CN112797917A - High-precision digital speckle interference phase quantitative measurement method - Google Patents

High-precision digital speckle interference phase quantitative measurement method Download PDF

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CN112797917A
CN112797917A CN202110069385.7A CN202110069385A CN112797917A CN 112797917 A CN112797917 A CN 112797917A CN 202110069385 A CN202110069385 A CN 202110069385A CN 112797917 A CN112797917 A CN 112797917A
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reliability
phase
map
pixel point
wrapped phase
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CN112797917B (en
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严利平
唐信永
黄柳
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
    • G01B11/254—Projection of a pattern, viewing through a pattern, e.g. moiré
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry

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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

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 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
Figure RE-GDA0003017709310000011
Step two: for wrapped phase diagram
Figure RE-GDA0003017709310000012
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 mapsesCalculating the average value L of the reliability corresponding to all residual points and the standard deviation H of the reliability graph, 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 graph by using the membership function to obtain slaveryA 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 TR；
Step five: using a mask threshold TRAnd 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 a space carrier digital speckle interferometry optical path to measure a circular plate type object to be measured, collects a digital speckle interference pattern which causes the object to be measured to generate in-plane deformation under 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 building a one-dimensional space carrier speckle interference measurement light path, collecting the speckle interference pattern as the deformed speckle interference pattern again after loading an in-plane horizontal force on the object to be measured, respectively carrying out Fourier transform on the two speckle interference patterns, selecting a positive-order frequency spectrum from the Fourier transform result to carry out Fourier inverse transform, carrying out 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
Figure RE-GDA0003017709310000021
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:
Figure RE-GDA0003017709310000022
Figure RE-GDA0003017709310000023
Figure RE-GDA0003017709310000024
Figure RE-GDA0003017709310000025
Figure RE-GDA0003017709310000026
wherein R isi,jRepresenting 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; hi,jAnd Vi,jSecond order differences in row and column directions for wrapping phase map pixel points (i, j); ci,jAnd Di,jRespectively 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);
Figure RE-GDA0003017709310000028
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 Res：
Figure RE-GDA0003017709310000027
Wherein Resi,jIndicating 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:
Figure RE-GDA0003017709310000031
wherein K represents the number of residual points;
3.3) calculating the standard deviation H of the reliability map:
Figure RE-GDA0003017709310000032
wherein the content of the first and second substances,
Figure RE-GDA0003017709310000033
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:
Figure RE-GDA0003017709310000034
Figure RE-GDA0003017709310000035
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 formulaR：
Figure RE-GDA0003017709310000036
Wherein: mu (R)i,j) Representing the membership value of a pixel point (i, j) in the reliability graph; ri,jRepresenting wrapped phasesThe reliability of the map at pixel (i, j), M, N, represents the number of rows and columns in the wrapped phase map, respectively, and i, j represent the row and column ordinal numbers in the wrapped phase map, respectively.
The fifth step is specifically as follows:
using the mask threshold T firstRCarrying out binarization segmentation on the reliability map to obtain a weight matrix w:
Figure RE-GDA0003017709310000041
wherein, wi,jRepresents the weight value at coordinate (i, j) in weight matrix w;
and 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 pick-up 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 number n and initial absolute phase phi0And calculating the weighted discrete partial differential sum of the wrapped phase diagram, and performing weighted least square solution 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 inverse transform, 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 wrapped phase pattern containing deformation information of the object to be measured and with the size of M multiplied by N
Figure RE-GDA0003017709310000051
Step two: the wrapped phase map is sine-cosine filtered to obtain the filtered wrapped phase map shown in fig. 2
Figure RE-GDA0003017709310000058
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
Figure RE-GDA0003017709310000059
The reliability of each pixel point in the image is calculated, and a reliability graph R is formed;
Figure RE-GDA0003017709310000052
Figure RE-GDA0003017709310000053
Figure RE-GDA0003017709310000054
Figure RE-GDA0003017709310000055
Figure RE-GDA0003017709310000056
wherein R isi,jRepresenting 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; hi,jAnd Vi,jSecond order differences in row and column directions for wrapping phase map pixel points (i, j); ci,jAnd Di,jRespectively 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); ,
Figure RE-GDA00030177093100000510
representing the phase value at pixel point (i, j) in the wrapped phase map.
Step three: identifying residual points R in wrapped phase mapsesCalculating 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 using the membership function to perform fuzzy classification on the reliability map to obtain a membership matrixMu.m. 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 Res：
Figure RE-GDA0003017709310000057
Wherein Resi,jIndicating 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:
Figure RE-GDA0003017709310000061
wherein K represents the number of residual points;
3.3) calculating the standard deviation H of the reliability map:
Figure RE-GDA0003017709310000062
wherein the content of the first and second substances,
Figure RE-GDA0003017709310000063
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:
Figure RE-GDA0003017709310000064
Figure RE-GDA0003017709310000065
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 TR：
Figure RE-GDA0003017709310000066
Wherein: mu (R)i,j) Representing the membership value of a pixel point (i, j) in the reliability graph; ri,jRepresenting 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 firstRThe reliability map is subjected to binarization segmentation to obtain a weight matrix w, as shown in fig. 4:
Figure RE-GDA0003017709310000071
wherein, wi,jRepresents the weight value at coordinate (i, j) in weight matrix w;
and 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 pick-up 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 phi0And (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 value of the wrapping phase is obtained in a self-adaptive mode, the problem of threshold value selection of a reliability mask weighting least square wrapping algorithm is solved, correct masking of an error point is guaranteed, and efficiency and 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 measurement method based on fuzzy theory is characterized in that:
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
Figure FDA0002905498440000011
Step two: for wrapped phase diagram
Figure FDA0002905498440000012
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 mapsesCalculating 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 TR；
Step five: using a mask threshold TRAnd 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 method for high-precision quantitative measurement of the digital speckle interferometry phase according to claim 1, wherein: the first step specifically comprises the following steps: obtaining a speckle interference pattern before deformation of an object to be measured by building a one-dimensional space carrier speckle interference measurement light path, collecting the speckle interference pattern as the deformed speckle interference pattern again after loading an in-plane horizontal force on the object to be measured, respectively carrying out Fourier transform on the two speckle interference patterns, selecting a positive-order frequency spectrum from the Fourier transform result to carry out Fourier inverse transform, carrying out 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
Figure FDA0002905498440000013
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:
Figure FDA0002905498440000021
Figure FDA0002905498440000022
Figure FDA0002905498440000023
Figure FDA0002905498440000024
Figure FDA0002905498440000025
wherein R isi,jRepresenting 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; hi,jAnd Vi,jSecond order differences in row and column directions for wrapping phase map pixel points (i, j); ci,jAnd Di,jRespectively 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,
Figure FDA0002905498440000026
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 1, wherein: 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 Res：
Figure FDA0002905498440000027
Wherein Resi,jIndicating 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:
Figure FDA0002905498440000028
wherein K represents the number of residual points;
3.3) calculating the standard deviation H of the reliability map:
Figure FDA0002905498440000029
wherein the content of the first and second substances,
Figure FDA00029054984400000210
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:
Figure FDA0002905498440000031
Figure FDA0002905498440000032
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 formulaR：
Figure FDA0002905498440000033
Wherein: mu (R)i,j) Representing the membership value of a pixel point (i, j) in the reliability graph; ri,jRepresenting 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 firstRCarrying out binarization segmentation on the reliability map to obtain a weight matrix w:
Figure FDA0002905498440000034
wherein, wi,jRepresents 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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