A related Hartmann fast wavefront recovery method

Abstract

This invention provides a fast Hartmann wavefront reconstruction method, comprising: acquiring an initial Hartmann image and sub-aperture arrangement detected by a Hartmann wavefront sensor; selecting a filter template in the initial Hartmann image; performing correlation filtering or kernel correlation filtering on the initial Hartmann image to obtain a response map, wherein the response map corresponds to multiple sub-response maps, and each sub-response map corresponds to a sub-aperture; traversing and finding the maximum pixel value of each sub-aperture in the sub-apertures corresponding to the multiple sub-response maps, and storing the coordinate position of the maximum pixel value to obtain a slope matrix; and performing Hartmann wavefront reconstruction using the response map and the slope matrix to obtain the reconstructed wavefront. This invention can achieve the transformation of an extended target into a spot image through a single correlation filtering, simplifying the algorithm, improving the calculation speed, and realizing fast wavefront reconstruction.

Description

Technical Field

[0001] This invention relates to the field of optical information measurement technology, and in particular to a correlated Hartmann fast wavefront recovery method. Background Technology

[0002] With the application of correlated Hartmann wavefront reconstruction to extended targets such as drones and automobiles, wavefront reconstruction is performed by convolving the Hartmann sub-response map target template to obtain the response image, and then calculating the reconstructed wavefront based on the response image. Therefore, correlated Hartmann wavefront reconstruction, through template convolution, plays a crucial role in wavefront reconstruction of extended target images.

[0003] Currently, correlation Hartmann algorithms for extended targets typically employ correlation filtering algorithms, such as the MOSSE (Minimum Output Sum of Squared Error) tracking algorithm. This algorithm uses filtering and correlation methods to perform Fourier transform on the image, trains a template to obtain a new filter, and updates the filter template in real time to achieve target tracking. However, traditional correlation Hartmann algorithms can only train and filter for a single target template. For Hartmann wavefront reconstruction, each sub-response map must be trained and filtered individually, requiring a 2-bit Fast Fourier Transform followed by Gaussian filtering and other processing. Therefore, the more sub-response maps there are, the more time-consuming the algorithm becomes. Furthermore, since traditional Hartmann algorithms can only process single sub-aperture images, image segmentation and the creation of multiple new arrays to receive data are necessary before image processing, further increasing time consumption and memory usage.

[0004] In addition, spatial domain algorithms are used to expand the target in some cases. This involves selecting a suitable template image from the Hartmann image and comparing its pixels with those in the continuously updated Hartmann image. The position with the highest similarity is the new location of the target in the Hartmann image. However, spatial domain algorithms require multiple iterations, resulting in high computational cost and slow processing speed.

[0005] Therefore, there is an urgent need for a method that can reduce the amount of computation, increase the computation speed, and quickly realize wavefront reconstruction. Summary of the Invention

[0006] Therefore, it is necessary to provide a relevant Hartmann fast wavefront recovery method to address the aforementioned technical problems.

[0007] A fast Hartmann wavefront reconstruction method includes the following steps: acquiring an initial Hartmann image and sub-aperture arrangement detected by a Hartmann wavefront sensor; selecting a filter template in the initial Hartmann image; placing the filter template into the initial Hartmann image and performing correlation filtering or kernel correlation filtering operations to obtain a response map, wherein the response map corresponds to multiple sub-response maps, and each sub-response map corresponds to a sub-aperture; traversing and finding the maximum pixel value of each sub-aperture in the sub-apertures corresponding to the multiple sub-response maps, and storing the coordinate position of the maximum pixel value to obtain a slope matrix; and performing Hartmann wavefront reconstruction using the response map and the slope matrix to obtain the reconstructed wavefront.

[0008] In one embodiment, selecting a filter template in the initial Hartmann image specifically includes: selecting a sub-image with clear pixels as a filter template at the center position of the initial Hartmann image.

[0009] In one embodiment, before acquiring the initial Hartmann image and sub-aperture arrangement detected by the Hartmann wavefront sensor, selecting a filter template in the initial Hartmann image, and placing the filter template into the initial Hartmann image for correlation filtering or kernel correlation filtering operations to obtain the response map, the method further includes: truncating the signal of the template image using a truncation function to obtain the filter template; wherein the formula for the truncation function is as follows:

[0010]

[0011] Where m and n represent the coordinates of the window function, and M and N represent the size of the template; the pixel gray values ​​of the filter template are normalized to an image with a mean of 0 and a variance of 1; the normalized filter template is multiplied by a cosine window to reduce the values ​​of the image edges to 0, thus obtaining the windowed filter template.

[0012] In one embodiment, after multiplying the normalized filter template by a cosine window to reduce the image edge values ​​to 0 and obtaining the windowed filter template, the method further includes: generating a correlation filter or a kernel correlation filter based on the windowed filter template, using the following formula:

[0013]

[0014] Where x is the template image or the template after windowing, and k xx Let x be the autocorrelation kernel function, and the kernel function k can be either a Gaussian kernel function or a linear kernel function; Indicates k xx Frequency domain after Fourier transform; For kernel correlation filters, λ is the Fourier transform of the standard response, and λ is the regularization term.

[0015] In one embodiment, the step of placing the filter template onto the initial Hartmann image for correlation filtering or kernel correlation filtering to obtain a response map is as follows:

[0016]

[0017] Where z is the initial Hartmann image; k xz Let x be the cross-correlation kernel function for x and z.

[0018] In one embodiment, the step of traversing and finding the maximum pixel value of each sub-aperture in the sub-apertures corresponding to the plurality of sub-response maps, and storing the coordinate position of the maximum pixel value to obtain a slope matrix specifically includes: traversing and comparing the pixels in the sub-apertures corresponding to each sub-response map to obtain the maximum pixel value, and storing the coordinate position of the maximum pixel value; performing sub-pixel fitting on the coordinate position of the maximum pixel value to obtain a sub-pixel offset; and obtaining the sub-pixel precision coordinate position based on the original pixel and the sub-pixel offset.

[0019] In one embodiment, the formula for sub-pixel fitting is:

[0020] T = 2·I n -I n-1 -I n+1 ;

[0021]

[0022] Among them, I n The pixel value at the coordinates of the maximum value, I n+1 I is the pixel value at the coordinate following the maximum value. n-1 is the pixel value of the coordinate preceding the maximum value, and F is the sub-pixel offset.

[0023] In one embodiment, the sub-pixel precision coordinate position is obtained by combining the original pixel with the sub-pixel offset, using the following formula:

[0024] X′ n =X n +F;

[0025] Where, X′ n For sub-pixel precision coordinates, X n F represents the original pixel position, and F represents the sub-pixel offset.

[0026] In one embodiment, the step of performing Hartmann wavefront reconstruction using the response map and slope matrix to obtain the reconstructed wavefront specifically includes: recovering multiple pieces of information of the wavefront within each sub-aperture using the phase inversion method based on the response map and slope matrix, and obtaining the sub-wavefront corresponding to the sub-response map; and reconstructing the sub-wavefront corresponding to the sub-response map into the entire reconstructed wavefront using a wavefront reconstruction algorithm or splicing method.

[0027] Compared with existing technologies, the advantages and beneficial effects of this invention are as follows: This invention acquires the initial Hartmann image and sub-aperture arrangement detected by a Hartmann wavefront sensor, selects a filter template in the initial Hartmann image, places the filter template into the initial Hartmann image for correlation filtering or kernel correlation filtering operations, and obtains a response map. The response map consists of multiple sub-response maps, each corresponding to a sub-aperture. In the sub-apertures corresponding to the multiple sub-response maps, the maximum pixel value of each sub-aperture is traversed and searched, and the coordinate position of the maximum pixel value is stored to obtain a slope matrix. Hartmann wavefront restoration is performed using the response map and the slope matrix to obtain the restored wavefront. This invention can achieve the transformation from an extended target to a spot image through a single correlation filtering, simplifying the algorithm, improving the calculation speed, and realizing fast wavefront restoration. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating a related Hartmann fast wavefront recovery method in one embodiment;

[0029] Figure 2 This is a schematic diagram comparing the template images before and after windowing in one embodiment;

[0030] Figure 3 This is a schematic diagram comparing the response diagrams before and after windowing in one embodiment;

[0031] Figure 4 This is an example of an equivalent overlay process of sub-images and response maps. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0033] In one embodiment, such as Figure 1 As shown, a correlation Hartmann fast wavefront recovery method is provided, including the following steps:

[0034] Step S101: Obtain the initial Hartmann image and sub-aperture arrangement detected by the Hartmann wavefront sensor, and select a filter template in the initial Hartmann image.

[0035] Specifically, an initial Hartmann image and sub-aperture arrangement are obtained by detecting the Hartmann wavefront sensor. A sub-response map with good detail near the center is selected from the initial Hartmann image as a filtering template, which facilitates subsequent filtering to obtain a more accurate response map.

[0036] The Hartmann wavefront sensor, consisting of a microlens array, matching lenses, and a CCD, is used to detect the wavefront of light. When a light beam is incident on the Hartmann wavefront sensor, the microlens array divides the beam into many tiny sub-apertures. Each portion of the light wave, after passing through the microlens, converges at the focal point of its respective sub-aperture, forming a sub-aperture spot array pattern. When the incident light wave is an ideal plane wave, a set of uniformly distributed focal points will be obtained at the focal point of the microlens array. When the incident light wave has wavefront distortion, the array image obtained at the focal plane of the microlens array will no longer be uniformly distributed, but will be offset from the aforementioned ideal wavefront focal points. This offset is the wavefront slope, and the wavefront phase distribution can be reconstructed based on the wavefront slope using a wavefront reconstruction algorithm.

[0037] Step S102: Place the filter template into the initial Hartman image to perform correlation filtering or kernel correlation filtering operations to obtain a response map. The response map has multiple sub-response maps, and each sub-response map has a sub-aperture.

[0038] Specifically, the initial Hartmann image is equivalent to the superposition of multiple sub-images. The filtering template is placed in the initial Hartmann image for correlation filtering or kernel correlation filtering. The multiple sub-images are filtered separately through the filtering template to obtain the corresponding sub-response maps. All sub-response maps are superimposed to obtain the response map corresponding to the initial Hartmann image. Thus, the initial Hartmann image can be directly filtered through the template image to obtain the final response map, realizing the transformation from an extended image to a spot array image.

[0039] Among them, the correlation filtering algorithm can be MOSSE, DCF, CN, DSST, etc., and the kernel correlation filtering algorithm can be CSK, KCF, BACF, SAMF, etc.

[0040] Step S103: In the sub-apertures corresponding to multiple sub-response maps, traverse and find the maximum pixel value of each sub-aperture, and store the coordinate position of the maximum pixel value to obtain the slope matrix.

[0041] Specifically, among the sub-apertures corresponding to multiple sub-response maps, the maximum pixel value of each sub-aperture is found to obtain the initial slope; by traversing and comparing the pixels in each sub-aperture, the maximum pixel value is obtained, and the coordinate position of the maximum pixel value is stored to obtain a coordinate slope matrix.

[0042] Step S104: Hartmann wavefront reconstruction is performed using the response map and slope matrix to obtain the reconstructed wavefront.

[0043] Specifically, in the initial Hartmann image, each pixel corresponds to an integer coordinate position. However, integer coordinate positions are often inaccurate. To achieve better accuracy, sub-pixel precision coordinates are needed. For example, sub-pixel localization methods can be used to calculate the true location of features in the image, thereby improving the accuracy of the Hartmann slope matrix and making wavefront reconstruction more precise, while also reducing computation time. Therefore, the initial Hartmann image can be reconstructed using wavefront reconstruction methods based on the response map and the slope matrix to obtain the reconstructed wavefront.

[0044] In this embodiment, an initial Hartmann image and sub-aperture arrangement detected by a Hartmann wavefront sensor are acquired. A filter template is selected from the initial Hartmann image. The filter template is then placed into the initial Hartmann image for correlation filtering or kernel correlation filtering to obtain a response map. The response map consists of multiple sub-response maps, each corresponding to a sub-aperture. Among the sub-apertures corresponding to the multiple sub-response maps, the maximum pixel value of each sub-aperture is found through traversal, and the coordinate position of the maximum pixel value is stored to obtain a slope matrix. Hartmann wavefront restoration is performed using the response map and the slope matrix to obtain the restored wavefront. This allows for the transformation of the extended target into a spot image through a single correlation filter, simplifying the algorithm, improving the computation speed, and achieving rapid wavefront restoration.

[0045] Specifically, step S101 includes: selecting a sub-image with clear pixels as a filtering template at the center position of the initial Hartman image.

[0046] Specifically, since the sub-images at the edges of the Hartman image are easily affected by edge noise, resulting in an unsatisfactory response map after filtering the edge sub-images, a sub-image that is close to the center, has clear pixels, and better details can be selected from the Hartman image as a filtering template to facilitate subsequent filtering and obtain an accurate response map.

[0047] The process, following step S101 and preceding step S102, further includes: truncating the signal of the template image using a truncation function to obtain a filtered template, wherein the formula for the truncation function is as follows:

[0048]

[0049] Where m and n represent the coordinates of the window function, and M and N represent the size of the template, respectively; the pixel gray values ​​of the filter template are normalized to an image with a mean of 0 and a variance of 1; the normalized filter template is multiplied by a cosine window to reduce the values ​​of the image edges to 0, thus obtaining the windowed filter template.

[0050] like Figure 2 As shown, these are the template images before and after windowing, such as... Figure 3The image shows the response maps before and after windowing. To reduce spectral energy leakage, different truncation functions can be used to truncate the signal; these functions are called window functions, or simply windows. Windowing the template image reduces the influence of its edges, resulting in a better response. During windowing, the pixel grayscale values ​​of the template image are first normalized to a mean of 0 and a variance of 1. This image is then multiplied by a cosine window, reducing the edge values ​​to 0. This allows more focus to be placed on the center of the target, reducing the impact of edges on the output and improving the algorithm's accuracy.

[0051] After obtaining the windowed filter template, the process also includes: generating a correlation filter or kernel correlation filter based on the windowed filter module, using the following formula:

[0052]

[0053] Where x is the template image or the template after windowing, and k xx Let x be the autocorrelation kernel function, and the kernel function k can be either a Gaussian kernel function or a linear kernel function; Indicates k xx Frequency domain after Fourier transform; For kernel correlation filters, λ is the Fourier transform of the standard response, and λ is the regularization term.

[0054] The formula for step S102 is as follows:

[0055]

[0056] Where z is the initial Hartmann image; k xz Let x be the cross-correlation kernel function for x and z.

[0057] Specifically, such as Figure 4 As shown, the initial Hartmann image is equivalent to the superposition of n sub-images. Then, the n sub-images are filtered separately by the windowed filter template to obtain the corresponding sub-response maps. All sub-response maps are superimposed to obtain the response map corresponding to the initial Hartmann image. The transformation from the extended image to the spot array image is achieved through a single correlation filter, which simplifies the algorithm and improves the computing speed.

[0058] Specifically, step S103 includes: traversing and comparing the pixels of each sub-aperture corresponding to each sub-response map to obtain the maximum pixel value, and storing the coordinate position of the maximum pixel value; performing sub-pixel fitting on the coordinate position of the maximum pixel value to obtain the sub-pixel offset; and obtaining the sub-pixel precision coordinate position based on the original pixel and the sub-pixel offset.

[0059] Specifically, each sub-response map corresponds to a sub-aperture. Pixels within each sub-aperture are iterated and compared to obtain the maximum pixel value in a single sub-response map, and the coordinates of this maximum pixel value are stored to obtain a slope. All sub-response maps in the initial Hartman image are iterated and compared to obtain the maximum pixel values ​​in all sub-response maps, and the corresponding coordinates are stored to obtain a coordinate slope matrix. Sub-pixel fitting is performed on the coordinates of the maximum pixel values ​​to obtain sub-pixel offsets. Sub-pixel precision coordinate positions are obtained by combining the original pixel values ​​with the sub-pixel offsets.

[0060] The formula for subpixel fitting is:

[0061] T = 2·I n -I n-1 -I n+1 ;

[0062]

[0063] Among them, I n The pixel value at the coordinates of the maximum value, I n+1 I is the pixel value at the coordinate following the maximum value. n-1 is the pixel value of the coordinate preceding the maximum value, and F is the sub-pixel offset.

[0064] The sub-pixel precision coordinate position is obtained by combining the original pixel with the sub-pixel offset, using the following formula:

[0065] X′ n =X n +F;

[0066] Where, X′ n X represents the pixel value at a sub-pixel precision coordinate position. n F represents the original pixel position, and F represents the sub-pixel offset.

[0067] Specifically, since each pixel corresponds to an integer coordinate position, but integer coordinate positions are not accurate enough in many cases, in order to improve their accuracy, a subpixel fitting method can be used to calculate the true position of the feature in the image. Based on the subpixel offset and the original pixel, the pixel value of the subpixel precision coordinate position is calculated and obtained, thereby obtaining the subpixel precision coordinate position of the maximum pixel value. This makes the slope matrix obtained by the relevant Hartmann more accurate, improves the accuracy of wavefront reconstruction, and also reduces the computation time.

[0068] Specifically, step S104 includes: based on the response map and slope matrix, recovering multiple information of the wavefront within each sub-aperture using the phase inversion method to obtain the sub-wavefront corresponding to the sub-response map; and reconstructing the sub-wavefront corresponding to the sub-response map into the entire restored wavefront using a wavefront restoration algorithm or splicing method.

[0069] Specifically, based on the slopes corresponding to the obtained sub-response maps, the wavefront can be reconstructed using the Zernike mode method by taking the slopes corresponding to all sub-apertures. This process yields all wavefront aberrations of the initial Hartman image. Based on all wavefront aberrations and the sub-aperture arrangement, the initial Hartman image is segmented to obtain the restoration matrix. The Zernike coefficients are obtained by multiplying the sub-aperture slope matrix and the restoration matrix. The restored wavefront is then obtained by weighted superposition of the Zernike coefficients and all wavefront aberrations.

[0070] Furthermore, multiple detailed information of the wavefront within each sub-aperture, such as aberration information and / or curvature information, can be recovered using phase inversion algorithms. Based on these detailed information, the sub-wavefront within the corresponding Hartmann wavefront sensor sub-aperture is obtained. Using the acquired sub-wavefronts, a wavefront stitching method is employed, starting with the sub-aperture located at a vertices position, such as the upper right corner, and sequentially connecting the corresponding sub-wavefronts of each sub-aperture to reconstruct the wavefront aberration of the entire initial Hartmann image. Based on the reconstructed wavefront aberration and the initial Hartmann image, the restored wavefront is obtained.

[0071] In one embodiment, a spatial domain algorithm can also be used, treating the image as a matrix, selecting a suitable template image in the Hartmann image, and comparing pixels of the template image with those of the real-time updated Hartmann image. The position of the target in the Hartmann image is the one with the highest similarity.

[0072] In one embodiment, the SAD (Sum of Absolute Differences, Image Matching Algorithm) algorithm can also be used. By constructing a window, similar to a convolution kernel, the window is used to cover the left side of the image, and all pixels within the covered area are selected. Similarly, the window is used to cover the right side of the image, and the covered pixels are selected. The left covered area is subtracted from the right covered area, and the sum of the absolute values ​​of all pixel differences is calculated. The window of the right image is moved, and the above actions are repeated to find the window with the smallest SAD value within the covered area, which is the best matching pixel block of the left image.

[0073] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for rapid wavefront reconstruction of correlated Hartmann waves, characterized in that, Includes the following steps: Acquire the initial Hartmann image and sub-aperture arrangement detected by the Hartmann wavefront sensor, and select a filter template in the initial Hartmann image; A truncation function is used to truncate the signal of the template image to obtain the filtered template; The formula for the truncation function is as follows: Where m and n represent the coordinates of the window function, and M and N represent the size of the template, respectively; The pixel grayscale values ​​of the filter template are normalized to an image with a mean of 0 and a variance of 1; Multiply the normalized filter template by a cosine window to reduce the value of the image edge to 0, and obtain the windowed filter template; The filter template is placed into the initial Hartmann image to perform kernel correlation filtering to obtain a response map. The response map corresponds to multiple sub-response maps, and the sub-response maps correspond to sub-apertures. In the sub-apertures corresponding to the multiple sub-response maps, the maximum pixel value of each sub-aperture is found through traversal, and the coordinate position of the maximum pixel value is stored to obtain the slope matrix. This includes: traversing and comparing the pixels of each sub-aperture corresponding to the sub-response map to obtain the maximum pixel value, and storing the coordinate position of the maximum pixel value; performing sub-pixel fitting on the coordinate position of the maximum pixel value to obtain the sub-pixel offset; and obtaining the sub-pixel precision coordinate position based on the original pixel and the sub-pixel offset. Hartmann wavefront reconstruction is performed using the response map and slope matrix to obtain the reconstructed wavefront.

2. The correlated Hartmann fast wavefront recovery method according to claim 1, characterized in that, The step of selecting a filter template in the initial Hartmann image specifically includes: At the center of the initial Hartmann image, a sub-image with clear pixels is selected as the filtering template.

3. The correlated Hartmann fast wavefront recovery method according to claim 1, characterized in that, After multiplying the normalized filter template by a cosine window to reduce the image edge values ​​to 0 and obtaining the windowed filter template, the process further includes: The kernel correlation filter is generated based on the windowed filter template, and the formula is as follows: Where x is the template image or the template after windowing, and k xx Let x be the autocorrelation kernel function, and the kernel function k can be either a Gaussian kernel function or a linear kernel function; Indicates k xx Frequency domain after Fourier transform; For kernel correlation filters, λ is the Fourier transform of the standard response, and λ is the regularization term.

4. The correlated Hartmann fast wavefront recovery method according to claim 3, characterized in that, The filter template is placed into the initial Hartmann image for kernel correlation filtering to obtain the response map, as shown in the formula: Where z is the initial Hartmann image; k xz Let x and z be the cross-correlation kernel function. Indicates k xz Frequency domain after Fourier transform.

5. The correlated Hartmann fast wavefront recovery method according to claim 1, characterized in that, The formula for subpixel fitting is: T=2·I n -I n-1 -I n+1 ; Among them, I n The pixel value at the coordinates of the maximum value, I n+1 I is the pixel value at the coordinate following the maximum value. n-1 is the pixel value of the coordinate preceding the maximum value, and F is the sub-pixel offset.

6. The correlated Hartmann fast wavefront recovery method according to claim 5, characterized in that, The sub-pixel precision coordinate position is obtained by combining the original pixel with the sub-pixel offset, using the following formula: X′ n =X n +F; Where, X′ n For sub-pixel precision coordinates, X n F represents the original pixel position, and F represents the sub-pixel offset.

7. The correlated Hartmann fast wavefront recovery method according to claim 1, characterized in that, The step of performing Hartmann wavefront reconstruction using the response map and slope matrix to obtain the reconstructed wavefront specifically includes: Based on the response map and slope matrix, multiple information of the wavefront within each sub-aperture is recovered by phase inversion method, and the sub-wavefront corresponding to the sub-response map is obtained. The sub-wavefronts corresponding to the sub-response maps are reconstructed into the entire restored wavefront using wavefront restoration algorithms or splicing methods.

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