CN112797917B - High-precision digital speckle interference phase quantitative measurement method - Google Patents
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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
Technical Field
The invention relates to an interference phase measuring method in the technical field of digital speckle interference, in particular to a high-precision digital speckle interference phase quantitative measuring method based on a fuzzy theory.
Background
Digital Speckle Interferometry (DSPI) is an important method in the modern measurement field due to the advantages of full-field measurement, high precision, high sensitivity, non-contact and the like, wherein phase unwrapping is a key step of DSPI quantitative measurement, and unwrapping results directly influence final measurement precision. The weighted least square phase unwrapping in the phase unwrapping algorithm is a high-efficiency and stable calculation method capable of suppressing errors, the method adopts a quality diagram to generate a weighting coefficient, and a discrete poisson equation with a weight is constructed to carry out iterative solution to obtain a continuous phase. The weighting coefficients are usually obtained by adopting a thresholding quality map, the selection of the threshold is the key for obtaining a proper 0-1 weighting coefficient, a proper threshold can obtain a high-precision unwrapping result, and conversely, an improper threshold can increase the error of the unwrapping result, reduce the calculation speed and cannot suppress noise.
Disclosure of Invention
In order to solve the technical problems, the invention provides a high-precision digital speckle interference phase quantitative measurement method which is high in processing efficiency, and can accurately mask errors and eliminate a smoothing effect.
The invention is realized by the following technical scheme:
the method comprises the following steps: the industrial camera equipment of the digital speckle interferometry optical path acquires speckle interference patterns before and after deformation of the object to be measured, and the speckle interference patterns are subjected to image processing to obtain a wrapped phase diagram which contains deformation information of the object to be measured and has the size of MxN
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 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 And 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 invention adopts the space carrier digital speckle interferometry light path to measure the circular plate type object to be measured, collects the digital speckle interferogram which causes the object to be measured to generate in-plane deformation under the action of external force, and then adopts the method for subsequent processing.
The object to be measured is a circular plate object to be measured.
The first step specifically comprises the following steps: obtaining a speckle interference pattern before deformation of an object to be measured by constructing a one-dimensional space carrier speckle interference measurement light path, collecting the speckle interference pattern again as the deformed speckle interference pattern after loading horizontal force in a plane on the object to be measured, and respectively carrying out two scattered speckle interference patternsFourier transformation is carried out on the spot interference pattern, a positive-order frequency spectrum is selected from the Fourier transformation result to carry out Fourier inverse transformation, then arc tangent operation is carried out to obtain phase patterns before and after deformation, finally, two phase patterns before and after deformation are subtracted 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
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 the phase value is wrapped in the wrapping operator by adding and subtracting integral multiple of 2 pi(-π,π]In the middle of;
representing the phase value at pixel point (i, j) in the wrapped phase map.
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 Indicating that the pixel point (i, j) in the wrapped phase diagram is a residual point, and others indicating that the pixel point (i, j) in the wrapped phase diagram is not a residual point;
3.2) calculating the average value L of the corresponding reliability of all 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.
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 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.
The fifth step specifically comprises:
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 then establishing a weighted least square equation set of the wrapped phase diagram according to the weight matrix w, and performing iterative solution on the weighted least square equation set by adopting a picocard method (PICARD) to obtain a continuous phase of each pixel point to form a continuous phase diagram so as to represent the deformation of the object to be measured.
In the fifth step, an iteration convergence condition is also set: iteration deviation epsilon, maximum iteration times n and initial absolute phase phi 0 CalculatingAnd (3) performing weighted least square solution on the weighted discrete partial differential sum of the wrapped phase map by adopting a Picard iteration method.
Compared with the background art, the invention has the beneficial effects that:
(1) the invention fuzzifies the mask threshold value of the reliability, constructs the membership function describing the threshold value, can self-adapt to one mask threshold value according to the input wrapped phase diagram, and realizes the automatic processing of the image.
(2) The mask threshold identified by the invention can accurately divide the reliability value with uncertainty to generate a proper mask plate, can effectively inhibit the global propagation of errors and improve the measurement precision.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a plot of the wrapped phase after filtering extracted by the spatial carrier phase shift technique;
FIG. 3 is a schematic representation of a membership function constructed in accordance with the present invention;
FIG. 4 is a schematic diagram of a 0-1 weighting coefficient matrix of the adaptive mask of the present invention;
FIG. 5 is a graph of unwrapped phase results from the present invention.
FIG. 6 is a graph of the phase result of the inventive repackaging.
Detailed Description
The invention is further illustrated by the following figures and examples.
The embodiment of the invention is shown in a flow chart of fig. 1, and comprises the following specific steps:
the method comprises the following steps: acquiring a speckle interference pattern before deformation of a circular plate object to be measured through a built two-dimensional digital speckle interference optical path system based on spatial carrier phase shift, acquiring the speckle interference pattern again after loading a horizontal force in a surface of the object to be measured as the speckle interference pattern after deformation of the circular plate object to be measured, respectively carrying out Fourier transform on the two speckle interference patterns, selecting a positive-level frequency spectrum from a Fourier transform result to carry out Fourier transform, then carrying out inverse tangent operation to obtain phase patterns before and after deformation, and finally subtracting the two phase patterns before and after deformation to obtain a phase pattern containing the phase patterns before and after deformationWrapped phase diagram with size of M multiplied by N of deformation information of object to be measured
Step two: the wrapped phase map is sine-cosine filtered to obtain the filtered wrapped phase map shown in fig. 2
Meanwhile, in order to show the unwrapping effect of a partial region, a white rectangular frame region is drawn at the position of the lower right corner of the filtered wrapped phase diagram shown in fig. 2 for comparison of subsequent unwrapping effects, and the filtered wrapped phase diagram is calculated
The reliability of each pixel point in the image is calculated, and a reliability graph R is formed;
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 Is a pack phaseSecond order difference of bitmap pixel point (i, j) in row direction and column direction; 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 the phase value is wrapped at (-pi, pi) by adding and subtracting integer multiples of 2 pi]To (c) to (d); ,
representing the phase value at pixel point (i, j) in the wrapped phase map.
Step three: identifying residual points R in wrapped phase maps es Calculating the average value L of the reliability corresponding to all residual points and the standard deviation H of the reliability map, using the average value L and the standard deviation H as the left end point and the right end point of the fuzzy interval, establishing a membership function, wherein the membership function is shown in FIG. 3, and performing fuzzy classification on the reliability map by using the membership function to obtain a membership matrix mu. The method specifically comprises the following steps:
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 Indicating that the pixel point (i, j) in the wrapped phase diagram is a residual point, and others indicating that the pixel point (i, j) in the wrapped phase diagram is not a residual point;
3.2) calculating the average value L of the corresponding reliability of all 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 graph; 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 denotes the coefficient of variation and P denotes the position of the vertex of the membership function.
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 ：
Wherein: mu (R) i,j ) Representing the membership value of a pixel point (i, j) in the reliability graph; r 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 represents the row number and column number in the wrapped phase map, respectively.
Step five: using the mask threshold T first R The reliability map is subjected to binarization segmentation to obtain a weight matrix w, as shown in fig. 4:
wherein, w i,j Represents the weight value at coordinate (i, j) in weight matrix w;
and then establishing a weighted least square equation set of the wrapped phase diagram according to the weight matrix w, and performing iterative solution on the weighted least square equation set by adopting a picocard method (PICARD) to obtain a continuous phase of each pixel point to form a continuous phase diagram so as to represent the deformation of the object to be measured.
In the fifth step, initialization parameters are also set: maximum iteration number n is 100, iteration cut-off threshold epsilon is 0.01, initial continuous phase phi 0 And (5) calculating the weighted discrete partial differential sum of each pixel point of the wrapped phase diagram, and performing weighted least square solution by adopting a Picard iteration method.
The continuous phase diagram obtained by phase unwrapping in this example is shown in fig. 5, and the gray level in the diagram gradually changes from black to white from top to bottom, which indicates that unwrapping by using the method can be successfully performed to obtain the continuous phase diagram, and it can be seen that the obtained result is relatively smooth. As shown in fig. 6, the unwrapped continuous phase map is subjected to a repackaging operation to obtain a repackaged phase map, which can be seen to coincide with the fringes of the original wrapped phase map, and as can be seen from the white rectangular box area of the unwrapped phase map of fig. 6 and the filtered wrapped phase map of fig. 2, the black jump points in the rectangular box in the repackaged phase map disappear, ensuring the effectiveness of the present invention.
Therefore, aiming at the problem that the mask threshold of the reliability map is difficult to determine in the reliability mask weighted least square, the fuzzy theory is utilized to carry out fuzzification processing on the reliability mask threshold, the mask threshold of the reliability map is obtained to carry out binarization processing on the reliability map to obtain a weight matrix, and continuous phases are obtained through iteration. The mask threshold of the wrapping phase is obtained in a self-adaptive mode, the problem of threshold selection of a reliability mask weighting least square wrapping algorithm is solved, correct masks of error points are guaranteed, and the efficiency and the precision of phase measurement can be effectively improved.
The foregoing detailed description is intended to illustrate and not limit the invention, and any modifications, equivalents, and improvements made within the spirit and scope of the claims are intended to be included within the scope of the invention.
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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