Least square phase unwrapping method based on residual point correction for unconnected regions

Abstract

The application discloses a least square unwrapping method based on residual point correction for unconnected regions, and the method comprises the following steps: collecting four original interference patterns of a measured sample containing unconnected regions; extracting an original wrapped phase pattern by a four-step phase shifting method; adding a digital carrier frequency to obtain a reference phase pattern; repairing the unconnected regions in the original wrapped phase pattern by using a sample block matching method, comparing with the reference phase, and repeatedly iterating to obtain a final wrapped phase pattern; obtaining an unwrapped phase pattern by using a least square unwrapping algorithm based on residual point correction; and obtaining a correction coefficient and finally obtaining a reconstructed phase pattern. The application combines the advantages of sample block matching and residual point correction, has a good unwrapping effect on the wrapped phase of unconnected, high-steep and high-noise regions, has high unwrapped phase precision, and has important significance for target pellet detection, optical element surface shape detection and other fields.

Description

Technical Field

[0001] This invention belongs to the field of phase unwrapping technology in optical phase-shifting interferometry, specifically, it relates to a least-squares phase unwrapping method based on residual point correction for disconnected regions. Background Technology

[0002] Phase, containing a wealth of crucial information about an object, has always been a focus in optical measurement. High-speed, efficient, and high-precision phase measurement has been a primary research direction for researchers. In practical measurements, due to the properties of the arctangent function, the phase of the measured object is often wrapped between (-π, π]. To obtain a high-precision true phase, various phase unwrapping algorithms have emerged. Least squares unwrapping is a commonly used algorithm, directly solving the Poisson equation on a rectangular grid with von Neumann boundary conditions using discrete cosine transform, fast Fourier transform, or other methods, avoiding the propagation of unwrapping errors caused by residual points. However, solving the noisy Poisson equation has a smoothing effect, leading to a decrease in the phase dynamic range. Weighted least squares methods can control error propagation caused by the smoothing effect, but the algorithm's performance depends on the choice of weighting coefficients. Correcting the difference map can eliminate phase jumps caused by noise, improving the performance of the least squares algorithm under strong noise. However, existing correction models cannot identify and distinguish residual points during the correction process, affecting the algorithm's reliability.

[0003] In actual measurements, due to the obstruction of the supporting structure, continuous optical elements are often divided into many segmented regions, and the corresponding segmented wrapped phase cannot represent the continuity of the original phase. If the previous method is used for unwrapping, height errors will appear between different phase regions. Moreover, when performing multiple averaging measurements, the height errors between these phase regions are even more severe. In summary, existing least squares-based unwrapping algorithms perform poorly in handling disconnected or steeply wrapped phases, and the unwrapping algorithm accuracy is not high. Therefore, a new unwrapping method is urgently needed to improve it. Summary of the Invention

[0004] To address the problem that existing least-squares unwrapping methods perform poorly on unconnected or steeply wrapped phases, this invention proposes a least-squares unwrapping method based on residual point correction for unconnected regions. This method demonstrates strong unwrapping capability for unconnected, steeply wrapped, and noisy phases, yielding high accuracy in the unwrapped phases. It expands the applicability of existing least-squares unwrapping methods and is of great significance for fields such as target detection and optical component surface shape detection.

[0005] The technical solution to achieve the purpose of this invention is: a least-squares unwrapping method for disconnected regions based on residual point correction, the method comprising:

[0006] Step 1: Construct a Fizeau-type reflective interferometry system, combine polarization phase shifting technology to realize four original interferograms of the test sample with equal phase difference, and use the four-step phase shifting method to calculate the original wrapped phase map;

[0007] Step 2: Add digital carrier frequencies to the original wrapped phase map and regenerate the interferogram. Use the least squares unwrapping method based on residual point correction to unwrap the phase. By removing the digital carrier frequencies, obtain the reference phase map.

[0008] Step 3: Use the sample block matching algorithm to perform image inpainting on the disconnected regions of the original wrapped phase to obtain the repaired phase;

[0009] Step 4: Compare the repaired phase with the reference phase map to obtain the error points of the repaired phase, and set the region where the error points of the repaired phase are located as the repair region for the next sample block matching algorithm;

[0010] Step 5: Repeat steps 3 and 4 until the absolute value of the difference between the repaired phase and the reference phase in the nth iteration is less than the set value or the error point no longer changes, to obtain the final wrapped phase containing information about disconnected regions.

[0011] Step 6: Use the least squares unwrapping method based on residual point correction to unwrap the final wrapped phase, obtain the correction coefficients, and obtain the reconstructed phase containing disconnected regions based on the correction coefficients.

[0012] Preferably, the method for phase unwrapping using the least squares unwrapping method based on residual point correction is as follows:

[0013] Step 2-1: Set the minimum iteration error ε and the upper limit of the number of iterations N. it Initial unwrapping phase The residual error of the initial unwrapped phase is δ0, W{} is the wrapping operator, W{δ0} = , and Φ is the original unwrapped phase map;

[0014] Step 2-2: Calculate the phase derivative of the package and residual point R i,j ,

[0015]

[0016]

[0017]

[0018] Based on residual point R i,j The value of the wrapping phase derivative Correction;

[0019]

[0020]

[0021] The corrected wrap phase derivative Substituting and solving the noise-free Poisson equation, we obtain the unwrapped phase.

[0022] Steps 2-3: Unwrap the phase With true phase The residual error δ between n Re-wrap the package and use the unwrapping method from step 2-2 to calculate the residual error δ from the unwrapping process. pun :

[0023] The residual error δ after unpacking pun Superimposed on unwrapping phase Above, we obtain an unwrapped phase that is closer to the true phase φ.

[0024]

[0025] Steps 2-4: Based on the updated unpacking phase Solving for the residual error δ pu(n+1) Calculate the residual error δ pu(n+1) The result of repackaging:

[0026]

[0027] Step 2-5: Repeat steps 2-3 and 2-4 to satisfy condition |W{δ pu(n+1)}-δ pun |<ε, or iteration count n>N it When the iteration stops, the final unwrapped phase is obtained.

[0028] Preferably, the image is inpainted by using a sample block matching algorithm to inpaint the disconnected regions of the original wrapped phase, and the specific method for obtaining the inpainted phase is as follows:

[0029] Step 3-1: Locate the region to be repaired in the input image and calculate the priority weight of all pixels on the boundary of the region to be repaired;

[0030] Step 3-2: Compare the priority of each pixel to find the pixel P with the highest priority, and create a sample block Ψ to be repaired with pixel P as the center. p The best matching block Ψ is found in the undamaged area Φ. q ;

[0031] Step 3-3: Find the best matching block Ψq The gray values ​​of the pixels in the image sample block are replaced with the gray values ​​of the corresponding pixels in the image sample block of the region to be repaired to complete the image repair, obtain the repair phase, and update the boundary of the region to be repaired and the related data items and confidence parameters of the image after one repair process.

[0032] Preferably, the boundary The priority value P(p) of any pixel p is calculated as follows:

[0033] P(p) = C(p) * D(p)

[0034] In the formula, C(p) represents the confidence term, specifically expressed as:

[0035]

[0036] D(p) represents the data item in the priority calculation, specifically as follows:

[0037]

[0038] |Ψ p | represents the number of pixels in the damaged sample block, α is the normalization factor, and n p This represents a unit vector that is orthogonal to the boundary curve of a pixel. Ψ represents the direction of the isoluminance lines of a pixel. p For the sample block to be repaired centered at p, Ψ p ∩Φ is the intersection of the sample block to be repaired and the undamaged sample block centered at p.

[0039] Preferably, a sample block Ψ to be repaired is created centered on pixel P. p The best matching block Ψ was found by searching the undamaged area. q The specific method is as follows:

[0040] The sample matching window is used to search in the undamaged area. During the search, the block with the closest color distance is defined as the best matching block. The color distance is defined as:

[0041] d(Ψ p ,Ψ q )=∑ i ∑ j |Ψ p (i,j)-Ψ q (i,j)| 2

[0042] A sample block that satisfies the following condition is called the optimal sample block:

[0043]

[0044] In the formula, argmin() represents the value of the variable when the above formula takes its minimum value. In this formula, it represents the value of Ψ when the color distance is the minimum. q The corresponding area in the undamaged area Φ.

[0045] Preferably, the correction coefficient k is as follows:

[0046]

[0047] In the formula, Φ represents the original wrapped phase map. This is the final unwrapping phase.

[0048] Preferably, the reconstructed phase including disconnected regions is obtained according to the correction coefficient k. Specifically:

[0049]

[0050] Compared with the prior art, the significant advantages of this invention are:

[0051] (1) The present invention connects the separated wrapped phase regions through an iterative sample block matching algorithm, and obtains a high-precision phase in the disconnected region without any processing of the wrapped phase. Even if the wrapped phase contains multiple speckle noise, the recovered phase is basically consistent with the actual phase, which verifies its excellent noise resistance performance.

[0052] (2) This invention identifies the residual points of the wrapped phase derivative model and corrects the wrapped phase derivative based on the values ​​of the residual points, thereby reducing the interference of noise on the least squares optimization function and avoiding the impact of unwrapping errors at the residual points on normal sampling points. This invention can achieve accurate unwrapping of wrapped phases containing strong noise and steep gradients, thus obtaining high-precision object phase information. Attached Figure Description

[0053] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0054] This paper proposes a least-squares unwrapping method based on residual point correction for disconnected regions, addressing the poor handling capability of existing least-squares unwrapping algorithms for connected, steep, and noisy wrapped phases. This method connects separated phase regions through sample block matching, achieving high-precision phases without any processing of the wrapped phases within disconnected regions. Furthermore, existing least-squares algorithm correction models have limited ability to correct for the phase dynamic range reduction caused by smoothing in traditional least-squares unwrapping algorithms, and cannot identify and distinguish residual points during the correction process, affecting the algorithm's reliability. The least-squares unwrapping method based on residual point correction identifies and corrects residual points in the difference model of the least-squares unwrapping algorithm, reducing the impact of noise on the least-squares optimization function and avoiding the influence of unwrapping errors at residual points on normal sampling points.

[0055] The present invention will now be described in further detail with reference to the accompanying drawings.

[0056] Combination Figure 1 The specific steps of the technical solution to achieve the purpose of this invention are as follows:

[0057] Step 1: Construct a Fizeau-type reflective interferometry system and combine it with polarization phase-shifting technology to simultaneously measure four original interferograms of the sample with equal phase difference. The polarization camera consists of multiple 2×2 micro-polarization arrays. The transmission angles of the four linear polarizers are 0°, 45°, 90°, and 135°, respectively. Additional phases of 0°, 90°, 180°, and 270° are introduced, and pixels containing the same additional phase are combined to form four interferograms, thereby achieving simultaneous acquisition of the four interferograms. Φ is calculated from the four interferograms with equal phase difference using a four-step phase-shifting method.

[0058]

[0059] Step 2: Add digital carrier frequency T to the original wrapped phase map Φ and regenerate the interferogram. Use the least squares unwrapping method based on residual point correction to unwrap the phase. By removing the digital carrier frequency, obtain the reference phase map Φ. R .

[0060] In a further embodiment, the specific method for adding a digital carrier frequency T to the original package phase map Φ and regenerating the interferogram is as follows:

[0061] The digital carrier frequency T is added to the package phase Φ using the following formula:

[0062] Φ T (x,y)=Φ(x,y)+T(x,y)

[0063] The digital carrier frequency T(x,y) can be written as:

[0064] T(x,y)=αx+βy+γ

[0065] Where α, β, and γ are carrier frequency coefficients. Using Φ T Reconstructing Interferogram I T

[0066] I T (x,y)=cos(Φ T (x,y))

[0067] In a further embodiment, the method of phase unwrapping using the least squares unwrapping method based on residual point correction is as follows:

[0068] Step 2-1: Set the minimum iteration error ε and the upper limit of the number of iterations N. it Initial unwrapping phase The residual error of the initial unwrapping phase is δ0, and W{} is the wrapping operator, W{δ0}=Φ;

[0069] Step 2-2: Calculate the phase derivative of the package and residual point R i,j ,

[0070]

[0071]

[0072]

[0073] Based on residual point R i,j The value of the wrapping phase derivative Correction;

[0074]

[0075]

[0076] The corrected wrap phase derivative Substituting and solving the noise-free Poisson equation, we obtain the unwrapped phase Ψ. n ;

[0077] The true phase contains significant noise or undersampling, causing some sampling points to fail to meet the sampling conditions. Points exceeding the sampling conditions result in a non-zero integral around the closed path in the derivative plot of the wrapped phase; these sampling points are called residuals in the wrapped phase. In this case, the unwrapping result depends on the integration path; when the integration path passes through the sampling point containing the residual, a correct unwrapping result cannot be obtained.

[0078] By connecting the adjacent pixels around each sampling point in the phase map in a certain order to form the minimum closed path and then calculating the integral, the residual points in the wrapped phase map can be detected. Let represent the wrapper phase derivatives of the four pixels near the sampling point (i,j), then the residual point can be determined by the following formula.

[0079]

[0080] Based on the properties of the package operator, R i,j The value of R can only be one of three possibilities: 2π, -2π, and 0. If R... i,j =2π, then there is a positive residual at the sampling point (i,j). If R i,j = -2π, then there exists a negative residual at the sampling point (i,j). Otherwise, if R i,j =0, then there is no residual. When there are no residual points on the entire M×N grid, the wrapped phase can be unwrapped by any method, including linear integration. A model of the derivative of the wrapped phase corrected for residual points is as follows:

[0081]

[0082]

[0083] By setting the derivative of the wrapped phase corresponding to the residual point to zero, noise or undersampled phase at sampling points with residuals can be removed from the difference map, thus correcting the residual points. At this point, the wrapped phase Φ is minimized using the least squares method to minimize the difference between the real phase and the residual phase. The difference between the difference plots can be used to obtain the following objective function:

[0084]

[0085] This expression can be equivalent to solving the discrete Poisson equation in a grid:

[0086]

[0087] in The input to the Poisson equation after residual correction is given. Solving the noise-free Poisson equation using the Discrete Cosine Transform (DCT) method yields the reciprocal solution of Φ in the DCT domain. Finally, the unwrapped phase in the least-squares sense is obtained through the inverse DCT transform.

[0088]

[0089] Steps 2-3: Unwrap Phase With true phase There exists an unwrapped residual error δ n However, due to the true phase Since the residual error δ is unknown, it is necessary to include it. n Re-wrap the package and use the unwrapping method from step 2-2 to calculate the residual unwrapping error:

[0090]

[0091] The residual error δ after unpacking pun Superimposed on unwrapping phase By doing so, an unwrapped phase that is closer to the true phase φ can be obtained.

[0092]

[0093] Steps 2-4: Updated Unpacking Phase Used to solve for the residual error δ again pu(n+1) Calculate the residual error δ pu(n+1) The result of repackaging:

[0094]

[0095] Step 2-5: Repeat steps 2-3 and 2-4 to satisfy condition |W{δ pu(n+1)}-δ pun |<ε, or iteration count n>N it When the iteration stops, the final unwrapped phase is obtained.

[0096] By removing the digital carrier frequency, the reference phase diagram Φ is obtained. R Specifically:

[0097]

[0098]

[0099] Where Ext{·} represents the interferogram continuation algorithm, F s This represents a positive first-order sideband Gaussian filter, where FT{·} and IFT{·} are the Fourier transform and inverse Fourier transform, respectively, and PU{·} represents the phase unwrapping algorithm. The unwrapped phase is obtained by the least squares unwrapping method based on residual point correction.

[0100] Step 3: Use a sample block matching algorithm to perform image inpainting on the disconnected regions of the original wrapped phase Φ to obtain the inpainted phase. The specific steps are as follows:

[0101] Step 3-1: Locate the area to be repaired using the mask obtained from the interferogram analysis software and set it as the target area. If the boundary is found to be empty, the entire sample matching algorithm process ends.

[0102] The priority value of all pixels on the boundary of the area to be repaired is calculated using a priority calculation formula. Since the priority value determines the order in which image patches are repaired, the calculation of the priority value has a significant impact on the repair effect. (Boundary) The priority value P(p) of any pixel is calculated as follows:

[0103] P(p) = C(p) * D(p)

[0104] In the formula, C(p) represents the confidence term, which can be specifically expressed as:

[0105]

[0106] D(p) represents the data item in the priority calculation, which can be specifically represented as:

[0107]

[0108] The priority of point P is determined by both the data term and the confidence term, where the confidence term estimates the proportion of undamaged pixels in all sample blocks, |Ψ p | Represents the number of pixels in the damaged sample block. The data term is a parameter used to measure the edge strength of pixels, where α is the normalization factor, and n... p This represents a unit vector that is orthogonal to the boundary curve of a pixel. Indicates the direction of maximum color change of a pixel. The isoluminance line direction represents the pixel, i.e., the orthogonal vector of the gradient vector at that point. The data term and confidence term serve as two important indicators for computational priority. The data term ensures that the algorithm prioritizes repairing sample blocks with significant changes in edge structure information of the region to be repaired, while the confidence term ensures that the algorithm prioritizes repairing sample blocks with abundant known edge information of the region to be repaired. By balancing these two parameters, an image with good structural and textural information can be repaired.

[0109] Step 3-2: Compare the priority of each pixel to find the pixel P with the highest priority, and create a sample block Ψ to be repaired with pixel P as the center. p The best matching block Ψ was found by searching the undamaged area. q In image restoration, square pixel blocks (sample blocks) are used, and the size of the sample block is called the sample matching window. Different sizes of image restoration windows affect the restoration effect; this method uses a 9×9 sample matching window. During the search process, the block with the closest color distance is defined as the best matching block. The color distance can be defined as:

[0110] d(Ψ p ,Ψ q)=∑ i ∑ j |Ψ p (i,j)-Ψ q (i,j)| 2

[0111] A sample block that satisfies the following condition is called the optimal sample block:

[0112]

[0113] Step 3-3: Replace the gray values ​​of the corresponding pixels in the damaged image sample block with the gray values ​​of the pixels in the matching block found in the search. Then update the boundary of the area to be repaired and related data items, confidence items and other parameters for the image after one repair process.

[0114] Preferably, the sample matching window selected in the sample block matching is 9×9, for the following reasons:

[0115] The size of the sample block matching window is related to the region to be repaired, the richness and roughness of the texture structure, etc. A larger window size can reduce time loss, but due to the large amount of data to be repaired, statistical errors are prone to occur during the calculation process, leading to inaccurate repair points and affecting subsequent image restoration. When the sample block matching window is smaller, the restoration accuracy is improved, but it takes more time. However, if the window is too small, it also affects the restoration effect and causes a large error. In the actual test, five different sample matching windows of 5×5, 7×7, 9×9, 11×11, and 13×13 were used for image restoration tests. The test results showed that the 9×9 sample matching window had the best restoration effect and the fewest residual points. Therefore, the 9×9 sample matching window was finally selected.

[0116] Step 4: Repair the phase With reference phase Φ R The errors in the phase correction are compared to identify the points where the phase correction errors are located. These points are then set as the correction regions for the next sample block matching algorithm.

[0117] Step 5: Repeat steps 3-3 and 3-4 until the phase is repaired in the nth iteration. With reference phase Φ R Between Until the error point no longer changes, obtain the final wrapped phase Φ containing information about disconnected regions. F .

[0118] Step 6: Use the least squares unwrapping method based on residual point correction to unwrap the final wrapped phase, obtain the correction coefficients, and obtain the reconstructed phase containing disconnected regions based on the correction coefficients.

[0119] The sample block matching algorithm copies the image information from the best matching block in the connected region to the disconnected region. However, this phase information is not the true phase information of the corresponding region. Therefore, the sample block matching algorithm is used to repair the final unwrapped phase obtained by image inpainting of the disconnected wrapped phase. There is an error between the actual phase and the true phase, but the error is small, and both are in the same 2π interval. This error can be used to solve for the correction coefficient k:

[0120]

[0121] In the formula, Φ represents the original wrapped phase map. Combining the correction coefficient k with the original wrapped phase Φ yields the true reconstructed phase. The reconstructed phase containing disconnected regions is obtained based on the correction factor k. Specifically:

[0122]

[0123] This invention can replace most existing algorithms for unwrapping disconnected wrapped phases. This method utilizes a sample block matching algorithm to connect separated wrapped phase regions, obtaining high-precision phases within disconnected regions. For noisy cross-shaped disconnected phases, the error points between the restored phase and the original phase are only 281, significantly improving the recovery effect. The least squares unwrapping method based on residual point correction described in this invention can replace most existing least squares unwrapping algorithms. This method uses a wrapped phase derivative model for residual correction. Using the "Peaks" function as the original phase, with PV set to 10 and the standard deviation of the added Gaussian noise set to 1 rad, the standard deviation of the residual between the restored phase and the original phase is only 0.35 rad, significantly improving the recovery effect.

[0124] The technical features of the embodiments described above can be combined arbitrarily. For the sake of brevity, not all combinations of the technical features in the above embodiments are described. However, as long as the combinations of these technical features do not contradict each other, they should be considered within the scope of this specification.

[0125] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A least-squares phase unwrapping method based on residual point correction for disconnected regions, characterized in that, The method includes: Step 1: Construct a Fizeau-type reflective interferometry system, combine polarization phase shifting technology to realize four original interferograms of the test sample with equal phase difference, and use the four-step phase shifting method to calculate the original wrapped phase map; Step 2: Add digital carrier frequencies to the original wrapped phase map and regenerate the interferogram. Use the least squares unwrapping method based on residual point correction to unwrap the phase. By removing the digital carrier frequencies, obtain the reference phase map. Step 3: Use a sample block matching algorithm to inpaint the disconnected regions of the original wrapped phase to obtain the repaired phase. The specific method is as follows: Step 3-1: Locate the region to be repaired in the input image, and calculate the priority weight of all pixels on the boundary of the region to be repaired. The priority value P(p) of any pixel p is calculated as follows: P(p) = C(p) * D(p) In the formula, C(p) represents the confidence term, specifically expressed as: D(p) represents the data item in the priority calculation, specifically as follows: |Ψ p | represents the number of pixels in the damaged sample block, α is the normalization factor, and n p This represents a unit vector that is orthogonal to the boundary curve of a pixel. Ψ represents the direction of the isoluminance lines of a pixel. p For the sample block to be repaired centered at p, Ψ p ∩φ represents the intersection of the sample block to be repaired and the undamaged sample block centered at p; Step 3-2: Compare the priority of each pixel to find the pixel P with the highest priority, and create a sample block Ψ to be repaired with pixel P as the center. p The best matching block Ψ is found in the undamaged area Φ. q The specific method is as follows: The sample matching window is used to search in the undamaged area. During the search, the block with the closest color distance is defined as the best matching block. The color distance is defined as: d(Ψ p ,P q )=∑ i ∑ j |P p (i,j)-Ψ q (i,j)| 2 A sample block that satisfies the following condition is called the optimal sample block: In the formula, argmin() represents the value of the variable when the above formula takes its minimum value. In this formula, it represents the value of Ψ when the color distance is the minimum. q The corresponding area in the undamaged area Φ Step 3-3: Find the best matching block Ψ q The gray values ​​of the pixels in the image sample block are replaced with the gray values ​​of the corresponding pixels in the image sample block of the region to be repaired to complete the image repair and obtain the repair phase. The boundary of the region to be repaired and the related data items and confidence parameters are updated for the image after one repair process. Step 4: Compare the repaired phase with the reference phase map to obtain the error points of the repaired phase, and set the region where the error points of the repaired phase are located as the repair region for the next sample block matching algorithm; Step 5: Repeat steps 3 and 4 until the absolute value of the difference between the repaired phase and the reference phase in the nth iteration is less than the set value or the error point no longer changes, to obtain the final wrapped phase containing information about disconnected regions. Step 6: Use the least squares unwrapping method based on residual point correction to unwrap the final wrapped phase, obtain the correction coefficients, and obtain the reconstructed phase containing disconnected regions based on the correction coefficients.

2. The least-squares phase unwrapping method for disconnected regions based on residual point correction according to claim 1, characterized in that, The specific method for phase unwrapping using the least squares unwrapping method based on residual point correction is as follows: Step 2-1: Set the minimum iteration error ε and the upper limit of the number of iterations N. it Initial unwrapping phase The residual error of the initial unwrapped phase is δ0, W{} is the wrapping operator, W{δ0} = , and Φ is the original unwrapped phase map; Step 2-2: Calculate the phase derivative of the package and residual point R i,j , Based on residual point R i,j The value of the wrapping phase derivative Correction; The corrected wrap phase derivative Substituting and solving the noise-free Poisson equation, we obtain the unwrapped phase. Steps 2-3: Unwrap the phase With true phase The residual error δ between n Re-wrap the package and use the unwrapping method from step 2-2 to calculate the residual error δ from the unwrapping process. pun : The residual error δ after unpacking pun Superimposed on unwrapping phase Above, we obtain an unwrapped phase that is closer to the true phase φ. Steps 2-4: Based on the updated unpacking phase Solving for the residual error δ pu(n+1) Calculate the residual error δ pu(n+1) The result of repackaging: Step 2-5: Repeat steps 2-3 and 2-4 to satisfy condition |W{δ pu(n+1) }-δ pun |<ε, or iteration count n>N it When the iteration stops, the final unwrapped phase is obtained.

3. The least-squares phase unwrapping method for disconnected regions based on residual point correction according to claim 1, characterized in that, The correction factor k is specifically: In the formula, Φ represents the original wrapped phase map. This is the final unwrapping phase.

4. The least-squares phase unwrapping method for disconnected regions based on residual point correction according to claim 1, characterized in that, The reconstructed phase containing disconnected regions is obtained based on the correction factor k. Specifically:

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