ₃, γ ₄, and γ ₁for phase retardation, the γ of λ/4 wavelet sheet ₂for phase retardation, the γ of λ/2 wavelet sheet ₃be the phase retardation of 3 λ/4 wavelet sheets, γ ₄for the phase retardation of λ wavelet sheet; Each sub-interferogram expression formula can be expressed as:

This system with other based on grating beam splitting scheme dynamic interferometry system compared with, difference is, the present invention adopts and postpones array as phase shifting device, the feature postponing array is: in the direction of the clock, each wavelet sheet is followed successively by λ/4 wave plate, λ/2 wave plate, 3 λ/4 wave plates, λ wave plate.

Composition graphs 2 ~ 4, the present invention is based on the dynamic interferometry method that random phase retardation postpones array, utilize random phase retardation to postpone array carries out interferometry method as the dynamic interferometry system of spacing phase shifter, to be measured is chosen spherical mirror is example, comprises the following steps:

Step 1, adopt and postpone the phase shifting device of array as dynamic interference system, described delay array comprises 4 sub-wave plates and each wavelet sheet is respectively λ/4 slice, λ/2 slice, 3 λ/4 slice, λ sheet, postpones array rear and arranges polaroid, and thoroughly shake direction and the horizontal direction angle of this polaroid are 45 °;

Step 2, places standard flat mirror in dynamic interferometer test arm, and the inclination pitching of adjustment standard flat mirror makes the fringe number in interferogram be greater than 20, collects 4 linear carrier frequency phase-shift interferences as shown in Figure 2 by CCD;

Step 3, carries out to each linear carrier frequency phase-shift interference the frequency spectrum that Fourier transform obtains as shown in Figure 3, demarcates and postpone array each wavelet sheet phase retardation; Concrete steps are as follows:

(1) Fourier transform is carried out to every sub-linear carrier frequency phase-shift interference and obtain corresponding frequency spectrum profile, extract+1 grade of secondary lobe of each frequency spectrum profile, resolve I _pi/2, I _π, I _{3 pi/2s}three sub-interferograms are relative to I _{2 π}the degree of modulation V of interferogram _i, that is:

$V_i=\frac{\mathrm{abs}\left\{{\mathrm{FT}}^{-1}{\{\mathrm{Filter}}_{+1}\right\{\mathrm{FT}\left\{i\right\}\left\}\right\}\}}{\mathrm{abs}\left\{{\mathrm{FT}}^{-1}\right\{{\mathrm{Filter}}_{+1}\left\{\mathrm{FT}\right\{I_{2\mathrm{\π}}\left\}\right\}\left\}\right\}},i=I_{\mathrm{\π}/2},I_{\mathrm{\π}},I_{3\mathrm{\π}/2}---\left(2\right)$

In formula, FT{} represents and carries out Fourier transform to interferogram, FT ^-1{ } represents inverse Fourier transform computing; Filter _{+ 1}{ } represents+1 grade of secondary lobe extracting frequency spectrum; Abs{} represents and takes absolute value;

Again according to the relation between the phase retardation of each wavelet sheet and contrast, can obtain:

$\left\{\begin{array}{c}{\mathrm{\γ}}_1=\±\frac{\arccos \sqrt{\frac{1+\sqrt{1-4(1-{V_I}_{\mathrm{\π}/2})}}{2}}}{2}\\ {\mathrm{\γ}}_2=\±\frac{{{\arccos V}_I}_{\mathrm{\π}}}{4}\\ {\mathrm{\γ}}_3=\±\frac{\arccos \sqrt{\frac{1+\sqrt{1-4(1-{V_I}_{3\mathrm{\π}/2})}}{2}}}{2}\end{array}\right.---\left(3\right)$

Wherein γ ₁for phase retardation, the γ of λ/4 wavelet sheet ₂for phase retardation, the γ of λ/2 wavelet sheet ₃it is the phase retardation of 3 λ/4 wavelet sheets;

(2) in order to determine azimuthal direction further, in calibration process, adjusting the light intensity a of test light and the light intensity b of reference light, make a>b, extract the amplitude C of 0 grade of frequency spectrum successively _κ, as shown in Figure 3, namely

C _κ＝abs{FT ^-1{Filter _x{FT{κ}}}}κ＝I _π/2，I _π，I _3π/2,I _2π

Filter in formula ₀{ } represents extraction 0 grade of frequency spectrum, assuming that wave plate phase retardation γ _ispan is that (-π/8, π/8) judge the direction of each wavelet sheet phase retardation according to following formula:

$\left\{\begin{array}{cc}{\mathrm{\γ}}_i\∈(0,\mathrm{\π}/2)& \mathrm{if}\frac{C_{\mathrm{\κ}}}{{C_I}_{2\mathrm{\π}}}>1\\ {\mathrm{\γ}}_i\∈(-\mathrm{\π}/\mathrm{2,0})& f\frac{C_{\mathrm{\κ}}}{{C_I}_{2\mathrm{\π}}}>1\end{array}\right.,\mathrm{\κ}=I_{\mathrm{\π}/2},I_{\mathrm{\π}},I_{3\mathrm{\π}/2},i=\mathrm{1,2,3}---\left(4\right)$

Namely the demarcation of each wavelet sheet phase retardation is completed through above step.

Step 4, puts into be measured in the test arm of dynamic interferometer, i.e. spherical mirror to be measured, regulates inclination pitching and the axial defocusing of to be measured, obtains simultaneous phase-shifting interferogram as shown in Figure 4;

Step 5, the simultaneous phase-shifting interferogram in each wavelet sheet phase retardation demarcated according to step 3 and step 4, process obtains the PHASE DISTRIBUTION of to be measured.Specific as follows: according to step 3 demarcate each wavelet sheet phase retardation and step 4 in simultaneous phase-shifting interferogram, solve system of linear equations:

B＝AX(5)

Wherein

B＝[I _π/2I _πI _3π/2I _2π] ^T

$A=\left[\begin{array}{cccc}1& \frac{1}{2}\sin 4{\mathrm{\γ}}_1& {\sin }^2{2\mathrm{\γ}}_1& -\cos 2{\mathrm{\γ}}_1\\ 1& \sin 4{\mathrm{\γ}}_2& -\cos 4{\mathrm{\γ}}_2& 0\\ 1& \frac{1}{2}\sin 4{\mathrm{\γ}}_3& {\sin }^{2}2{\mathrm{\γ}}_3& \cos 2{\mathrm{\γ}}_3\\ 1& 0& 1& 0\end{array}\right]$

Unknown vector X can be obtained by following formula:

X＝A ^-1B(6)

Assuming that the inverse matrix of coefficient matrices A can be represented by the formula:

$A^{-1}=\left[\begin{array}{cccc}{a}_{11}^{\′}& a_{12}^{\′}& a_{13}^{\′}& a_{14}^{\′}\\ a_{21}^{\′}& a_{22}^{\′}& a_{23}^{\′}& a_{24}^{\′}\\ a_{31}^{\′}& a_{32}^{\′}& a_{33}^{\′}& a_{34}^{\′}\\ a_{41}^{\′}& a_{42}^{\′}& a_{43}^{\′}& a_{44}^{\′}\end{array}\right]---\left(7\right)$

To be measured phase place distribution can be solved by following formula:

By above step, the kinetic measurement that just can realize phase place under the condition that wave plate group phase retardation is calibrated can not needed, measure the PHASE DISTRIBUTION figure of spherical mirror to be measured as shown in Figure 5, compare the PHASE DISTRIBUTION figure that Fig. 6 adopts traditional four step phase-shifting methods to obtain, the traditional four step Phase-shifting algorithm of direct use can introduce obvious ripple error in the measurement results, and the measuring method adopting the present invention to propose, can significantly suppress ripple error as shown in Figure 5.

Claims (2)

1. postpone a dynamic interferometry method for array based on random phase retardation, it is characterized in that, comprise the following steps:

Step 1, adopt and postpone the phase shifting device of array as dynamic interference system, described delay array comprises 4 sub-wave plates and each wavelet sheet is respectively λ/4 slice, λ/2 slice, 3 λ/4 slice, λ sheet, postpones array rear and arranges polaroid, and thoroughly shake direction and the horizontal direction angle of this polaroid are 45 °;

Step 2, places standard flat mirror in dynamic interferometer test arm, and the inclination pitching of adjustment standard flat mirror makes the fringe number in interferogram be greater than 20, collects 4 linear carrier frequency phase-shift interferences by CCD;

Step 3, carries out Fourier transform to each linear carrier frequency phase-shift interference, demarcates and postpones array each wavelet sheet phase retardation;

Step 4, puts into be measured in the test arm of dynamic interferometer, regulates inclination pitching and the axial defocusing of to be measured, obtains simultaneous phase-shifting interferogram;

Step 5, according to step 3 demarcate each wavelet sheet phase retardation and step 4 in simultaneous phase-shifting interferogram, process obtains the PHASE DISTRIBUTION of to be measured, specific as follows: the simultaneous phase-shifting interferogram in each wavelet sheet phase retardation demarcated according to step 3 and step 4, solves system of linear equations:

B＝AX

Wherein

B＝[I _π/2I _πI _3π/2I _2π] ^T

$A=\left[\begin{array}{cccc}1& \frac{1}{2}sin4{\mathrm{\γ}}_1& {\sin }^{2}2{\mathrm{\γ}}_1& -cos2{\mathrm{\γ}}_1\\ 1& \sin 4{\mathrm{\γ}}_2& -cos4{\mathrm{\γ}}_2& 0\\ 1& \frac{1}{2}sin4{\mathrm{\γ}}_3& {\sin }^{2}2{\mathrm{\γ}}_3& \cos 2{\mathrm{\γ}}_3\\ 1& 0& 1& 0\end{array}\right]$

Unknown vector X can be obtained by following formula:

X＝A ^-1B

Assuming that the inverse matrix of coefficient matrices A can be represented by the formula:

$A^{-1}=\left[\begin{array}{cccc}{a}_{11}^{\′}& a_{12}^{\′}& a_{13}^{\′}& a_{14}^{\′}\\ a_{21}^{\′}& a_{22}^{\′}& a_{23}^{\′}& a_{24}^{\′}\\ a_{31}^{\′}& a_{32}^{\′}& a_{33}^{\′}& a_{34}^{\′}\\ a_{41}^{\′}& a_{42}^{\′}& a_{43}^{\′}& a_{44}^{\′}\end{array}\right]$

To be measured phase place distribution can be solved by following formula:

Wherein, I _pi/2, I _π, I _{3 pi/2s}, I _{2 π}represent 4 sub-interferograms respectively:

γ ₁for phase retardation, the γ of λ/4 wavelet sheet ₂for phase retardation, the γ of λ/2 wavelet sheet ₃be the phase retardation of 3 λ/4 wavelet sheets, a represents the light intensity of test light, and b represents the light intensity of reference light, represent to be measured phase place.

2. the dynamic interferometry method postponing array based on random phase retardation according to claim 1, is characterized in that, the concrete steps of demarcating delay array each wavelet sheet phase retardation described in step 3 are as follows:

(1) Fourier transform is carried out to every sub-linear carrier frequency phase-shift interference and obtain corresponding frequency spectrum profile, extract+1 grade of secondary lobe of each frequency spectrum profile, resolve I _pi/2, I _π, I _{3 pi/2s}three sub-interferograms are relative to I _{2 π}the degree of modulation V of interferogram _i, that is:

$V_i=\frac{abs\left\{{\mathrm{FT}}^{-1}\right\{{\mathrm{Filter}}_{+1}\left\{FT\right\{i\left\}\right\}\left\}\right\}}{abs\left\{{\mathrm{FT}}^{-1}\right\{{\mathrm{Filter}}_{+1}\left\{FT\right\{I_{2\mathrm{\π}}\left\}\right\}\left\}\right\}},i=I_{\mathrm{\π}/2},I_{\mathrm{\π}},I_{3\mathrm{\π}/2}$

In formula, FT{} represents and carries out Fourier transform to interferogram, FT ^-1{ } represents inverse Fourier transform computing; Filter _{+ 1}{ } represents+1 grade of secondary lobe extracting frequency spectrum; Abs{} represents and takes absolute value;

Again according to the relation between the phase retardation of each wavelet sheet and contrast, can obtain:

Wherein γ ₁for phase retardation, the γ of λ/4 wavelet sheet ₂for phase retardation, the γ of λ/2 wavelet sheet ₃it is the phase retardation of 3 λ/4 wavelet sheets;

(2) adjust the light intensity a of test light and the light intensity b of reference light, make a>b, extract the amplitude C of 0 grade of frequency spectrum successively _κ, namely

C _κ＝abs{FT ^-1{Filter ₀{FT{κ}}}}κ＝I _π/2，I _π，I _3π/2,I _2π

Filter in formula ₀{ } represents extraction 0 grade of frequency spectrum, judges the direction of each wavelet sheet phase retardation according to following formula:

$\left\{\begin{array}{cc}{\mathrm{\&gamma;}}_i\&Element;(0,\mathrm{\&pi;}/2)& if\frac{C_{\mathrm{\&kappa;}}}{C_{I_{2\mathrm{\&pi;}}}}>1\\ {\mathrm{\&gamma;}}_i\&Element;(-\mathrm{\&pi;}/2,0)& if\frac{C_{\mathrm{\&kappa;}}}{C_{I_{2\mathrm{\&pi;}}}}<1\end{array}\right.,\mathrm{\&kappa;}=I_{\mathrm{\&pi;}/2},I_{\mathrm{\&pi;}},I_{3\mathrm{\&pi;}/2},i=1,2,3.$