A phase shift interferometric image surface shape reconstruction method, device, equipment and storage medium

Abstract

The application discloses a phase shift interferometric image surface shape reconstruction method and device, equipment and storage medium, relates to the field of optical interferometry, and comprises the following steps: constructing a common aperture of a phase shift interferometric image sequence and independent masks corresponding to each frame of the phase shift interferometric image, determining an interferogram intensity model, determining target image parameters of each phase shift interferometric image by using the interferogram intensity model, determining predicted interference intensity based on a leave-one-out prediction mode, determining consistency residuals and corresponding frame quality weights, and judging whether the interferogram intensity model meets a preset model iteration condition; when the interferogram intensity model meets the preset model iteration condition, a new interferogram intensity model is iteratively obtained, and the step of determining target image parameters corresponding to each phase shift interferometric image by using the current interferogram intensity model is jumped to; if not, the surface shape result of the measured object is determined based on the interferogram intensity model and the wrapped phase. The application realizes phase shift interferometric image surface shape reconstruction.

Description

Technical Field

[0001] This invention relates to the field of optical interferometry, and in particular to a method, apparatus, device, and storage medium for reconstructing the surface shape of a phase-shifting interferometric image. Background Technology

[0002] In engineering testing, platform vibration, micro-motion of the tested component, reference mirror disturbance, air disturbance in long optical paths, and camera exposure or transmission anomalies can cause inter-frame pistoning, tilting, defocusing, or local non-rigid body changes. A small number of anomalous frames may still have normal average grayscale and fringe contrast, but they no longer satisfy the same set of phase-shift interferometry parameters. When anomalous frames are used in the solution with equal weight to normal frames, their errors are propagated to the frame-by-frame phase-shift state, background, modulation, and phase parameters, manifesting as surface ripples, low-order drift, local jumps, phase unwrapping failure, or decreased repeatability. Existing vibration-resistant techniques mainly include increasing acquisition speed, active or passive vibration isolation, synchronous or instantaneous phase shift, phase shift increment estimation, iterative fitting based on cavity models, averaging multiple measurements, robust statistical phase demodulation, and general image quality screening. These solutions address issues such as vibration during acquisition, inaccurate phase shift, model parameter coupling, or general outliers. However, for sequences that have already been acquired and contain only a few extremely bad frames, a surface reconstruction scheme that can preserve information from normal frames is still lacking. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a method, apparatus, device, and storage medium for reconstructing the surface shape of a phase-shifting interferometric image, which can preserve the sequence of normal frame information when reconstructing the surface shape of a phase-shifting interferometric image. The specific solution is as follows: In a first aspect, this application discloses a method for reconstructing the surface shape of a phase-shifting interferometric image, comprising: The phase-shifted interferometric image sequence of the object under test and the corresponding acquisition parameters are acquired, and the phase-shifted interferometric image sequence is processed to construct an independent mask corresponding to each frame of the phase-shifted interferometric image and a common aperture corresponding to the phase-shifted interferometric image sequence; the acquisition parameters include nominal phase shift, exposure parameters and timestamp; Based on the common aperture, preset weights, and the phase-shifted interferometric images, the interferogram intensity model corresponding to the phase-shifted interferometric image sequence is determined. The target image parameters corresponding to each phase-shifted interferometric image are determined using the current interferogram intensity model, and the corresponding predicted interferometric intensity is determined based on the leave-one-out prediction method. The target image parameters include background intensity, modulation degree, wrapping phase, and phase shift state. Based on the predicted interference intensity and the observed interference intensity corresponding to the phase-shifted interferogram, a consistency residual is determined; based on the consistency residual, a frame quality weight corresponding to the phase-shifted interferogram is determined; and based on each frame quality weight, it is determined whether the current interferogram intensity model satisfies the preset model iteration conditions. When the interferogram intensity model satisfies the preset model iteration condition, the interferogram intensity model is updated based on the independent mask, the target image parameters, and the frame quality weight to obtain a new interferogram intensity model, and then the process jumps to the step of determining the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model; When the interferogram intensity model does not meet the preset model iteration conditions, the wrapped phase is expanded based on the current interferogram intensity model to obtain the expanded phase, and surface shape conversion is performed based on the expanded phase to determine the surface shape result corresponding to the measured object.

[0004] Optionally, determining the corresponding predicted interference intensity based on the leave-one-out prediction method includes: The current interferogram intensity model is modified using the target influence function, and the predicted interferometric intensity corresponding to each phase-shifted interferogram is determined using the modified interferogram intensity model.

[0005] Optionally, determining the consistency residual based on the predicted interferometric intensity and the observed interferometric intensity corresponding to the phase-shifted interferometric image, and determining the frame quality weight corresponding to the phase-shifted interferometric image based on the consistency residual, includes: The observed interference intensity corresponding to the phase-shifted interferometric image is determined based on the intensity value corresponding to each pixel in the phase-shifted interferometric image, and the consistency residual between the predicted interference intensity and the observed interference intensity is determined based on the modulation index. Based on the common aperture, the consistency residuals are aggregated to determine the frame quality vector corresponding to the phase-shifted interferometric image, and the frame quality weight corresponding to the phase-shifted interferometric image is determined based on the frame quality vector.

[0006] Optionally, determining the frame quality weights corresponding to the phase-shifted interferometric image based on the frame quality vector includes: A normalized vector corresponding to each frame quality vector is determined, and the normalized vectors are fused based on non-negative fusion coefficients to determine the target anomaly score corresponding to the frame quality vector. The target anomaly score is then mapped to the frame quality weight corresponding to the phase-shifting interferometric image using a target weight mapping function.

[0007] Optionally, determining whether the current interferogram intensity model satisfies the preset model iteration conditions based on the quality weights of each frame includes: The target weighted effective number of frames is determined based on the frame quality weights of each frame, the proportion of low-weight frame images corresponding to the phase-shifted interferometric image sequence is determined based on a preset low-weight threshold, and a phase-shift design matrix corresponding to the target pixel set of the phase-shifted interferometric image is constructed. Based on the target weighted effective frame count, the proportion of low-weighted frame images, and the phase-shift design matrix, it is determined whether the current interferogram intensity model meets the preset model iteration conditions.

[0008] Optionally, determining whether the current interferogram intensity model satisfies the preset model iteration conditions includes: The target weight difference and target phase mean square change value corresponding to the current interferogram intensity model are determined. When the target weight difference is less than a preset weight difference and the target phase mean square change value is less than a preset mean square change value, or when the current interferogram intensity model iteration round reaches a preset iteration round, it is determined that the current interferogram intensity model does not meet the preset model iteration condition. The target weight difference is the maximum weight difference between the frame quality weight corresponding to the current interferogram intensity model and the frame quality weight corresponding to the previous interferogram intensity model. The target phase mean square change value is the root mean square value of the difference between the wrapping phase corresponding to the current interferogram intensity model and the wrapping phase corresponding to the previous interferogram intensity model.

[0009] Optionally, updating the interferogram intensity model based on the independent mask, the target image parameters, and the frame quality weights to obtain a new interferogram intensity model includes: Based on the phase shift state in the target image parameters, the motion field parameters corresponding to the current interferogram intensity model are determined, and the motion field parameters are updated based on the frame quality weights. The interferogram intensity model is then updated based on the updated motion field parameters, the independent mask, the target image parameters, and the frame quality weights to obtain a new interferogram intensity model.

[0010] Secondly, this application discloses a phase-shifting interferometric image surface shape reconstruction device, comprising: The image processing module is used to acquire the phase-shifted interferometric image sequence of the object under test and the corresponding acquisition parameters, and to process the phase-shifted interferometric image sequence to construct an independent mask corresponding to each frame of the phase-shifted interferometric image and a common aperture corresponding to the phase-shifted interferometric image sequence; the acquisition parameters include nominal phase shift, exposure parameters and timestamp; The interference intensity prediction module is used to determine the interferogram intensity model corresponding to the phase-shifted interferogram sequence based on the common aperture, preset weights, and the phase-shifted interferogram; to determine the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model; and to determine the corresponding predicted interference intensity based on a leave-one-out prediction method. The target image parameters include background intensity, modulation degree, wrapping phase, and phase shift state. The iterative judgment module is used to determine the consistency residual based on the predicted interference intensity and the observed interference intensity corresponding to the phase-shifted interferogram, determine the frame quality weight corresponding to the phase-shifted interferogram based on the consistency residual, and determine whether the current interferogram intensity model satisfies the preset model iteration conditions based on each of the frame quality weights. The model iteration module is used to update the interferogram intensity model based on the independent mask, the target image parameters, and the frame quality weight to obtain a new interferogram intensity model when the interferogram intensity model satisfies the preset model iteration condition, and then jump to the step of determining the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model; The surface shape result acquisition module is used to perform phase unfolding on the wrapped phase based on the current interferogram intensity model to obtain the unfolded phase when the interferogram intensity model does not meet the preset model iteration conditions, and to perform surface shape conversion based on the unfolded phase to determine the surface shape result corresponding to the measured object.

[0011] Thirdly, this application discloses an electronic device, comprising: Memory, used to store computer programs; A processor is used to execute the computer program to implement the aforementioned phase-shifting interferometric image surface reconstruction method.

[0012] Fourthly, this application discloses a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned phase-shifting interferometric image surface reconstruction method.

[0013] In this application, during phase-shift interferometric image surface reconstruction, a phase-shift interferometric image sequence of the object under test and corresponding acquisition parameters are acquired. The phase-shift interferometric image sequence is then processed to construct an independent mask corresponding to each frame of the phase-shift interferometric image and a common aperture corresponding to the phase-shift interferometric image sequence. The acquisition parameters include nominal phase shift, exposure parameters, and timestamps. Based on the common aperture, preset weights, and the phase-shift interferometric images, an interferogram intensity model corresponding to the phase-shift interferometric image sequence is determined. The current interferogram intensity model is used to determine the target image parameters corresponding to each phase-shift interferometric image, and a leave-one-out prediction method is used to determine the corresponding predicted interferometric intensity. The target image parameters include background intensity, modulation, wrapping phase, and phase shift state. Based on the predicted interferometric intensity and the observed interferometric intensity corresponding to the phase-shift interferometric images, a... Consistency residuals are used to determine the frame quality weights corresponding to the phase-shifted interferometric images. Based on the consistency residuals, it is determined whether the current interferogram intensity model meets the preset model iteration conditions. When the interferogram intensity model meets the preset model iteration conditions, the interferogram intensity model is updated based on the independent mask, the target image parameters, and the frame quality weights to obtain a new interferogram intensity model. Then, the process jumps to the step of determining the target image parameters corresponding to each phase-shifted interferometric image using the current interferogram intensity model. When the interferogram intensity model does not meet the preset model iteration conditions, the wrapped phase is phase-unfolded based on the current interferogram intensity model to obtain the unfolded phase. Based on the unfolded phase, surface shape conversion is performed to determine the surface shape result corresponding to the measured object. As can be seen, the frame quality evaluation in this application is driven by the consistency residual between the observed interferometric intensity and the intensity predicted by the phase-shifting interferometric physical model. This allows for the detection of anomalous frames with normal average grayscale and fringe appearance but mismatched phase relationships. The leave-one-out prediction method reduces the influence of anomalous frames on the evaluation benchmark, making the frame quality evaluation results less susceptible to the influence of bad frames and improving the detectability of extreme outliers. Furthermore, the frame quality weights are not only used for reporting but also participate in the update process of the interferogram intensity model, directly reducing the contribution of anomalous frames to phase and surface parameters. Mildly anomalous frames retain some phase shift information, while severely anomalous frames are nearly eliminated, which helps maintain phase shift diversity. In addition, this application does not rely on additional hardware or repeated acquisitions and can be used as a post-processing module in existing interferometer reconstruction software for offline remediation of acquired sequences. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0015] Figure 1 This is a flowchart of a phase-shifting interferometric image surface shape reconstruction method disclosed in this application; Figure 2 This is a schematic diagram of a specific phase-shifting interferometric image surface reconstruction system architecture disclosed in this application; Figure 3 This is a schematic diagram of a specific phase-shifting interferometric image surface shape reconstruction process disclosed in this application; Figure 4 This is a comparative schematic diagram of a specific phase-shifting interferometric image surface reconstruction result disclosed in this application, wherein... Figure 4 (a) is the acquired original phase-shifted interferometry image. Figure 4 (b) for Figure 4 (a) The surface shape result obtained by direct solution. Figure 4 (c) To utilize the phase-shifting interferometric image surface shape reconstruction method provided in this application for... Figure 4 (a) The surface reconstruction result obtained by performing surface reconstruction; Figure 5 This is a schematic diagram of the structure of a phase-shifting interferometric image surface shape reconstruction device disclosed in this application; Figure 6 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] In engineering testing, platform vibration, micro-motion of the tested component, reference mirror disturbance, air disturbance in long optical paths, and camera exposure or transmission anomalies can cause inter-frame pistoning, tilting, defocusing, or local non-rigid body changes. A small number of anomalous frames may still have normal average grayscale and fringe contrast, but they no longer satisfy the same set of phase-shift interferometry parameters. When anomalous frames are used in the solution with equal weight to normal frames, their errors are propagated to the frame-by-frame phase-shift state, background, modulation, and phase parameters, manifesting as surface ripples, low-order drift, local jumps, phase unwrapping failure, or decreased repeatability. Existing vibration-resistant techniques mainly include increasing acquisition speed, active or passive vibration isolation, synchronous or instantaneous phase shift, phase shift increment estimation, iterative fitting based on cavity models, averaging multiple measurements, robust statistical phase demodulation, and general image quality screening. These solutions address issues such as vibration during acquisition, inaccurate phase shift, model parameter coupling, or general outliers. However, for sequences that have already been acquired and contain only a few extremely bad frames, a surface reconstruction scheme that can preserve information from normal frames is still lacking. To address the aforementioned technical problems, this application discloses a method for reconstructing the surface shape of a phase-shifting interferometric image, which can preserve the sequence of normal frame information when reconstructing the surface shape of a phase-shifting interferometric image.

[0018] See Figure 1 As shown, this embodiment of the invention discloses a method for reconstructing the surface shape of a phase-shifting interferometric image, comprising: Step S11: Obtain the phase-shifted interferometric image sequence of the object under test and the corresponding acquisition parameters, and process the phase-shifted interferometric image sequence to construct the independent mask corresponding to each frame of the phase-shifted interferometric image and the common aperture corresponding to the phase-shifted interferometric image sequence; the acquisition parameters include nominal phase shift, exposure parameters and timestamp.

[0019] In this embodiment, the phase-shifting interferometric image sequence consists of K consecutively acquired phase-shifting interferometric images belonging to the same measurement and targeting the same object under test. K is typically no less than three, and preferably five or more. The object under test can be an optical mirror, optical system, extreme ultraviolet or deep ultraviolet element, optical element in a semiconductor device, etc., and this embodiment does not limit this. The phase shift can be generated by a piezoelectric phase shifter, mechanical displacement, wavelength tuning, electro-optic modulation, acousto-optic modulation, or environmental disturbance; the phase shift amount can be predetermined, or it can be used as an unknown parameter frame by frame, alternately estimated with the phase to be measured. Accordingly, the type of phase-shifting interferometry is not limited to fixed step size phase shift, unknown step size phase shift, random phase shift, wavelength tuning, multi-wavelength, polarization synchronization, digital holography, or low coherence scanning. As long as a model relationship between multi-frame observations and the parameters to be determined can be established, the method of this embodiment can be used. The acquisition parameters include the nominal phase shift amount corresponding to each frame, exposure parameters, and timestamps, and may also include optional acquisition status information such as vibration sensor data. The nominal phase shift can be used as an initial value or prior for estimating the phase shift state, exposure parameters can be used to determine saturation and underexposure, and timestamps can be used to establish the temporal relationship between frames. After acquiring the phase-shifted interferometric image sequence, the range of frames to be processed can be determined based on the timestamps, acquisition status, or user settings. For example, frames that are obviously not part of this measurement can be removed, or only frames within a specified time window can be selected for processing.

[0020] In this embodiment, Figure 2This is a schematic diagram of a specific phase-shift interferometric image surface reconstruction system architecture. In this system, the image acquisition unit acquires multiple frames of phase-shift interferometric images belonging to the same measurement, along with nominal phase shift, exposure parameters, timestamps, and optional vibration sensor data. The preprocessing unit performs image size checks, dark field or flat field correction, bad pixel processing, grayscale normalization, saturation and underexposure detection, and generates independent effective masks and common apertures for each frame. The baseline reconstruction unit calculates background intensity, modulation, and baseline wrapping phase under equal or preset initial weights, and estimates scalar phase shift, piston, tilt, defocus, or other motion parameters for each frame. The frame quality evaluation unit generates predicted interferograms for each frame based on the baseline reconstruction results and calculates model consistency residuals, available pixel ratio, saturation ratio, modulation coverage, and other frame quality indicators. The weight solvability determination unit performs robust normalization and fusion of frame quality indicators, generates continuous frame quality weights, and calculates the number of effective frames, the rank of the design matrix, and the condition number to determine whether the weighted solution conditions are met. The weighted iterative reconstruction unit incorporates frame quality weights and pixel local reliability weights into motion parameter updates and pixel-by-pixel phase calculations. Based on the updated results, it re-evaluates frame quality and recalculates weights until convergence conditions are met or the maximum number of iterations is reached. The results and diagnosis unit performs phase unwrapping and surface shape conversion, outputting wrapped phase, unwrapped phase, surface shape height, peak-to-valley value, root mean square value, frame quality index, frame weight, effective frame count, matrix condition number, and quality alarm information. The interface unit connects to the area array camera, interferometer controller, and instrument host computer, receiving multiple frames of phase-shifted interferometric images and acquisition parameters, and sending reconstruction results, quality diagnoses, and alarm information to the instrument terminal or production database. A feedback relationship exists between the frame quality evaluation unit and the weighted iterative reconstruction unit: the weighted reconstruction results are used to update the predicted image and frame quality weights; the updated frame quality weights are then re-entered into the weighted reconstruction process until convergence conditions are met or the preset number of iterations is reached.

[0021] Understandably, the aforementioned system can be deployed on interferometer host computers, instrument controllers, servers, edge computing boxes, graphics processing units (GPUs), or field-programmable gate arrays (FPGAs) acceleration platforms, and can serve as an independent frame quality assessment service to output frame weights to other reconstruction algorithms. Quality assessment and weight updates can be performed after a baseline reconstruction, or dynamically during multi-scale reconstruction, each iteration, before and after phase unrolling, or during online acquisition. Frame quality weights can be frame-level scalars, or extended to frame group weights, channel weights, region weights, pixel weights, or multi-scale weights. Multiple weights can be multiplied, weighted fused, or applied hierarchically.

[0022] In this embodiment, Figure 3This is a schematic diagram of a specific phase-shift interferometric image surface reconstruction process. After acquiring the phase-shift interferometric image sequence, the sequence is preprocessed. Preprocessing may include image size checking, dark field or flat field correction, bad pixel processing, grayscale normalization, and saturation and underexposure detection. Specifically, image size checking confirms that each frame has a consistent size and matches the calibration information; dark field or flat field correction eliminates fixed camera bias and response inhomogeneity; bad pixel processing marks or repairs sensor defects; grayscale normalization can employ camera bit depth normalization, dark field and gain correction, quantile scaling, or reference exposure calibration; and saturation or underexposure thresholds are preferably determined according to camera calibration and are used to detect pixels with truncated grayscale values.

[0023] Based on the preprocessing results above, an independent mask is constructed for each frame. Let the image sequence contain K frames, and the observation intensity at pixel i in the k-th frame be... Independent and valid markers are , This indicates that the pixel is valid in the k-th frame. Indicates invalid. The valid marker comprehensively considers finite values, sensor dynamic range, dead pixels, occlusion, low-modulation settings, and user aperture. Specifically, a pixel is marked invalid in a frame if its intensity is not finite, exceeds the sensor dynamic range, is a dead pixel, is occluded, its modulation is below the minimum requirement, or it is outside the user-defined aperture. Independent mask for the k-th frame. That is, the set of all valid pixels in the frame.

[0024] Based on the construction of independent masks for each frame, a common aperture corresponding to the phase-shifted interferometric image sequence is constructed. If the strict intersection of the independent masks for each frame is directly taken as the common aperture, a single abnormal frame (e.g., a frame with large-area occlusion) will cause the common aperture to shrink excessively, resulting in the loss of a large amount of effective information from normal frames. Therefore, this embodiment preferably constructs the common aperture according to the effective number of times across frames: (1); in, For common aperture, Indicates rounding up. The coverage factor for the common aperture can be set from 0.7 to 1, depending on the detection task. When the common aperture equals 1, the common aperture is a strict intersection. Thus, only when the common aperture is not less than 1... Only valid pixels within a frame enter the common aperture, thus avoiding excessive erosion of the common aperture by a few abnormal frames while ensuring that pixels within the common aperture are observable in the vast majority of frames. Simultaneously, each frame retains its independent mask. This is so that the proportion of available pixels in the frame and the pixel-level local reliability weights can be calculated later.

[0025] Step S12: Based on the common aperture, preset weights and the phase-shifted interferometric images, determine the interferogram intensity model corresponding to the phase-shifted interferometric image sequence, use the current interferogram intensity model to determine the target image parameters corresponding to each phase-shifted interferometric image, and determine the corresponding predicted interferometric intensity based on leave-one prediction method; the target image parameters include background intensity, modulation degree, wrapping phase and phase shift state.

[0026] In this embodiment, the interferogram intensity model is a physical model describing the relationship between the observed intensity of each frame of the phase-shifted interferogram and the background intensity, modulation degree, measured phase, and frame-by-frame phase shift state. In one implementation, the interferometric intensity of the i-th pixel in the k-th frame is expressed as: (2); in, Let i be the background intensity at pixel i. The modulation depth at pixel i. Let i be the phase of the envelope to be measured. This represents the phase shift state or motion phase at pixel i in the k-th frame. This includes noise and unmodeled errors. Phase shift state. It can be scalar phase shift only At this point, all pixels within the same frame have the same phase shift; it can also be expanded using spatial basis functions to describe the spatial phase shift caused by inter-frame pistoning, tilting, defocusing, and other motions, i.e.: (3); in, The value of the l-th spatial basis function at pixel i can be a constant term, horizontal and vertical coordinates, defocus term, astigmatism term, Zernike term, polynomial term, spline basis function, or optical flow basis function. Let be the motion coefficients corresponding to the l-th basis function in the k-th frame. The scalar phase shift of the k-th frame. With each motion coefficient The motion field parameters that together constitute this frame are the motion coefficient vector. .

[0027] The interferogram intensity model is determined based on a common aperture, preset weights, and phase-shifted interferometric images; this is the baseline reconstruction process. Within the model, K-frame phase-shifted interferometric images are solved using preset weights to obtain the model parameters in equations (2) and (3), thus obtaining the initial interferogram intensity model. The preset weights can be equal weights, meaning each frame has a weight of 1; or they can be initial weights set based on prior information, such as initial weights set based on vibration sensor data or exposure parameters. The baseline reconstruction can employ a fixed phase-shift algorithm, least squares, maximum likelihood, model iteration, or other algorithms capable of outputting... , , and The phase-shifting interferometry algorithm is used. The background intensity, modulation, reference wrapping phase, and scalar phase shift, piston, tilt, defocus, or other motion parameters of each frame obtained from the reference reconstruction are the target image parameters corresponding to each frame of the phase-shifting interferogram under the initial interferogram intensity model. It should be noted that when this step is executed for the first time, the current interferogram intensity model is the initial interferogram intensity model obtained from the reference reconstruction.

[0028] After determining the target image parameters, the predicted interference intensity corresponding to each frame of phase-shifted interferometric image is determined based on the leave-one-out prediction method. If the intensity of the k-th frame is directly predicted using the current model containing all frames, then when the k-th frame is an anomalous frame, this frame has already exerted a pull on the model parameters in the baseline solution, causing the model to "explain" the anomalousness of the frame to a certain extent, thereby reducing its apparent residual and causing missed detections. Therefore, this embodiment adopts the leave-one-out prediction method to evaluate the k-th frame: the k-th frame is excluded from the baseline solution, the model parameters are solved using the data of the remaining K-1 frames, and then the obtained model is used to predict the intensity of the k-th frame at each pixel. Alternatively, lever values ​​and influence functions can be used to make equivalent corrections to the fitting results of the entire sequence, resulting in a prediction model that excludes the k-th frame, and then the intensity of the k-th frame can be predicted. This can reduce the missed detections caused by using the model to evaluate itself after the abnormal frame pulls the model.

[0029] In practical implementation, when there are many frames, one frame can be left out each time, meaning that the solution and prediction for each frame are performed separately. When there are few frames, to avoid insufficient phase shift information in the remaining frames after excluding one frame, grouped cross-prediction can be used. This involves dividing the sequence into several groups and using the data from the remaining groups to predict the intensity of each frame in the current group. Alternatively, influence correction can be used, which involves using leverage values ​​or influence functions to equivalently correct the fitting results of the entire sequence without actually repeating the solution. Furthermore, when a historical calibration model is available, the intensity of each frame can be predicted directly from the historical calibration model, or a full-sequence baseline prediction can be used as a rapid evaluation method. In one specific implementation, determining the corresponding predicted interferometric intensity based on the leave-one prediction method includes: correcting the current interferogram intensity model using the target influence function, and using the corrected interferogram intensity model to determine the predicted interferometric intensity corresponding to each phase-shifted interferogram. The target influence function is used to characterize the degree of influence of the observation of the k-th frame on the current model parameter estimate, and can be determined, for example, by the leverage value of that frame in the weighted equation and the fitting residual of that frame. The contribution of the k-th frame is subtracted from the current model parameters using the objective influence function, resulting in a corrected model equivalent to excluding the k-th frame. This corrected model is then used to calculate the predicted interferometry intensity for the k-th frame. This influence correction method avoids performing a complete solution for every frame, reducing computational load while maintaining leave-one-out prediction performance. It is particularly suitable for scenarios with a small number of frames or high processing speed requirements.

[0030] Step S13: Determine the consistency residual based on the predicted interference intensity and the observed interference intensity corresponding to the phase-shifted interferogram, determine the frame quality weight corresponding to the phase-shifted interferogram based on the consistency residual, and determine whether the current interferogram intensity model satisfies the preset model iteration conditions based on each frame quality weight.

[0031] In this embodiment, the observed interference intensity is the actual intensity value of each pixel in the phase-shifted interferometric image. The frame quality weights can be determined after preprocessing such as dark field or flat field correction and grayscale normalization. In one embodiment, a consistency residual is determined based on the predicted interference intensity and the observed interference intensity corresponding to the phase-shifted interferometric image, and the frame quality weights corresponding to the phase-shifted interferometric image are determined based on the consistency residual. This includes: determining the observed interference intensity corresponding to the phase-shifted interferometric image based on the intensity value corresponding to each pixel in the phase-shifted interferometric image, and determining the consistency residual between the predicted interference intensity and the observed interference intensity based on the modulation index; aggregating each consistency residual based on the common aperture to determine the frame quality vector corresponding to the phase-shifted interferometric image, and determining the frame quality weights corresponding to the phase-shifted interferometric image based on the frame quality vector.

[0032] Specifically, to eliminate the impact of modulation differences between different pixels on the residual magnitude, it is preferable to use modulation-normalized residuals as consistency residuals: (4); in, Let i be the consistency residual at pixel i in the k-th frame. Let be the predicted interference intensity at pixel i in the k-th frame. To prevent positive numbers with a denominator of zero, pixels with large modulation levels are inherently allowed to have larger intensity fluctuations, while the intensity fluctuations of pixels with small modulation levels are more easily masked by noise. After modulation normalization, the residuals of different pixels have comparable scales.

[0033] After obtaining the pixel-level consistency residuals, the consistency residuals are aggregated based on the common aperture to obtain the frame-level model consistency index. . Common aperture can be used The median, truncated mean, quantiles, mean Huber loss, or mean Tukey loss of the effective sample residuals are robust statistics that prevent extreme residuals of individual pixels from dominating frame-level metrics. (Except for model consistency metrics...) In addition, the frame quality vector may also include: the proportion of available pixels. This represents the proportion of pixels within the common aperture that can be used to solve for this frame, and can be determined by an independent mask. With common aperture The saturation ratio is obtained by the ratio of the intersection size to the common aperture size. This indicates the proportion of pixels in the frame that are saturated, underexposed, or truncated; modulation coverage. This represents the proportion of pixels that meet the minimum tone condition; the degree of temporal abrupt change. This indicates the degree of abrupt change in the motion coefficients of a frame relative to adjacent frames or robust temporal trends, and can be calculated based on timestamps and motion field parameters of each frame; regional anomaly degree. , representing the degree of anomaly in areas such as aperture edges, local occlusion, or fringe breaks. Therefore, the frame quality vector of the k-th frame can be represented as: Or a combination of several of these indicators, which characterize the data quality of the frame from multiple aspects such as model consistency, aperture availability, exposure status, temporal stability and regional integrity.

[0034] It should be noted that the model consistency index is not limited to the intensity residual form mentioned above. It can also use normalized intensity residual, wrapping phase difference, complex phasor difference, frequency transfer function mismatch, local fringe direction difference, gradient consistency, or a combination of the above indices. For example, the wrapping phase difference can be obtained by comparing the difference between the wrapping phase obtained when the frame is involved in the solution and when it is not involved in the solution. The complex phasor difference can be obtained by comparing the difference between the complex phasor corresponding to the observed intensity of the frame and the phasor predicted by the model.

[0035] In one specific implementation, determining the frame quality weights corresponding to the phase-shifted interferometric image based on the frame quality vector includes: determining the normalized vector corresponding to each frame quality vector, and fusing each normalized vector based on a non-negative fusion coefficient to determine the target anomaly score corresponding to the frame quality vector, so as to map the target anomaly score to the frame quality weights corresponding to the phase-shifted interferometric image using a target weight mapping function. Specifically, since the absolute values ​​of indicators such as residual levels and available pixel ratios differ among different sequences, it is necessary to normalize each component of the frame quality vector. For the model consistency index of each frame, robust normalization is preferably performed using the sequence median and median absolute deviation. For example: (5); in, Let be the normalized outlier of the model consistency index for the k-th frame, median(R) be the median of the model consistency index sequence R for the k-frames, MAD(R) be the median absolute deviation of the sequence, and 1.4826 be the scaling factor that makes the median absolute deviation consistent with the standard deviation of the normal distribution. Equation (5) uses the robust statistics of the sequence itself as a benchmark. The normalized outlier of frames with residuals below the median level is 0, and the normalized outlier of frames with residuals significantly higher than the median level increases with the degree of deviation. Moreover, the median and median absolute deviation are not easily affected by a few extreme frames. Available pixel ratio saturation ratio Adjustment of system coverage and degree of temporal mutation It can be converted according to the direction of "normalized outliers increase when quality deteriorates" , , and For example, the lower the available pixel ratio and modulation coverage, and the higher the saturation ratio and temporal abrupt change, the larger the corresponding normalized outlier. An upper limit is applied to each normalized outlier to prevent the extreme values ​​of a single indicator from overwhelming other indicators. All normalized outliers together constitute the normalized vector of the frame.

[0036] After determining the normalized vector, the normalized vector is fused based on the non-negative fusion coefficients to determine the target anomaly score. One implementation of the comprehensive anomaly score is as follows: (6); in, The target anomaly score in the k-th frame. , , , and These are non-negative fusion coefficients, which can be calibrated to sum to 1. The magnitude of each fusion coefficient reflects the importance of the corresponding indicator in frame quality evaluation. For example, in cases where vibration is the main disturbance source, it can improve the frame quality. and It can improve performance in situations where exposure is unstable. When the frame quality vector also includes the degree of regional anomalies. At that time, an item can be added accordingly. .

[0037] After determining the target anomaly score, the target anomaly score is mapped to frame quality weights using a target weight mapping function. One implementation of the frame quality weights is as follows: (7); in, Here, `clip` represents the frame quality weight for the k-th frame. The weight is set as a minimum. As shown in equation (7), the weight of a normal frame with a target anomaly score of 0 is 1, and the weight of a frame with a higher target anomaly score is lower, and the weight is not lower than the minimum weight. This preserves some phase shift information of the frame under normal abnormal conditions. For frames with an effective pixel ratio lower than the hard threshold, a saturation ratio higher than the hard threshold, file corruption, or model residuals much higher than the safety threshold, the phase shift information can be directly set without using equation (7). This means completely removing the frame. For typical abnormal frames, Maintain a continuous value between 0 and 1 to avoid sudden loss of phase shift information.

[0038] In this embodiment, the weight mapping is not limited to an exponential function. The target weight mapping function can also be a logistic function, a piecewise linear function, Huber weights, Tukey's double-weight function, a lookup table function, Bayesian posterior probability, fuzzy rules, or a calibrated lightweight learning model. Regardless of the mapping method used, it is preferable that the target weight mapping function satisfies the following condition: the frame weights do not monotonically increase when the model mismatch increases, the proportion of available pixels decreases, or the saturation proportion increases; that is, frames with deteriorating data quality will not receive higher weights.

[0039] In this embodiment, after determining the frame quality weights of each frame, it is determined whether the current interferogram intensity model meets the preset model iteration conditions based on the frame quality weights. The preset model iteration conditions are used to determine whether it is worthwhile and safe to perform weighted solving: if the weights of each frame are almost the same, the results of weighted solving and equal-weighted solving are basically the same, and resolving is unnecessary; if the remaining effective information after weight reduction is insufficient to solve all unknown parameters, or the phase shift distribution is ill-conditioned, then forcibly resolving will produce spurious results. Therefore, the preset model iteration conditions in this embodiment include resolving trigger conditions and numerical safety conditions, and convergence judgment conditions are also included in the iteration process.

[0040] In one specific implementation, determining whether the current interferogram intensity model meets the preset model iteration conditions based on the quality weights of each frame includes: determining the target weighted effective frame number based on the quality weights of each frame, determining the proportion of low-weight frame images corresponding to the phase-shifted interferogram image sequence based on the preset low-weight threshold, and constructing the phase-shift design matrix corresponding to the target pixel set of the phase-shifted interferogram; and determining whether the current interferogram intensity model meets the preset model iteration conditions based on the target weighted effective frame number, the proportion of low-weight frame images, and the phase-shift design matrix.

[0041] Specifically, the target weighted effective frame count is calculated using the following formula: (8); in, The target is weighted effective frame count, reflecting the equivalent number of independent frames corresponding to consecutive weights. When the weight of each frame is 1... Equal to K; when the weight of some frames is reduced, The weight is reduced accordingly; when only one frame has a weight of 1 and the weights of the remaining frames are 0. Equal to 1. The preset low-weight threshold is the weight threshold for determining whether a frame is a low-weight frame. Frames with a weight lower than the preset low-weight threshold are recorded as low-weight frames. The ratio of the number of low-weight frames to the total number of frames K is the proportion of low-weight frames.

[0042] In this embodiment, the phase shift design matrix is ​​a coefficient matrix composed of the phase shift states of each frame during pixel-by-pixel solution. For each pixel or representative pixel set (i.e., the target pixel set), the phase shift state of the current model is used as the basis for the design matrix. Construct a phase-shift design matrix and check the rank and condition number of its weighted normal equations. The target pixel set can be all pixels within a common aperture, or representative pixels extracted from the common aperture according to certain rules, such as uniformly grid sampled pixels or several pixels with the highest modulation, to reduce computational load. A fixed phase-shift three-parameter model (background intensity, modulation, and phase, or equivalent three linear parameters) requires at least a rank of 3 for the phase-shift design matrix; when estimating more motion parameters simultaneously, the number of effective frames should not be less than the dimension of the corresponding unknown parameters, and preferably, at least one frame should be retained for redundancy. Based on this, a preferred re-solution triggering condition and numerical safety condition are: at least one frame weight is lower than a preset low-weight threshold or the frame weight range exceeds a discrimination threshold, to ensure that weighted solution is practically meaningful compared to equal-weight solution; the target weighted effective frame number... The interferogram intensity model is determined to meet the following conditions: The number of frames must be at least the minimum effective number to ensure sufficient equivalent frames for solving unknown parameters after weighting; the weighted phase shift design matrix of representative pixels must be full rank and the condition number must be less than the upper limit of the condition number to ensure the weighted equations are solvable and numerically stable; the proportion of low-weighted frames must not exceed a safe proportion to avoid most frames being weighted and losing representativeness; the baseline reconstruction must have a minimum modulation coverage to ensure a sufficient proportion of pixels within the common aperture possess solvable fringe information. If all the above conditions are met, the current interferogram intensity model is deemed to satisfy the preset model iteration conditions, and weighted solution is initiated; if any condition is not met, the current interferogram intensity model is deemed not to satisfy the preset model iteration conditions. Furthermore, safety determination can also use one or more of the following criteria as supplementary criteria: matrix determinant, phase shift coverage angle, residual improvement rate, or prediction uncertainty.

[0043] During the iteration process, the preset model iteration conditions also include convergence criteria. In one implementation, determining whether the current interferogram intensity model meets the preset model iteration conditions includes: determining the target weight difference and target phase mean square change value corresponding to the current interferogram intensity model, and determining that the current interferogram intensity model does not meet the preset model iteration conditions when the target weight difference is less than the preset weight difference and the target phase mean square change value is less than the preset mean square change value, or when the current interferogram intensity model iteration round reaches the preset iteration round; wherein, the target weight difference is the maximum weight difference between the frame quality weight corresponding to the current interferogram intensity model and the frame quality weight corresponding to the previous interferogram intensity model, and the target phase mean square change value is the root mean square value of the difference between the wrapping phase corresponding to the current interferogram intensity model and the wrapping phase corresponding to the previous interferogram intensity model. That is, when the maximum change of frame weights between two adjacent rounds is less than the threshold and the mean square change of the wrapping phase is also less than the threshold, it indicates that the frame weights and model parameters have stabilized, and continuing iteration will not bring significant improvement, so the iteration stops at this time; when the iteration round reaches the preset iteration round, the iteration also stops to avoid infinite loop. The convergence determination condition, together with the aforementioned triggering condition and safety condition, constitutes the preset model iteration condition: the interferogram intensity model will only continue to be updated if the model fails to converge, fails to reach the preset iteration round, and both the triggering condition and the safety condition are met.

[0044] Step S14: When the interferogram intensity model satisfies the preset model iteration condition, update the interferogram intensity model based on the independent mask, the target image parameters, and the frame quality weight to obtain a new interferogram intensity model, and then proceed to the step of determining the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model.

[0045] In this embodiment, updating the interferogram intensity model is a weighted solution process. The frame quality weights are applied in two ways: first, through cross-frame coupled motion field parameter updates; and second, through pixel-by-pixel phase parameter solutions. In one implementation, updating the interferogram intensity model based on an independent mask, target image parameters, and frame quality weights to obtain a new interferogram intensity model includes: determining the motion field parameters corresponding to the current interferogram intensity model based on the phase shift state in the target image parameters, updating the motion field parameters based on the frame quality weights, and then updating the interferogram intensity model based on the updated motion field parameters, independent mask, target image parameters, and frame quality weights to obtain a new interferogram intensity model.

[0046] In this embodiment, when the frame quality weight is solved pixel by pixel, the intensity model shown in equation (2) is written in linear form: (9); in, , Let the design matrix The k-th action , Let i be a column vector consisting of the observed intensities at pixel i across all frames, with local reliability weights. It is obtained from the independent mask, modulation, saturation state, and region confidence of the k-th frame. For example, when pixel i is outside the independent mask in the k-th frame... When it is 0, it is in a saturated state. When the value is 0 or a small value, the higher the modulation index and regional confidence level, the better. The closer it is to 1, the better. The weight matrix is... The product of the frame quality weight and the local reliability weight forms a diagonal weight matrix. Therefore, the weighted least squares solution is: (10); in, Let I be the estimated value of the linear parameter at pixel i, and let I be the identity matrix. is an optional regularization coefficient used to improve numerical stability when the normal equations approach ill-conditioned conditions. The updated package phase is obtained by The updated tuning system was obtained. This is the updated background intensity. If a linear form is not used, weighted nonlinear least squares, maximum likelihood, or robust optimization can also be performed under the original cosine model shown in equation (2). As can be seen from equation (10), the frame quality weight... The contribution of the k-th frame to each pixel's normal equation is directly scaled. Outlier frames with weights close to 0 have almost no impact on the estimation of background intensity, modulation, and wrapping phase, while the local reliability weights... This further suppresses the effects of local occlusion, low-key settings, and saturated pixels at the pixel level.

[0047] In this embodiment, when the frame quality weight is incorporated into the motion field parameter update, it is based on the phase shift state in the target image parameters. According to the parameterization of equation (3), the motion field parameters of each frame, i.e., the motion coefficient vector, can be determined. . Using the motion coefficient vector of each frame For the variables to be optimized, the following weighted objective function can be constructed: (11); in, The updated motion field parameters consist of two terms: the first term is the weighted sum of squared fitted residuals at each pixel in each frame, and the second term is the temporal smoothing constraint on the motion coefficients of adjacent frames. For temporal regularization coefficients. Since the objective function includes cross-frame temporal constraints and shared model parameters such as background intensity, modulation, and wrapping phase across frames, the frame quality weights... This approach can alter the contribution of each frame to the overall motion field estimation, preventing motion coefficients in anomalous frames from influencing the estimation of adjacent frames and shared parameters; this differs from methods that only label the motion parameters after independently solving each frame. The motion field can employ scalar phase shift, piston, lateral and longitudinal tilt, defocus, astigmatism, coma, Zernike higher-order terms, local polynomials, spline fields, optical flow fields, low-rank fields, or parametric models driven by vibration sensors. Weighted solutions can employ weighted linear least squares, weighted nonlinear least squares, maximum likelihood, iterative reweighted least squares, alternating orientation optimization, stochastic optimization, or parallel solutions using a graphics processor. Pixel-by-pixel solutions are independent between pixels, making them suitable for parallel acceleration.

[0048] In specific implementation, the interferogram intensity model is updated by alternating iteration: the frame weights are fixed, the motion field parameters are solved according to equation (11), and the pixel-by-pixel parameters are solved according to equation (10) to obtain a new interferogram intensity model; then, the process jumps to step S12, where the target image parameters of each frame are re-determined using the new interferogram intensity model, and the predicted interferogram intensity is recalculated based on leave-one prediction; then, step S13 is executed to recalculate the quality index and frame weights, and to determine whether the preset model iteration conditions are met. If they are met, the next round of weighted solution is performed. The iteration stops when the maximum change in weight between two adjacent rounds is less than the threshold, the mean square change in the wrapping phase is less than the threshold, or the maximum number of iterations is reached. If the rank of the phase shift design matrix is ​​insufficient or the condition number exceeds the limit in a certain round, the process reverts to the previous round's valid result and outputs an alarm.

[0049] Step S15: When the interferogram intensity model does not meet the preset model iteration conditions, the wrapped phase is expanded based on the current interferogram intensity model to obtain the expanded phase, and surface shape conversion is performed based on the expanded phase to determine the surface shape result corresponding to the measured object.

[0050] In this embodiment, the interferogram intensity model not meeting the preset model iteration conditions includes two cases. The first case is when the iteration has converged or reached the preset iteration round. In this case, the current interferogram intensity model is the effective model obtained from the last round of weighted solution, and the phase unwrapping phase of this model is directly used for phase expansion. The second case is when the triggering condition or safety condition is not met, such as when the weights of each frame are almost the same, the number of target weighted effective frames is lower than the minimum effective frame number, the rank of the phase shift design matrix is ​​insufficient or the condition number exceeds the limit, the proportion of low-weighted frame images exceeds the safety proportion, or the modulation coverage is insufficient. For cases where the triggering condition is not met, it indicates that there are no abnormal frames in the sequence that require weight reduction, and the baseline reconstruction result can be retained as the current interferogram intensity model. For cases where the safety condition is not met, a degradation strategy can be adopted, including: retaining the baseline result; switching to a low-degree-of-freedom model, i.e., reducing the degrees of freedom of the motion field model, for example, only estimating the scalar phase shift without estimating the tilt and defocus terms, to reduce unknown parameters and restore solvability; using only reliable regions for solution, i.e., solving only within regions where the weight and availability requirements are met; prompting manual review or suggesting re-acquisition; or marking the result as unacceptable. The model obtained after downgrading is used as the current interferogram intensity model for subsequent phase expansion.

[0051] After determining the current interferogram intensity model, its wrapped phase is expanded to obtain the expanded phase. Phase expansion can employ path-following, quality-guided, least-squares, or other phase expansion algorithms; this embodiment does not limit this approach. Then, surface shape conversion is performed based on the expanded phase. That is, according to the interferometer's optical path structure and the measurement wavelength, the expanded phase is converted into the height or wavefront deviation of the measured object's surface, yielding the surface shape result. The surface shape result can include the surface height distribution and its peak-to-valley (PV) and root-mean-square (RMS) values. For example... Figure 4 The image shown is a comparative schematic diagram of specific phase-shifting interferometry image surface reconstruction results, in which... Figure 4 (a) is the acquired original phase-shifted interferometry image. Figure 4 (b) for Figure 4 (a) The surface shape result obtained by direct solution. Figure 4 (c) To utilize the phase-shifting interferometric image surface shape reconstruction method provided in this application for... Figure 4(a) Surface reconstruction results obtained through surface reconstruction. A comparison reveals that the direct solution results contain local anomaly regions and striped errors introduced by damaged frames, especially near the locations corresponding to the original damaged areas, where the surface distribution exhibits discontinuities, local abrupt changes, or abnormal textures. This indicates that under extreme vibration, image occlusion, or frame corruption, traditional equal-weighted solutions treat abnormal frames as normal observations in the solution process, causing bad frame errors to propagate to the phase retrieval and surface reconstruction results. The method provided in this embodiment first constructs a common aperture and performs benchmark reconstruction on multiple frames of phase-shifting interferometric images to obtain the initial phase, background intensity, modulation degree, and frame-by-frame motion parameters; then, it generates a predicted image for each frame based on the benchmark model and calculates the residual between the observed image and the model's predicted image, while simultaneously calculating quality indicators such as effective pixel ratio, local reliability, and aperture integrity. For Figure 4 The corrupted frame shown in (a) exhibits low quality in both model consistency and usability metrics because its central dark bands and local anomalies cannot be reasonably explained by the phase-shifting interferometry physical model. Therefore, the system automatically assigns it a lower frame quality weight. During the weighted solution stage, the frame quality weight is introduced into the motion field update and pixel-by-pixel phase solution process, reducing the contribution of the corrupted frame to the final phase parameters while strengthening the constraint effect of the normal frame on the reconstruction result. After processing by the method provided in this embodiment, Figure 4 In (b), the local anomalies and striped errors caused by the damaged frame are significantly suppressed, the overall continuity and stability of the surface shape result are improved, the abnormal textures within the aperture are weakened, and the reconstruction result is closer to the true surface shape trend reflected by the normal frame.

[0052] It is understood that, in addition to the surface shape results, this embodiment can also output quality diagnostic information, including frame quality indicators such as wrapping phase, unfolding phase, model consistency index of each frame, available pixel ratio, saturation ratio, etc.; frame quality weight of each frame; target weighted effective frame count; matrix stability information such as rank and condition number of the phase shift design matrix; a list of downweighted frames; trigger status; and quality alarm information. This information can serve as the basis for measurement reception, re-acquisition, or manual verification, making the reconstruction results interpretable and traceable. Based on this, this embodiment can be used in scenarios such as optical mirror surface shape inspection, optical system wavelet aberration detection, extreme ultraviolet or deep ultraviolet component inspection, vacuum or low pressure inspection, motion platform inspection, vehicle-mounted or airborne optical inspection, semiconductor equipment inspection, and offline repair of abnormal data in production lines.

[0053] As can be seen, this application, through residual evaluation between observed intensity and phase-shift interferometry predicted intensity, can identify anomalous frames with normal average grayscale and fringe appearance but mismatched phase relationships. Leave-one prediction reduces the pull of anomalous frames on their own evaluation benchmark, making the frame quality evaluation results less susceptible to the influence of bad frames and improving the detectability of extreme outliers. Continuous weighting balances information preservation and anomaly suppression, preserving some phase shift information in mildly anomalous frames and nearly eliminating severely anomalous frames, which is more conducive to maintaining phase shift diversity than hard deletion with a fixed threshold. The layered effect of frame-level and pixel-level weights means that frame-wide vibration or exposure anomalies are controlled by frame quality weights, while local occlusion, low-key settings, and saturated pixels are controlled by local reliability weights, avoiding the expansion of local defects into frame-wide deletion. The weights are incorporated into the reconstruction model itself; frame quality weights are not only used for reporting but also enter the cross-frame coupled motion field objective function and pixel-by-pixel normal equations, directly reducing the contribution of anomalous frames to phase and surface parameters. The checks on effective frame count, matrix rank, and condition number can avoid spurious results caused by insufficient model degrees of freedom or ill-conditioned phase shift distribution after weighting, providing solvability and numerical stability protection. Furthermore, the phase-shifting interferometric image surface shape reconstruction system based on the architecture of this application does not rely on additional hardware or repeated acquisitions. It can be used as a post-processing module for existing interferometer reconstruction software and has offline remediation capabilities for acquired sequences. The system outputs the residual, usable ratio, saturation ratio, weight, effective frame number, matrix condition number, and trigger status for each frame. The results are interpretable and traceable and can be used as the basis for measurement reception, re-acquisition, or manual verification.

[0054] See Figure 5 As shown, this application discloses a phase-shifting interferometric image surface shape reconstruction device, comprising: Image processing module 11 is used to acquire the phase-shifted interferometric image sequence of the object under test and the corresponding acquisition parameters, and to process the phase-shifted interferometric image sequence to construct an independent mask corresponding to each frame of the phase-shifted interferometric image and a common aperture corresponding to the phase-shifted interferometric image sequence; the acquisition parameters include nominal phase shift, exposure parameters and timestamp; The interference intensity prediction module 12 is used to determine the interferogram intensity model corresponding to the phase-shifted interferogram sequence based on the common aperture, preset weights and the phase-shifted interferogram, determine the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model, and determine the corresponding predicted interference intensity based on leave-one prediction method; the target image parameters include background intensity, modulation degree, wrapping phase and phase shift state; The iterative judgment module 13 is used to determine the consistency residual based on the predicted interference intensity and the observed interference intensity corresponding to the phase-shifted interference image, determine the frame quality weight corresponding to the phase-shifted interference image based on the consistency residual, and determine whether the current interferogram intensity model meets the preset model iteration conditions based on each of the frame quality weights. The model iteration module 14 is used to update the interferogram intensity model based on the independent mask, the target image parameters and the frame quality weight to obtain a new interferogram intensity model when the interferogram intensity model satisfies the preset model iteration condition, and then jump to the step of determining the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model; The surface shape result acquisition module 15 is used to perform phase expansion on the wrapped phase based on the current interferogram intensity model to obtain the expanded phase when the interferogram intensity model does not meet the preset model iteration conditions, and to perform surface shape conversion based on the expanded phase to determine the surface shape result corresponding to the measured object.

[0055] As can be seen, the frame quality evaluation in this application is driven by the consistency residual between the observed interferometric intensity and the intensity predicted by the phase-shifting interferometric physical model. This allows for the detection of anomalous frames with normal average grayscale and fringe appearance but mismatched phase relationships. The leave-one-out prediction method reduces the influence of anomalous frames on the evaluation benchmark, making the frame quality evaluation results less susceptible to the influence of bad frames and improving the detectability of extreme outliers. Furthermore, the frame quality weights are not only used for reporting but also participate in the update process of the interferogram intensity model, directly reducing the contribution of anomalous frames to phase and surface parameters. Mildly anomalous frames retain some phase shift information, while severely anomalous frames are nearly eliminated, which helps maintain phase shift diversity. In addition, this application does not rely on additional hardware or repeated acquisitions and can be used as a post-processing module in existing interferometer reconstruction software for offline remediation of acquired sequences.

[0056] In one specific implementation, the interference intensity prediction module 12 may include: The interferometric intensity prediction submodule is used to modify the current interferogram intensity model using the target influence function, and to determine the predicted interferometric intensity corresponding to each phase-shifted interferometric image using the modified interferogram intensity model.

[0057] In one specific implementation, the iterative judgment module 13 may include: The consistency residual determination submodule is used to determine the observed interference intensity corresponding to the phase-shifted interferometric image based on the intensity value corresponding to each pixel in the phase-shifted interferometric image, and to determine the consistency residual between the predicted interference intensity and the observed interference intensity based on the modulation index; The frame quality weight determination submodule is used to aggregate the consistency residuals based on the common aperture to determine the frame quality vector corresponding to the phase-shifted interferometric image, and to determine the frame quality weight corresponding to the phase-shifted interferometric image based on the frame quality vector.

[0058] In one specific implementation, the frame quality weight determination submodule may include: The frame quality weight determination unit is used to determine the normalized vector corresponding to each frame quality vector, and to fuse each normalized vector based on a non-negative fusion coefficient to determine the target anomaly score corresponding to the frame quality vector, so as to map the target anomaly score to the frame quality weight corresponding to the phase-shifted interferometric image using a target weight mapping function.

[0059] In one specific implementation, the iterative judgment module 13 may include: The image sequence analysis submodule is used to determine the target weighted effective frame number based on the quality weight of each frame, determine the proportion of low-weight frame images corresponding to the phase-shifted interferometric image sequence based on a preset low-weight threshold, and construct the phase-shift design matrix corresponding to the target pixel set of the phase-shifted interferometric image. The first iteration judgment submodule is used to determine whether the current interferogram intensity model meets the preset model iteration conditions based on the target weighted effective frame number, the proportion of low-weight frame images, and the phase shift design matrix.

[0060] In one specific implementation, the iterative judgment module 13 may include: The second iteration judgment submodule is used to determine the target weight difference and target phase mean square change value corresponding to the current interferogram intensity model, and to determine that the current interferogram intensity model does not meet the preset model iteration conditions when the target weight difference is less than a preset weight difference and the target phase mean square change value is less than a preset mean square change value, or when the current interferogram intensity model iteration round reaches a preset iteration round; wherein, the target weight difference is the maximum weight difference between the frame quality weight corresponding to the current interferogram intensity model and the frame quality weight corresponding to the previous interferogram intensity model, and the target phase mean square change value is the root mean square value of the difference between the wrapping phase corresponding to the current interferogram intensity model and the wrapping phase corresponding to the previous interferogram intensity model.

[0061] In one specific implementation, the model iteration module 14 may include: The model iteration submodule is used to determine the motion field parameters corresponding to the current interferogram intensity model based on the phase shift state in the target image parameters, and update the motion field parameters based on the frame quality weights, so as to update the interferogram intensity model based on the updated motion field parameters, the independent mask, the target image parameters and the frame quality weights to obtain a new interferogram intensity model.

[0062] Furthermore, embodiments of this application also disclose an electronic device, Figure 6This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.

[0063] Figure 6 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the phase-shifting interferometric image surface shape reconstruction method disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0064] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0065] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0066] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the phase-shifting interferometric image surface reconstruction method executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0067] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned phase-shifting interferometric image surface shape reconstruction method. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0068] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0069] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0070] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0071] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0072] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for reconstructing the surface shape of a phase-shifting interferometric image, characterized in that, include: The phase-shifted interferometric image sequence of the object under test and the corresponding acquisition parameters are acquired, and the phase-shifted interferometric image sequence is processed to construct an independent mask corresponding to each frame of the phase-shifted interferometric image and a common aperture corresponding to the phase-shifted interferometric image sequence; the acquisition parameters include nominal phase shift, exposure parameters and timestamp; Based on the common aperture, preset weights, and the phase-shifted interferometric images, the interferogram intensity model corresponding to the phase-shifted interferometric image sequence is determined. The target image parameters corresponding to each phase-shifted interferometric image are determined using the current interferogram intensity model, and the corresponding predicted interferometric intensity is determined based on the leave-one-out prediction method. The target image parameters include background intensity, modulation degree, wrapping phase, and phase shift state. Based on the predicted interference intensity and the observed interference intensity corresponding to the phase-shifted interferogram, a consistency residual is determined; based on the consistency residual, a frame quality weight corresponding to the phase-shifted interferogram is determined; and based on each frame quality weight, it is determined whether the current interferogram intensity model satisfies the preset model iteration conditions. When the interferogram intensity model satisfies the preset model iteration condition, the interferogram intensity model is updated based on the independent mask, the target image parameters, and the frame quality weight to obtain a new interferogram intensity model, and then the process jumps to the step of determining the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model; When the interferogram intensity model does not meet the preset model iteration conditions, the wrapped phase is expanded based on the current interferogram intensity model to obtain the expanded phase, and surface shape conversion is performed based on the expanded phase to determine the surface shape result corresponding to the measured object.

2. The phase-shifting interferometric image surface shape reconstruction method according to claim 1, characterized in that, The determination of the corresponding predicted interference intensity based on the leave-one-out prediction method includes: The current interferogram intensity model is modified using the target influence function, and the predicted interferometric intensity corresponding to each phase-shifted interferogram is determined using the modified interferogram intensity model.

3. The method for reconstructing the surface shape of a phase-shifting interferometric image according to claim 1, characterized in that, The step of determining the consistency residual based on the predicted interferometric intensity and the observed interferometric intensity corresponding to the phase-shifted interferometric image, and determining the frame quality weight corresponding to the phase-shifted interferometric image based on the consistency residual, includes: The observed interference intensity corresponding to the phase-shifted interferometric image is determined based on the intensity value corresponding to each pixel in the phase-shifted interferometric image, and the consistency residual between the predicted interference intensity and the observed interference intensity is determined based on the modulation index. Based on the common aperture, the consistency residuals are aggregated to determine the frame quality vector corresponding to the phase-shifted interferometric image, and the frame quality weight corresponding to the phase-shifted interferometric image is determined based on the frame quality vector.

4. The phase-shifting interferometric image surface shape reconstruction method according to claim 3, characterized in that, Determining the frame quality weights corresponding to the phase-shifted interferometric image based on the frame quality vector includes: A normalized vector corresponding to each frame quality vector is determined, and the normalized vectors are fused based on non-negative fusion coefficients to determine the target anomaly score corresponding to the frame quality vector. The target anomaly score is then mapped to the frame quality weight corresponding to the phase-shifting interferometric image using a target weight mapping function.

5. The method for reconstructing the surface shape of a phase-shifting interferometric image according to claim 1, characterized in that, The step of determining whether the current interferogram intensity model satisfies the preset model iteration conditions based on the quality weights of each frame includes: The target weighted effective number of frames is determined based on the frame quality weights of each frame, the proportion of low-weight frame images corresponding to the phase-shifted interferometric image sequence is determined based on a preset low-weight threshold, and a phase-shift design matrix corresponding to the target pixel set of the phase-shifted interferometric image is constructed. Based on the target weighted effective frame count, the proportion of low-weighted frame images, and the phase-shift design matrix, it is determined whether the current interferogram intensity model meets the preset model iteration conditions.

6. The method for reconstructing the surface shape of a phase-shifting interferometric image according to claim 1, characterized in that, The step of determining whether the current interferogram intensity model satisfies the preset model iteration conditions includes: The target weight difference and target phase mean square change value corresponding to the current interferogram intensity model are determined. When the target weight difference is less than a preset weight difference and the target phase mean square change value is less than a preset mean square change value, or when the current interferogram intensity model iteration round reaches a preset iteration round, it is determined that the current interferogram intensity model does not meet the preset model iteration condition. The target weight difference is the maximum weight difference between the frame quality weight corresponding to the current interferogram intensity model and the frame quality weight corresponding to the previous interferogram intensity model. The target phase mean square change value is the root mean square value of the difference between the wrapping phase corresponding to the current interferogram intensity model and the wrapping phase corresponding to the previous interferogram intensity model.

7. The method for reconstructing the surface shape of a phase-shifting interferometric image according to any one of claims 1 to 6, characterized in that, The step of updating the interferogram intensity model based on the independent mask, the target image parameters, and the frame quality weights to obtain a new interferogram intensity model includes: Based on the phase shift state in the target image parameters, the motion field parameters corresponding to the current interferogram intensity model are determined, and the motion field parameters are updated based on the frame quality weights. The interferogram intensity model is then updated based on the updated motion field parameters, the independent mask, the target image parameters, and the frame quality weights to obtain a new interferogram intensity model.

8. A phase-shifting interferometric image surface shape reconstruction device, characterized in that, include: The image processing module is used to acquire the phase-shifted interferometric image sequence of the object under test and the corresponding acquisition parameters, and to process the phase-shifted interferometric image sequence to construct an independent mask corresponding to each frame of the phase-shifted interferometric image and a common aperture corresponding to the phase-shifted interferometric image sequence; the acquisition parameters include nominal phase shift, exposure parameters and timestamp; The interference intensity prediction module is used to determine the interferogram intensity model corresponding to the phase-shifted interferogram sequence based on the common aperture, preset weights, and the phase-shifted interferogram; to determine the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model; and to determine the corresponding predicted interference intensity based on a leave-one-out prediction method. The target image parameters include background intensity, modulation degree, wrapping phase, and phase shift state. The iterative judgment module is used to determine the consistency residual based on the predicted interference intensity and the observed interference intensity corresponding to the phase-shifted interferogram, determine the frame quality weight corresponding to the phase-shifted interferogram based on the consistency residual, and determine whether the current interferogram intensity model satisfies the preset model iteration conditions based on each of the frame quality weights. The model iteration module is used to update the interferogram intensity model based on the independent mask, the target image parameters, and the frame quality weight to obtain a new interferogram intensity model when the interferogram intensity model satisfies the preset model iteration condition, and then jump to the step of determining the target image parameters corresponding to each phase-shifted interferogram using the current interferogram intensity model; The surface shape result acquisition module is used to perform phase unfolding on the wrapped phase based on the current interferogram intensity model to obtain the unfolded phase when the interferogram intensity model does not meet the preset model iteration conditions, and to perform surface shape conversion based on the unfolded phase to determine the surface shape result corresponding to the measured object.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the phase-shifting interferometric image surface reconstruction method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the phase-shifting interferometric image surface reconstruction method as described in any one of claims 1 to 7.

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