Weight function phase shift method for deformation field measurement

Abstract

The invention discloses a weight function phase shift method for deformation field measurement, belongs to the technical field of optical measurement, is suitable for phase extraction and deformation field measurement of periodic structure images such as gratings and stripes, and has the characteristics of high speed and high precision. Weight function windows (a rectangular window, a triangular window, a cosine window and a Gaussian window) are applied in image processing, discrete Fourier transform is carried out after pixel gray values in the windows are multiplied by corresponding weights, and image phases at the center pixel positions of the windows are obtained. After the weight function window traverses all image pixels, the phase distribution of the whole image is obtained. And solving an image deformation field by using the phase difference of the images before and after deformation. Compared with the existing phase-based deformation field method, the method does not need complex image processing operation, and can solve the high-precision phase in one step and obtain full-field deformation only by using the weight function and the global pixel gray scale.

Description

Technical Field

[0001] The invention belongs to the technical field of optical measurement and is a weighted function phase shift method for deformation field measurement. Background Art

[0002] In recent years, the fields of aerospace, national defense equipment, advanced manufacturing, new materials, etc. have developed rapidly, and the demand for material and structural performance testing has increased. The focus of research on the detection of mechanical properties of materials and structures is the measurement of deformation and strain. In recent years, optical deformation measurement technology has become an important means of measuring material and structural deformation due to its advantages of full-field, non-contact, and strong environmental adaptability. Images used for optical deformation measurement are roughly divided into speckle images and images with periodic structures. The latter usually require phase extraction to obtain the position information of the periodic structure in the image, and the deformation field is obtained by using the relationship between phase and deformation. It can be seen that high-quality phase extraction is the key to obtaining the deformation field of images with periodic structures.

[0003] Existing image phase extraction deformation field measurement technologies include Fourier transform method, windowed Fourier transform method, wavelet transform method, sampling moiré method, phase shift method, etc. Among them, the windowed Fourier transform method, wavelet transform method and phase shift method are easily affected by image noise and the algorithm is time-consuming. In actual deformation measurement scenarios, the noise cannot be eliminated, resulting in large errors in the calculated phase distribution. The sampling moiré method is a high-precision deformation measurement method based on phase resolution and has strong anti-noise ability. However, the sampling moiré method usually only obtains high-precision phase and deformation field at a single frequency. When the periodicity in the image is unequal, there is multi-frequency information, and the deformation is too large, a non-negligible phase error will occur.

[0004] Traditional deformation measurement methods based on phase extraction, such as Fourier transform and windowed Fourier transform, usually intercept a frequency band of a window in the spectrum and use positive and negative Fourier transforms to obtain the phase. Wavelet transform uses the distribution of wavelet ridges to obtain the phase. The sampling moiré rule downsamples the pixel grayscale at the same interval, obtains multiple phase-shifted fringes after interpolation, and uses discrete Fourier transform to obtain the phase. The traditional phase shift method is used in the three-dimensional morphology measurement of objects. By taking multiple images with continuously changing phases, the phase distribution of the measured object is extracted. For the phase extraction of a single periodic image, there is still no technology with high precision, strong noise resistance, high computational efficiency and suitable for multi-frequency phase extraction for deformation field measurement.

[0005] In order to solve the above problems, we improve the image phase extraction based on the underlying discrete Fourier principle and propose a new deformation field measurement method based on phase analysis, called the weighted function phase shift method. The image pixel grayscale is weighted using a weight function window, and the weighted pixel grayscale is directly phase shifted to obtain the phase at the center of the window. Then, the relationship between phase and deformation is used to obtain the full-field deformation of the image. The present invention aims to extract multi-frequency phase information using a window with a certain length, so as to achieve high-precision, high-noise resistance and high-efficiency deformation field measurement of images with periodic structures. Summary of the invention

[0006] The technology of the present invention solves the problem: In view of the shortcomings of the existing technology, the present invention improves the image phase extraction based on the underlying discrete Fourier principle. We propose a new deformation field measurement method based on phase analysis, called the weighted function phase shift method. The image pixel grayscale is weighted using a weight function window, and the weighted pixel grayscale is directly phase shifted to obtain the phase at the center of the window. Subsequently, the relationship between phase and deformation is used to obtain the full-field deformation of the image. The present invention aims to extract multi-frequency phase information using a window with a certain length, so as to achieve high-precision, high-noise resistance and high-efficiency deformation field measurement of images with periodic structures.

[0007] The technical solution of the present invention is a weighted function phase shift method for deformation field measurement, and its implementation steps are as follows: (1) Apply a weight function window to the image. The center of the window corresponds to the pixel position of the phase to be determined. Multiply the grayscale value of all pixels in the window by the weight of the corresponding position. (2) Perform discrete Fourier transform on all weighted pixel grayscale values ​​in the window in turn, and accumulate them to obtain the phase value of the pixel position at the center of the window; (3) Use the weight function window to traverse all pixels of the image and calculate the phase distribution of the entire image; (4) Repeat steps 1, 2, and 3 for each image to solve the phase distribution of multiple images and obtain the phase difference of the image before and after deformation; (5) Using the relationship between phase difference, strain and displacement, the image deformation field is obtained.

[0008] The image used for deformation measurement has a periodic pattern, including but not limited to a grating, a dot matrix, a letter array, etc.

[0009] The weight functions in step 1 include: rectangular window, triangular window, cosine window, and Gaussian window. Represents the periodic pixel interval in the image, the image width is w, the length is h, W is the weight value, then the rectangular window weight The calculation formula is:

[0010] Triangular window weight calculation The formula is:

[0011] Cosine window weight calculation The formula is:

[0012] Gaussian window weight calculation The formula is:

[0013] in, Indicates the position of the pixel in the window, at the center of each window , the left and right edges of the window Equal to , ,in The length of the weight function window is specified as . In step 1, When the grating grayscale is , the grayscale value of all pixels in the window multiplied by the weight of the corresponding position can be expressed as:

[0014] In step 2, the weighted pixel grayscale value is directly used for discrete Fourier transform, and the phase value at the center of the window is obtained after accumulation. , which can be expressed as:

[0015] in It is expressed as the phase distribution in the x direction obtained by traversing the weight function window along the image width direction (x direction), It is expressed as the phase distribution in the x direction obtained by traversing the weight function window along the image width direction (y direction).

[0016] In step 4, after phase extraction of multiple images containing deformation information, the phase difference before and after deformation is obtained. for:

[0017]

[0018] in and Respectively represent the phase distribution after deformation in the x and y directions, and Respectively represent the phase distribution after deformation in the x and y directions, and Represent the phase difference in the x and y directions respectively.

[0019] In step 5, after the phase difference is obtained, the full-field displacement and strain are obtained by the following formula:

[0020]

[0021]

[0022]

[0023]

[0024] in , represent the displacement fields in the x and y directions respectively, , Represents the distance in the x and y directions respectively, , represent the strain field in the x and y directions respectively, represents the shear strain field.

[0025] Each pixel position in the weight function window has a corresponding weight value, which is given by the weight function. Different weight function types have different weight values, and the maximum weight value is P.

[0026] The phase is solved using the global grayscale value of the image. The phase shift step of the discrete Fourier transform is based on the weighted function window length. The weighted grayscale values ​​of all pixels in the window are phase shifted and accumulated each time, and the obtained phase is assigned to the center position of the weighted function window.

[0027] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention combines the weight function with the discrete Fourier transform, which can directly shift the phase of the pixel grayscale value after weighting the periodic structure image to obtain the phase distribution of a single image, and use the relationship between phase, strain and displacement to obtain the full-field deformation of the image. By selecting different weight function window types and window lengths, high-precision, high-noise and efficient image phase analysis of periodic images with different waveforms and frequencies can be achieved.

[0028] (2) The present invention is beneficial to the high-precision deformation field measurement of images by virtue of the technological progress of image phase extraction. In actual deformation measurement experiments, the image has a certain amount of noise, and the deformed periodic structure image will change the original spacing and have phase information of different frequencies. Traditional methods cannot overcome multi-frequency phase extraction under background noise. Thanks to the present invention, the phase is extracted by a weight function window with a certain length. The existence of the window can reduce the influence of background noise and obtain phase information of different frequencies. The phase information carries the deformation information of the periodic structure of the image. The high-precision phase extraction of the deformed image greatly improves the accuracy of deformation field measurement.

[0029] (3) The present invention greatly simplifies the steps of the traditional phase extraction method. Starting from the mathematical principle of discrete Fourier transform, the weight function is used to establish the relationship between the grayscale value and the phase value of the image pixel, thereby realizing one-step extraction of the image phase. The rapid extraction of the image phase can realize real-time dynamic deformation measurement.

[0030] (4) In addition to being used in deformation measurement, the image phase extraction in the present invention can also be combined with all phase-based optical methods such as optical morphology measurement, and has certain transferability and wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Schematic diagram of the relationship between the weight function window length and pixel position.

[0032] Figure 2 Schematic diagram of the rectangular weight function window when P=4.

[0033] Figure 3 Schematic diagram of the triangular weight function window when P=4.

[0034] Figure 4 Schematic diagram of the cosine weight function window when P=4.

[0035] Figure 5 Schematic diagram of the Gaussian weight function window when P=4.

[0036] Figure 6 Schematic diagram of the principle of calculating the x-direction grating phase for the cosine weight function window.

[0037] Figure 7 Flowchart for solving the grating phase for the cosine weight function window by traversing the grating pixels in the x direction.

[0038] Figure 8 Flowchart for solving the deformation field of orthogonal grating image using the weighted function phase shift method.

[0039] Fig. 9 The simulated raster images are without noise before and after deformation.

[0040] Fig.10 The simulated raster images with 50% noise before and after deformation.

[0041] Fig.11 This is the RMS error diagram of the phase difference of the triangular window and cosine window with different window lengths in the noise-free environment.

[0042] Fig.12 The RMS error diagram of the phase difference of the triangular window and cosine window with different window lengths under 50% noise. DETAILED DESCRIPTION

[0043] The present invention is further described below in conjunction with the accompanying drawings and implementation modes.

[0044] The present invention provides a weighted function phase shift method for deformation field measurement, wherein the weighted function window length and pixel position are as shown in the schematic diagram. Figure 1 As shown in the figure, P is the grating pitch of the grating image, k is the pixel position, the window length is 2P-1, and the window center pixel position k=0.

[0045] Furthermore, schematic diagrams of window types such as rectangular window, triangular window, cosine window and Gaussian window are shown as follows: Figure 2 , 3 , 4, and 5. Before calculating the deformation field, the present invention needs to select a weight function window to weight the pixel grayscale value, and the length and type of the weight function window can be flexibly changed. Weight functions of different lengths and types have different weights for the corresponding pixel positions, indicating different degrees of weighting of the image pixel grayscale values. The formulas for different types of weight function windows are as follows: Rectangular window weight The calculation formula is:

[0046] Triangular window weight calculation The formula is:

[0047] Cosine window weight calculation The formula is:

[0048] Gaussian window weight calculation The formula is:

[0049] Among them, the image width is w, the length is h, and W is the weight value. Indicates the position of the pixel in the window, at the center of each window , the left and right edges of the window Equal to , ,in The length of the weight function window is specified as .

[0050] In order to further explain how the weight function window calculates the grating phase value directly from the weighted grating pixel grayscale, the cosine weight function window is used as an example to show the principle of calculating the x-direction grating phase using the cosine weight function window. The schematic diagram is shown in Figure 6 As shown. The upper row is the grating pixel grayscale. First, the pixel grayscale value in the cosine window is multiplied by the weight of each position. The weighted pixel grayscale value is used as the data of discrete Fourier transform. The grating phase of the window center pixel position (k=0) is directly calculated through discrete Fourier transform. When other types of windows are selected, the calculation process is the same. The grayscale value of all pixels in the window is multiplied by the weight of the corresponding position. It can be expressed as:

[0051] A single Fourier transform can only solve the phase of one pixel position. In order to solve the phase of the entire grating image, it is necessary to use a weight function window to traverse all pixel positions of the image. The cosine weight function window is used as an example. Figure 7 The flowchart of solving the grating phase by traversing the grating pixels in the x-direction with a window is shown. First, for a one-dimensional x-direction grating image, the length direction of the weight function window is preferably perpendicular to the main direction of the grating, so as to obtain a high-precision grating phase using the grating grayscale value of the optimal waveform. Taking the first pixel of the grating as the center of the cosine window, the phase of the pixel position is obtained by discrete Fourier transform after weighting the grayscale of the pixels in the window, and stored in the pixel position. Subsequently, the window is moved one pixel in the x-direction, and the above operation is repeated to obtain the phase of the second pixel position and store it. Next, the window is used to traverse all pixel positions, and the phase extraction operation is repeated to obtain the phase of the entire grating image. , which can be expressed as:

[0052] in It is expressed as the phase distribution in the x direction obtained by traversing the weight function window along the image width direction (x direction). For the grating in the y direction, the traversal direction is changed from the above x direction to the y direction. It is expressed as the phase distribution in the y direction obtained by traversing the weight function window along the image width direction (x direction).

[0053] After obtaining the grating phase, the image deformation field can be solved. For orthogonal gratings, the weighted function phase shift method solves the deformation field flow chart as follows: Figure 8As shown in the figure, firstly, a low-pass filter is applied to the orthogonal grating to obtain a one-dimensional grating in the x and y main directions. Then, the phase of the grating is solved by the weighted function phase shift method to obtain the phase difference of the image before and after deformation. Then, the full-field deformation of the image is obtained by using the relationship between the phase difference and the strain field and the displacement field. It is expressed as:

[0054]

[0055] and Respectively represent the phase distribution after deformation in the x and y directions, and Respectively represent the phase distribution after deformation in the x and y directions, and Represent the phase difference in the x and y directions respectively.

[0056] The formula for solving the strain field and displacement field based on the phase difference is expressed as:

[0057]

[0058]

[0059]

[0060]

[0061] in , represent the displacement fields in the x and y directions respectively, , Represents the distance in the x and y directions respectively, , represent the strain field in the x and y directions respectively, represents the shear strain field.

[0062] In order to verify the accuracy and noise resistance of this method, a set of grating images before and after deformation were simulated by Matlab. Fig. 9 shows the noise-free orthogonal raster image. Fig.10 The orthogonal grating image under 50% noise is shown. For the simulated grating image, its grayscale It can be expressed as: Among them, P is 8 pixels, Represents random noise, which is a built-in function of Matlab. The existence of the function can deform the raster, Indicates the degree of deformation, respectively expressed as:

[0063]

[0064] Here, n is the number of images. Five simulated gratings were generated without noise and with 50% noise, respectively, with deformation degrees of 0%, 20%, 40%, 60%, and 80%. The grating with a deformation degree of 0% was regarded as the grating before deformation, and the rest were regarded as the grating after deformation. Fig. 9 The simulated raster image without noise before and after deformation is shown. Fig.10 The simulated grating image with 50% noise before and after deformation is shown. The theoretical phase difference is obtained from the generated simulated grating , which can be expressed as:

[0065] In order to verify the accuracy of phase extraction by this method, we use the weighted function phase shift method to Fig. 9 , Fig.10 The simulated grating in the image was phase extracted to obtain the calculated phase difference. , the root mean square error (RSM) is used to evaluate the proposed method and compare it with the theoretical phase difference The phase error between them, where the root mean square error RMS can be expressed as: Depend on Fig.11 It can be obtained that when the phase of the deformed grating under noise-free conditions is extracted using the weighted function phase shift method, the greater the degree of grating deformation, the higher the phase difference root mean square error. When the window length is 6-8 pixels, the highest accuracy is achieved, and the analytical root mean square error of the phase difference between the triangular window and the cosine window is below 0.4%. When extracting the phase of the deformed grating under 50% noise, the greater the degree of grating deformation, the higher the phase difference root mean square error. When the window length is 8 pixels, the highest accuracy is achieved, and the analytical root mean square error of the phase difference between the triangular window and the cosine window is below 4%. It can be seen that the present invention can extract the grating phase with high accuracy in the presence or absence of noise.

[0066] Parts of the present invention that are not disclosed in detail belong to the common knowledge in the art.

[0067] Although the above illustrative specific embodiments of the present invention are described to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

Claims

1. A weighted function phase shift method for deformation field measurement, characterized in that: The specific steps are: S1: Apply a weight function window to the image, with the center of the window corresponding to the pixel position of the phase to be determined, and multiply the grayscale values ​​of all pixels in the window by the weight of the corresponding position; S2: Perform discrete Fourier transform on all weighted pixel grayscale values ​​in the window in turn, and obtain the phase value of the pixel position at the center of the window after accumulation; S3: Use the weight function window to traverse all pixels of the image and calculate the phase distribution of the entire image; S14: repeating steps 1, 2, and 3 for each image, solving the phase distribution of the multiple images, and obtaining the image phase difference before and after deformation; S5: Using the relationship between phase difference, strain and displacement, the image deformation field is obtained.

2. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that: The image used for deformation measurement has a periodic pattern, including but not limited to a grating, a dot matrix, a letter array, etc.

3. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that: The weight functions in S1 include: rectangular window, triangular window, cosine window, Gaussian window; Represents the periodic pixel interval in the image, the image width is w, the length is h, W is the weight value, then the rectangular window weight The calculation formula is: ； Triangular window weight calculation The formula is: ； Cosine window weight calculation The formula is: ； Gaussian window weight calculation The formula is: ； in, Indicates the position of the pixel in the window, at the center of each window , the left and right edges of the window Equal to , ,in The length of the weight function window is specified as .

4. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that: In S1, let When the grating grayscale is , the grayscale value of all pixels in the window multiplied by the weight of the corresponding position can be expressed as: 。 5. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that: In S2, the weighted pixel grayscale value is directly used for discrete Fourier transform, and the phase value at the center of the window is obtained after accumulation. , which can be expressed as: ； in, It is expressed as the phase distribution in the x direction obtained by traversing the weight function window along the image width direction (x direction), It is expressed as the phase distribution in the x direction obtained by traversing the weight function window along the image width direction (y direction).

6. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that: In S4, after phase extraction is performed on multiple images containing deformation information, the phase difference before and after deformation is obtained as: ； ； in, and Respectively represent the phase distribution after deformation in the x and y directions, and Respectively represent the phase distribution after deformation in the x and y directions, and Represent the phase difference in the x and y directions respectively.

7. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that: In S5, after the phase difference is obtained, the full-field displacement and strain are obtained by the following formula: ； ； ； ； ； in, , represent the displacement fields in the x and y directions respectively, , Represents the distance in the x and y directions respectively, , represent the strain field in the x and y directions respectively, represents the shear strain field.

8. The weighted function phase shift method for deformation field measurement according to claim 3, characterized in that: Each pixel position in the weight function window has a corresponding weight value, which is given by the weight function. Different weight function types have different weight values, and the maximum weight value is P.

9. A weighted function phase shift method for deformation field measurement according to claim 5, characterized in that: The phase is solved by using the global grayscale value of the image. The phase shift step of the discrete Fourier transform is based on the weighted function window length. The weighted grayscale values ​​of all pixels in the window are phase-shifted and accumulated each time, and the obtained phase is assigned to the center position of the weighted function window.

Images