CN111964876A - LRTE-NUFFT (line-of-the-earth-non-uniform Fourier transform) -based parallel plate optical uniformity measurement method - Google Patents

LRTE-NUFFT (line-of-the-earth-non-uniform Fourier transform) -based parallel plate optical uniformity measurement method Download PDF

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CN111964876A
CN111964876A CN202010743163.4A CN202010743163A CN111964876A CN 111964876 A CN111964876 A CN 111964876A CN 202010743163 A CN202010743163 A CN 202010743163A CN 111964876 A CN111964876 A CN 111964876A
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郭仁慧
刘成兴
宋萍萍
廖之山
许雅
付航
李建欣
何勇
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Nanjing University of Science and Technology
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Abstract

The invention discloses a method for measuring the optical uniformity of a parallel flat plate based on the non-uniform fast Fourier transform of low-rank approximation and Taylor expansion. Firstly, wavelength tuning phase-shifting interference is carried out by using a Fizeau type wavelength phase-shifting interferometer, and interferograms placed under a parallel flat plate to be detected and a cavity are respectively obtained; then, carrying out non-uniform fast Fourier transform based on low-rank approximation and Taylor expansion on interference light intensity data of each point of the interference pattern, and converting the interference light intensity data into a frequency domain for spectrum analysis; and finally, extracting corresponding frequency components under different interference cavity lengths, and performing inverse Fourier transform to obtain phase information of the interference pattern. And after the wave surface information is recovered, calculating to obtain the optical uniformity of the parallel plate to be measured. The invention adopts the spectrum analysis method based on LRTE-NUFFT, does not need to adopt an oversampling technology, can greatly save the memory space when a computer runs, and can quickly calculate the spectrum estimation of the non-uniform interference data.

Description

LRTE-NUFFT (line-of-the-earth-non-uniform Fourier transform) -based parallel plate optical uniformity measurement method
Technical Field
The invention relates to the field of optical interference measurement testing, in particular to a method for measuring the optical uniformity of a parallel plate based on low-rank approximation and Taylor expansion non-uniform fast Fourier transform (LRTE-NUFFT).
Background
The optical parallel plate is a commonly used optical element, and the quality of the optical performance of the optical parallel plate directly affects the normal operation of the system. The optical uniformity is an important index for evaluating the performance of the optical parallel plate, and reflects the inconsistency of the internal refractive indexes of the same optical material. If the optical uniformity of the optical parallel plate is poor, the change of the transmitted wavefront can be directly caused, the wave aberration of the optical system is changed, and the performance of the optical system is further influenced. Therefore, it is necessary and important to measure the optical uniformity of the optical parallel plate with high precision.
Among the numerous optical uniformity measurement methods, interferometry is the most accurate measurement method. The interferometry includes sample inversion, direct measurement, absolute measurement, and the like. The absolute Measurement method proposed in 1991 by Chiayu Ai and James C Wyant et al of Measurement of the innovative nature of a window (Journal of Fluids Engineering,1991,30(9): 602) 610) has been developed to date, and has high detection precision because it takes into account the surface shape error of the front and back surfaces of the material to be detected and the system error of the interferometer. DeGroot et al, in the Grating interferometer for warping testing (ol/21/3/ol-21-3-228.pdf,1996,21(3):228-0), put two diffraction gratings in front of a parallel plate, and when the light beam passes through, the light beam is first split and then combined, and the light beam can be combined on a certain surface of a sample by controlling the incident angle, so that the influence of interference of the front and rear surfaces is avoided. Novak et al, Analysis of a micropolarizer array-based homogeneous phase-shifting interferometer, propose a phase-shifting interferometer based on a micro-polarization array, and measure optical uniformity by obtaining interference of a specific surface by interference of short coherent polarized light.
In order to avoid phase shift errors caused by hardware phase shift, Deck et al, Multiple-surface phase-shifting interferometry (Proceedings of SPIE-The International Society for Optical Engineering,2001,4451: 424-. The method uses a wavelength phase-shifting interferometer to measure an optical parallel flat interference cavity and a cavity respectively, and separates interference fringes between a flat plate to be measured and a reference surface to realize high-precision measurement of optical uniformity. In 2019, Guo ren Hui et al, in Optical horizontal measurement of parallel plates by way of fast Gaussian grid non-uniform fast Fourier transform (Opt Express 2019; 27(9): 13072) also proposed a method for measuring Optical uniformity of parallel plates based on fast Gaussian grid non-uniform fast Fourier transform, which can effectively solve the problem of non-uniform phase shift but still needs a lot of calculations. The measuring method provided by the invention has small calculated amount on the basis of solving the non-uniform phase-shifting interference, and can save the storage space of a computer in operation.
Disclosure of Invention
The invention aims to provide a method for measuring the optical uniformity of a parallel plate based on LRTE-NUFFT, which avoids using an oversampling technology, reduces the operation amount and the storage space, and simultaneously carries out quick calculation on the frequency spectrum estimation of non-uniform interference data.
The technical solution for realizing the purpose of the invention is as follows: a method for measuring the optical uniformity of a parallel plate based on LRTE-NUFFT comprises the following steps:
step 1, sequentially placing a transmission reference plane T, a to-be-detected parallel flat plate (the front surface is A, and the rear surface is B) and a reflection reference plane R in an interference cavity of a Fizeau wavelength phase-shifting interferometer; setting a phase-shifting step length and acquiring the number N of interferograms, wherein the number N of interferograms satisfies the condition that N is 2nN is in accordance with the accuracyA positive integer; then, phase-shifting sampling is carried out to obtain interference light intensity data of the N interference patterns. Because the area of the parallel plate to be detected is smaller than that of the transmission plate and the reflection plate, the interference light intensity data of each interference image is divided into a non-multi-surface interference superposition region (only the planes T and R participate in interference) and a multi-surface interference superposition region (the planes T, A, B and R both participate in interference), non-uniform interference data of the multi-surface interference superposition region are collected and are recorded as non-uniform interference data c, and the step 2 is carried out;
step 2, selecting the non-multi-surface interference superposition area of each interference pattern, performing phase recovery on the non-multi-surface interference superposition area, and calculating to obtain the non-uniform phase shift quantity of each wavelength phase shift
Figure BDA0002607428620000021
Let the set of all non-uniform phase-shift quantities be the original non-uniform sampling sequence xjTurning to step 3;
step 3, calculating a rank parameter K according to the required measurement precision and the maximum offset gamma in the phase shift quantity with unequal intervals, and then calculating the rank parameter K according to the K value and the original non-uniform sampling sequence xjComputing a low rank matrix AKAnd vectors u, v, go to step 4;
step 4, carrying out matrix calculation on the vectors u and v and the non-uniform interference data c of a single pixel point of the multi-surface interference area in the interference image in the step 1 to obtain frequency spectrum data f, and completing the non-uniform discrete Fourier transform of the pixel point; then all pixel points of the multi-surface interference region are calculated in the same mode to obtain a frequency spectrum data set FdeconvTurning to step 5;
step 5, the frequency spectrum data set FdeconvThe peak value area in the step (1) is subjected to windowing extraction, inverse Fourier transform is carried out to obtain phase information corresponding to each group of interference fringes, and the phase information is converted into wave surface information W1～W6Turning to step 6;
step 6, carrying out cavity measurement, keeping the positions of the transmission reference plane T and the reflection reference plane R in the interference cavity constant, removing the parallel flat plate to be measured, carrying out wavelength tuning phase shift measurement, and calculating in the same way to obtain wave surface information W7And turning to step 7;
step 7, synthesizing wave surface information W1～W7And calculating to obtain the optical uniformity information delta n of the parallel plate to be measured.
Compared with the prior art, the invention has the following remarkable advantages: (1) the oversampling technology is not needed, and the storage space of the computer in operation is saved. (2) The method can reduce the system error caused by the wavelength tuning nonlinear phase shift, and solves the problem that the FFT cannot directly process the non-uniform data. (3) The operation is simple, and only two times of measurement are needed.
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FIG. 1 is a schematic flow chart of a method for measuring the optical uniformity of a parallel plate based on LRTE-NUFFT according to the present invention.
FIG. 2 is a schematic diagram of the wavelength-tuned interferometry principle of the present invention.
FIG. 3 is an interferogram obtained by sampling wavelength tuned interference in accordance with the present invention.
FIG. 4 is a schematic diagram of the phase shift amount of the nonlinear error in the wavelength tuning interference sampling process according to the present invention.
FIG. 5 is a spectral diagram of interference fringe data after non-uniform Fourier transform.
Fig. 6 is a diagram of simulation results of the present invention, in which (a) is a diagram of simulation results and (b) is a diagram of camera interference calculation results.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
Referring to fig. 1, the method for measuring the optical uniformity of the parallel plate based on LRTE-NUFFT of the present invention includes the following steps:
step 1, sequentially placing a transmission reference plane T, a to-be-detected parallel flat plate (the front surface is A, and the rear surface is B) and a reflection reference plane R in an interference cavity of a Fizeau wavelength phase-shifting interferometer; setting a phase-shifting step length and acquiring the number N of interferograms, wherein the number N of interferograms satisfies the condition that N is 2nN is a positive integer meeting the precision requirement; then, phase-shifting sampling is carried out to obtain interference light intensity data of the N interference patterns. Because the area of the parallel flat plate to be measured is more flat than the transmissionThe plate and the reflective plate are small, and the interference intensity data of each interference pattern obtained is divided into a non-multi-surface interference superimposed region (only the planes T and R participate in interference) and a multi-surface interference superimposed region (both the planes T, A, B and R participate in interference). As shown in fig. 2, TF is a transmission reference mirror, RF is a reflection reference mirror, the middle is a parallel plate to be measured, T, A, B and R are sequentially a reflecting surface of TF, front and back surfaces of the parallel plate to be measured, and a reflecting surface of RF. If only one reflection is considered, the superposed regions of multi-surface interference together generate six groups of interference fringes of T and A, T and B, T and R, A and B, A and R and B and R, and the light intensity c of each group of interference fringesiCan be expressed as:
Figure BDA0002607428620000041
Figure BDA0002607428620000042
i≈-4πhikΔλ/λ0 2(3) the non-uniform interference data c is formed by superposing six groups of interference data:
Figure BDA0002607428620000043
in the formula, aiAs background light intensity, biIn order to adjust the degree of modulation of the light intensity,
Figure BDA0002607428620000044
in order to be the initial phase position,iis a phase shift quantity, λ0Is the initial wavelength, hiIs the length of the interference cavity, WiK is the number of phase shifts, Δ λ is the wavelength conversion amount at the time of phase shift, and i is 1 to 6.
Step 2, selecting the non-multi-surface interference superposition area of each interference pattern, performing phase recovery, and calculating to obtain the non-uniform phase shift quantity of each wavelength phase shift
Figure BDA0002607428620000045
Let the set of all non-uniform phase-shift quantities be the original non-uniform sampling sequence xj. As shown in fig. 3, since the cross-sectional area of the interference cavity is larger than that of the parallel flat plate to be measured, only the cross-sectional portion of the middle parallel flat plate to be measured is a multi-surface interference overlapping region, and the rest is a non-multi-surface interference overlapping region, that is, only the T and R generate interference. And (3) carrying out phase reconstruction on the interference data in the non-multi-surface interference superposition area by utilizing a Fourier transform phase measurement method to obtain corresponding phase shift quantity. Fourier transform phase measurement, also called additive spatial linear carrier phase measurement, introduces a linearly varying phase in the fringe pattern by making the reflected light of T and R a fixed angle, and in general, for the sake of simplicity of calculation, only the phase change along the x-axis is considered, and the intensity of the interference fringe in this region in the first interferogram is:
Il(x)＝al+bl cos(φl+2πfxx) (5)
in the formula, philIs the total phase, i.e. the sum of the initial phase and the amount of phase shift, fxL is 2 to N, which is the spatial frequency of the interference fringes.
The formula (5) is transformed by using the euler formula to obtain:
Figure BDA0002607428620000046
in the formula, i is an imaginary number.
Fourier transform is simultaneously carried out on two sides of the formula (6) to obtain:
Figure BDA0002607428620000047
in the formula, al(0) The frequency spectrum has positive and negative first-order sidelobes of interference light intensity frequency and phase phi of interference patternlIs locked at the peak position f of the amplitude spectrumv＝±fxIn the method, a proper filter is used to select a positive-order (or negative-order) spectrum for windowingTo obtain the spectrum psi (f)v)：
Figure BDA0002607428620000051
Performing inverse fourier transform on equation (8) to obtain:
Figure BDA0002607428620000052
the amplitude angle is calculated according to the formula (9) to obtain the phase phil：
Figure BDA0002607428620000053
The same operation is carried out on the N interference patterns, and the phase phi corresponding to each interference pattern is obtained through calculationlObtaining the non-uniform phase shift quantity of each wavelength phase shift
Figure BDA0002607428620000054
Figure BDA0002607428620000055
Wherein k is 1 to N. Let the set of all non-uniform phase-shift quantities be the original non-uniform sampling sequence xj：
Figure BDA0002607428620000056
The resulting original non-uniform sampling sequence is shown in fig. 4.
Step 3, calculating a rank parameter K according to the required measurement precision and the maximum offset gamma in the phase shift quantity with unequal intervals, and then calculating the rank parameter K according to the K value and the original non-uniform sampling sequence xjComputing a low rank matrix AKAnd vectors u, v. To distinguish from the identity matrix I, the non-uniform interference data is denoted by c instead, where c is (c)1，c2，c3，...，cN)TOriginal non-uniform sampling sequence xjNormalized to [0,1]X isj＝(x1，x2，x3，...，xN)T. c non-uniform discrete fourier transform:
Figure BDA0002607428620000057
in the formula 1<<j，k<<And N is added. Order to
Figure BDA0002607428620000058
Fjk＝e-2πijk/N(hereinafter, each F is used2A, F simplified representation), then:
Figure BDA0002607428620000059
in the formula (I), the compound is shown in the specification,
Figure BDA00026074286200000514
is the product of Hadamard, i.e. if Cij＝Aij×Bij，
Figure BDA00026074286200000513
If the sampling is approximately uniform, i.e. sample point xjThe existence parameter of j/N of the ideal uniform sampling point is 0 < gamma < 1/2, which satisfies the condition
Figure BDA00026074286200000510
At this time
Figure BDA00026074286200000511
Sufficiently small, AjkCan be approximated as a low rank matrix of rank K, decomposed into the product of two vectors:
Figure BDA00026074286200000512
let x be (x)0，x1，...，xN-1)T，e＝(0，1/N，...，(N-1)/N)T，ω＝(0，1，...，N-1)TIt is possible to obtain:
Figure BDA0002607428620000061
in the formula, A is
Figure BDA0002607428620000062
The simplification of (1) is that K is an integer related to precision and maximum offset gamma, when a polynomial is approximated to a finite polynomial by an infinite polynomial, the precision requirement can be just met when the polynomial is approximated to the K term, and the number of the polynomial is the value of K, namely, | | A-AK||maxWhen the content is less than or equal to the standard value,
Figure BDA0002607428620000063
vectors u and v are obtained according to equation (17):
u＝(N(x-j/N))r (18)
Figure BDA0002607428620000064
and 4, carrying out matrix calculation on the vectors u and v and the non-uniform interference data c of a single pixel point of the multi-surface interference region in the interference pattern in the step 1 to obtain frequency spectrum data f, and completing the non-uniform discrete Fourier transform of the pixel point. Rewriting equation (13) into a matrix form, there are:
f＝F2·c (20)
approximation of A by formula (14) and AKThe relationship of (1) is as follows:
Figure BDA0002607428620000065
in the formula, F2Is composed of
Figure BDA0002607428620000066
In a simplification of (1), F is Fjk＝e-2πijk/NSimplification of (D)uAnd DvFor diagonal matrices, the values of the u vectors lie in matrix DuOn the diagonal of (a), the values of the v vectors lie in the matrix DvOn the diagonal of (c). Then all pixel points of the multi-surface interference region are calculated in the same mode to obtain a frequency spectrum data set Fdeconv。
Step 5, the frequency spectrum data set FdeconvThe peak value area in the step (1) is subjected to windowing extraction, inverse Fourier transform is carried out to obtain phase information corresponding to each group of interference fringes, and the phase information is converted into wave surface information W1～W6. As shown in fig. 5, the frequency spectrum data f of each pixel point in the multi-surface interference region includes six peak values, which correspond to the cavity length values of six groups of different interference fringes. Windowing extraction and inverse Fourier transformation are respectively carried out on six frequency peak values of each pixel point to obtain phase information of the whole multi-surface interference area under each group of interference fringe frequency, and corresponding wave surface information W can be obtained through unwrapping and tilt elimination1～W6. The relationship between each wavefront information and the length of the interference cavity is shown in the following table:
TABLE 1 optical path difference and interference cavity Length for each set of fringes
Serial number Interference surface Optical path difference Length of interference cavity
1 T and A W1＝2A-2T h1＝L1
2 T and B W2＝2A-2T+2n0(B-A)+2Δn·t h2＝2(L1+n0t)
3 T and R W3＝2R-2T+2n0(B-A)+2Δn·t+2A-2B h3＝2(L1+L2+n0t)
4 A and B W4＝2n0(B-A)+2Δn·t h4＝2n0t
5 A and R W5＝2R+2n0(B-A)+2Δn·t-2B h5＝2(L2+n0t)
6 B and R W6＝2R-2B h6＝2L2
In the table, the number of the first and second,n0is the refractive index of the parallel plate to be measured, and t is the thickness of the parallel plate to be measured.
Step 6, carrying out cavity measurement, keeping the positions of the transmission reference plane T and the reflection reference plane R in the interference cavity constant, removing the parallel flat plate to be measured, carrying out wavelength tuning phase shift measurement, and obtaining wave surface information W7. In this case, interference fringes are generated only by interference of T and R, and wavefront information W7And the interference cavity length is respectively:
W7＝2R-2T (22)
h7＝2(L1+L2+t) (23)
step 7, synthesizing wave surface information W1～W7And calculating to obtain optical uniformity information delta n of the parallel plate to be detected:
Figure BDA0002607428620000071
examples
In order to verify the feasibility of the algorithm, the measured wavefront data are utilized to simulate the surface profiles of the transmission reference plane T, the reflection reference plane R, the front surface A of the board to be measured and the rear surface B of the board to be measured and the optical uniformity of the board to be measured, a quadratic equation is used for simulating uneven phase shift, and the interference result is simulated through formulas (1) to (4). And then, calculating the simulated interference result by adopting the text algorithm to obtain the optical uniformity of the plate to be tested, and comparing the optical uniformity with the simulated optical uniformity to verify the feasibility of the algorithm.
Suppose L1＝45mm，t＝60mm，L2＝165mm，n0And setting the quadratic coefficient to be 0.0065nm/V according to the nonlinear relation between the wavelength of the wavelength tuning laser and the control voltage so as to obtain non-uniform phase shift. A total of 256 phase-shifted interferograms are obtained by generating a total of six sets of interference fringes through simulation and then obtaining the total interference intensity by superimposing the six sets of intensities. Finally, the 256 phase-shifted interferograms are calculated by the algorithm presented herein to yield an optical uniformity distribution that is correlated with the simulated optical powerUniformity distributions were compared. As shown in fig. 6, the left graph is the simulated optical uniformity distribution, and the right graph is the optical uniformity distribution calculated by the phase-shift interferogram, and the optical uniformity distributions of the two are substantially the same, which illustrates the feasibility of the algorithm.

Claims (7)

1. A method for measuring the optical uniformity of a parallel plate based on LRTE-NUFFT is characterized by comprising the following steps:
step 1, sequentially placing a transmission reference plane T, a to-be-detected parallel flat plate and a reflection reference plane R in an interference cavity of a Fizeau wavelength phase-shifting interferometer; the front surface of the parallel flat plate to be detected is A, the rear surface of the parallel flat plate to be detected is B, the number N of the acquired interferograms and the phase-shifting step length are set, wherein the number N of the interferograms satisfies that N is 2nN is a positive integer meeting the precision requirement; and performing phase-shifting sampling to obtain interference light intensity data of the N interference patterns. The area of the parallel flat plate to be detected is smaller than that of the transmission flat plate and the reflection flat plate, so that the interference light intensity data of each interference image is divided into a non-multi-surface interference superposition area and a multi-surface interference superposition area, non-uniform interference data of the multi-surface interference superposition area are collected and recorded as non-uniform interference data c, and the step 2 is carried out;
step 2, selecting a non-multi-surface interference superposition area in the interference light intensity data of each interference pattern, carrying out phase recovery on the non-multi-surface interference superposition area, and calculating to obtain the non-uniform phase shift quantity of each wavelength phase shift
Figure FDA0002607428610000011
Let the set of all non-uniform phase-shift quantities be the original non-uniform sampling sequence xjTurning to step 3;
step 3, calculating a rank parameter K according to the required measurement precision and the maximum offset gamma in the phase shift quantity with unequal intervals, and calculating the rank parameter K according to the K and the original non-uniform sampling sequence xjComputing a low rank matrix AKAnd vectors u, v, go to step 4;
step 4, carrying out matrix calculation on the vectors u and v and the non-uniform interference data c of the single pixel point of the multi-surface interference area in the step 1 to obtain frequency spectrum data f, and finishing the pairNon-uniform discrete Fourier transform of the pixel point; calculating all pixel points of the multi-surface interference region in the same mode to obtain a frequency spectrum data set FdeconvTurning to step 5;
step 5, the frequency spectrum data set FdeconvThe peak value area in the step (1) is subjected to windowing extraction, inverse Fourier transform is carried out to obtain phase information corresponding to each group of interference fringes, and the phase information is converted into wave surface information W1～W6Turning to step 6;
step 6, carrying out cavity measurement, keeping the positions of a transmission reference plane T and a reflection reference plane R in an interference cavity of the Fizeau wavelength phase-shifting interferometer fixed, removing the parallel flat plate to be measured, carrying out wavelength tuning phase-shifting measurement, and calculating in the same way to obtain wave surface information W7And turning to step 7;
step 7, synthesizing wave surface information W1～W7And calculating to obtain the optical uniformity information delta n of the parallel plate to be measured.
2. The method of claim 1, wherein the method comprises the following steps: the non-multi-surface interference superposition area in the interference light intensity data of the interference pattern is an area where a transmission reference plane T and a reflection reference plane R participate in interference; the multi-surface interference superposition area is an area where the transmission reference plane T, the front surface A of the parallel flat plate to be detected, the rear surface B of the parallel flat plate to be detected and the reflection reference plane R all participate in interference.
3. The method of claim 1, wherein the method comprises the following steps: the multi-surface interference superposition area of the interference light intensity data in the interference pattern in the step 1 is formed by superposing six groups of multi-surface interference under different cavity lengths, and the light intensity c of each group of interference fringesiComprises the following steps:
Figure FDA0002607428610000021
Figure FDA0002607428610000022
i≈-4πhikΔλ/λ0 2 (3)
the non-uniform interference data c is formed by superposing six groups of interference data:
Figure FDA0002607428610000023
in the formula, aiAs background light intensity, biIn order to adjust the degree of modulation of the light intensity,
Figure FDA0002607428610000024
in order to be the initial phase position,iis a phase shift quantity, λ0Is the initial wavelength, hiIs the length of the interference cavity, WiK is the number of phase shifts, Δ λ is the wavelength conversion amount at the time of phase shift, and i is 1 to 6.
4. The method of claim 1, wherein the method comprises the following steps: the original non-uniform sampling sequence x of step 2jFor each set of non-uniform phase-shift quantities, the formula is as follows:
Figure FDA0002607428610000025
Figure FDA0002607428610000026
in the formula (I), the compound is shown in the specification,
Figure FDA0002607428610000027
non-uniform phase shift amount for each wavelength phase shift, philTotal phase of the first interferogram obtained for phase recovery，k＝1～N，l＝2～N。
5. The method of claim 1, wherein the method comprises the following steps: the step 3 is that the low rank matrix AkAnd vectors u, v, the calculation formula is as follows:
Figure FDA0002607428610000028
u＝(N(x-j/N))r (18)
Figure FDA0002607428610000029
in which A is an intermediate variable
Figure FDA00026074286100000210
For simplicity, x, e and ω are all intermediate variables, x ═ x0，x1，...，xN-1)T，e＝(0，1/N，...，(N-1)/N)T，ω＝(0，1，...，N-1)TK is an integer related to the maximum offset γ and the precision, and N is the number of interferograms acquired.
6. The method of claim 1, wherein the method comprises the following steps: the calculation formula of the frequency spectrum data f in the step 4 is as follows:
Figure FDA0002607428610000031
in the formula, F2As an intermediate variable
Figure FDA0002607428610000032
In a simplification of (1), F is an intermediate variable Fjk＝e-2πij/NSimplification of (D)uAnd DvFor diagonal matrices, the values of the u vectors lie in matrix DuOn the diagonal of (a), the values of the v vectors lie in the matrix DvOn the diagonal of (a) the line of the,
Figure FDA0002607428610000033
is the product of Hadamard, i.e. if Cij＝Aij×Bij，
Figure FDA0002607428610000034
7. The method of claim 1, wherein the method comprises the following steps: and 7, calculating the optical uniformity information delta n of the parallel plate to be detected according to the formula:
Figure FDA0002607428610000035
in the formula, W1～W7Sequentially comprises a transmission reference plane T, a front surface A of a parallel flat plate to be measured, a transmission reference plane T, a rear surface B of the parallel flat plate to be measured, a transmission reference plane T, a reflection reference plane R, a front surface A of the parallel flat plate to be measured, a rear surface B of the parallel flat plate to be measured, a front surface A of the parallel flat plate to be measured, a rear surface R of the parallel flat plate to be measured, a rear surface B of the parallel flat plate to be measured, a reflection reference plane R and wave surface information under cavity measurement interference, n0Is the refractive index of the parallel plate to be measured, and t is the thickness of the parallel plate to be measured.
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