A phase-shifting interferometry method for non-iterative calculation of phase tilt parameters

Abstract

The application 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 an interferogram as an initial value; constructing a least square fitting according to the initial value of the tilt term to obtain a constant term in the phase; constructing a least square fitting according to the obtained constant term of the phase and the estimated tilt term in the x direction to obtain a tilt term in the y direction; constructing a least square fitting according to the obtained constant term of the phase and the obtained tilt term in the y direction to obtain a tilt term in the x direction; repeating the previous steps to obtain tilt parameters of a phase of a phase-shifting interferogram for each frame of the interferogram; obtaining a phase shift by subtracting the tilt parameters of the phase-shifting interferogram; obtaining a phase distribution according to a least square phase shifting algorithm to complete the phase-shifting interferometry. The application can efficiently and accurately complete the phase-shifting interferometry in a vibration environment.

Description

Technical Field

[0001] This invention belongs to the field of optical interferometry technology, and in particular, it is a phase-shifting interferometric measurement method for non-iterative calculation of phase tilt parameters. Background Technology

[0002] In phase-shifting interferometry, the phase shift is used as a known condition to solve for the phase. However, in reality, due to factors such as environmental vibration or nonlinear errors of the phase shifter, the phase shift deviates from the theoretical value, becoming an unknown quantity. To solve the problem of phase solution when the phase shift is unknown, scholars have proposed random phase-shifting techniques. Random phase-shifting techniques have also developed alongside research on the error sensitivity of traditional fixed-step phase-shifting algorithms. Early random phase-shifting techniques were based on least-squares phase-shifting algorithms, obtaining the phase shift through iteration and other methods to recover the phase. The most representative work is Wang, ZY and BTHan (2004). "Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms." OPTICS LETTERS The Advanced Iterative Algorithm (AIA) proposed in 29(14):1671-1673. requires only more than three interferograms to simultaneously calculate the phase shift and phase. AIA not only has no requirements on the phase shift of the interferogram but also has high accuracy. However, the large number of least squares operations in the iteration process makes the computational efficiency low. In 2009, Hao (Hao,Q., et al.(2009). "Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts."OPTICS LETTERS 34(8):1288-1290.) proposed a method to process a large number of random phase-shifting interferograms by normalizing the background light intensity and modulation of the interferogram. This method requires small-angle phase shifts and the acquisition of a large number of interferograms, which is very 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) from mathematical statistics to interferogram analysis. PCA does not require the calculation of phase shifts, which greatly improves the computational speed of random phase-shifting algorithms, but the computational accuracy is affected by the number of fringes in the interferogram.

[0003] It is worth noting that the above studies only apply to random translational phase shifts, that is, the phase shift is only a time-varying quantity and the spatial distribution is consistent. In reality, however, tilt changes between the reference mirror and the test mirror are unavoidable. For example, the tilting and shaking of the mirror caused by environmental vibrations, and the tilting of the reference mirror caused by inconsistent PZT step sizes at multiple points. For random tilt phase shifts, in 2000, Chen (Chen, MY, et al. (2000). "Algorithm immune to tilt phase-shifting error for phase-shifting interferometers." APPLIED OPTICS 39(22):3894-3898.) et al. performed a first-order Taylor expansion of the interferogram and used least squares iteration to achieve small-amplitude tilt phase shift error compensation. In 2008, Xu, JC (Xu, JC, et al. (2008). "Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts." APPLIED OPTICS 47(3):480-485.) improved upon the AIA algorithm by dividing the interferogram into blocks to calculate the phase shift and constructing a plane fit to calculate the tilt phase shift. This method has a small error when the background and contrast of the interferogram are uniform, but when the two are unevenly distributed, it will have a coupling effect on the calculation of the tilt coefficient. In 2009, Deck, LL (Deck, LL (2009). "Suppressing phase errors from vibration in phase-shifting interferometry." APPLIED OPTICS 48(20):3948-3960.) proposed an MPSI method based on a multi-parameter physical model, which uses the background and modulation as time-independent quantities to compensate for the tilt error of the phase shift. In 2013, Li (Li,JX,etal.(2013).Phase-tilting interferometry for optical testing.OPTICS LETTERS38(15):2838-2841.) et al. solved the tilt phase shift parameters based on the idea of ​​Hough transform to detect straight lines, and realized the phase solution of 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 variation." OPTICS EXPRESS 22(4):4738-4750.) proposed using least squares fitting to obtain the background light intensity and modulation index of each frame of the interferogram, thereby normalizing the interferogram. For the normalized interferogram, the least squares method is used to calculate the phase shift and obtain the phase distribution from the phase shift. In this method, the phase shift, background light intensity, and modulation index can vary not only in the time domain but also in the spatial domain, which greatly improves the universality of the random phase-shifting algorithm. The only drawback is that it requires a large number of fringes in the interferogram. In 2021, Lu (Lu,W., et al. (2021). "Anti-Vibration Interferometric Shape Measurement Based on TiltPhase." Acta Optica Sinica 41(2).) et al. calculated the tilted phase plane of each frame of the interferogram based on Fourier transform, obtained the phase shift, and used the least squares phase shift algorithm to obtain the phase distribution. Due to the spectral overlap problem, the restoration accuracy of this method is not high. In the same year, Mingliang Duan (Duan, ML, et al. (2021). "Phase-tilt iteration: Accurate and robust phase extraction from random tilt-shift interferograms." OPTICS AND LASERS IN ENGINEERING 142.) proposed an iterative method for solving tilt-shift interferograms. This method constructs a system of linear equations about the tilt parameters of the interferogram to solve for the phase shift between interferograms. The phase distribution is then solved using least squares, and the obtained phase distribution is iterated back into the solution for the phase shift. This process is repeated until convergence, yielding accurate tilt parameters and phase distribution of the interferogram. This method has high accuracy, but the algorithm involves a large number of least squares operations, resulting in long computation time. It is a method that sacrifices time for accuracy.In 2022, Chenhui Hu (Hu, CH, et al. (2022). "Parameter mismatch phase extraction method for spatial phase-shifting interferograms." OPTICS AND LASERS IN ENGINEERING 154.) proposed a phase extraction method for spatially synchronized phase-shifting interferograms. This method establishes a linear relationship between the contrast, carrier frequency error, and phase shift error of the interferogram, and iterates repeatedly after giving initial values ​​to achieve phase extraction. This method can achieve phase extraction of interferograms with random tilted phase shifts and time-varying contrast, but the initial values ​​required for solving the phase are relatively high. Summary of the Invention

[0004] The purpose of this invention is to provide a non-iterative method for calculating phase tilt parameters in phase-shifting interferometry, which enables the calibration and phase solution of random tilted phase-shifting interferograms, and achieves high-precision phase-shifting interferometry under vibration conditions.

[0005] The technical solution to achieve the objective of this invention is: a phase-shifting interferometry method for non-iterative calculation of phase tilt parameters, comprising the following steps:

[0006] Step 1: Estimate the phase tilt term in the interferogram as an initial value;

[0007] Step 2: Based on the initial value of the tilt term, construct a least-squares fit to obtain the constant term in the phase;

[0008] Step 3: Based on the obtained phase constant term and the estimated x-direction tilt term, construct a least squares fit to obtain the y-direction tilt term;

[0009] Step 4: Based on the obtained constant term of the phase and the obtained tilt term in the y direction, construct a least squares fit to obtain the tilt term in the x direction.

[0010] Step 5: For each frame of the interferogram, repeat steps 1 to 4 to obtain the tilt parameters of the phase of the phase-shifted interferogram.

[0011] Step 6: Subtract the tilt parameters of the phase-shifted interferogram to obtain the phase shift amount, and obtain the phase distribution according to the least squares phase shift algorithm to complete the phase-shifted interferometry measurement.

[0012] Furthermore, in step 1, the tilt term of the phase in the interferogram is estimated as an initial value, as follows:

[0013] Performing a Fourier transform on the interferogram yields its spectrum, which is represented as follows:

[0014]

[0015] Where u and v are coordinates in the frequency spectrum domain, f x with f y Let λ be the carrier frequency of the interference light intensity in the x and y directions, A be the Fourier transform of the background of the interference pattern, λ be the wavelength, i be the imaginary unit, and C be the Fourier transform of the cosine component of the interference pattern.

[0016] Based on the spectrum of the interferogram, the positive first-order spectrum is extracted, and the centroid is calculated to obtain the centroid coordinates of the positive first-order spectrum, that is, the phase tilt terms in the x and y directions are obtained, which are used as initial values.

[0017] Furthermore, the least squares fit constructed in step 2 based on the initial value of the tilt term is as follows:

[0018] The intensity of the interference light is represented as:

[0019]

[0020] Where I is the interference light intensity, a is the background of the interferogram, b is the modulation degree, m and n are the phase tilt coefficients in the x and y directions, respectively, and k is the phase constant. For higher-order terms of phase;

[0021] Phase omitted The constructed least squares are as follows:

[0022]

[0023] Where α = mi + nj, M and N are the number of rows and columns of the interferogram, I ij The light intensity values ​​are in the i-th row and j-th column of the interferogram;

[0024] After obtaining the parameters A1, B1, and C1, the coefficient k of the constant term is expressed as:

[0025] k = tan- 1 (-C1 / B1)

[0026] Furthermore, the least squares fit constructed in step 3 based on the obtained phase constant term and the estimated x-direction tilt term is as follows:

[0027] The intensity of the interference light is represented as:

[0028]

[0029] Phase omitted The constructed least squares are as follows:

[0030]

[0031] After obtaining parameters A2, B2, and C2, the coefficient m of the first-order term is expressed as:

[0032] mx + k = tan- 1 (-C2 / B2)

[0033] Furthermore, the least squares fit constructed in step 4 based on the obtained phase constant term and the obtained y-direction tilt term is as follows:

[0034] The intensity of the interference light is represented as:

[0035]

[0036] Phase omitted The constructed least squares are as follows:

[0037]

[0038] After obtaining parameters A3, B3, and C3, the first-order term coefficient m is expressed as:

[0039] ny+k=tan- 1 (-C3 / B3)

[0040] A phase-shifting interferometry system for non-iterative calculation of phase tilt parameters includes an initial value estimation module, a constant term solution module, a tilt term solution module in the y-direction, a tilt term solution module in the x-direction, a tilt parameter solution module for the phase of the phase-shifting interferogram, and a phase distribution solution module, wherein:

[0041] The initial value estimation module is used to estimate the phase tilt term in the interferogram as an initial value;

[0042] The constant term solution module is used to construct a least-squares fit based on the initial value of the tilt term and obtain the constant term in the phase.

[0043] The module for solving the tilt term in the y-direction is used to construct a least-squares fit based on the obtained phase constant term and the estimated tilt term in the x-direction to obtain the tilt term in the y-direction.

[0044] The x-direction tilt term solution module is used to construct a least-squares fit based on the obtained phase constant term and the obtained y-direction tilt term to obtain the x-direction tilt term.

[0045] The tilt parameter solution module for the phase of the phase-shifted interferogram is used to repeat the processing of the initial value estimation module, the constant term solution module, the tilt term solution module in the y direction, and the tilt term solution module in the x direction for each frame of the interferogram to obtain the tilt parameter of the phase of the phase-shifted interferogram.

[0046] The phase distribution solution module is used to calculate the phase shift by subtracting the tilt parameters of the phase-shifted interferogram, and then to obtain the phase distribution using the least squares phase-shifting algorithm to complete the phase-shifted interferometry measurement.

[0047] A mobile terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the non-iterative calculation method for phase tilt parameters by phase-shifting interferometry.

[0048] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the non-iterative calculation of phase tilt parameters by phase-shifting interferometry.

[0049] Compared with the prior art, the present invention has the following significant advantages: (1) The phase tilt parameter of the interferogram can be accurately obtained by least squares fitting, so as to achieve high-precision calibration of the interferogram; (2) It is not sensitive to the error of the initial value and can quickly solve the phase tilt parameter of the interferogram without iteration; (3) It has no requirements for the phase-shifting interferogram. The phase shift between the interferograms can be either a time change or a spatial change. The method is simple and efficient, has low requirements for the measurement environment, and is suitable for the calibration and phase extraction of most phase-shifting interferometers. Attached Figure Description

[0050] Figure 1 This is a flowchart of the phase-shifting interferometry measurement method for non-iterative calculation of phase tilt parameters according to the present invention.

[0051] Figure 2 The figure shows the simulation results in an embodiment of the present invention.

[0052] Figure 3 The figure shows the experimental results in an embodiment of the present invention. Detailed Implementation

[0053] Combination Figure 1 The present invention provides a non-iterative calculation method for phase tilt parameters by phase-shifting interferometry, comprising the following steps:

[0054] Step 1: Estimate the phase tilt term in the interferogram as an initial value;

[0055] Step 2: Based on the initial value of the tilt term, construct a least-squares fit to obtain the constant term in the phase;

[0056] Step 3: Based on the obtained phase constant term and the estimated x-direction tilt term, construct a least squares fit to obtain the y-direction tilt term;

[0057] Step 4: Based on the obtained constant term of the phase and the obtained tilt term in the y direction, construct a least squares fit to obtain the tilt term in the x direction.

[0058] Step 5: For each frame of the interferogram, repeat steps 1 to 4 to obtain the tilt parameters of the phase of the phase-shifted interferogram.

[0059] Step 6: Subtract the tilt parameters of the phase-shifted interferogram to obtain the phase shift amount, and obtain the phase distribution according to the least squares phase shift algorithm to complete the phase-shifted interferometry measurement.

[0060] As a specific example, in step 1, the tilt term of the phase in the interferogram is estimated as an initial value, specifically:

[0061] Performing a Fourier transform on the interferogram yields its spectrum, which is represented as follows:

[0062]

[0063] Where u and v are coordinates in the frequency spectrum domain, f x with f y Let λ be the carrier frequency of the interference light intensity in the x and y directions, A be the Fourier transform of the background of the interference pattern, λ be the wavelength, i be the imaginary unit, and C be the Fourier transform of the cosine component of the interference pattern.

[0064] Based on the spectrum of the interferogram, the positive first-order spectrum is extracted, and the centroid is calculated to obtain the centroid coordinates of the positive first-order spectrum, that is, the phase tilt terms in the x and y directions are obtained, which are used as initial values.

[0065] As a specific example, the least squares fit constructed in step 2 based on the initial values ​​of the skew term is as follows:

[0066] The light intensity expression for a single-frame interferogram can be represented as:

[0067]

[0068] Where I is the interference light intensity, a is the background of the interferogram, b is the modulation degree, m and n are the phase tilt coefficients in the x and y directions, respectively, and k is the phase constant. This is a higher-order term of the phase.

[0069] For a single-frame interferogram, m, n, and k are collectively referred to as the phase tilt parameters. Based on the Fourier transform, the tilt parameters m and n can be easily estimated and are called the initial values ​​of the tilt parameters, denoted as m0 and n0.

[0070] The interference light intensity of equation (2) can be rewritten as:

[0071]

[0072] Where I is the interference light intensity, a is the background of the interferogram, b is the modulation degree, m and n are the phase tilt coefficients in the x and y directions, respectively, and k is the phase constant. For higher-order terms of phase;

[0073] Considering the actual satisfaction Therefore, omitted. Based on the initial values ​​m0 and n0 of the tilt parameters, a least-squares form can be constructed for parameters A1, B1, and C1. The variance between the theoretical light intensity and the actual light intensity can be expressed as:

[0074] E=∑(A1+B1cos(mx+ny)+C1sin(mx+ny)-I) 2 (4)

[0075] To minimize variance, phase is neglected. The constructed least squares are as follows:

[0076]

[0077] Where α = mi + nj, M and N are the number of rows and columns of the interferogram, I ij The light intensity values ​​are in the i-th row and j-th column of the interferogram;

[0078] After obtaining the parameters A1, B1, and C1, the coefficient k of the constant term is expressed as:

[0079] k = tan- 1 (-C1 / B1) (6)

[0080] It should be noted that there will inevitably be some error between the initial values ​​m0 and n0 and the actual values, but even so, the constant term coefficient k obtained by this method is still very accurate.

[0081] As a specific example, the least squares fit constructed in step 3 based on the obtained phase constant term and the estimated x-direction tilt term is as follows:

[0082] After obtaining the precise constant coefficient k, equation (2) is rewritten, and the interference light intensity is expressed as:

[0083]

[0084] Similarly, omitted Given an initial value n0, take a column of data from the interferogram (making mx a constant), and construct a least-squares form for parameters A2, B2, and C2. The solution is as follows:

[0085]

[0086] After obtaining parameters A2, B2, and C2, the coefficient m of the first-order term is expressed as:

[0087] mx + k = tan- 1 (-C2 / B2) (9)

[0088] As a specific example, the least squares fit constructed in step 4 based on the obtained phase constant term and the obtained y-direction tilt term is as follows:

[0089] Similarly, based on the initial value m0 (or the precise m calculated from the initial value n0), by taking a certain row of data in the interferogram (making ny a constant), a least squares form for solving the coefficient n of the first-order term can be constructed. The form of the solution is similar to that of equation (8), except that n in equation (8) is replaced with m, as shown in equation (10):

[0090]

[0091] Phase omitted The constructed least squares are as follows:

[0092]

[0093] After obtaining parameters A3, B3, and C3, the first-order term coefficient m is expressed as:

[0094] ny+k=tan- 1 (-C3 / B3) (13)

[0095] Thus, for a single-frame interferogram, the first-order and constant coefficients of the interference phase have been accurately obtained. For multi-frame tilted phase-shifted interferograms, the tilt parameters of the interferogram can be obtained frame by frame, and then the difference can be used to obtain the phase shift amount containing the tilt change. This can be used for the calibration of the phase shifter, or combined with the least squares phase shifting algorithm to realize phase solution.

[0096] This invention also provides a phase-shifting interferometry system for non-iterative calculation of phase tilt parameters, comprising an initial value estimation module, a constant term solution module, a tilt term solution module in the y-direction, a tilt term solution module in the x-direction, a tilt parameter solution module for the phase of the phase-shifting interferogram, and a phase distribution solution module, wherein:

[0097] The initial value estimation module is used to estimate the phase tilt term in the interferogram as an initial value;

[0098] The constant term solution module is used to construct a least-squares fit based on the initial value of the tilt term and obtain the constant term in the phase.

[0099] The module for solving the tilt term in the y-direction is used to construct a least-squares fit based on the obtained phase constant term and the estimated tilt term in the x-direction to obtain the tilt term in the y-direction.

[0100] The x-direction tilt term solution module is used to construct a least-squares fit based on the obtained phase constant term and the obtained y-direction tilt term to obtain the x-direction tilt term.

[0101] The tilt parameter solution module for the phase of the phase-shifted interferogram is used to repeat the processing of the initial value estimation module, the constant term solution module, the tilt term solution module in the y direction, and the tilt term solution module in the x direction for each frame of the interferogram to obtain the tilt parameter of the phase of the phase-shifted interferogram.

[0102] The phase distribution solution module is used to calculate the phase shift by subtracting the tilt parameters of the phase-shifted interferogram, and then to obtain the phase distribution using the least squares phase-shifting algorithm to complete the phase-shifted interferometry measurement.

[0103] The present invention also provides a mobile terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the non-iterative calculation of phase tilt parameters phase-shifting interferometry measurement method.

[0104] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the non-iterative calculation of phase tilt parameters phase-shifting interferometry method.

[0105] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0106] Example

[0107] This embodiment employs the non-iterative calculation method for the phase tilt parameter of the interferogram according to the present invention to extract the phase of a randomly tilted phase-shifting interferogram. Figure 2 The simulation results are shown below. Figure 2 (a) is a 16-frame phase-shifted interferogram generated to simulate random tilt phase shift. Figure 2 (b) represents the actual phase implied in the interferogram. Figure 2 (c) is the phase extracted using the non-iterative calculation method for the interferogram phase tilt parameter of this invention. Figure 2 (d) is the calculation of the difference between the phase and the actual phase. Figure 3 The experimental results are as follows, in which Figure 3 (a) 16 frames of phase-shifted interferograms acquired by a 32-inch Fizzo interferometer. Figure 3 (b) is the phase obtained using the four-step method. Figure 3 (c) is the phase obtained using AIA. Figure 3 (d) represents the phase obtained using the PTI algorithm. Figure 3 (e) is the phase extracted using the non-iterative calculation method for the phase tilt parameter of the interferogram according to the present invention.

[0108] according to Figure 2, Figure 3 As can be seen, the present invention solves the phase tilt parameters of the interferogram based on least squares fitting, without the need for complex iterations. The algorithm runs fast and has high calculation accuracy, which can provide a high-efficiency and high-precision solution for phase-shifting interferometry under vibration environment.

Claims

1. A phase-shifting interferometry method for non-iterative calculation of phase tilt parameters, characterized in that, The method comprises the following steps: Step 1, estimate the tilt term of the phase in the interference pattern as an initial value; Step 2, construct a least squares fitting according to the initial value of the tilt term to obtain a constant term in the phase; Step 3, construct a least squares fitting according to the obtained constant term of the phase and the estimated tilt term in the x direction to obtain a tilt term in the y direction; Step 4, construct a least squares fitting according to the obtained constant term of the phase and the obtained tilt term in the y direction to obtain a tilt term in the x direction; Step 5, repeat steps 1-4 for each frame of interference pattern to obtain the tilt parameters of the phase of the phase-shifting interference pattern; Step 6, difference the tilt parameters of the phase-shifting interference pattern to obtain a phase-shifting amount, and obtain a phase distribution according to a least squares phase-shifting algorithm to complete the phase-shifting interference measurement.

2. The non-iterative phase tilt parameter calculation phase-shifting interferometry method of claim 1, wherein, In step 1, the tilt term of the phase in the interference pattern is estimated as an initial value, which is specifically as follows: Perform Fourier transform on the interference pattern to obtain a frequency spectrum, and the frequency spectrum of the interference pattern is represented as: where u, v are the coordinates in the spectral domain, f x and f y is the carrier frequency of the interference light in the x and y direction, A is the Fourier transform of the interference pattern background, λ is the wavelength, i is the imaginary unit, and C is the Fourier transform of the cosine component of the interference pattern. According to the frequency spectrum of the interference pattern, extract the positive first-order spectrum, calculate the centroid to obtain the centroid coordinates of the positive first-order spectrum, and obtain the tilt terms of the phase in the x and y directions as the initial values.

3. The non-iterative phase tilt parameter calculation phase-shifting interferometry method of claim 2, wherein, In step 2, the least squares fitting constructed according to the initial value of the tilt term is specifically as follows: The interference light intensity is represented as: where I is the intensity of interference, a is the background of the interferogram, b is the modulation, m, n are the tilt coefficients of the phase in the x and y directions, respectively, k is the constant term of the phase, are the high-order terms of the phase. neglecting phase After, the least square is constructed as follows: where a = mi + nj, M, N are the number of rows and columns of the interferogram, I ij is the light intensity value in the i-th row and j-th column of the interferogram; After obtaining the parameters A1, B1 and C1, the constant term coefficient k is represented as: k = tan -1 (-C1 / B1).

4. The non-iterative phase tilt parameter calculation phase-shifting interferometry method of claim 3, wherein, In step 3, the least squares fitting constructed according to the obtained constant term of the phase and the estimated tilt term in the x direction is specifically as follows: The interference light intensity is represented as: neglecting phase After, the least square is constructed as follows: After obtaining the parameters A2, B2 and C2, the first-order term coefficient m is represented as: mx+k = tan -1 (-C2 / B2).

5. The non-iterative phase tilt parameter calculation phase-shifting interferometry method of claim 3, wherein, In step 4, the least squares fitting constructed according to the obtained constant term of the phase and the obtained tilt term in the y direction is specifically as follows: The interference light intensity is represented as: neglecting phase After, the least square is constructed as follows: After obtaining the parameters A3, B3 and C3, the first-order term coefficient m is represented as: ny+k = tan -1 (-C3 / B3).

6. A phase-shifting interferometry system that calculates phase tilt parameters without iteration, the system comprising: The method 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 interference pattern phase tilt parameter solving module, and a phase distribution solving module, wherein: The initial value estimation module is configured to estimate the tilt term of the phase in the interference pattern as an initial value; The constant term solving module is configured to construct a least squares fitting according to the initial value of the tilt term to obtain a constant term in the phase; The y-direction tilt term solving module is configured to construct a least squares fitting according to the obtained constant term of the phase and the estimated tilt term in the x direction to obtain a tilt term in the y direction; The x-direction tilt term solving module is configured to construct a least squares fitting according to the obtained constant term of the phase and the obtained tilt term in the y direction to obtain a tilt term in the x direction; The phase-shifting interference pattern phase tilt parameter solving module is configured to repeat the processing of the initial value estimation module, the constant term solving module, the y-direction tilt term solving module and the x-direction tilt term solving module for each frame of interference pattern to obtain the tilt parameters of the phase of the phase-shifting interference pattern; The phase distribution solving module is configured to difference the tilt parameters of the phase-shifting interference pattern to obtain a phase-shifting amount, and obtain a phase distribution according to a least squares phase-shifting algorithm to complete the phase-shifting interference measurement.

7. A mobile terminal comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The program, when executed by the processor, implements the non-iterative phase-shifting parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt parameter calculation phase tilt 8. A computer-readable storage medium having stored thereon a computer program, characterized in that, ​

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