A method for compressively encoding a computer-generated hologram based on constructing tangent lines

Abstract

This invention discloses a computational hologram compression coding method based on tangent construction. It extracts the phase contour lines of the computational hologram as the etched fringe boundaries; adaptively selects the start and end points and matches ascending or descending scanning directions according to different fringe spatial topologies; constructs a one-sided auxiliary error boundary based on the overall distribution characteristics of the phase gradient field and a preset coding error precision; and uses a tangent compression algorithm to solve for the tangent points on the auxiliary error boundary and directly generate a sparse discrete point sequence, completing the compressed coding of the fringe boundaries. This invention eliminates the need for pre-dense sampling of the fringe boundaries, obtaining discrete points of the fringe boundaries through tangent sampling constructed from the auxiliary error boundaries, achieving compressed coding and coding error control, and significantly improving coding efficiency while ensuring coding accuracy.

Description

Technical Field

[0001] This invention relates to the fields of optical inspection and advanced manufacturing technology, specifically to a computational hologram compression coding method based on constructed tangents. Background Technology

[0002] Computational holograms (CGHs) are diffractive optical elements used for high-precision detection of aspherical surfaces. They compensate for wavefront aberrations of the aspherical surface under test by designing a specific phase distribution at the compensation phase plane, achieving null-position interferometry detection. In the design phase, a continuous phase distribution function is obtained. This phase distribution is then converted into a fringe distribution using specific contour lines of the phase function as etching fringe boundaries, and finally encoded into layout data recognizable by the processing equipment.

[0003] Since the phase distribution is continuous, and processing equipment can only read discrete point coordinate data, a smooth fringe boundary curve is usually approximated by a polygonal contour formed by a series of discrete points in engineering. The sampling density of the discrete points of the fringe boundary directly determines the accuracy of the representation of the ideal boundary, and the two are directly proportional. For CGH substrates with conventional diameters of tens to hundreds of millimeters, if uniform discrete sampling is performed with micrometer-level steps, the amount of encoded data obtained will be extremely large, exceeding the data reading limit of the processing machine and causing excessively long encoding calculation time, seriously affecting engineering efficiency. Therefore, effectively compressing the amount of encoded data while ensuring a certain encoding accuracy is a key technical issue in CGH processing data preparation.

[0004] To address the aforementioned issues, existing literature has proposed various compression coding schemes. Li Chunqi et al. proposed a method using circular arcs as primitives to fit discrete coordinates. First, they obtain a large number of discrete points on the etched stripe boundary using traditional binary encoding. Then, they fit circular arcs to these discrete points in each local region, replacing the coordinate information of a large number of discrete points with the arc parameters. Wang Rumo, Gao Qixiang et al. proposed an efficient compression coding method for computational holograms. This method also first uses conventional coding methods to obtain a large number of discrete sampling points on the stripe boundary. Then, they set a thinning threshold and use an iterative Douglas-Peucker algorithm to continuously check and segment the maximum distance from the sampling points to the connecting lines until the maximum distance of each segment is less than the threshold, thus selecting some key points from a large number of discrete points to represent the stripe boundary. Both of these methods rely on conventional coding methods to pre-obtain a large number of discrete sampling points, and then post-process these dense point sets to extract a small number of effective points. The entire process still includes a dense sampling step, resulting in significant computational and storage overhead.

[0005] In the fabrication of large-aperture off-axis aspherical optical components, accurate detection and feedback correction of surface shape accuracy are crucial for achieving high-precision manufacturing. Computational holograms (CGHs), as the core diffractive optical element for null-interference detection, are used to compare the deviation between the actual processed surface shape and the ideal surface shape, thereby guiding subsequent processing steps such as polishing or ion beam shaping. The quality of the etching fringe coding of the CGH directly determines the accuracy of detecting surface shape deviations, thus affecting the closed-loop control level of the entire aspherical manufacturing process. With the increasing demand for high-precision large-aperture asphericals in fields such as space optics and lithography objectives, the speed and manufacturability of CGH coding have become one of the bottlenecks restricting the efficiency of advanced manufacturing. Therefore, achieving efficient compression while ensuring a certain level of coding accuracy is a crucial technical issue supporting the high-precision fabrication of large-aperture asphericals in advanced manufacturing. Summary of the Invention

[0006] To address the technical problem that existing computational hologram compression coding methods rely on traditional scanning methods for dense and uniform sampling of etched fringe boundaries, resulting in long coding times and large amounts of pre-stored data, making it difficult to meet the real-time requirements of high-efficiency and high-precision surface shape detection in advanced manufacturing fields for large-diameter aspherical surface processing, this invention provides a computational hologram compression coding method based on constructed tangents. This method is used to convert the designed phase distribution into etched fringe processing pattern data to manufacture holographic detection elements for detecting processed surface shapes and accurately guiding the manufacturing of high-precision aspherical optical elements.

[0007] The specific method includes the following steps:

[0008] S1: Obtain the phase distribution function of the hologram and set the boundary function for extracting etching fringes;

[0009] S2: Based on the topological morphology of the stripe space, an adaptive start and end point coordinate information acquisition method is used to determine the start and end point coordinate information of the stripe boundary line of each sub-region;

[0010] S3: Based on the overall distribution characteristics of the gradient field in the effective region of the phase function and the preset coding error accuracy, a preset phase error is superimposed on the target phase constant corresponding to the extracted etching stripe boundary function to construct a one-sided auxiliary error boundary.

[0011] S4: Using the tangent compression algorithm, under the premise of limiting the encoding error, by solving the tangent contact point on the auxiliary error boundary and the encoded data point on the ideal equiphase line, a sparse discrete point column is directly generated to complete the compressed encoding of the stripe discrete sampling; the tangent compression algorithm does not require pre-dense uniform sampling of the stripe boundary.

[0012] Furthermore, based on the preset stripe order n iThe corresponding target phase constant is determined, and the equiphase lines corresponding to each target phase constant are extracted as the boundaries of the etching stripes to be compressed.

[0013] Furthermore, the etched stripes are divided. For stripes with inflection points, the stripe boundary is divided into several sub-segments at each inflection point, so that the stripe boundary in each sub-segment remains purely concave or purely convex. For stripes without inflection points, they are directly treated as a sub-region stripe.

[0014] Furthermore, the start and end coordinates of the fringe boundary lines of each sub-region and the traversal scanning direction of the tangent points on the auxiliary error boundary are determined, and a classification adaptive collaborative configuration strategy based on the fringe spatial topology is adopted:

[0015] Based on the spatial distribution area and boundary closure properties of the current sub-region stripes within the effective etching boundary of the computational hologram, the stripes are divided into several topological morphology categories. For different topological morphology categories, corresponding start and end point selection rules are adopted, and a unique matching ascending or descending scanning direction is bound to the selected start and end point intervals.

[0016] The spatial distribution area includes at least: distributed only in the lower half of the region, and spanning both the upper and lower halves of the region; the boundary closure attributes include: non-closed circular arc shape and closed elliptical shape;

[0017] The classification adaptive collaborative configuration strategy specifically includes:

[0018] (a) For stripes that are distributed only in the lower half of the region and are non-closed: take the leftmost and rightmost endpoints along the X direction in the lower half of the region as the start and end points, and bind an ascending scan within the interval between the start and end points;

[0019] (b) For stripes that span the upper and lower halves and are non-closed, and whose absolute X coordinate of the starting point of the upper half is less than that of the starting point of the lower half: take the extreme endpoints of the upper half along the X direction and the extreme endpoints of the lower half along the X direction as independent starting and ending points of their respective halves, and bind descending scans in the upper half and ascending scans in the lower half.

[0020] (c) For stripes that span the upper and lower halves and are non-closed, with the absolute value of the X coordinate of the starting point of the upper half being greater than that of the starting point of the lower half: First, a trial advance is made using the common starting and ending points. If the number of tangent points generated is less than the preset threshold, the corrected starting and ending points are searched again inside the boundary of the upper half and a descending scan is performed using the corrected starting and ending points. At the same time, the original starting and ending points of the lower half are retained and an ascending scan is performed, so that the node sequences generated in the upper and lower halves are spatially complementary and connected.

[0021] (d) For stripes that span the upper and lower halves and are closed: obtain the start and end points of the upper half and the lower half respectively, select the one with the larger absolute value of the X coordinate as the global start point and global end point, use the range of X coordinates corresponding to the global start point and global end point as the search interval, and perform descending scan and ascending scan in the search interval to make the two sequences merge to form a complete closed boundary node chain.

[0022] (e) For stripes that are only distributed in the upper half of the region and are closed: take the extreme endpoints along the X direction in the upper half of the region as the start and end points, and perform descending and ascending scans in the interval between the start and end points, so that the two sequences are merged to form a complete closed boundary node chain.

[0023] The ascending order scan refers to progressing point by point from the lower limit of the current search interval to the upper limit to solve for the cutting contact point; the descending order scan refers to progressing point by point from the upper limit of the current search interval to the lower limit to solve for the cutting contact point.

[0024] The classification-adaptive collaborative configuration strategy ensures that the advancing direction of the contact point sequence along the stripe boundary remains singular in each sub-region and consistent with the global iteration direction of the tangent compression algorithm, thereby eliminating the multi-valued ambiguity in root solution and node entanglement conflicts caused by multiple intersections of a single phase boundary at a single scan coordinate.

[0025] Furthermore, for the upper boundary stripes, the compression encoding starting point A(x) A y A ) and the contact point B(x) B y B The normal vector at point B is () , (Conditions met:)

[0026] ;

[0027] In the formula , Phase function for auxiliary error boundary Partial derivatives with respect to x and y;

[0028] For the contact point B(x) B y B )satisfy:

[0029] ;

[0030] Solve for the contact point B(x) B y B From this, we can obtain the equation of the tangent line:

[0031] ;

[0032] Combining the tangent equation and the curve on the ideal etching fringe Solve the system of equations to find the two intersection points of the tangent line and the curve. One of the intersection points should be A(x). A y A Excluding that point, the other intersection point is one of the valid solutions for solving the etching boundary position using the error boundary tangent method, denoted as point C(x). C y C ).

[0033] Furthermore, each etched stripe includes an upper boundary line and a lower boundary line, and the upper and lower boundary lines use the same compression encoding method.

[0034] In summary, the present invention has the following beneficial effects:

[0035] 1. Direct sparse coding is achieved. Unlike existing methods that require pre-dense sampling and then thinning, this invention directly generates a sparse point sequence that meets the accuracy requirements by constructing tangents and iteratively obtaining discrete points. This eliminates the need for generating, storing, and post-processing a large number of discrete points, significantly reducing computation time and storage overhead, and making it possible to quickly encode large-aperture, high-stripe-density computational holograms.

[0036] 2. Error parameters are explicitly controllable, based on preset phase error. Construct auxiliary error boundaries to directly constrain the upper limit of the geometric approximation error of each step of tangent construction. This can be flexibly set in engineering. To achieve the optimal balance between the amount of encoded data and the accuracy of reconstruction.

[0037] 3. The encoded data generated by this method can be directly used in manufacturing equipment such as laser direct writing to output standard GDSII format layout files, providing technical support for the rapid preparation of large-aperture, high-density CGH etching stripes, thereby ensuring the timeliness and accuracy of surface deviation detection during aspherical processing, and serving the advanced manufacturing closed-loop process of high-precision optical components. Attached Figure Description

[0038] Figure 1 This is a flowchart of the computational hologram compression encoding method for constructing tangents according to the present invention.

[0039] Figure 2 This is a schematic diagram of the stripe type in the selected embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram illustrating the principle of the tangent compression algorithm of this invention.

[0041] Figure 4 This is a schematic diagram of the coding error solving method described in this invention.

[0042] Figure 5 For order n i=-1562~922 encoded discrete points construct the overall schematic diagram of the stripe boundary.

[0043] Figure 6 For order n i =923~2345 coded discrete points to construct the overall schematic diagram of the stripe boundary.

[0044] Figure 7 For order n i =-1562~922 encoded discrete points to construct a locally magnified image of the stripe boundary.

[0045] Figure 8 For order n i =923~2345 coded discrete points to construct a locally enlarged image of the stripe boundary.

[0046] Figure 9 A schematic diagram of the overall layout drawn in KLayout software to represent the complete encoded data.

[0047] Figure 10 A magnified view of the layout drawn in KLayout software, showing the complete encoded data. Detailed Implementation

[0048] To more accurately describe the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0049] Example 1:

[0050] This embodiment provides a computational hologram compression coding method based on tangent construction, the specific implementation steps of which are as follows: Figure 1 As shown:

[0051] S1: Obtain the phase distribution function of the hologram and set the boundary function for extracting the etching stripes.

[0052] In phase The CGH phase is quantized periodically to obtain the total number of periodic fringes n, with a preset fringe duty cycle of 50%.

[0053] The phase condition is satisfied at the upper and lower boundaries of the etched stripes to be compressed: ;

[0054] .

[0055] in The formula for the phase distribution at the upper boundary of the fringe is as follows: The formula for the phase distribution at the lower boundary of the fringes is as follows: and All are expressed by 37 Zernike Feinge phase polynomials, which can be directly read by optical design software after the optical design stage is completed. To classify stripe levels.

[0056] S2: Based on the topological morphology of the stripe space, an adaptive start and end point coordinate information acquisition method is used to determine the start and end point coordinate information of the stripe boundary lines of each sub-region.

[0057] S3: Based on the overall distribution characteristics of the gradient field in the effective region of the phase function and the preset coding error accuracy, a preset phase error is superimposed on the target phase constant corresponding to the extracted etching stripe boundary function to construct a one-sided auxiliary error boundary.

[0058] S4: Using the tangent compression algorithm, under the premise of limiting the encoding error, by solving the tangent contact point on the auxiliary error boundary and the encoded data point on the ideal equiphase line, a sparse discrete point column is directly generated to complete the compressed encoding of the stripe discrete sampling; the tangent compression algorithm does not require pre-dense uniform sampling of the stripe boundary.

[0059] For stripes that are distributed only in the lower half of the region and are non-closed: take the leftmost and rightmost endpoints along the X direction in the lower half of the region as the start and end points, and bind an ascending scan within the interval between the start and end points.

[0060] For stripes that span the upper and lower halves and are non-closed, and whose absolute X-coordinate of the starting point of the upper half is less than that of the starting point of the lower half: take the extreme endpoints of the upper half along the X direction and the extreme endpoints of the lower half along the X direction as independent starting and ending points of their respective halves, and bind descending scans in the upper half and ascending scans in the lower half.

[0061] For stripes that span the upper and lower halves and are non-closed, with the absolute value of the X-coordinate of the starting point in the upper half greater than that in the lower half: First, a trial advance is made using a common starting and ending point. If the number of tangent points generated is less than a preset threshold, the corrected starting and ending points are searched again inside the boundary of the upper half and a descending scan is performed using the corrected starting and ending points. At the same time, the original starting and ending points of the lower half are retained and an ascending scan is performed, so that the node sequences generated in the upper and lower halves are spatially complementary and connected.

[0062] For stripes that span the upper and lower halves and are closed: obtain the start and end points of the upper half and the lower half respectively, select the one with the larger absolute value of the X coordinate as the global start point and global end point, use the range of X coordinates corresponding to the global start point and global end point as the search interval, and perform descending scan and ascending scan in sequence within the search interval so that the two sequences are merged to form a complete closed boundary node chain.

[0063] For stripes that are only distributed in the upper half of the region and are closed in shape: take the extreme endpoints along the X direction in the upper half of the region as the start and end points, and perform descending and ascending scans in the interval between the start and end points, so that the two sequences are merged to form a complete closed boundary node chain.

[0064] For the upper boundary stripe, the compression encoding starts at A(x) A y A ) and the contact point B(x) B y B The normal vector at point B is Conditions met:

[0065] ;

[0066] In the formula , Phase function for auxiliary error boundary Partial derivatives with respect to x and y;

[0067] For the contact point B(x) B y B )satisfy:

[0068] ;

[0069] Solve for the contact point B(x) B y B From this, we can obtain the equation of the tangent line:

[0070] ;

[0071] Combining the tangent equation and the curve on the ideal etching fringe Solve the system of equations to find the two intersection points of the tangent line and the curve. One of the intersection points should be A(x). A y A Excluding that point, the other intersection point is one of the valid solutions for solving the etching boundary position using the error boundary tangent method, denoted as point C(x). C y C ).

[0072] Each etched stripe includes an upper boundary line and a lower boundary line, and the upper and lower boundary lines use the same compression encoding method.

[0073] Example 2:

[0074] The CGH principal region phase diagram shown in this embodiment is used to test a large-aperture off-axis parabolic mirror. The off-axis parabolic mirror under test has an aperture of 835 mm, an off-axis distance of 2600 mm, and a radius of curvature of -12000 mm. The total number of periodic fringes in the CGH principal region phase distribution is n=3907, and the fringe order is n... i Divide into n i=-1562~2345, minimum fringe spacing is about 4.26um, phase region range is elliptical, its short semi-axis length is about 44mm, and its long semi-axis length is about 63mm.

[0075] Various stripe types such as Figure 2 As shown, types 1, 2, and 3 stripes are non-closed monotonic arcs, while types 4 and 5 stripes are closed arcs. None of them have inflection points, so there is no need to divide them into sub-region stripes.

[0076] The aforementioned type division has defined intervals. Within each fringe definition interval, discrete scanning is performed along both the positive and negative x-axis directions. Sign change detection and bisection / interpolation (fzero) methods are used to solve the problem. The root is obtained to obtain the encoding start and end points of the stripe boundaries within each defined interval.

[0077] The start and end points of the obtained fringes are the leftmost and rightmost endpoints in the X-direction within the defined interval of the fringe. The traversal scanning direction of the contact point is generally clockwise and counterclockwise along the x-direction from the start point to the end point, and can be further divided according to the fringe type:

[0078] Stripe Type 1: The phase region is divided into an elliptical region by the x-axis, into upper and lower halves. Within the constraints of the lower half, ascending compression is performed on the stripe boundaries from the start point to the end point.

[0079] Fringe Type 2: The phase region is divided into an elliptical region by the x-axis, into upper and lower halves. Within the upper half, descending compression is performed on the fringe boundaries from the start to the end. Within the lower half, ascending compression is performed on the fringe boundaries from the start to the end.

[0080] Stripe Type 3: The elliptical phase region is divided into upper and lower halves by the line connecting the start and end points of the stripes. Within the upper half, the stripe boundaries in the upper half are compressed in descending order from the start to the end. Within the lower half, the stripe boundaries in the lower half are compressed in ascending order from the start to the end.

[0081] Stripe Type 4: Within an elliptical phase region, ascending and descending compression are performed on the stripe boundaries from the start to the end point.

[0082] Stripe Type 5: Within an elliptical phase region, ascending and descending compression are performed on the stripe boundaries from the start to the end point.

[0083] Ascending and descending order are core parameters controlling the tangent compression scan direction; they determine the "winding direction" of the node sequence as it advances along the equiphase line during the tangent point determination process. When determining the tangent point, given the x-coordinate and the current reference point A(x...A ,y A Under the condition of ), solve for the phase that satisfies the error boundary. The coordinates of the points, in ascending order, will be in the y A -5 increases linearly to y A +5 means scanning upwards from the bottom. It will prioritize finding the root below the current point and output a smaller y-value; the descending order approach will output a smaller y-value. A +5 linearly decreases to y A -5 This means scanning downwards from top to bottom. It prioritizes finding roots higher than the current point and outputs a larger y-value. Since the tangent point B is also used to calculate the tangent direction and find the ideal equiphase line C... ideal The intersection point C, with its ascending / descending order, effectively controls the macroscopic direction of the entire compressed sequence. By combining the ascending / descending method with the start and end points of different stripe types to make corresponding decisions, we ensure that the node sequences generated in the upper and lower halves of the region are spatially connected or cover each other, avoiding entanglement and conflict.

[0084] The equation of an ideal equiphase line is: The rules for constructing the auxiliary error boundary are as follows: based on the phase function... The overall distribution characteristics of the gradient field within the effective region are used to determine the offset sign of the auxiliary error boundary, ensuring that the auxiliary error boundary is always located on one side of the curvature center of the ideal equiphase line in space. In this embodiment, the phase function exhibits a monotonically varying distribution characteristic from the origin outwards; therefore, a uniform selection is used. As an auxiliary error boundary, this boundary is spatially closer to the origin than the ideal boundary. Regardless of whether the sub-region fringes are locally concave or convex, the tangent point can always fall correctly inside the ideal boundary, thus ensuring that the next compressed discrete point can be effectively searched along the tangent direction.

[0085] A schematic diagram of the tangent compression algorithm is shown below. Figure 3 As shown. Solve for the tangent point B on the auxiliary error boundary, such that the line AB connecting the compression coding starting point A and the tangent point B is tangent to the auxiliary error boundary curve at the tangent point B. Search for the next discrete point C on the ideal isophase line along the direction of the tangent line AB; use the next discrete point C as the new compression coding starting point, and repeat the solution for new tangent points and the next discrete point on the ideal isophase line until the endpoint is reached, completing the compression coding of this stripe boundary segment. Iterate the stripe level n times. i This completes the compressed encoding of all stripe boundaries.

[0086] In this invention, the specific solution method for the contact point B is as follows: taking the currently encoded point A as the starting point, scanning is performed along the positive x direction with a set step size; for each scanning position x, on the error equiphase line... The corresponding coordinates are determined by detecting the sign change in the y-direction and numerical root calculation to obtain candidate contact points; the displacement vector AB and phase gradient g at the candidate point are calculated. B The absolute value of the inner product is used as the residual, and the minimum residual and its corresponding point are dynamically recorded during the scanning process. The candidate point corresponding to the minimum residual is selected as the contact point B.

[0087] The computational hologram compression coding method based on constructed tangents proposed in this invention has a coding accuracy that directly depends on the accuracy of the tangent point calculation. For example... Figure 4 As shown, the accuracy of the contact point solution is initially quantified using the normal deviation distance d: during the search for the contact point B along the error equiphase line, the phase gradient g of the displacement vector AB at the contact point is calculated using the currently encoded point A as the reference. B The projected length in the direction, i.e.:

[0088] .

[0089] The deviation distance d is essentially the distance between the desired contact point B and the ideal contact point (satisfying AB perpendicular to g). B The normal geometric offset of the point is calculated; the smaller the value, the more accurate the solution of the tangent point, and the more accurate the constructed tangent direction. This ensures the accuracy of subsequent searches for intersection points and fringe boundary path compression along the tangent direction, providing an effective quantitative control basis for the local accuracy of holographic compression coding. d serves as an engineering approximation index for determining the minimum residual during the tangent point solution process. This error value is greater than the theoretical error. When the wavefront aberration introduced by d is lower than the target error threshold, it indicates that the theoretical error is also lower than the target error. This method can be used to quickly evaluate the accuracy of the coding method.

[0090] It should be noted that 'd', as an engineering approximation index used to determine the minimum residual during the tangent point solution process, is calculated as the projection length of vector Ab at the actual tangent point b along the phase gradient direction, a value greater than the theoretical error. Therefore, when the wavelet aberration introduced by 'd' is lower than the preset target error threshold, it can be determined that the theoretical error must also be lower than that threshold. Based on this, 'd' can be used as a rapid criterion for evaluating coding accuracy, eliminating the need for precise error calculation in each iteration, thus balancing coding accuracy and computational efficiency.

[0091] When the wavelet aberration introduced by d is lower than the target error threshold, the precise coding error needs to be solved further to verify the coding accuracy. The cause of the precise coding error is as follows: the actual tangent point b has a slight offset relative to the theoretical tangent point B, causing the line segment Ab constructed by the currently coded point A and the actual tangent point b to not be precisely tangent to the preset error boundary, but rather to be in an intersecting state. The maximum positional deviation caused by this intersection state along the normal direction at the theoretical tangent point B is the precise coding error D. max .

[0092] Since the theoretical tangent point B is difficult to solve directly without error, and the X-coordinate step size of the tangent contact point scanning sampling is 2μm, the deviation between the actual X-coordinate of the tangent contact point b and the theoretical X-coordinate of the tangent point B is less than 1μm. Therefore, we can set xB = xb + 0.001mm, and let x... B Substituting into the auxiliary error boundary equation, the corresponding y can be obtained. B This allows us to determine the coordinates of the theoretical tangency point B. At this point, the coordinates of points A, B, and b are all known. Based on vector geometry, we can use the dot product formula to solve for the angle θ between vectors Ab and AB.

[0093] Then, the exact solution is obtained. .

[0094] Phase boundary error Set to 0.000159 The error accuracy meets the design requirements. In this embodiment of the invention, the CGH main region stripes are compressed and encoded using the method described in this invention. The tangent compression encoding algorithm obtains the coordinate information of discrete points on each stripe boundary. A schematic diagram of the adjacent encoded discrete polygons representing the stripe boundaries is shown below. Figure 5 , Figure 6 As shown in the figure. The results indicate that the coordinates of the discrete points at the boundary of each fringe obtained by tangent compression coding are all within the phase region of the CGH main region and do not exceed the boundary limits. Further examination of the details of the local coded discrete points of each fringe, as shown... Figure 7 , Figure 8 As shown, the discrete points do not overlap, and the lines connecting adjacent discrete points do not overlap or misalign, thus accurately depicting the fringe shape. Random sampling was performed on all fringe levels. A systematic test and statistical analysis were conducted on 652,990 contact points covering the entire fringe level range (n from -1562 to 2345). The maximum positional deviation D of each contact point was determined. max The weighted average is 1.91 × 10⁻⁶. -7 mm, introducing wavelet aberration of 0.0000119λ, the total coding error is approximately 1.7 × 10⁻⁶. -4 λ provides a reliable accuracy guarantee for the compressed encoding of high-precision computational holograms.

[0095] Computer-generated holograms (CGHs) typically require electron beam lithography or laser direct writing to fabricate precise stepped or continuous relief structures on a substrate. This micro-nano fabrication characteristic dictates that pixel-based files such as BMP and PNG cannot be used, as these formats cannot define continuous physical boundaries at the sub-micron level. The GDSII format is specifically designed for integrated circuits and micro-nano structure layouts. It matches the vector scanning method used by direct writing devices—that is, the electron beam or laser beam does not fill pixels line by line, but rather follows the boundary path of the graphic, defining closed polygons through a series of precise vertex coordinates. This corresponds precisely to the curved phase step contours in CGHs.

[0096] A data reading script was written using the layout software KLayout to sequentially read the discrete point coordinates of each stripe boundary output by the tangent compression encoding algorithm, and connect these points one by one into a closed polygon according to the original spatial order, so as to accurately represent the contour shape of each stripe boundary, such as... Figure 9 , Figure 10 As shown, the drawn polygon boundary lines are continuous and unbroken, with no overlap or gaps between adjacent polygons, and perfectly match the original elliptical calculation area, indicating that the layout drawing result is correct. All striped boundary polygons are output as a GDSII format processing file, with a file size of approximately 580MB, which does not exceed the maximum data capacity allowed by conventional photolithography and mask processing equipment, and can be loaded and processed normally.

[0097] The encoding results show that the fringe order n within the full aperture of the CGH main region phase distribution shown in the embodiment of the present invention is... i Encoding is performed for values ​​from -1562 to 2345. Using the encoding method of this invention, existing computers can encode levels n... i Encoding the boundary of stripes from -1562 to 2345 to obtain the coordinates of all discrete points took 255.8 minutes, approximately 4.26 hours. If the entire range of order n is then encoded... i For values ​​from -1562 to 2345, the traditional uniform scanning encoding method with a step size of 2μm is used, and the total time is estimated to be at least 70 hours. Therefore, the method of this invention improves the encoding efficiency by more than 16 times compared to the traditional uniform scanning encoding method, significantly shortens the encoding calculation time, and significantly improves the efficiency of engineering applications.

[0098] In summary, the tangent coding compression method proposed in this invention effectively solves the problems of large data volume in holographic stripe calculation and difficulty in balancing traditional coding accuracy and processing compatibility. It significantly compresses the data size while maintaining high-precision representation, and has the advantages of high coding accuracy, significant compression effect, and strong processing adaptability.

[0099] The above embodiments are merely one specific implementation of the technical solution of the present invention and should not be construed as limiting the scope of application of the present invention in any way. Reasonable deductions, modifications, or combinations made by those skilled in the art based on the technical essence disclosed in the present invention, without departing from the core inventive points of the present invention, are all within the scope of protection of the present invention.

Claims

1. A method for compressively encoding a computer-generated hologram based on constructing tangents, characterized by, Includes the following steps: S1: Obtain the phase distribution function of the hologram and set the boundary function for extracting etching fringes; S2: Based on the topological morphology of the stripe space, an adaptive start and end point coordinate information acquisition method is used to determine the start and end point coordinate information of the stripe boundary line of each sub-region; S3: Based on the overall distribution characteristics of the gradient field in the effective region of the phase function and the preset coding error accuracy, a preset phase error is superimposed on the target phase constant corresponding to the extracted etching stripe boundary function to construct a one-sided auxiliary error boundary. S4: Using the tangent compression algorithm, under the premise of limiting the encoding error, by solving the tangent contact point on the auxiliary error boundary and the encoded data point on the ideal equiphase line, a sparse discrete point column is directly generated to complete the compressed encoding of the stripe discrete sampling; the tangent compression algorithm does not require pre-dense uniform sampling of the stripe boundary.

2. The method for compressively encoding a computer-generated hologram based on a construction tangent according to claim 1, wherein, In step S1, specific etching stripes are divided as needed. For stripes with inflection points, the stripe boundary is divided into several sub-segments at each inflection point, so that the stripe boundary in each sub-segment remains purely concave or purely convex after division. For stripes without inflection points, they are directly treated as a sub-region stripe.

3. The method for compressively encoding a computer-generated hologram based on construction sheaf according to claim 1, wherein, In step S2, the start and end coordinates of the stripe boundary lines of each sub-region are determined, and in step S4, the traversal scanning direction of the tangent points on the auxiliary error boundary is configured, using a classification adaptive collaborative configuration strategy based on the stripe spatial topology. Based on the spatial distribution area and boundary closure properties of the current sub-region stripes within the effective etching boundary of the computational hologram, the stripes are divided into several topological morphology categories. For different topological morphology categories, corresponding start and end point selection rules are adopted, and a unique matching ascending or descending scanning direction is bound to the selected start and end point intervals. The spatial distribution area includes at least: distributed only in the lower half of the region, and spanning both the upper and lower halves of the region; the boundary closure attributes include: non-closed circular arc shape and closed elliptical shape; The classification adaptive collaborative configuration strategy specifically includes: (a) For stripes that are distributed only in the lower half of the region and are non-closed: take the leftmost and rightmost endpoints along the X direction in the lower half of the region as the start and end points, and bind an ascending scan within the interval between the start and end points; (b) For stripes that span the upper and lower halves and are non-closed, and whose absolute X coordinate of the starting point of the upper half is less than that of the starting point of the lower half: take the extreme endpoints of the upper half along the X direction and the extreme endpoints of the lower half along the X direction as independent starting and ending points of their respective halves, and bind descending scans in the upper half and ascending scans in the lower half. (c) For stripes that span the upper and lower halves and are non-closed, with the absolute value of the X coordinate of the starting point of the upper half being greater than that of the starting point of the lower half: First, a trial advance is made using a common starting and ending point. If the number of tangent points generated is less than the preset threshold, the corrected starting and ending points are searched again inside the boundary of the upper half and a descending scan is performed using the corrected starting and ending points. At the same time, the original starting and ending points of the lower half are retained and an ascending scan is performed, so that the node sequences generated in the upper and lower halves are spatially complementary and connected. (d) For stripes that span the upper and lower halves and are closed: obtain the start and end points of the upper half and the lower half respectively, select the one with the larger absolute value of the X coordinate as the global start point and global end point, use the range of X coordinates corresponding to the global start point and global end point as the search interval, and perform descending scan and ascending scan in the search interval to make the two sequences merge to form a complete closed boundary node chain. (e) For stripes that are only distributed in the upper half of the region and are closed: take the extreme endpoints along the X direction in the upper half of the region as the start and end points, and perform descending and ascending scans in the interval between the start and end points, so that the two sequences are merged to form a complete closed boundary node chain. The ascending order scan refers to progressing point by point from the lower limit of the current search interval to the upper limit to solve for the cutting contact point; the descending order scan refers to progressing point by point from the upper limit of the current search interval to the lower limit to solve for the cutting contact point. The classification-adaptive collaborative configuration strategy ensures that the advancing direction of the contact point sequence along the stripe boundary remains singular in each sub-region and consistent with the global iteration direction of the tangent compression algorithm, thereby eliminating the multi-valued ambiguity in root solution and node entanglement conflicts caused by multiple intersections of a single phase boundary at a single scan coordinate.

4. The computational hologram compression coding method based on constructed tangents according to claim 3, wherein the traversal scanning direction is specifically the traversal scanning direction for solving the tangent contact points on the auxiliary error boundary.

5. The method of claim 1, wherein the method is characterized by: In step S4, for the tangent compression algorithm, at the upper boundary stripe, the compression encoding starting point A(x) is... A y A ) and the contact point B(x) B y B The normal vector at point B is () , (Conditions met:) ； wherein , is the auxiliary error boundary phase function partial derivative of x, partial derivative of y; For the contact point B(x) B y B )satisfy: ； Solve the tangent point B(x B , y B ), the tangent equation: ； Combining the tangent equation and the curve on the ideal etching fringe Solve the system of equations to find the two intersection points of the tangent line and the curve. One of the intersection points should be A(x). A y A Excluding that point, the other intersection point is one of the valid solutions for solving the etching boundary position using the error boundary tangent method, denoted as point C(x). C y C ).

6. The computational hologram compression coding method based on constructed tangents according to claim 1, characterized in that, Each etched stripe includes an upper boundary line and a lower boundary line, and the upper and lower boundary lines use the same compression encoding method.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method of claim 1.

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