A weighted phase-shifting method for deformation field measurement

Abstract

This invention discloses a weighted phase-shifting method for deformation field measurement, belonging to the field of optical measurement technology. It is applicable to phase extraction and deformation field measurement of periodic structure images such as gratings and fringes, and features high speed and high accuracy. In image processing, this invention applies a weighted function window (rectangular window, triangular window, cosine window, Gaussian window). After multiplying the pixel grayscale values ​​within the window by the corresponding weights, a discrete Fourier transform is performed to obtain the image phase at the center pixel position of the window. After the weighted function window traverses all image pixels, the phase distribution of the entire image is obtained. The image deformation field is solved using the phase difference between the images before and after deformation. Compared with existing phase-based deformation field methods, this invention does not require complex image processing operations; it can obtain a high-precision phase and full-field deformation in one step using only weighted functions and global pixel grayscale values.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement technology, and is a weighted function phase shift method for deformation field measurement. Background Technology

[0002] In recent years, the aerospace, defense equipment, advanced manufacturing, and new materials industries have experienced rapid development, leading to an increasing demand for material and structural performance testing. Research on the testing of material and structural mechanical properties focuses on 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 such as full-field, non-contact, and strong environmental adaptability. Images used for optical deformation measurement are broadly classified into speckle images and images with periodic structures. The latter typically requires phase extraction to obtain the location information of the periodic structure in the image, and the deformation field is obtained using the relationship between phase and deformation. Therefore, high-quality phase extraction is crucial for obtaining the deformation field of images with periodic structures.

[0003] Existing image phase extraction and deformation field measurement techniques include Fourier transform, windowed Fourier transform, wavelet transform, sampling moiré pattern method, and phase shift method. Among these, windowed Fourier transform, wavelet transform, and phase shift method are susceptible to image noise and are time-consuming. In practical deformation measurement scenarios, the inability to eliminate noise leads to significant errors in the calculated phase distribution. The sampling moiré pattern method is a high-precision deformation measurement method based on phase analysis and has strong noise resistance. However, the sampling moiré pattern method typically obtains high-precision phase and deformation fields only at a single frequency. When the image has unequal periodicity, contains multi-frequency information, or 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, typically extract a frequency window from the spectrum and obtain the phase using positive and negative Fourier transforms. Wavelet transform utilizes the distribution of wavelet ridges to obtain the phase. The sampling moiré method downsamples pixel grayscale at equal intervals, interpolates to obtain multiple phase-shifted fringes, and then uses discrete Fourier transform to obtain the phase. Traditional phase-shifting methods are applied in the measurement of three-dimensional object topography by capturing multiple images with continuously changing phases to extract the phase distribution of the measured object. For phase extraction from single periodic images, there is currently no high-precision, noise-resistant, computationally efficient technique suitable for multi-frequency phase extraction in deformation field measurement.

[0005] To address the aforementioned challenges, we propose a novel deformation field measurement method based on phase analysis, named the weighted function phase-shifting method, which improves image phase extraction from the underlying Discrete Fourier transform principle. This method uses a weighted function window to weight the gray levels of image pixels and directly performs a phase shift on these weighted pixel gray levels to obtain the phase at the center of the window. Then, using the relationship between phase and deformation, the overall image deformation is calculated. This invention aims to extract multi-frequency phase information using a window of a certain length, achieving high-precision, high-noise-resistance, and efficient deformation field measurement of images with periodic structures. Summary of the Invention

[0006] This invention addresses the shortcomings of existing technologies by improving image phase extraction based on the underlying Discrete Fourier Transform principle. We propose a novel deformation field measurement method based on phase analysis, named the weighted function phase-shift method. This method uses a weighted function window to weight the gray levels of image pixels and directly performs a phase shift on these weighted pixel gray levels to obtain the phase at the center of the window. Then, using the relationship between phase and deformation, the overall image deformation is calculated. This invention aims to extract multi-frequency phase information using a window of a certain length, achieving high-precision, high-noise-resistance, and efficient deformation field measurement of images with periodic structures.

[0007] The technical solution of this invention: a weighted function phase shift method for deformation field measurement, the implementation steps of which are as follows:

[0008] (1) 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 gray values ​​of all pixels in the window by the weight of the corresponding position.

[0009] (2) Perform discrete Fourier transform on all weighted pixel gray values ​​in the window in sequence, and sum them to obtain the phase value of the pixel position at the center point of the window;

[0010] (3) Use the weight function window to traverse all pixels of the image and calculate the phase distribution of the entire image;

[0011] (4) Repeat steps one, two, and three for each image to solve the phase distribution of multiple images and obtain the phase difference between the images before and after deformation;

[0012] (5) The image deformation field is obtained by using the relationship between phase difference and strain and displacement.

[0013] Images used for deformation measurement have periodic patterns, including but not limited to gratings, dot matrices, and letter arrays.

[0014] The weighting functions in step one include: rectangular window, triangular window, cosine window, and Gaussian window. Let... Representing the periodic pixel intervals in an image, with image width w and length h, and W being the weight value, the rectangular window weight... The calculation formula is:

[0015]

[0016] Triangular window weight calculation The formula is:

[0017]

[0018] Cosine window weight calculation The formula is:

[0019]

[0020] Gaussian window weight calculation The formula is:

[0021]

[0022] in, This indicates the position of a pixel within the window, at the center of each window. The left and right edges of the window They are respectively equal to , ,in The length of the weight function window is specified as follows: .

[0023] In step one, let When the raster grayscale is 0, the grayscale value of all pixels within the window multiplied by the weight of the corresponding position can be expressed as:

[0024]

[0025] In step two, the weighted pixel grayscale values ​​are directly used to perform a discrete Fourier transform, and the phase value at the center of the window is obtained after accumulation. , can be represented as:

[0026]

[0027] in This is represented as the phase distribution in the x-direction obtained by traversing the weighted function window along the image width direction (x-direction). This is represented as the phase distribution in the y-direction obtained by traversing the weighted function window along the length direction (y-direction) of the image.

[0028] In step four, after performing phase extraction on multiple images containing deformation information, the phase difference before and after deformation is calculated. for:

[0029]

[0030]

[0031] in and These represent the phase distributions in the x and y directions before deformation, respectively. and These represent the phase distributions after deformation in the x and y directions, respectively. and These represent the phase difference in the x and y directions, respectively.

[0032] In step five, after obtaining the phase difference, the total displacement and strain are derived from the following formulas:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] in , These represent the displacement fields in the x and y directions, respectively. , These represent the distances in the x and y directions, respectively. , These represent the strain fields in the x and y directions, respectively. This represents the shear strain field.

[0039] 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, with the maximum weight value being P.

[0040] The phase is solved using the global grayscale values ​​of the image. The phase shift step of the discrete Fourier transform is obtained by using the length of the weighted function window. The grayscale values ​​of all pixels in the window are phase shifted and accumulated each time. The resulting phase is assigned to the center position of the weighted function window.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) This invention combines the weighting function with the discrete Fourier transform, which can directly phase shift the phase of the pixel gray values ​​after weighting the periodic structure image to obtain the phase distribution of a single image. The full-field deformation of the image is obtained by using the relationship between phase, strain, and displacement. By selecting different weighting function window types and window lengths, high-precision, high-noise-resistance, and efficient image phase analysis of periodic images with different waveforms and frequencies can be achieved.

[0043] (2) This invention, leveraging advancements in image phase extraction technology, is beneficial for high-precision deformation field measurement of images. In actual deformation measurement experiments, images often contain noise, and the deformed periodic structure image alters the original spacing, resulting in phase information with different frequencies. Traditional methods cannot overcome the challenge of multi-frequency phase extraction under background noise. Thanks to this invention, phase extraction is achieved through a window with a weighted function of a certain length. The presence of the window mitigates the influence of background noise and allows for the acquisition of phase information at different frequencies. The phase information carries the deformation information of the image's periodic structure, and the high-precision phase extraction of the deformed image significantly improves the accuracy of deformation field measurement.

[0044] (3) This invention greatly simplifies the steps of traditional phase extraction methods. Starting from the mathematical principles of the Discrete Fourier Transform, a weighting function is used to establish the relationship between image pixel gray values ​​and phase values, realizing one-step image phase extraction. Rapid image phase extraction enables real-time dynamic deformation measurement.

[0045] (4) In addition to deformation measurement, the image phase extraction in this invention can also be combined with all phase-based optical methods such as optical topography measurement, and has a certain degree of transferability and wide applicability. Attached Figure Description

[0046] Figure 1 This is a schematic diagram illustrating the relationship between the length of the weighting function window and the pixel position.

[0047] Figure 2 This is a schematic diagram of the rectangular weight function window when P=4.

[0048] Figure 3 This is a schematic diagram of the trigonometric weight function window when P=4.

[0049] Figure 4 This is a schematic diagram of the cosine weight function window when P=4.

[0050] Figure 5 This is a schematic diagram of the Gaussian weight function window when P=4.

[0051] Figure 6 A schematic diagram illustrating the principle of calculating the x-direction grating phase using a cosine weighted function window.

[0052] Figure 7The flowchart shows the process of solving the grating phase by traversing the grating pixels in the x-direction using the cosine weight function window.

[0053] Figure 8 The flowchart shows the process of solving the deformation field of orthogonal grating images using the phase-shifting method with weighted functions.

[0054] Figure 9 This is a simulated raster image before and after deformation without noise.

[0055] Figure 10 The image shows a simulated raster image with 50% noise before and after deformation.

[0056] Figure 11 This is a graph showing the root mean square error of the phase difference between triangular and cosine windows of different window lengths under noise-free conditions.

[0057] Figure 12 The root mean square error of the phase difference between the triangular window and the cosine window with different window lengths under 50% noise is plotted. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0059] This invention provides a weighted function phase shift method for deformation field measurement, wherein the weighted function window length and pixel position are shown in the simplified diagram below. Figure 1 As shown in the figure. Where P is the raster spacing of the raster image, k is the pixel position, the window length is 2P-1, and the center pixel position of the window is set to k=0.

[0060] Furthermore, schematic diagrams of window types such as rectangular windows, triangular windows, cosine windows, and Gaussian windows are shown below. Figure 2 , 3 As shown in Figures 4 and 5. Before calculating the deformation field, this invention requires selecting a weighting function window to weight the pixel grayscale values. The length and type of the weighting function window can be flexibly changed. Different lengths and types of weighting functions correspond to different weights at the pixel positions, indicating different degrees of weighting on the image pixel grayscale values. The formulas for different types of weighting function windows are shown below: Rectangular window weights The calculation formula is:

[0061]

[0062] Triangular window weight calculation The formula is:

[0063]

[0064] Cosine window weight calculation The formula is:

[0065]

[0066] Gaussian window weight calculation The formula is:

[0067]

[0068] Where the image width is w, the length is h, and W is the weight value. This indicates the position of a pixel within the window, at the center of each window. The left and right edges of the window They are respectively equal to , ,in The length of the weight function window is specified as follows: .

[0069] To further explain how the weighted function window directly calculates the grating phase value from the weighted grating pixel grayscale, a cosine weighted function window is used as an example to demonstrate the principle of calculating the grating phase in the x-direction. A schematic diagram is shown below. Figure 6 As shown. The top row represents the grayscale values ​​of the raster pixels. First, the grayscale values ​​of the pixels within the cosine window are multiplied by their respective position weights. These weighted pixel grayscale values ​​are then used as data for the Discrete Fourier Transform (DFT). The raster phase at the center pixel position (k=0) of the window is directly obtained via the DFT. The calculation process is the same when other window types are selected. The grayscale values ​​of all pixels within the window are multiplied by their corresponding position weights. It can be represented as:

[0070]

[0071] A single Fourier transform can only solve for the phase of a single pixel. To solve for the phase of the entire raster image, a weighted function window is needed to traverse all pixel positions of the image. A cosine weighted function window is used as an example. Figure 7 This document presents a flowchart illustrating the process of calculating the grating phase by traversing grating pixels along the x-direction using a window. First, for a one-dimensional grating image along the x-direction, the length of the weighting function window is ideally perpendicular to the principal direction of the grating to obtain a high-precision grating phase using the optimal waveform grating grayscale values. Using the first pixel of the grating as the center of the cosine window, the phase of each pixel within the window is obtained using a discrete Fourier transform after weighting the grayscale values, and stored at that pixel location. 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 location, which is also stored. Then, the phase extraction operation is repeated by traversing all pixel locations using the window to obtain the phase of the entire grating image. , can be represented as:

[0072]

[0073] in This represents 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 x-direction to the y-direction. This is represented as the phase distribution in the y-direction obtained by traversing the weighted function window along the length direction (y-direction) of the image.

[0074] Once the grating phase is obtained, the image deformation field can be solved. For orthogonal gratings, the flowchart for solving the deformation field using the weighted function phase-shifting method is as follows: Figure 8 As shown in the diagram, firstly, a low-pass filter is applied to the orthogonal grating to obtain a one-dimensional grating in the x and y principal directions. Then, the grating phase is solved using the weighted function phase-shift method to obtain the phase difference between the images before and after deformation. Finally, the full-field deformation of the image is calculated using the relationship between the phase difference and the strain and displacement fields. The phase difference... Represented as:

[0075]

[0076]

[0077] and These represent the phase distributions in the x and y directions before deformation, respectively. and These represent the phase distributions after deformation in the x and y directions, respectively. and These represent the phase difference in the x and y directions, respectively.

[0078] The formulas for solving the strain field and displacement field based on the phase difference are expressed as follows:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] in , These represent the displacement fields in the x and y directions, respectively. , These represent the distances in the x and y directions, respectively. , These represent the strain fields in the x and y directions, respectively. This represents the shear strain field.

[0085] To verify the accuracy and noise resistance of this method, a set of raster images before and after deformation were simulated using Matlab, in which... Figure 9 This demonstrates orthogonal raster images without noise. Figure 10 This demonstrates an orthogonal raster image with 50% noise. For analog raster images, their grayscale values ​​are... It can be represented as:

[0086]

[0087] Where P represents 8 pixels. This represents random noise and is a built-in function in Matlab. The existence of a function can deform the grating. The degree of deformation is represented as follows:

[0088]

[0089]

[0090] Where n is the number of frames. Here, five simulated gratings were generated for both noise-free and 50% noise conditions, with deformation degrees of 0%, 20%, 40%, 60%, and 80%, respectively. The grating with a deformation degree of 0% is considered as the grating before deformation, and the rest are considered as the grating after deformation. Figure 9 The simulated raster images before and after deformation without noise are shown. Figure 10 The simulated grating images with 50% noise before and after deformation are shown. The theoretical phase difference is obtained from the generated simulated grating. , can be represented as:

[0091]

[0092] To verify the accuracy of phase extraction using this method, we used the weighted function phase shift method. Figure 9 , Figure 10 Phase extraction was performed on the simulated grating to obtain the calculated phase difference. The root mean square (RSM) error was used to evaluate the proposed method and compared it with the theoretical phase difference. The phase error between them, where the root mean square error (RMS) can be expressed as:

[0093]

[0094] Depend on Figure 11It can be seen that when extracting the phase of a deformed grating under noise-free conditions using the weighted function phase-shifting method, the greater the degree of grating deformation, the higher the root mean square error of the phase difference. The highest accuracy is achieved when the window length is 6-8 pixels, with the resolved root mean square error of the phase difference between the triangular window and the cosine window below 0.4%. When extracting the phase of a deformed grating under 50% noise, the same pattern applies: the greater the degree of grating deformation, the higher the root mean square error of the phase difference. The highest accuracy is achieved when the window length is 8 pixels, with the resolved root mean square error of the phase difference between the triangular window and the cosine window below 4%. Therefore, it is evident that this invention can extract the grating phase with high accuracy under both noise-free and noise-free conditions.

[0095] The parts of this invention not disclosed in detail are well-known technologies in the field.

[0096] Although the foregoing has described illustrative specific embodiments of the present invention to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions 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 as follows: S1: Apply a weighted function window to the image, with the center of the window corresponding to the pixel position of the phase to be determined. Multiply the gray values ​​of all pixels within the window by the weights corresponding to their positions. In S1, let... Represented as image pixel position The raster grayscale value, This represents the position of the pixel in the weighted function window. Represents the periodic pixel intervals in an image, where the image width is... , length is , For a weighted function window, the grayscale value of all pixels within the window is multiplied by the weight at the corresponding position to obtain the weighted raster grayscale value. Represented as: ； in, This indicates the weight type, which includes four types: Represented as a rectangular window type Represented as a triangular window type, Represented as a cosine window type, Represented as a Gaussian window type; S2: Perform Discrete Fourier Transform on all weighted pixel grayscale values ​​within the window sequentially, and accumulate the results to obtain the phase value at the pixel position at the center of the window; in S2, the phase value at the center of the window is obtained by directly performing Discrete Fourier Transform on the weighted pixel grayscale values ​​and accumulating the results. , can be represented as: ； ； in, This can be represented as the phase distribution in the x-direction obtained by traversing the weighted function window along the width of the image. This is represented as the y-direction phase distribution obtained by traversing the weighted function window along the length of the image; S3: Use a weighted function window to traverse all pixels of the image and calculate the phase distribution of the entire image; S4: Repeat steps one, two, and three for each image to solve for the phase distribution of multiple images and obtain the phase difference between the images before and after deformation; in S4, after performing phase extraction on multiple images containing deformation information, the phase difference before and after deformation is obtained as follows: ； ； in, and These represent the phase distribution in the x and y directions before deformation, respectively. and These represent the phase distribution in the x and y directions after deformation, respectively. and These represent the phase difference in the x and y directions, respectively. S5: The image deformation field is obtained by utilizing the relationship between phase difference, strain, and displacement. In S5, after obtaining the phase difference, the overall displacement and strain are derived from the following formulas: ； ； ； ； ； in, and These represent the displacement fields in the x and y directions, respectively. and These represent the spacing of the raster image in the x and y directions, respectively. and These represent the strain fields in the x and y directions, respectively. This represents the shear strain field.

2. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that: Images used for deformation measurement contain periodic patterns, including gratings, dot matrices, and letter arrays.

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, and Gaussian window; let Given a rectangular window representing periodic pixel intervals in an image with width w and length h, then the weights are as follows: 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, This indicates the position of a pixel within the window, at the center of each window. The left and right edges of the window They are respectively equal to , ,in The length of the weight function window is specified as follows: .

4. The weighted function phase shift method for deformation field measurement according to claim 1, characterized in that, The phase is solved using the global grayscale values ​​of the image. The phase shift step size of the discrete Fourier transform is used as the length of the weighting function window. The grayscale values ​​of all pixels in the window are phase shifted and accumulated each time. The resulting phase is assigned to the center position of the weighting function window.

Images