An adaptive phase-shifting method applied to a wavelength-tunable phase-shifting interferometer

Abstract

The application discloses a kind of wavelength tuning phase-shifting interferometer applied adaptive phase-shifting method, the relationship between the step voltage of wavelength tuning phase-shifting interferometer and cavity length is calibrated, and the relationship function of step voltage and cavity length is obtained by calibration;Input cavity length is in the value of set range, according to the relationship function of step voltage and cavity length calibrated, the step voltage value under the cavity length value is obtained;With the step voltage value under the cavity length value, phase shifting is carried out, and the phase-shifting interferogram with set phase interval is obtained, and then based on the least square principle and the phase solution algorithm of iterative method, wavelength tuning phase-shifting interference of adaptive interference cavity length is realized.The wavelength tuning phase-shifting interference method based on the wavelength tuning phase-shifting interference technology principle can realize adaptive phase-shifting operation, and improve the precision and stability of detection.

Description

Technical Field

[0001] This invention relates to the field of optical technology, and in particular to an adaptive phase-shifting method for use in wavelength-tuned phase-shifting interferometers. Background Technology

[0002] Phase-shifting interferometry (PSI) is the eye and the benchmark of modern optical manufacturing. Due to its characteristics of non-contact detection, fast response speed, and high detection accuracy, it is widely used in the production and testing process of various optical components.

[0003] Since the 20th century, phase-shifting interferometry has been applied to the field of optical metrology. Through continuous technological innovation, the bottleneck limiting its development is no longer just the relevant hardware conditions, but more importantly, the phase-shifting method and the corresponding phase-solution algorithm. Traditional laser interferometers generally use piezoelectric ceramic (PZT) to carry a reference mirror for micro-displacement, thereby introducing a phase difference. However, with the increasing development of various fields, large-aperture optical elements are increasingly widely used in various large and medium-sized optical systems. Faced with the increasing size and mass of the objects being measured, PZT phase-shifting technology is insufficient due to the limitations of the piezoelectric ceramic's load-bearing capacity. During the phase-shifting process, internal vibrations of the detection system are easily induced, introducing mechanical errors. This error is introduced from within the interferometer and is a defect of the phase-shifting principle, making its occurrence almost unavoidable.

[0004] Wavelength phase-shifting interferometry has garnered significant attention because it solves the phase-shifting problem of large-aperture optical elements by precisely controlling and adjusting the output wavelength of the light source through electrical signal input, without requiring changes to the interference cavity length. However, since phase shifting is introduced through the laser's output wavelength, the amount of phase shift is influenced by both the laser's wavelength tuning and the cavity length, leading to variations in the associated image processing algorithms. Therefore, studying the principles of wavelength phase-shifting interferometry and developing suitable processing algorithms for wavelength-tuned phase shifting techniques is of significant practical importance.

[0005] Modern phase-shifting interferometry integrates research findings from multiple fields, combining laser technology, image processing technology, electronic measurement technology, and computer technology, among other high-precision metrology techniques. The rapid development of devices such as piezoelectric crystals has provided the hardware foundation for the development of phase-shifting interferometry. Thanks to these advancements in hardware technology, phase-shifting interferometry can accurately determine the wavefront phase distribution. While integrating multiple high-precision metrology techniques, in the early stages of its development, limitations in hardware conditions restricted the advancement of interferometry, making it difficult to improve measurement accuracy.

[0006] Over the past thirty years, related hardware technologies have developed rapidly, and the pixel precision of photodetectors and the computing power of computers have been continuously improved, breaking through the bottleneck in the development of phase-shifting interferometry. Having overcome the limitations of hardware technology, the measurement accuracy and stability of phase-shifting interferometry are mainly determined by two aspects: (1) the phase-shifting method. According to the principle of phase-shifting interferometry, the optical path difference between the reference light and the test light needs to be changed during the measurement process to achieve the same-direction displacement of the interference fringes. The accuracy and stability of the phase shift determine the measurement accuracy. (2) the phase-decomposition algorithm. After obtaining the interferogram sequence with ordered phase changes through phase-shifting technology, the computer needs to perform a series of phase-decomposition calculations to obtain the wavefront distribution of the affected side. Therefore, the accuracy of the phase-decomposition algorithm directly affects the measurement results. A high-precision phase-decomposition algorithm can not only improve the phase extraction accuracy but also strongly suppress random errors caused by air disturbances, artificial vibrations, etc.

[0007] In existing technologies, wavelength-tuned phase-shifting algorithms generally employ a constant-step least squares iterative algorithm to calculate and statistically analyze the phase distribution of the interferogram. The least squares iterative algorithm is a recursive iterative algorithm with low phase-shifting accuracy requirements, good stability, and high computational accuracy, and has been widely used in wavelength-tuned phase-shifting technology. However, in practical applications, this algorithm still has the following three problems: 1) It requires an accurate value of the interferometric cavity length to calibrate the phase shift amount as the initial value for iteration; 2) When the phase shift amount is close to Nπ (N = 0, 1, 2, ...), the phase extraction error is relatively large; 3) When there are contrast differences between multiple frames of interferograms, it will significantly affect the phase extraction accuracy. Summary of the Invention

[0008] To address the problems existing in the prior art, the purpose of this invention is to provide an adaptive phase-shifting method for wavelength-tuned phase-shifting interferometers. This method adaptively adjusts the step phase-shifting voltage based on the coarse calibration value of the cavity length, effectively improving the accuracy of phase shifting. This results in obtaining high-quality interferograms that are less affected by interference and meet quality requirements. It solves the problem that current wavelength-tuned phase-shifting interferometers require recalibration every time the cavity length is changed, greatly improving the intelligence of the detection process. Furthermore, combined with a phase-solution algorithm based on the least squares principle and iterative method, adaptive wavelength-tuned phase-shifting interferometry with an adaptive interferometric cavity length is achieved, resulting in superior detection performance.

[0009] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0010] An adaptive phase-shifting method for use in wavelength-tuned phase-shifting interferometers, the method comprising:

[0011] The relationship between the step voltage and cavity length of the wavelength-tuned phase-shifting interferometer is calibrated, and the relationship function between the step voltage and cavity length is obtained through calibration.

[0012] Input the cavity length within the set range, and obtain the step voltage value for that cavity length value according to the calibrated step voltage and cavity length relationship function;

[0013] Phase shifting is performed using the step voltage value under the cavity length to obtain a phase-shifted interferogram with a set phase interval. Then, based on the least squares principle and the iterative phase solution algorithm, wavelength-tuned phase-shifted interferometry with adaptive interferometric cavity length is realized.

[0014] Preferably, in the above-described adaptive phase-shifting method applied to a wavelength-tuned phase-shifting interferometer,

[0015] The process of calibrating the relationship between the step voltage and cavity length of the wavelength-tuned phase-shifting interferometer, and obtaining the relationship function between the step voltage and cavity length through calibration, includes:

[0016] First, the interferogram is masked and the regions containing interference fringe information are extracted to obtain the relationship between the interference light intensity of each pixel and the background light intensity, modulation light intensity, wavefront phase and step shift term.

[0017] Next, an interferogram sequence is obtained by phase shifting at equal steps. The adjacent interferogram sequences are used for calculation. During calibration, the phase shift of each pixel is calculated separately to obtain the phase shift of all pixels in the mask.

[0018] Finally, the number of pixels falling within different angle intervals is counted to obtain a set of phase shift statistical histograms of interferograms. The peak value of the histogram is the preliminary calibration value of the phase shift of this set of interferograms.

[0019] Preferably, in the above-described adaptive phase-shifting method applied to a wavelength-tuned phase-shifting interferometer,

[0020] The process of performing phase shifting using the step voltage value at the cavity length to obtain a phase-shifted interferogram with a set phase interval, and then realizing wavelength-tuned phase-shifted interferometry with adaptive interferometric cavity length based on the least squares principle and iterative phase-solving algorithm includes:

[0021] When the input cavity length is within the set range, the step voltage that makes the phase shift amount reach the set threshold can be determined according to the calibrated relationship function between the step voltage and the cavity length under the cavity length condition. When the phase shift amount is known, the wavefront phase is calculated by least squares fitting.

[0022] Increase the contrast compensation amount so that the background light intensity and the modulation light intensity are iteratively compensated during the calculation process. After adding the compensation coefficient, it is considered that the contrast difference is mainly between different interferograms. The background light intensity and the modulation light intensity are equal between different pixels in the same interferogram. Therefore, the compensation coefficient is only related to the interferogram number.

[0023] In the first iteration, the compensation coefficient is set to 1. The wavefront phase is calculated using the calibrated phase shift estimate. The phase is solved point by point. When the wavefront phase is known, the phase shift can be solved through the same fitting process. When solving the phase shift, each frame is used as the object to calculate and solve, so that the phase shift is closer to the true value.

[0024] Preferably, in the above-described adaptive phase-shifting method applied to a wavelength-tuned phase-shifting interferometer,

[0025] The process of solving for the phase shift using the same fitting procedure when the wavefront phase is known, and calculating the phase shift by taking each frame as the object to make the phase shift closer to the true value, also includes:

[0026] When solving for the phase shift using the same fitting process, the background light intensity and the modulated light intensity can be obtained simultaneously, and the compensation coefficient in the next iteration can be calculated accordingly.

[0027] The two processes described above are repeated to form an iterative cycle. After repeated iterations, the wavefront phase and phase shift continuously approach the true value.

[0028] Preferably, in the above-described adaptive phase-shifting method applied to a wavelength-tuned phase-shifting interferometer,

[0029] The repeated iterations control the number of iterations by setting an iteration threshold. The difference between the phase shift of different interferograms after n iterations and the average phase shift is used as an indicator to measure the fluctuation range of the calculation results. The difference between the result of the nth iteration and the result of the (n-1)th iteration is used to obtain the iteration accuracy. The iteration ends when the iteration accuracy reaches the set threshold.

[0030] Compared with existing technologies, this invention proposes an adaptive phase-shifting method for wavelength-tuned phase-shifting interferometers based on the principle of laser wavelength tuning. According to the calibrated phase-shifting voltage and cavity length curve, the user only needs to input a rough value of the cavity length, and the algorithm can adaptively adjust the step voltage to complete the phase shift, thereby obtaining a high-quality interferogram group with ideal phase shift. Combined with the anti-vibration algorithm based on the least squares method, phase extraction can be performed to achieve better detection results.

[0031] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 Flowchart of the adaptive phase-shifting method of this invention applied to a wavelength-tuned phase-shifting interferometer;

[0034] Figure 2 The embodiment of the present invention shows a 9-frame phase-shifted interference fringe pattern with a phase-shifting interval of 90°.

[0035] Figure 3 : A schematic diagram of the tuning of the Littman-type grating structure according to an embodiment of the present invention;

[0036] Figure 4 : A schematic diagram illustrating the linear relationship between cavity length and wavelength tuning when the step phase shift is π / 2 in an embodiment of the present invention;

[0037] Figure 5 The phase shift statistical histogram calculated from an interferogram with a phase shift of 30° in this embodiment of the invention;

[0038] Figure 6 The phase shift statistical histogram calculated from the interferogram with a phase shift of 90° in this embodiment of the invention;

[0039] Figure 7 The phase shift statistical histogram calculated from an interferogram with a phase shift of 140° in this embodiment of the invention;

[0040] Figure 8 : A schematic diagram of the phase resolution algorithm in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0042] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0043] like Figure 1 As shown, the present invention provides an adaptive phase-shifting method for use in a wavelength-tuned phase-shifting interferometer, the method comprising:

[0044] The relationship between the step voltage and cavity length of the wavelength-tuned phase-shifting interferometer is calibrated, and the relationship function between the step voltage and cavity length is obtained through calibration.

[0045] Input the cavity length within the set range, and obtain the step voltage value for that cavity length value according to the calibrated step voltage and cavity length relationship function;

[0046] Phase shifting is performed using the step voltage value under the cavity length to obtain a phase-shifted interferogram with a set phase interval. Then, based on the least squares principle and the iterative phase solution algorithm, wavelength-tuned phase-shifted interferometry with adaptive interferometric cavity length is realized.

[0047] In practice, the phase-shifting interferometry technique of this invention is based on an interferometer, typically employing two interference structures: the Fizeau interferometer and the Thyman interferometer. During measurement, the laser beam is split into two beams after being expanded by a beam expander. The reference beam is reflected from the upper surface of the reference surface, while the measured beam is reflected from the side surface, carrying the wavefront information of that side. The two coherent beams converge at the CMOS target surface, forming interference fringes, which are recorded by a photodetector and stored in a computer. The wavefronts of the reference beam and the measured beam can be written as follows:

[0048]

[0049]

[0050] In the formula, (x, y) refers to the spatial coordinates of the pixel, and a r (x, y) and a t (x, y) represents the wavefront amplitudes of the two light beams, φ r (x, y) and φ r (x, y) represents the wavefront phase of the two waves.

[0051] On the surface of the imaging system, the intensity of the superimposed light beams can be expressed as:

[0052] I(x, y) = |W r (x, y) + W t (x, y)| 2 ;

[0053] In the figure, I(x, y) represents the gray value of pixel (x, y) in the interference pattern, and y represents the light intensity signal received by the CMOS. Expanding the above equation into a trigonometric function form, we can obtain:

[0054] I(x,y)=A(x,y)+B(x,y)cos[φt(x,y)-φ r [(x, y)];

[0055] In the formula, The average light intensity, also known as the background light intensity, is B(x, y) = 2a. r(x, y)a t (x, y) represents the modulation intensity of the interference fringes.

[0056] Fixed text Let be the wavefront phase of the interfering light. Based on the wavefront phase distribution, the wavefront to be measured can be fitted, thereby obtaining the morphological information of the surface to be measured. The relationship between the wavefront phase distribution and the length of the interferometer cavity is as follows:

[0057]

[0058] In the formula, h is the cavity length of the interferometer, and λ0 is the center wavelength of the emitted laser.

[0059] Therefore, traditional laser-based phase-shifting interferometers change the optical path difference between the reference and test beams by controlling the piezoelectric ceramic actuator (PZT) to move the reference mirror, thereby altering the interference cavity length. The resulting displacement of the interference fringes can be observed in the interference image. Figure 2 This is a 9-frame phase-shifted interference fringe pattern with a phase-shifting interval of 90°.

[0060] Unlike traditional phase-shifting methods, wavelength-tuned phase-shifting interferometry achieves phase shifting by adjusting the center wavelength of the laser emitted from the laser. Therefore, the wavelength-tuned laser is a key component of the wavelength-tuned interferometer. By achieving single-longitudinal-mode output in an external resonant cavity containing a wavelength selection device within a semiconductor diode laser (i.e., an external cavity semiconductor laser), precise tuning of the laser's output wavelength can be achieved.

[0061] like Figure 3 The diagram shows a tuning schematic of a Littman grating structure. In this semiconductor laser structure, the first-order diffracted light is reflected onto an additional mirror, reflected back to the grating, and then the second-order diffracted light returns to the laser tube, while the zero-order light serves as the laser output. When the angle between the incident light and the grating normal changes, assuming the change is Δθ (Δθ is sufficiently small), it is easy to deduce that the change in wavelength of the incident light is:

[0062] Δλ=Δθ·d·cosθ.

[0063] Therefore, precise phase shifting can be achieved simply by changing the angle between the mirror plane and the grating plane when the PZT pushes the mirror. After obtaining multiple frames of interferograms with fixed phase shifts, the pixel data I of the interferogram group can be processed using a phase decomposition algorithm. i (x, y) can be calculated Furthermore, the surface shape information P(x, y) is obtained to complete the detection work. Common phase-shifting algorithms include the four-step phase-shifting method, the nine-step phase-shifting method, and so on.

[0064] From the above principle of wavelength-tuned phase-shifting interference, it can be seen that the phase change of the wavelength-tuned phase-shifting technology is related to both the cavity length and the wavelength tuning. Therefore, when studying wavelength-tuned phase-shifting technology, it is necessary to study the laws governing wavelength-tuned phase shifting under different interference cavity lengths. As mentioned above, in this embodiment of the invention, the laser achieves wavelength tuning of the emitted laser by driving a reflector with a PZT. Since the displacement of the piezoelectric ceramic is proportional to the input voltage, the relationship between the laser wavelength tuning and the input voltage can be written as:

[0065] Δλ=G·(Δv) k .

[0066] In the formula, G and k are constants related to piezoelectric ceramics, which can be obtained through calibration. Their values ​​vary depending on the laser. The better the linearity of the laser, the closer the value of k will be to 1.

[0067] The relationship between laser wavelength tuning and input voltage shows that, for a given cavity length, the phase change is related to both the laser's center wavelength and the wavelength tuning. Taking the G60U wavelength-tuned phase-shifting interferometer as an example, with a laser center wavelength of 638nm and an interferometer cavity length ranging from 10-60cm, using constant-step phase-shifting technology, the relationship between the phase shift and wavelength tuning can be obtained as follows:

[0068]

[0069] When the step phase shift is π / 2, the phase change can be obtained as:

[0070]

[0071]

[0072] It can be seen that, given a fixed step phase shift, the voltage tuning is inversely proportional to the interference cavity length, and the proportionality coefficient is linearly related to the laser wavelength tuning. Taking the logarithm of both sides of the above equation yields:

[0073]

[0074] Therefore, the relationship between the voltage tuning amount and the interference cavity length can be calibrated based on the above formula. In this embodiment of the invention, the relationship between the voltage tuning amount Δv and the interference cavity length h within the range of cavity length variation of the interferometer is as follows: Figure 4 As shown.

[0075] from Figure 4 As can be seen, with a fixed phase shift, the voltage tuning amount decreases as the cavity length increases, and the wavelength tuning amount also decreases. This means that higher wavelength tuning resolution is required for the laser. When the interference cavity length is 60 cm, the required wavelength change per phase shift step is 8.5 × 10⁻⁶. -5nm. In the phase shifting method adopted in the embodiments of the present invention, the total phase change during the phase shifting process is 9π / 2. Within the adjustable cavity length range, the maximum change in laser wavelength is 0.0045nm. Therefore, the laser wavelength tunable range exceeding 0.0045nm can meet the requirements for phase shifting.

[0076] In summary, by calibrating and obtaining the relationship between the step voltage and the cavity length during the detection process, the step voltage that results in a phase shift of π / 2 at that cavity length can be obtained from the approximate value of the cavity length.

[0077] Preferably, in the embodiments of the present invention, the method for adaptive phase shifting of a wavelength-tuned phase-shifting interferometer is applied. The process of calibrating the relationship between the step voltage and the cavity length of the wavelength-tuned phase-shifting interferometer, and obtaining the relationship function between the step voltage and the cavity length through calibration, includes:

[0078] First, the interferogram is masked and the regions containing interference fringe information are extracted to obtain the relationship between the interference light intensity of each pixel and the background light intensity, modulation light intensity, wavefront phase and step shift term.

[0079] Next, an interferogram sequence is obtained by phase shifting at equal steps. The adjacent interferogram sequences are used for calculation. During calibration, the phase shift of each pixel is calculated separately to obtain the phase shift of all pixels in the mask.

[0080] Finally, the number of pixels falling within different angle intervals is counted to obtain a set of phase shift statistical histograms of interferograms. The peak value of the histogram is the preliminary calibration value of the phase shift of this set of interferograms.

[0081] In practice, after obtaining 5 interferograms with a phase shift of ΔV, the interferograms are first masked to extract the regions containing interference fringe information. The interference light intensity of each pixel within the mask extracted from the k-th interferogram can be written as:

[0082]

[0083] In the formula: I represents light intensity, A(x, y) is background light intensity, and B(x, y) is modulated light intensity. Let δ(x, y) represent the wavefront phase at each point in the figure, and δ(x, y) represent the step phase shift. In wavelength-tuned phase shifting technology, And δ can be expressed as:

[0084]

[0085]

[0086] In the formula: h is the interference cavity length, λ0 is the initial center wavelength of the laser, and Δλ is the wavelength tuning amount for each phase shift. An interferogram sequence is obtained by phase shifting in equal steps. Using five adjacent frames of interferograms for calculation, the phase shift amount at each pixel can be expressed as:

[0087]

[0088] During calibration, the phase shift at each point is calculated individually to obtain the phase shift of all pixels within the mask. The number of pixels falling within different angular intervals is counted, resulting in a set of phase shift statistical histograms of the interferograms. The peak value of the histogram is the preliminary calibration value of the phase shift for this set of interferograms. Figures 5-7 The figure shows the statistical histograms of phase shifts calculated from three sets of interferograms with different phase shifts.

[0089] Preliminary calibration values ​​for the phase shift were obtained. The aperture width and peak height of the histogram directly reflect the phase shift accuracy of this set of interferograms, which can be measured by the standard deviation of the histogram. Calibration accuracy is related to the quality of the interferogram and the magnitude of the phase shift. To study the influence of the phase shift magnitude on accuracy, the standard deviation of the phase shift variation within the interval 0 to π was measured using a G60U interferometer. The data are shown in the table below:

[0090]

[0091]

[0092] As can be seen from the table, when the standard deviation of the phase shift is below 6 within the range of 70° to 110°, considering slight vibrations and other interferences in the actual shooting environment, this value is within an acceptable range. Therefore, during the calibration process, it is necessary to measure the step voltage that makes the phase shift π / 2 under different cavity lengths. Assuming N sets of measured data are obtained, the least squares fitting formula can be used, according to the following formula:

[0093]

[0094] available:

[0095] V = a - bH;

[0096] In the formula, V = log(Δv), H = log(h), Where 'a' is related to the center wavelength of the laser and the PZT elastic coefficient, it can be regarded as a constant.

[0097] Based on the principle of least squares, the least squares residual function can be established:

[0098]

[0099] The solution to the residual function coefficient matrix is:

[0100] β=(X T X) -1 XV = A -1 B;

[0101] in:

[0102]

[0103] β=[ab] T ,

[0104]

[0105] As can be seen from the above formula, when N is greater than or equal to 2, the formula has a solution. However, in order to ensure the accuracy of the calibrated function curve, it is generally required that the amount of calibration data be no less than 15 sets, and the cavity length be set evenly and uniformly.

[0106] Preferably, the present invention is applied to the adaptive phase-shifting method of a wavelength-tuned phase-shifting interferometer. The process of performing phase shifting with a step voltage value under the cavity length value to obtain a phase-shifted interferogram with a set phase interval, and then realizing the wavelength-tuned phase-shifting interferometry of the adaptive interferometric cavity length based on the least squares principle and the iterative phase-solving algorithm includes:

[0107] When the input cavity length is within the set range, the step voltage that makes the phase shift amount reach the set threshold can be determined according to the calibrated relationship function between the step voltage and the cavity length under the cavity length condition. When the phase shift amount is known, the wavefront phase is calculated by least squares fitting.

[0108] Increase the contrast compensation amount so that the background light intensity and the modulation light intensity are iteratively compensated during the calculation process. After adding the compensation coefficient, it is considered that the contrast difference is mainly between different interferograms. The background light intensity and the modulation light intensity are equal between different pixels in the same interferogram. Therefore, the compensation coefficient is only related to the interferogram number.

[0109] In the first iteration, the compensation coefficient is set to 1. The wavefront phase is calculated using the calibrated phase shift estimate. The phase is solved point by point. When the wavefront phase is known, the phase shift can be solved through the same fitting process. When solving the phase shift, each frame is used as the object to calculate and solve, so that the phase shift is closer to the true value.

[0110] Preferably, the input cavity length within the set range is based on the current cavity adjustment state of the interferometer, combined with the auxiliary scale of the interferometer, to estimate the cavity length value of the interferometer, accurate to one decimal place.

[0111] In this invention, to address the issue of contrast differences affecting calculation accuracy when there are discrepancies between interferograms in the same group, a contrast compensation factor is added to the original least squares algorithm. This allows for iterative compensation between the background light intensity and the modulated light intensity during the calculation process. After adding the compensation factor, the following formula is used:

[0112] I(x,y)=A(x,y)+B(x,y)cos[φ t (x, y) - φ r [(x, y)],

[0113] Rewritten as:

[0114] In the formula: i represents the sequence number of different pixels, j represents the sequence number of the interferogram, and P Aj With P Bj Let represent the compensation coefficients of the background light intensity and modulation light intensity of the j-th frame interferogram relative to the first frame interferogram. Considering that the contrast difference is mainly between different interferograms, the background light intensity and modulation light intensity are considered to be equal between different pixels in the same interferogram. Therefore, the compensation coefficients are only related to the interferogram number.

[0115] In the implementation, the compensation coefficient is set to 1 in the first iteration calculation. The wavefront phase is calculated using the estimated phase shift obtained from calibration, and the phase is solved point by point. For the pixel with index i, let... A linear equation was established to obtain the theoretical value of light intensity. for:

[0116]

[0117] Calculate theoretical values With the true value I ij The difference between them is used to construct a least-squares residual function:

[0118]

[0119] In the formula: N represents the number of frames in a set of interferogram sequences, β i The coefficient matrix representing wavefront phase information has a solution in its determinant when the number of interferogram frames is greater than or equal to 3, according to the least squares principle. The solution for the residual function coefficient matrix is:

[0120]

[0121] in:

[0122]

[0123] β i =[a i b i c i ]T ,,

[0124]

[0125] The coefficient matrix β is obtained. i Then, the wavefront phase can be obtained as:

[0126]

[0127] When the wavefront phase is known, the phase shift can be solved using the same fitting process, making the phase shift closer to the true value. When solving for the phase shift, the calculation is performed on a per-frame basis. Let:

[0128] α j =P Aj A ij b j =P Bj B ij cos(δ j ), c j =-P Bj B ij sin(δ j If the light intensity is 0, then the theoretical value of the light intensity is:

[0129]

[0130] Calculate theoretical values With the true value I ij The difference between them is used to establish a least squares residual function:

[0131]

[0132] In the formula: M represents the total number of pixels in an image, β j The coefficient matrix representing the phase shift information, according to the least squares principle, yields the solution for the residual function coefficient matrix as follows:

[0133]

[0134] in:

[0135]

[0136] β j =[a j b j c j ] T ,,

[0137]

[0138] The coefficient matrix β is obtained. i Then, the phase shift can be obtained as follows:

[0139] δ j =arctan(-c j / b j );

[0140] Preferably, in the embodiments of the present invention, the adaptive phase-shifting method of a wavelength-tuned phase-shifting interferometer is applied. When the wavefront phase is known, the phase shift can be solved using the same fitting process. The process of calculating the phase shift by treating each frame as an object, making the phase shift closer to the true value, further includes:

[0141] When solving for the phase shift using the same fitting process, the background light intensity and the modulated light intensity can be obtained simultaneously, and the compensation coefficient in the next iteration can be calculated accordingly.

[0142] The two processes described above are repeated to form an iterative cycle. After repeated iterations, the wavefront phase and phase shift continuously approach the true value.

[0143] In practice, the phase shift amount obtained in this embodiment of the invention can be simultaneously obtained from the coefficient matrix along with the background light intensity and the modulated light intensity. The compensation coefficient for the next iteration is then calculated as follows:

[0144]

[0145] The above two processes are repeated to form an iterative loop. After repeated iterations, the wavefront phase and phase shift continuously approach the true value. When the calculation result reaches a certain accuracy, the result obtained by further iterative calculation changes very little, and continuing the calculation is not very meaningful. To improve the efficiency of the algorithm, the repeated iteration described in this embodiment controls the number of iterations by setting an iteration threshold. The difference between the phase shift of different interferograms after n iterations and the average phase shift is taken as an indicator to measure the fluctuation range of the calculation result. The difference between the result of the nth iteration and the result of the (n-1)th iteration is taken to obtain the iteration accuracy. When the iteration accuracy reaches the set threshold, the iteration can be terminated.

[0146]

[0147] Through the above phase solution process, the wavefront phase can be solved using the phase shift calibration value as the initial value for iteration. The algorithm flow for phase solution in this embodiment of the invention is as follows: Figure 8 As shown.

[0148] As the principle of the least squares fitting algorithm states, a minimum of 3 frames are needed for the coefficient matrix to have a solution in the interferogram sequence. The calibration algorithm requires at least 5 interferogram frames, and the phase resolution algorithm can solve the problem with 5 frames. However, to improve the accuracy of the iterative algorithm and to reduce errors caused by vibration, air disturbance, etc., during the measurement process, 9 frames are typically taken as a set of interferogram sequences for each measurement. In practice, after 6 to 8 iterations, the numerical and phase calculation values ​​no longer change significantly, so 8 iterations are generally sufficient.

[0149] This invention provides an adaptive wavelength-tuned phase-shifting method combining phase shift calibration and dephase calculation. When using a wavelength-tuned phase-shifting interferometer for the first time, it is necessary to calibrate the relationship between the interferometer's step voltage and cavity length. First, multiple experiments are conducted at different interferometric cavity lengths to obtain the step voltage that results in a phase shift of π / 2. At least 15 sets of data should be obtained, and the cavity length data should be distributed across the entire adjustable cavity length range as much as possible. Five interferograms are captured for each set of experiments. A 271×271 pixel area is taken from the center region of each image and used as a sample area for phase shift calibration using the aforementioned calibration principle. Every five frames in the interferogram set form a phase shift calculation group. Based on a specific phase shift calculation formula, the phase shift corresponding to each pixel can be calculated. Among them I k(i，j) Let be the grayscale value of the pixel in the i-th row and j-th column of the k-th frame. Calculate the grouped phase shift value for each phase shift. Statistical analysis was performed, rounding the phase shift values ​​corresponding to all pixels to the nearest integer. The number of pixels corresponding to each integer value within the 0-180° range was then counted. The integer value with the most pixels was used as the phase shift value for this group of interferograms. Adjust the step voltage to a phase shift of π / 2; this step voltage is the ideal step voltage for this cavity length. Based on the data obtained in the previous step, and using the least squares algorithm, the relationship function between the cavity length and the step voltage can be obtained. This relationship is linearly related to the change in laser wavelength; the better the linearity of the laser, the closer the relationship function is to an inverse proportional relationship. The obtained phase shift calibration curve is recorded in the program. After completing the phase shift calibration, measurement can begin. First, input the approximate cavity length value. Based on the calibrated curve of step voltage and interference cavity length, the step voltage value that results in a phase shift of π / 2 for this cavity length can be obtained. Using this step voltage, phase shifting is performed, acquiring 9 frames of phase-shifted interferograms. The first 5 frames are used for a selection sequence operation, filtering high-quality interferogram groups and extracting the phase.

[0150] This invention significantly improves the adaptive phase-shifting capability of phase-shifting interferometry systems at the algorithmic level, which has been well-received by customers. Furthermore, it requires no additional hardware costs, meeting the actual development needs of enterprises. The wavelength-tuned phase-shifting interferometry method based on the principle of wavelength-tuned phase-shifting interferometry in this invention can achieve adaptive phase-shifting operation, improving detection accuracy and stability.

[0151] In summary, the adaptive wavelength tuning phase-shifting method of this invention consists of a phase-shifting calibration algorithm and an adaptive phase-shifting algorithm, which complement each other. The phase shift amount in wavelength tuning phase-shifting technology is affected by the interference cavity length. Therefore, when the cavity length is unknown, the phase shift amount needs to be calibrated for accurate phase extraction. By calibrating to find the relationship between the step voltage and the cavity length, a suitable step voltage can be obtained by inputting a coarse calibration value of the cavity length during the detection process. This allows for the acquisition of a set of interferograms with appropriate phase intervals, achieving a better voltage selection effect.

[0152] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0153] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. An adaptive phase-shifting method applied to a wavelength-tuned phase-shifting interferometer, characterized in that, The method includes: The relationship between the step voltage and cavity length of the wavelength-tuned phase-shifting interferometer is calibrated, and the relationship function between the step voltage and cavity length is obtained through calibration. Input the cavity length within the set range, and obtain the step voltage value for that cavity length value according to the calibrated step voltage and cavity length relationship function; Phase shifting is performed using the step voltage value under the cavity length to obtain a phase-shifted interferogram with a set phase interval. Then, based on the least squares principle and the iterative method of phase solution algorithm, wavelength-tuned phase-shifted interferometry with adaptive interferometric cavity length is realized. The process of performing phase shifting using the step voltage value at the cavity length to obtain a phase-shifted interferogram with a set phase interval, and then realizing wavelength-tuned phase-shifted interferometry with adaptive interferometric cavity length based on the least squares principle and iterative phase-solving algorithm includes: When the input cavity length is within the set range, the step voltage that makes the phase shift amount equal to the set threshold is determined according to the calibrated relationship function between the step voltage and the cavity length. When the phase shift amount is known, the wavefront phase is calculated by least squares fitting. Increase the contrast compensation amount so that the background light intensity and the modulation light intensity are iteratively compensated during the calculation process. After adding the compensation coefficient, it is considered that the contrast difference is mainly between different interferograms. The background light intensity and the modulation light intensity are equal between different pixels in the same interferogram. Therefore, the compensation coefficient is only related to the interferogram number. In the first iteration, the compensation coefficient is set to 1. The wavefront phase is calculated using the calibrated phase shift estimate. The phase is solved point by point. When the wavefront phase is known, the phase shift is solved through the same fitting process. When solving the phase shift, each frame is used as the object to calculate and solve, so that the phase shift is closer to the true value. The process of solving for the phase shift using the same fitting process when the wavefront phase is known, and calculating the phase shift by taking each frame as the object to make the phase shift closer to the true value, also includes: When solving for the phase shift using the same fitting process, the background light intensity and the modulated light intensity are obtained simultaneously, and the compensation coefficient in the next iteration is calculated accordingly. The two processes of calculating the phase shift and calculating the phase are repeated to form an iterative loop. After repeated iterations, the wavefront phase and the phase shift continuously approach the true value.

2. The adaptive phase-shifting method for a wavelength-tuned phase-shifting interferometer according to claim 1, characterized in that: The process of calibrating the relationship between the step voltage and cavity length of the wavelength-tuned phase-shifting interferometer, and obtaining the relationship function between the step voltage and cavity length through calibration, includes: First, the interferogram is masked and the regions containing interference fringe information are extracted to obtain the relationship between the interference light intensity of each pixel and the background light intensity, modulation light intensity, wavefront phase and step shift term. Next, an interferogram sequence is obtained by phase shifting at equal steps. The adjacent interferogram sequences are used for calculation. During calibration, the phase shift of each pixel is calculated separately to obtain the phase shift of all pixels in the mask. Finally, the number of pixels falling within different angle intervals is counted to obtain a set of phase shift statistical histograms of interferograms. The peak value of the histogram is the preliminary calibration value of the phase shift of this set of interferograms.

3. The adaptive phase-shifting method for a wavelength-tuned phase-shifting interferometer according to claim 1, characterized in that: The repeated iterations control the number of iterations by setting an iteration threshold. The difference between the phase shift of different interferograms after n iterations and the average phase shift is used as an indicator to measure the fluctuation range of the calculation results. The difference between the result of the nth iteration and the result of the (n-1)th iteration is used to obtain the iteration accuracy. The iteration ends when the iteration accuracy reaches the set threshold.

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