CN116481655A - Phase-shifting interferometry method for non-iterative calculation of phase tilt parameters - Google Patents
Phase-shifting interferometry method for non-iterative calculation of phase tilt parameters Download PDFInfo
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Abstract
The invention discloses a phase-shifting interferometry method for non-iterative calculation of phase tilt parameters, which comprises the following steps: estimating a tilt term of a phase in the interferogram as an initial value; constructing least square fitting according to the initial value of the inclination term, and obtaining a constant term in the phase; constructing least square fitting according to the constant term of the obtained phase and the estimated inclination term of the x direction, and obtaining the inclination term of the y direction; constructing least square fitting according to the constant term of the obtained phase and the obtained inclination term of the y direction, and obtaining the inclination term of the x direction; repeating the previous steps for each frame of interference pattern to obtain the inclination parameters of the phase-shifting interference pattern; and (3) taking the difference of the inclination parameters of the phase-shifting interferogram to obtain a phase-shifting quantity, and obtaining phase distribution according to a least square phase-shifting algorithm to finish phase-shifting interferometry. The invention can finish phase-shifting interferometry in a vibration environment with high efficiency and high precision.
Description
Technical Field
The invention belongs to the technical field of optical interferometry, and particularly relates to a phase-shifting interferometry method for non-iterative calculation of phase tilt parameters.
Background
In phase-shifting interferometry, the phase-shifting quantity is used as a known condition and is actually influenced by factors such as environmental vibration or nonlinear errors of a phase shifter, the phase-shifting quantity deviates from a theoretical value, the known value is changed into an unknown quantity, in order to solve the phase-solving problem of unknown phase-shifting quantity, scholars propose a random phase-shifting technology which is also developed along with error sensitivity research on a traditional fixed-step phase-shifting algorithm, the early random phase-shifting technology is based on a least square phase-shifting algorithm, the phase-shifting quantity is obtained by an iterative mode and the like, and then the phase is restored, and the most typical Advanced Iterative Algorithm (AIA) is proposed by 2004 Wang (Wang, Z.Y.and B.T.Han (2004), "Advanced iterative algorithm for phase extraction of randomly phase-shifted interferometers." OPTICS LETTERS 29 (14): 1-1673.) and the AIA can simultaneously calculate the phase-shifting quantity only by more than 3 interferograms, and the AIA has no requirement on the interference pattern and has high minimum iterative operation accuracy in the two iterative processes. In 2009, hao (q., et al (2009), "Random phase-shifting interferometry without accurately controlling or calibrating the phase shift," OPTICS litters 34 (8): 1288-1290) proposed a method for processing a large number of Random phase-shifting interferograms by normalization of interferogram background light intensity and modulation, which requires phase shifting at a small angle, collecting a large number of interferograms, which is time-consuming. In 2011, vargas (Vargas, j., et al (2011), "Phase-shifting interferometry based on principal component analysis," OPTICS LETTERS 36 (8): 1326-1328.) applied Principal Component Analysis (PCA) in mathematical statistics to interferogram analysis. PCA does not need to calculate the phasor, greatly improves the calculation speed of the random phase shift algorithm, but the calculation accuracy is affected by the number of fringes in the interferogram.
It is noted that the above study is only directed to random translational phase shift, i.e., the phase shift amount is only a time variation amount, the spatial distribution is uniform, in practice, the tilt variation of the reference mirror and the test mirror is unavoidable, for example, the tilt shake of the mirror due to environmental vibration, the tilt of the reference mirror due to inconsistent stepping amount of the multi-point PZT, etc., and the interference pattern is first-order developed by using least square iteration for random tilt phase shift, chen (Chen, m.y., et al (2000), "Algorithm immune to tilt phase-shifting error for phase-shifting interference factors", "APPLIED OPTICS 39 (22): 3894-3898), etc., to realize small-amplitude tilt phase shift error compensation. In 2008, xu, J.C. (Xu, J.C., et al (2008), "Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shift," APPLIED OPTICS 47 (3): 480-485.) is improved on the basis of AIA algorithm, the interferogram is divided into blocks to calculate the phasors, and a plane fit is constructed to realize the calculation of the oblique phasors. The method has small error when the interference pattern background and the contrast are uniform, but can generate coupling effect on the calculation of the inclination coefficient when the interference pattern background and the contrast are not uniformly distributed. In 2009, deck, l.l. (2009), "Suppressing phase errors from vibration in phase-shifting intermediate," applies operation 48 (20): 3948-3960) proposes a multi-parameter physical model-based mps i method that compensates for phase-shifting tilt errors with background and modulation as time-independent amounts. In 2013, li (Li, J.X.), et al (2013), "Phase-tilting interferometry for optical testing," OPTICS LETTERS 38 (15): 2838-2841.) et al solve for tilt Phase shift parameters based on the idea of detecting straight lines by Hough transform, and achieve Phase solution for random tilt Phase shift. In 2014, juarez-Salazar (Juarez-Salazar, r., et al (2014), "Generalized phase-shifting algorithm for inhomogeneous phase shift and spatio-temporal fringe visibility variationj OPTICS EXPRESS 22 (4): 4738-4750.), et al proposed using least squares fitting to find the background light intensity and modulation degree of each frame of interferogram, thereby normalizing the interferograms, calculating the phase shift amount using least squares for the normalized interferograms, and finding the phase distribution from the phase shift amount. In the method, the phase shift amount, the background light intensity and the modulation degree can be changed in time domain and space domain, so that the universality of a random phase shift algorithm is greatly improved, and the only disadvantage is that the interference pattern is required to contain more stripes. In 2021, lu (Lu, w., et al (2021), "Anti-Vibration Interferometric Shape Measurement Based on Tilt phase," Acta Optica Sinica (2)), et al calculated the inclined phase plane of each frame of the interferogram based on fourier transform, obtained the phasors and used a least squares phase shift algorithm to obtain the phase distribution. The restoration accuracy of this method is not high due to the spectrum overlap problem. In the same year, mingliang Duan (Duan, M.L., et al (2021), "Phase-tilt Phase: accurate and robust Phase extraction from random tilt-shift interferometers," OPTICS AND LASERS IN ENGINEERING., "proposes an iterative method for solving a tilt Phase-shifting interferogram, which constructs a system of linear equations for tilt parameters of the interferogram, for solving the Phase shift between interferograms, and solving the Phase distribution by least squares, and iterating the obtained Phase distribution into the solution of the Phase shift, and repeating so on until convergence, to obtain the exact tilt parameters and Phase distribution of the interferogram. The method has high precision, but the algorithm involves a large number of least square operations, and the calculation time is long, so that the method is a method for sacrificing time to exchange precision. In 2022, chenhui Hu (Hu, c.h., et al (2022), "Parameter mismatch phase extraction method for spatial phase-shifting interference graphs," OPTICS AND LASERS IN ENGINEERING 154.) proposed a phase extraction method for spatially synchronized phase-shifting interferograms, which constructed a linear relationship between the contrast of the interferograms, carrier frequency error, and phase-shifting error, and iterated after a given initial value to achieve phase extraction. The method realizes the phase extraction of the interferogram with random tilt phase shifting and contrast time variation, and has higher requirement on the initial value on the solution phase.
Disclosure of Invention
The invention aims to provide a phase-shifting interferometry method for non-iterative calculation of phase tilt parameters, which can realize the calibration of a random tilt phase-shifting interferogram and a phase solving method, and realize high-precision phase-shifting interferometry in a vibration environment.
The technical solution for realizing the purpose of the invention is as follows: a phase-shifting interferometry method for non-iterative calculation of phase tilt parameters includes the following steps:
step 1, estimating an inclination term of a phase in an interferogram as an initial value;
step 2, constructing least square fitting according to initial values of the inclination terms, and obtaining constant terms in the phase;
step 3, constructing least square fitting according to the constant term of the obtained phase and the estimated inclination term of the x direction, and obtaining the inclination term of the y direction;
step 4, constructing least square fitting according to the constant term of the obtained phase and the obtained inclination term of the y direction, and obtaining the inclination term of the x direction;
step 5, repeating the steps 1 to 4 for each frame of interference pattern to obtain the inclination parameters of the phase-shifting interference pattern;
and 6, differencing the inclination parameters of the phase-shifting interferogram to obtain a phase-shifting quantity, and obtaining phase distribution according to a least square phase-shifting algorithm to finish phase-shifting interferometry.
Further, in step 1, the inclination term of the phase in the interferogram is estimated as an initial value, specifically as follows:
fourier transforming the interferogram to obtain a spectrogram, wherein the spectrum of the interferogram is expressed as:
wherein u and v are coordinates of a spectrum domain, f x And f y The carrier frequency of the interference light intensity in the x and y directions is represented by A, the Fourier transform of the interference pattern background is represented by lambda, the wavelength is represented by i, the imaginary unit is represented by i, and the Fourier transform of the cosine component of the interference pattern is represented by C;
and extracting a positive primary frequency spectrum according to a spectrogram of the interference pattern, and calculating a centroid to obtain centroid coordinates of the positive primary frequency spectrum, namely obtaining an inclination term of the phase in the x and y directions as an initial value.
Further, the least square fitting constructed according to the initial value of the inclination term in the step 2 is specifically:
the intensity of the interference light is expressed as:
wherein I is the interference light intensity, a is the interference pattern background, b is the modulation degreeM and n are tilt coefficients of the phase in the x direction and the y direction respectively, k is a constant term of the phase,is a higher-order term of the phase;
omitting phaseAfter that, the least squares of the construction are as follows:
where α=mi+nj, M, N is the row, column number, I of the interferogram ij Light intensity values of the ith row and the jth column in the interference diagram;
obtaining parameter A 1 、B 1 、C 1 The constant term coefficient k is then expressed as:
k＝tan- 1 (-C 1 /B 1 )
further, in step 3, a least square fitting constructed according to the constant term of the obtained phase and the estimated inclination term of the x direction is specifically as follows:
the intensity of the interference light is expressed as:
omitting phaseAfter that, the least squares of the construction are as follows:
obtaining parameter A 2 、B 2 、C 2 The first order term coefficient m is then expressed as:
mx+k＝tan- 1 (-C 2 /B 2 )
further, in step 4, a least square fit constructed from the constant term of the obtained phase and the inclination term of the obtained y direction is specifically as follows:
the intensity of the interference light is expressed as:
omitting phaseAfter that, the least squares of the construction are as follows:
obtaining parameter A 3 、B 3 、C 3 The first order term coefficient m is then expressed as:
ny+k＝tan- 1 (-C 3 /B 3 )
a phase-shifting interferometry system for non-iterative calculation of phase tilt parameters comprises an initial value estimation module, a constant term solving module, a y-direction tilt term solving module, an x-direction tilt term solving module, a phase-shifting interferogram phase tilt parameter solving module and a phase distribution solving module, wherein:
the initial value estimation module is used for estimating the inclination term of the phase in the interferogram as an initial value;
the constant term solving module is used for constructing least square fitting according to the initial value of the inclination term to obtain a constant term in the phase;
the y-direction inclination term solving module is used for constructing least square fitting according to the constant term of the obtained phase and the estimated x-direction inclination term to obtain the y-direction inclination term;
the system comprises an inclination term solving module in the x direction, a phase calculating module and a phase calculating module, wherein the inclination term solving module in the x direction is used for constructing least square fitting according to a constant term of the obtained phase and an inclination term in the y direction to obtain an inclination term in the x direction;
the phase-shifting interferogram phase inclination parameter solving module is used for repeating the processing of the initial value estimating module, the constant term solving module, the y-direction inclination term solving module and the x-direction inclination term solving module for each frame of interferogram to obtain phase-shifting interferogram phase inclination parameters;
and the phase distribution solving module is used for carrying out difference on the inclination parameters of the phase-shifting interferogram to obtain a phase-shifting quantity, and obtaining phase distribution according to a least square phase-shifting algorithm to finish phase-shifting interferometry.
A mobile terminal comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the phase-shifting interferometry method of non-iteratively calculating phase tilt parameters when executing the program.
A computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps in a phase shifting interferometry method of non-iteratively calculating a phase tilt parameter.
Compared with the prior art, the invention has the remarkable advantages that: (1) The phase inclination parameter of the interference pattern can be accurately obtained through least square fitting, and high-precision calibration of the interference pattern is realized; (2) The method is insensitive to errors of initial values, and phase inclination parameters of the interferograms can be rapidly solved without iteration; (3) The method has no requirement on phase-shifting interferograms, the phase-shifting quantity between the interferograms can be time variable quantity or space variable quantity, the method is simple and efficient, the requirement on the measuring environment is low, and the method is suitable for calibration and phase extraction of most phase-shifting interferometers.
Drawings
FIG. 1 is a flow chart of a phase-shifting interferometry method for non-iteratively calculating phase tilt parameters according to the present invention.
Fig. 2 is a diagram of simulation results in an embodiment of the present invention.
FIG. 3 is a graph showing experimental results in the examples of the present invention.
Detailed Description
Referring to fig. 1, the phase-shifting interferometry method for non-iterative calculation of phase tilt parameters of the present invention includes the steps of:
step 1, estimating an inclination term of a phase in an interferogram as an initial value;
step 2, constructing least square fitting according to initial values of the inclination terms, and obtaining constant terms in the phase;
step 3, constructing least square fitting according to the constant term of the obtained phase and the estimated inclination term of the x direction, and obtaining the inclination term of the y direction;
step 4, constructing least square fitting according to the constant term of the obtained phase and the obtained inclination term of the y direction, and obtaining the inclination term of the x direction;
step 5, repeating the steps 1 to 4 for each frame of interference pattern to obtain the inclination parameters of the phase-shifting interference pattern;
and 6, differencing the inclination parameters of the phase-shifting interferogram to obtain a phase-shifting quantity, and obtaining phase distribution according to a least square phase-shifting algorithm to finish phase-shifting interferometry.
As a specific example, in step 1, the tilt term of the phase in the interferogram is estimated as an initial value, specifically:
fourier transforming the interferogram to obtain a spectrogram, wherein the spectrum of the interferogram is expressed as:
wherein u and v are coordinates of a spectrum domain, f x And f y The carrier frequency of the interference light intensity in the x and y directions is represented by A, the Fourier transform of the interference pattern background is represented by lambda, the wavelength is represented by i, the imaginary unit is represented by i, and the Fourier transform of the cosine component of the interference pattern is represented by C;
and extracting a positive primary frequency spectrum according to a spectrogram of the interference pattern, and calculating a centroid to obtain centroid coordinates of the positive primary frequency spectrum, namely obtaining an inclination term of the phase in the x and y directions as an initial value.
As a specific example, the least squares fit constructed from the initial values of the tilt terms in step 2 is specifically:
the light intensity expression for a single frame interferogram can be expressed as:
wherein I is interference light intensity, a is interference pattern background, b is modulation degree, m and n are respectively inclination coefficients of phase in x direction and y direction, k is constant term of phase,is a higher order term of the phase.
For a single-frame interferogram, m, n and k are collectively called as tilt parameters of phases, and based on Fourier transformation, the tilt parameters m and n can be conveniently estimated and are called as initial values of the tilt parameters and recorded as m 0 、n 0 。
The interference light intensity of formula (2) is rewritten as:
wherein I is interference light intensity, a is interference pattern background, b is modulation degree, m and n are respectively inclination coefficients of phase in x direction and y direction, k is constant term of phase,is a higher-order term of the phase;
considering that in practice it is satisfied thatTherefore, omit->According to the initial value m of the inclination parameter 0 、n 0 Can construct the parameter A 1 、B 1 、C 1 The variance of the theoretical light intensity and the actual light intensity can be expressed as:
E＝∑(A 1 +B 1 cos(mx+ny)+C 1 sin(mx+ny)-I) 2 (4)
to minimize variance, the phase is omittedAfter that, the least squares of the construction are as follows:
where α=mi+nj, M, N is the row, column number, I of the interferogram ij Light intensity values of the ith row and the jth column in the interference diagram;
obtaining parameter A 1 、B 1 、C 1 The constant term coefficient k is then expressed as:
k＝tan- 1 (-C 1 /B 1 ) (6)
the initial value m 0 、n 0 There must be some error from the actual value, but even so, the constant term coefficient k obtained by this method is still very accurate.
As a specific example, the least squares fit constructed from the constant term of the obtained phase and the estimated inclination term in the x-direction in step 3 is specifically as follows:
after obtaining the exact constant term coefficient k, re-writing equation (2), the interference light intensity is expressed as:
likewise, omitAccording to the initial value n 0 Taking a certain column of data (so that mx is a fixed value) in the interference diagram, constructing a related parameter A 2 、B 2 、C 2 Is a least squares form of (c) and can be solved:
obtaining parameter A 2 、B 2 、C 2 The first order term coefficient m is then expressed as:
mx+k＝tan- 1 (-C 2 /B 2 ) (9)
as a specific example, further, the least square fitting constructed from the constant term of the obtained phase and the inclination term of the obtained y direction in step 4 is specifically as follows:
similarly, according to the initial value m 0 (or from an initial value n 0 The calculated accurate m), taking a certain line data (so that ny is a constant value) in the interferogram, the least square form for solving the first-order term coefficient n can be constructed, and the solution form is similar to the formula (8), so long as n in the formula (8) is replaced by m, as shown in the formula (10):
omitting phaseAfter that, the least squares of the construction are as follows:
obtaining parameter A 3 、B 3 、C 3 The first order term coefficient m is then expressed as:
ny+k＝tan- 1 (-C 3 /B 3 ) (13)
thus, for a single-frame interferogram, the first-order term coefficient and the constant term coefficient of the interference phase are accurately obtained. For multi-frame oblique phase-shifting interferograms, the inclination parameters of the interferograms can be obtained frame by frame, and then the phase-shifting quantity containing the inclination quantity change is obtained by difference, so that the phase-shifting quantity can be used for calibrating a phase shifter or combining a least square phase-shifting algorithm to realize phase calculation.
The invention also provides a phase-shifting interferometry system for non-iterative calculation of phase tilt parameters, which comprises an initial value estimation module, a constant term solving module, a y-direction tilt term solving module, an x-direction tilt term solving module, a phase-shifting interferogram phase tilt parameter solving module and a phase distribution solving module, wherein:
the initial value estimation module is used for estimating the inclination term of the phase in the interferogram as an initial value;
the constant term solving module is used for constructing least square fitting according to the initial value of the inclination term to obtain a constant term in the phase;
the y-direction inclination term solving module is used for constructing least square fitting according to the constant term of the obtained phase and the estimated x-direction inclination term to obtain the y-direction inclination term;
the system comprises an inclination term solving module in the x direction, a phase calculating module and a phase calculating module, wherein the inclination term solving module in the x direction is used for constructing least square fitting according to a constant term of the obtained phase and an inclination term in the y direction to obtain an inclination term in the x direction;
the phase-shifting interferogram phase inclination parameter solving module is used for repeating the processing of the initial value estimating module, the constant term solving module, the y-direction inclination term solving module and the x-direction inclination term solving module for each frame of interferogram to obtain phase-shifting interferogram phase inclination parameters;
and the phase distribution solving module is used for carrying out difference on the inclination parameters of the phase-shifting interferogram to obtain a phase-shifting quantity, and obtaining phase distribution according to a least square phase-shifting algorithm to finish phase-shifting interferometry.
The invention also provides a mobile terminal, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the phase-shifting interferometry method for calculating the phase tilt parameter in a non-iterative way when executing the program.
The present invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps in the phase-shifting interferometry method of non-iteratively calculating a phase tilt parameter.
The invention will now be described in further detail with reference to the drawings and examples.
Examples
In this embodiment, the non-iterative calculation method of the phase tilt parameter of the interferogram of the present invention is adopted to perform phase extraction on the random tilt phase-shifting interferogram, fig. 2 is a simulation result, where fig. 2 (a) is a 16-frame phase-shifting interferogram generated by simulating the random tilt phase shift, fig. 2 (b) is an actual phase contained in the interferogram, fig. 2 (c) is a phase extracted by the non-iterative calculation method of the phase tilt parameter of the interferogram of the present invention, and fig. 2 (d) is a difference value between the calculated phase and the actual phase. Fig. 3 shows experimental results, in which fig. 3 (a) shows a 16-frame phase-shifting interferogram acquired by a 32-inch fizeau interferometer, fig. 3 (b) shows a phase solved by a four-step method, fig. 3 (c) shows a phase solved by AIA, fig. 3 (d) shows a phase solved by PTI algorithm, and fig. 3 (e) shows a phase extracted by a non-iterative calculation method of the phase tilt parameter of the interferogram according to the present invention.
According to fig. 2 and 3, the method solves the phase tilt parameter of the interferogram based on least square fitting, does not need complex iteration, has high algorithm running speed and high calculation precision, and can provide a high-efficiency and high-precision solution for phase-shifting interferometry in a vibration environment.
Claims (8)
1. A phase-shifting interferometry method for non-iterative calculation of phase tilt parameters is characterized by comprising the following steps:
step 1, estimating an inclination term of a phase in an interferogram as an initial value;
step 2, constructing least square fitting according to initial values of the inclination terms, and obtaining constant terms in the phase;
step 3, constructing least square fitting according to the constant term of the obtained phase and the estimated inclination term of the x direction, and obtaining the inclination term of the y direction;
step 4, constructing least square fitting according to the constant term of the obtained phase and the obtained inclination term of the y direction, and obtaining the inclination term of the x direction;
step 5, repeating the steps 1 to 4 for each frame of interference pattern to obtain the inclination parameters of the phase-shifting interference pattern;
and 6, differencing the inclination parameters of the phase-shifting interferogram to obtain a phase-shifting quantity, and obtaining phase distribution according to a least square phase-shifting algorithm to finish phase-shifting interferometry.
2. The phase-shifting interferometry method of claim 1, wherein in step 1, the phase tilt term in the interferogram is estimated as an initial value, specifically as follows:
fourier transforming the interferogram to obtain a spectrogram, wherein the spectrum of the interferogram is expressed as:
wherein u and v are coordinates of a spectrum domain, f x And f y The carrier frequency of the interference light intensity in the x and y directions is represented by A, the Fourier transform of the interference pattern background is represented by lambda, the wavelength is represented by i, the imaginary unit is represented by i, and the Fourier transform of the cosine component of the interference pattern is represented by C;
and extracting a positive primary frequency spectrum according to a spectrogram of the interference pattern, and calculating a centroid to obtain centroid coordinates of the positive primary frequency spectrum, namely obtaining an inclination term of the phase in the x and y directions as an initial value.
3. The phase-shifting interferometry method of non-iterative calculation of phase tilt parameters according to claim 2, wherein the least squares fit constructed from the initial values of the tilt terms in step 2 is specifically:
the intensity of the interference light is expressed as:
wherein I is interference light intensity, a is interference pattern background, b is modulation degree, m and n are respectively inclination coefficients of phase in x direction and y direction, k is constant term of phase,is a higher-order term of the phase;
omitting phaseAfter that, the least squares of the construction are as follows:
where α=mi+nj, M, N is the row, column number, I of the interferogram ij Light intensity values of the ith row and the jth column in the interference diagram;
obtaining parameter A 1 、B 1 、C 1 The constant term coefficient k is then expressed as:
k＝tan- 1 (-C 1 /B 1 )。
4. the phase-shifting interferometry method of non-iterative phase tilt parameter according to claim 3, wherein the least squares fit constructed from the constant term of the obtained phase and the estimated tilt term in the x-direction in step 3 is specifically as follows:
the intensity of the interference light is expressed as:
omitting phaseAfter that, the least squares of the construction are as follows:
obtaining parameter A 2 、B 2 、C 2 The first order term coefficient m is then expressed as:
mx+k＝tan- 1 (-C 2 /B 2 )。
5. the phase-shifting interferometry method of non-iterative phase tilt parameter according to claim 3, wherein in step 4, a least squares fit constructed from the constant term of the obtained phase and the tilt term of the obtained y-direction is specifically as follows:
the intensity of the interference light is expressed as:
omitting phaseAfter that, the least squares of the construction are as follows:
obtaining parameter A 3 、B 3 、C 3 The first order term coefficient m is then expressed as:
ny+k＝tan- 1 (-C 3 /B 3 )。
6. the phase-shifting interferometry system for non-iterative calculation of phase tilt parameters is characterized by comprising an initial value estimation module, a constant term solving module, a y-direction tilt term solving module, an x-direction tilt term solving module, a phase-shifting interferogram phase tilt parameter solving module and a phase distribution solving module, wherein:
the initial value estimation module is used for estimating the inclination term of the phase in the interferogram as an initial value;
the constant term solving module is used for constructing least square fitting according to the initial value of the inclination term to obtain a constant term in the phase;
the y-direction inclination term solving module is used for constructing least square fitting according to the constant term of the obtained phase and the estimated x-direction inclination term to obtain the y-direction inclination term;
the system comprises an inclination term solving module in the x direction, a phase calculating module and a phase calculating module, wherein the inclination term solving module in the x direction is used for constructing least square fitting according to a constant term of the obtained phase and an inclination term in the y direction to obtain an inclination term in the x direction;
the phase-shifting interferogram phase inclination parameter solving module is used for repeating the processing of the initial value estimating module, the constant term solving module, the y-direction inclination term solving module and the x-direction inclination term solving module for each frame of interferogram to obtain phase-shifting interferogram phase inclination parameters;
and the phase distribution solving module is used for carrying out difference on the inclination parameters of the phase-shifting interferogram to obtain a phase-shifting quantity, and obtaining phase distribution according to a least square phase-shifting algorithm to finish phase-shifting interferometry.
7. A mobile terminal comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements a phase shifting interferometry method for non-iteratively calculating a phase tilt parameter according to any of claims 1 to 5 when the program is executed by the processor.
8. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the steps in the phase-shifting interferometry method of non-iteratively calculating a phase tilt parameter according to any of claims 1 to 5.
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