CN112797917B - A high-precision digital speckle interference phase quantitative measurement method - Google Patents

Abstract

The invention discloses a high-precision digital speckle interference phase measurement method based on a fuzzy theory. Acquiring speckle interference patterns of an object to be measured before and after deformation, and processing the speckle interference patterns to obtain a wrapped phase diagram; calculating to obtain a reliability map after filtering and denoising; identifying residual points in the wrapped phase diagram, calculating the average value of the reliability corresponding to all the residual points and the standard deviation of the reliability diagram, establishing a membership function according to the average value, and carrying out fuzzy classification on the reliability diagram by using the membership function to obtain a membership matrix; taking the membership matrix as the weight of the reliability graph to carry out weighted average to obtain a mask threshold value; and binarizing the reliability map by using the mask threshold value to obtain a weight matrix, and iteratively solving by using the weight matrix as a weight to obtain a continuous phase map, so as to present the deformation of the object to be measured. The method solves the problem of threshold selection in the reliability mask, can self-adapt the mask threshold according to the input parcel phase, and improves the efficiency and the precision of phase measurement.

Description

A high-precision digital speckle interference phase quantitative measurement method

technical field

The invention relates to an interference phase measurement method in the technical field of digital speckle interference, in particular to a high-precision digital speckle interference phase quantitative measurement method based on fuzzy theory.

Background technique

Digital Speckle Pattern Interferometry (DSPI) has become an important method in the modern measurement field due to its advantages of full-field measurement, high precision, high sensitivity, and non-contact. Among them, phase unwrapping is a key step in quantitative measurement of DSPI. The unpacking result directly affects the final measurement accuracy. The weighted least squares phase unwrapping in the phase unwrapping algorithm is an efficient, robust and error-suppressing calculation method. The iterative solution obtains the continuous phase. The weighting coefficient is usually obtained by thresholding the quality map, and the selection of the threshold is the key to obtaining a suitable 0-1 weighting coefficient. A suitable threshold can obtain high-precision unpacking results, on the contrary, an unsuitable threshold will cause unpacking. As a result, the error becomes larger, and the calculation speed is also reduced, and the noise cannot be suppressed.

SUMMARY OF THE INVENTION

In order to solve the above technical problems, the present invention provides a high-precision digital speckle interference phase quantitative measurement method, which has high processing efficiency, can accurately mask errors and eliminate smoothing effects.

The present invention is achieved through the following technical solutions:

Step 1: Obtain the speckle interferogram before and after the deformation of the object to be measured through the industrial camera equipment that measures the optical path through digital speckle interferometry. The speckle interferogram is processed by image processing to obtain a package phase map containing the deformation information of the object to be measured and the size is M×N

进行滤波降噪，计算滤波后的包裹相位图中每个像素点的可靠度，进而组成可靠度图R；Step 2: Plot the phase map of the package

Perform filtering and noise reduction, calculate the reliability of each pixel in the filtered package phase map, and then form a reliability map R;

Step 3: Identify the residual points R _es in the wrapped phase map, calculate the average L of the reliability corresponding to all the residual points and the standard deviation H of the reliability map, and use the average L and standard deviation H as the fuzzy interval to establish the degree of membership function, and use the membership function to fuzzy classify the reliability map to obtain the membership matrix μ;

Step 4: Use the membership matrix μ as the weight of the reliability map R to perform a weighted average to obtain the mask threshold _TR ;

Step 5: Use the mask threshold TR to binarize the reliability map _R to obtain a weight matrix w, and use the weight matrix w as the weight of the weighted least squares equations to iteratively solve to obtain a continuous phase map. Displays the amount of deformation of the object to be measured.

The invention adopts the space carrier digital speckle interferometry optical path to measure the circular plate to be measured, collects the digital speckle interferogram which is subjected to external force to cause the in-plane deformation of the measured object, and then adopts the method for subsequent processing.

The test object is a circular plate test object.

The step 1 is specifically: obtaining the speckle interferogram before the deformation of the object to be measured by building a one-dimensional space carrier speckle interferometry optical path, and collecting the speckle interferogram as the deformation after the object to be measured is loaded with a horizontal force in the plane. After the speckle interferogram, the Fourier transform is performed on the two speckle interferograms respectively. In the Fourier transform result, the positive first-order spectrum is selected as the inverse Fourier transform, and then the arc tangent operation is performed to obtain the phase diagram before and after the deformation. Finally, the two phase images before and after the deformation are subtracted to obtain a wrapped phase map of size M×N containing the deformation information of the object to be tested

In the second step, after filtering and noise reduction, the following formula is used to obtain the reliability of each pixel in the wrapped phase map:

表示包裹相位图中在像素点(i,j)处的相位值。Among them, R _{i, j} represents the reliability of the wrapped phase map at the pixel point (i, j), i, j represent the index of the row and column where the pixel point is located, and 1≤i≤M-2, 1≤j≤N- 2; H _i,j and V _i,j are the second-order differences of the wrapped phase map pixel point (i,j) in the row and column directions; C _i,j and D _i,j represent the wrapped phase map pixel point respectively The second-order difference of the diagonal line from the upper left corner to the lower right corner and the diagonal line from the lower left corner to the upper right corner at (i, j); W is the wrapping operator, wrapping the phase value by adding or subtracting an integer multiple of 2π between (-π,π];

Represents the phase value at pixel (i,j) in the wrapped phase map.

The third step is specifically:

3.1) Identify whether each pixel point in the wrapped phase map is a residual point by the following formula, and then obtain the residual point set R _es :

Among them, Res _{i, j} indicates that the pixel point (i, j) in the wrapped phase image is a residual point, and others indicates that the pixel point (i, j) in the wrapped phase image is not a residual point;

3.2) Use the following formula to calculate the average value L of the corresponding reliability of all residual points:

Among them, K represents the number of residual points;

3.3) Calculate the standard deviation H of the reliability map:

代表可靠度图中所有像素点的平均值；M、N分别表示包裹相位图中的行数和列数；in,

Represents the average value of all pixels in the reliability map; M and N represent the number of rows and columns in the wrapped phase map, respectively;

3.4) Construct the following membership function, and calculate the membership matrix μ corresponding to the reliability graph R:

P=L+(H-L)/(k+1)

Among them: μ(R _i,j ) represents the membership value at the pixel point (i,j) in the reliable graph; k represents the coefficient of variation, and P represents the abscissa position of the vertex of the membership function.

The step 4 is specifically: according to the membership matrix μ and the reliability map R, the weighted mean is calculated as the mask threshold _TR according to the following formula:

Among them: μ(R _i,j ) represents the membership value at the pixel point (i,j) in the reliability map; R _i,j represents the reliability of the wrapped phase map at the pixel point (i,j), M, N Represent the number of rows and columns in the wrapped phase diagram, respectively, and i and j represent the number of rows and columns in the wrapped phase diagram, respectively.

The fifth step is specifically:

First use the mask threshold _TR to binarize the reliability map to obtain the weight matrix w:

Among them, w _{i, j} represents the weight value at the coordinate (i, j) in the weight matrix w;

Then, according to the weight matrix w, the weighted least squares equation system of the wrapped phase map is established, and the PICARD method is used to iteratively solve the weighted least squares equation system, and the continuous phase of each pixel point is obtained to form a continuous phase map, and then characterize The amount of deformation of the test object.

In the fifth step, iterative convergence conditions are also set: iterative deviation ε, maximum iteration number n, initial absolute phase φ ⁰ , the weighted discrete partial differential sum of the wrapped phase map is calculated, and the Picard iteration method is used to solve the weighted least squares.

Compared with the background technology, the beneficial effects of the present invention are:

(1) The present invention fuzzifies the mask threshold value of reliability, and constructs a membership function describing the threshold value, which can adapt a mask threshold value according to the input package phase map, and realizes the automatic processing of images.

(2) The mask threshold identified by the present invention can more accurately divide the reliability value with uncertainty, generate a suitable mask, can effectively suppress the global propagation of errors, and improve the measurement accuracy.

Description of drawings

Fig. 1 is the flow chart of the method of the present invention;

Fig. 2 is the wrapped phase diagram after filtering extracted by space carrier phase shift technology;

3 is a schematic diagram of a membership function constructed by the present invention;

4 is a schematic diagram of a 0-1 weighting coefficient matrix of an adaptive mask of the present invention;

FIG. 5 is a graph of the phase results of unwrapping according to the present invention.

FIG. 6 is a graph of the phase results of the repackaging of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and embodiments.

The embodiment of the present invention is shown in the flowchart of FIG. 1, and the specific steps are as follows:

Step 1: Collect and obtain the speckle interferogram before the deformation of the object to be measured on the circular plate through the built two-dimensional digital speckle interference optical path system based on the phase shift of the space carrier, and collect the speckle again after the object to be measured is loaded with in-plane horizontal force The interferogram is used as the speckle interferogram after the deformation of the circular plate to be measured, and the Fourier transform is performed on the two speckle interferograms respectively, and the positive first-order spectrum is selected for the inverse Fourier transform in the Fourier transform result. Arctangent operation obtains the phase map before and after deformation, and finally subtracts the two phase maps before and after deformation to obtain a packaged phase map of size M×N containing the deformation information of the object to be tested

同时为了展示部分区域的解包裹效果，在图2所示的滤波后的包裹相位图的右下角的位置绘制了白色矩形框区域用于后续解包裹效果对比，计算滤波后的包裹相位图

中每个像素点的可靠度，进而组成可靠度图R；Step 2: After performing sine and cosine filtering on the wrapped phase map, the filtered wrapped phase map shown in Figure 2 is obtained.

At the same time, in order to show the unwrapping effect of some areas, a white rectangular frame area is drawn at the lower right corner of the filtered wrapped phase map shown in Figure 2 for the comparison of subsequent unwrapping effects, and the filtered wrapped phase map is calculated.

The reliability of each pixel in the , and then form the reliability map R;

表示包裹相位图中在像素点(i,j)处的相位值。Among them, R _{i, j} represents the reliability of the wrapped phase map at the pixel point (i, j), i, j represent the index of the row and column where the pixel point is located, and 1≤i≤M-2, 1≤j≤N- 2; H _i,j and V _i,j are the second-order differences of the wrapped phase map pixel point (i,j) in the row and column directions; C _i,j and D _i,j represent the wrapped phase map pixel point respectively The second-order difference of the diagonal line from the upper left corner to the lower right corner and the diagonal line from the lower left corner to the upper right corner at (i, j); W is the wrapping operator, wrapping the phase value by adding or subtracting an integer multiple of 2π between (-π,π];,

Represents the phase value at pixel (i,j) in the wrapped phase map.

Step 3: Identify the residual points R _es in the wrapped phase map, calculate the average value L of the reliability corresponding to all the residual points and the standard deviation H of the reliability map, and use the average value L and standard deviation H as the left and right ends of the fuzzy interval Point, establish the membership function, the membership function is shown in Figure 3, and use the membership function to classify the reliability map fuzzy, and obtain the membership matrix μ. Specifically:

3.1) Identify whether each pixel point in the wrapped phase map is a residual point by the following formula, and then obtain the residual point set R _es :

Among them, Res _{i, j} indicates that the pixel point (i, j) in the wrapped phase image is a residual point, and others indicates that the pixel point (i, j) in the wrapped phase image is not a residual point;

3.2) Use the following formula to calculate the average value L of the corresponding reliability of all residual points:

Among them, K represents the number of residual points;

3.3) Calculate the standard deviation H of the reliability map:

代表可靠度图中所有像素点的平均值；M、N分别表示包裹相位图中的行数和列数；in,

Represents the average value of all pixels in the reliability map; M and N represent the number of rows and columns in the wrapped phase map, respectively;

3.4) Construct the following membership function, and calculate the membership matrix μ corresponding to the reliability graph R:

P=L+(H-L)/(k+1)

Among them: μ(R _i,j ) represents the membership value at the pixel point (i,j) in the reliable graph; k represents the coefficient of variation, and P represents the position of the vertex of the membership function.

Step 4: Use the membership matrix μ as the weight of the reliability map R to perform a weighted average to obtain the mask threshold T _R :

Among them: μ(R _i,j ) represents the membership value at the pixel point (i,j) in the reliability map; R _i,j represents the reliability of the wrapped phase map at the pixel point (i,j), M, N represent the number of rows and columns in the wrapped phase diagram, respectively, and i, j represent the number of rows and columns in the wrapped phase diagram, respectively.

Step 5: First use the mask threshold _TR to binarize the reliability map to obtain the weight matrix w, as shown in Figure 4:

Among them, w _{i, j} represents the weight value at the coordinate (i, j) in the weight matrix w;

Then, according to the weight matrix w, the weighted least squares equation system of the wrapped phase map is established, and the PICARD method is used to iteratively solve the weighted least squares equation system, and the continuous phase of each pixel point is obtained to form a continuous phase map, and then characterize The amount of deformation of the test object.

In step 5, the initialization parameters are also set: the maximum number of iterations n=100, the iteration cut-off threshold ε=0.01, the initial continuous phase φ ⁰ =0, the weighted discrete partial differential sum of each pixel point of the wrapped phase map is calculated, and the Picard iteration method is used. Perform a weighted least squares solution.

The continuous phase map obtained by phase unwrapping in this example is shown in Figure 5. The grayscale in the figure gradually changes from black to white from top to bottom, which indicates that the unwrapping method can be successfully unwrapped to obtain a continuous phase map, and It can be seen that the obtained results are smoother. As shown in Figure 6, the unwrapped continuous phase map is rewrapped to obtain the rewrapped phase map. It can be seen that the fringes of the rewrapped phase map are consistent with the original wrapped phase map, and from the rewrapped phase map of Figure 6 and It can be seen from the white rectangular frame area of the filtered wrapped phase diagram in FIG. 2 that the black transition points in the rectangular frame in the repacked phase diagram disappear, which ensures the effectiveness of the present invention.

From this, it can be seen that, aiming at the problem that the mask threshold value of the reliability map is difficult to determine in the reliability mask weighted least squares method, the present invention uses fuzzy theory to fuzzify the reliability mask threshold value to obtain the mask threshold value of the reliability map. A weight matrix is obtained by binarizing the reliability map using the membrane threshold, and the continuous phase is obtained by iteration. The mask threshold of the wrapped phase is obtained adaptively, which solves the threshold selection problem of the reliability mask weighted least squares unwrapping algorithm, and ensures the correct mask of the error point, which can effectively improve the efficiency and accuracy of the phase measurement.

The above-mentioned specific embodiments are used to explain the present invention, rather than limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit of the present invention and the protection scope of the claims should be included in the protection scope of the present invention. within.

Claims (6)

1. A high-precision digital speckle interference phase quantitative measurement method is characterized by comprising the following steps:

the method comprises the following steps: obtaining speckle interference patterns before and after deformation of the object to be measured through a digital speckle interference measuring light path, and obtaining a wrapped phase diagram which contains deformation information of the object to be measured and has a size of MxN through image processing of the speckle interference patterns

Step two: for wrapped phase diagram

Filtering and denoising are carried out, and the reliability of each pixel point in the filtered wrapped phase diagram is calculated, so that a reliability diagram R is formed;

step three: identifying residual points R in wrapped phase maps _es Calculating the average value L of the reliability corresponding to all the residual points and the standard deviation H of the reliability map, establishing a membership function by using the average value L and the standard deviation H as fuzzy intervals, and carrying out fuzzy classification on the reliability map by using the membership function to obtain a membership matrix mu;

step four: taking the membership matrix mu as the weight of the reliability graph R to carry out weighted average to obtain a mask threshold value T _R ；

Step five: using a mask threshold T _R Carrying out binarization on the reliability map R to obtain a weight matrix w, carrying out iterative solution by taking the weight matrix w as a weight of a weighted least square equation set to obtain a continuous phase map, and presenting the deformation of the object to be measured by the continuous phase map;

the object to be measured is a circular plate object to be measured.

2. The high-precision quantitative measurement of digital speckle interferometry phase according to claim 1The method is characterized in that: the first step specifically comprises the following steps: obtaining a speckle interference pattern of an object to be measured before deformation by constructing a one-dimensional space carrier speckle interference measurement optical path, collecting the speckle interference pattern as the deformed speckle interference pattern again after loading a horizontal force in a surface on the object to be measured, performing Fourier transform on the two speckle interference patterns respectively, selecting a positive-level frequency spectrum from Fourier transform results, performing Fourier inversion on the positive-level frequency spectrum, performing arc tangent operation to obtain phase patterns before and after deformation, and finally subtracting the two phase patterns before and after deformation to obtain a wrapped phase pattern which contains deformation information of the object to be measured and has the size of M multiplied by N

3. The method for high-precision quantitative measurement of the digital speckle interferometry phase according to claim 1, wherein: in the second step, after filtering and noise reduction, the following formula is adopted to process and obtain the reliability of each pixel point in the wrapped phase diagram:

wherein R is _i,j Representing the reliability of the wrapped phase diagram at the pixel point (i, j), wherein i, j respectively represent the row and column index of the pixel point, i is more than or equal to 1 and less than or equal to M-2, and j is more than or equal to 1 and less than or equal to N-2; h _i,j And V _i,j Second order differences in row and column directions for wrapping phase map pixel points (i, j); c _i,j And D _i,j Respectively representing second-order differences of a diagonal line from the upper left corner to the lower right corner and a diagonal line from the lower left corner to the upper right corner at the wrapped phase map pixel point (i, j); w is a wrapping operator, and W is a wrapping operator,

representing the phase value at pixel point (i, j) in the wrapped phase map.

4. The method for high-precision quantitative measurement of the digital speckle interferometry phase according to claim 3, wherein the method comprises the following steps: the third step is specifically as follows:

3.1) identifying whether each pixel point in the wrapped phase diagram is a residual error point or not by the following formula, and further obtaining a residual error point set R _es ：

Wherein Res _i,j Representing that the pixel point (i, j) in the wrapped phase diagram is a residual error point, and others representing that the pixel point (i, j) in the wrapped phase diagram is not a residual error point;

3.2) calculating the average value L of the corresponding reliability of all the residual points by adopting the following formula:

wherein K represents the number of residual points;

3.3) calculating the standard deviation H of the reliability map:

wherein,

representing the average value of all pixel points in the reliability map; m, N denotes the number of rows and columns in the wrapped phase diagram, respectively;

3.4) constructing the following membership function, and calculating a membership matrix mu corresponding to the reliability graph R:

P＝L+(H-L)/(k+1)

wherein: mu (R) _i,j ) Representing the membership value of a pixel point (i, j) in the reliability graph; k represents the coefficient of variation and P represents the abscissa position where the vertex of the membership function is located.

5. The method for high-precision quantitative measurement of the digital speckle interferometry phase according to claim 1, wherein: the fourth step is specifically as follows: calculating a weighted mean value as a mask threshold value T according to the membership matrix mu and the reliability graph R according to the following formula _R ：

Wherein: mu (R) _i,j ) Representing the membership value of a pixel point (i, j) in the reliability graph; r is _i,j Representing the reliability of the wrapped phase map at pixel point (i, j), M, N represents the number of rows and columns in the wrapped phase map, respectively, and i, j represent the row number and column number in the wrapped phase map, respectively.

6. The method for high-precision quantitative measurement of the digital speckle interferometry phase according to claim 1, wherein: the fifth step is specifically as follows:

using the mask threshold T first _R Carrying out binarization segmentation on the reliability map to obtain a weight matrix w:

wherein, w _i,j Represents the weight value at coordinate (i, j) in weight matrix w;

and establishing a weighted least square equation set wrapping the phase diagram according to the weight matrix w, and performing iterative solution on the weighted least square equation set by adopting a pick-up method to obtain a continuous phase diagram so as to represent the deformation of the object to be measured.

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