Refraction correction reverse ray tracing method for additive manufacturing
The optical refraction effect in volumetric additive manufacturing is corrected by the reverse ray tracing method, which solves the problem of model distortion, achieves high-precision automatic compensation, and ensures the geometric and dimensional accuracy of the molded structure.
Patent Information
- Application Number
- CN202511291146.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-10
- Publication Date
- 2025-10-17
AI Technical Summary
In existing volumetric additive manufacturing technology, the problem of model distortion caused by optical refraction effect has not been effectively solved, which affects the geometric precision and dimensional accuracy of the molded structure, and there is a lack of automated compensation methods.
The additive manufacturing refraction-corrected reverse ray tracing method is adopted to obtain the parallel light in the resin vial through reverse ray tracing, reconstruct it into a real projection pattern, correct the optical refraction effect, and ensure that the light is parallel lines in the resin.
The model distortion caused by optical refraction is effectively corrected, the geometric precision and dimensional accuracy of the molded structure are improved, and the robustness and automation of the method are enhanced.
Smart Images
Figure CN120792149A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the field of computer aided manufacturing (CAM) technology and additive manufacturing, and particularly relates to an additive manufacturing refraction correction reverse ray tracing method. BACKGROUND
[0002] Additive manufacturing technology has made great progress in the past few decades and has formed a relatively mature technical system. The core principle of its mainstream technology (such as fused deposition modeling (FDM) and stereolithography (SLA)) is to discretize a three-dimensional digital model into a two-dimensional cross section, that is, a "slicing" process, and to gradually reconstruct a three-dimensional entity by layer-by-layer accumulation. However, this layer-by-layer accumulation manufacturing method essentially has several limitations: interlayer texture is inevitably produced; additional support structures need to be added when manufacturing structures with overhangs or cavities, increasing material consumption and post-processing difficulty; and the overall manufacturing time is usually long, especially for large or complex components.
[0003] Under this background, volumetric additive manufacturing as a new additive manufacturing technology has gradually emerged in recent years. Volumetric additive manufacturing breaks through the constraints of traditional layer-by-layer manufacturing, and its core idea is to realize synchronous forming in three-dimensional space. This technology projects a series of precisely spatially and temporally modulated light field patterns onto a high-speed rotating container filled with transparent photosensitive resin. Under precise spatiotemporal control, these pre-calculated patterns are non-coherently superimposed. Only when the accumulated light dose in the three-dimensional target region inside the resin exceeds the material's solidification threshold, will it trigger the selective photopolymerization reaction of the resin in that region. This mechanism enables the target structure to be formed almost synchronously inside the resin, thereby greatly shortening the manufacturing time from the traditional hours to minutes.
[0004] In current volumetric printing technology, the process of analyzing a three-dimensional digital model into a two-dimensional projection image is usually called forward projection. This process is mathematically analogous to the inverse problem of computed tomography (CT) imaging, which reconstructs images from projection data, and can be achieved through mathematical tools such as Radon Transform. However, unlike traditional CT scanning, the light projection of volumetric printing usually needs to penetrate a transparent container (such as a vial) containing photosensitive resin. When light rays enter the resin medium from the air medium, according to Snell's law, refraction will occur at the container wall interface. This optical effect, if not compensated, will severely distort the geometric correspondence between the projection image and the target three-dimensional model inside the resin, ultimately leading to spatial distortion problems in the formed structure.
[0005] In the published volume printing projection generation related patents and technical solutions, the systematic analysis of the influence of optical refraction on the projection geometric accuracy and the corresponding compensation correction algorithm are still relatively scarce. Due to the lack of effective physical model correction, the current voxel generation method often shows obvious geometric distortion and size deviation in the finally manufactured model. At present, it often needs to rely on the experience of manual post-compensation (such as manual adjustment of the projection image) to improve the molding effect, which not only reduces the robustness and engineering practicability of the method itself, but also becomes one of the key bottlenecks restricting the volume printing technology to move towards the field of high-precision, automatic additive manufacturing. SUMMARY
[0006] In order to solve the model distortion problem caused by refraction effect in the process of volume additive manufacturing, the present application provides an additive manufacturing refraction correction reverse ray tracing method, which obtains the refracted line of parallel light in the resin vial containing additive manufacturing resin material as the actual projection line by reverse ray tracing method, and reorganizes it into a real projection pattern. Further ensure that the light in the resin vial is parallel line, complete the correction of refraction effect.
[0007] The object of the present application is achieved by the following technical solutions: An additive manufacturing refraction correction reverse ray tracing method, comprising the following steps: Step one: receiving the STL model to be printed, calculating the rectangular envelope box of the STL model; receiving the user input of the number of voxels in the longitudinal resolution res, determining the voxel size; receiving the user input of the number of forward projection frames n , calculating the angle interval θ step between different frames; Step two: calculating the volume additive manufacturing forward projection data; Step three: receiving the user input of the refraction coefficient, the radius of the container containing the additive manufacturing resin material, first calculating the maximum distance of the incident parallel light and the center of the corresponding projection plane and the Y direction voxel number required by the real projection plane considering the refraction effect, and calculating the exit light Y coordinate and the corresponding rotation angle of each voxel on the real projection plane, and generating a refraction sequence set, each element in the refraction sequence set is a two-tuple composed of the rotation angle and the exit light Y coordinate of each voxel; Step four: calculating the updated forward projection data according to the refraction sequence set and the forward projection data.
[0008] Further, in the step one, the minimum point of the rectangular envelope box is represented as min 3 D (X min ,Y min ,Z min), the maximum point is expressed as max3D(X max ,Y max ,Z max ), wherein X min , Y min , Z min , X max , Y max , Z max respectively represent the minimum and maximum values of the rectangular envelope box in three directions; the voxel size v l =(Z max -Z min ) / res.
[0009] Further, the step two includes the following sub-steps: S2.1: dividing a regular voxel grid with the number of x-direction grid N x , the number of y-direction grid N y , and the number of z-direction grid N z in the rectangular envelope box, wherein: N z =res; N x =(X max -X min ) / v l ; N y =(Y max -Y min ) / v l ; S2.2: in the regular voxel grid, constructing a voxel model based on the STL model target geo according to the STL model to be printed, and assigning the voxel in the internal region of the STL model as 1 and the voxel in the external region as 0; S2.3: using Radon transform to perform forward projection on the voxel model target geo to obtain forward projection data prog_ori(n h , n i , n j ), wherein n h represents the number of image frames when the container rotates one circle, n i represents the number of voxels in the x-direction of the two-dimensional projection plane, and n j represents the number of voxels in the y-direction of the two-dimensional projection plane; wherein n i =n j =n r , and n r represents half of the number of voxels in a single direction on the two-dimensional square projection plane, and when N x >Ny n = N / 2; otherwise, n = N / 2. r x r y
[0010] Further, the step three includes the following sub-steps: S3.1: Calculate the horizontal and vertical coordinates (p Max , p Max.x ) of the intersection point p Max.y of the maximum refracted parallel light and the container; p Max.y = v l× n r ; p Max.x = ; S3.2: According to the law of refraction, calculate the exit angle theta out and the incident angle theta in corresponding to the maximum refracted parallel light: theta out = arcsin(p Max.y / R) ; theta in = arcsin(k x sin theta out ) ; wherein k is the refractive coefficient input by the user, and R is the radius of the container containing the additive manufacturing resin material; S3.3: Calculate the maximum refracted distance refMax.y of the real projection plane: refMax.y = R x sin theta in ; S3.4: Calculate the number of voxels in Y direction refMax.n required for the real projection plane after considering the refraction effect according to the number of longitudinal grid division according to the voxel size: refMax.n = ceil((reMax.y) / v v l ) x 2 + 1; wherein ceil() represents the upward rounding operation; S3.5: Calculate the incident light Y coordinate p_in i .y, the exit light Y coordinate p_out i .y and the corresponding rotation angle theta rotate,i and generate a set of refraction sequences refPairs, each element of which is a pair of each voxel theta rotate,i , p_in i .y): p_in i .y=i×v l -refMax.y; p_out i .y= p_in i .y×n1 / n2; theta out,i =arcsin(p_out i .y / R) ; theta in,i = arcsin(k×sin theta out,i ); theta rotate,i = theta in,i - theta out,i ; wherein i represents the serial number of the voxel, taking values from 0 to refMax.n-1, theta out,i and theta in,i respectively represent the incident angle and the exit angle corresponding to the i-th voxel.
[0011] Further, the step four comprises the following sub-steps: S4.1: according to the set of refraction sequences refPairs and the forward projection data prog_ori(n h , n i , n j ) obtained in step two, calculate the updated forward projection data proj_update(n h ,updata_n i , n j ), wherein updata_n i represents the number of voxels in the x direction of the two-dimensional projection plane, and its value is equal to refMax.n; S4.2: perform triple loop traversal on the updated forward projection data proj_update(n h ,updata_n i , n j ), and for each element position, perform the following mapping operation: (1) Calculate the corresponding container projection light Y position of each element: ori_i.y =[(i -refMax.n / 2) / k + n r ] ; Wherein, [ ] represents the rounding operation; (2) Calculate the light intensity resinValue after the light intensity is reduced due to the change caused by the increase of the number of voxels: resinValue=proj_ori(h.ori_i.y,j) / k; Wherein, proj_ori(h.ori_i.y,j) represents the original light intensity of the voxel position ori_i.y; (3) Calculate the corrected rotation angle : =[ theta rotate,i + θ step × h) % 360] ; θ step =360 / n; Wherein, theta rotate,i ori_i represents the original rotation angle of the i-th voxel, θ step represents the angle interval between different frames; % represents the remainder function, [ ] represents the rounding operation; h represents the forward projection specified position image frame number, and its value range is 0~n h ; (4) Calculate the real rotation projection Y coordinate: proj(h,i,j).y= p_in i .y + n j ; (5) Accumulate and update the target light intensity: proj_update[ , proj(h,i,j).y,j]+= resinValue。
[0012] The beneficial effects of the present application are as follows: (1) The present application is aimed at the refraction problem of light from air to resin vial, and sets the projection pattern incident to the resin vial as parallel light through the reverse ray tracing method, so as to deduce the position and angle of the incident light, and then correspond to different projection planes. This method can effectively correct the refraction distortion problem, and can adapt to all forward projection technologies.
[0013] (2) The present application is based on the existing forward projection data, and has good adaptation ability.
[0014] (3) The scheme of the present application has high processing efficiency due to small amount of calculation, simple algorithm logic and good robustness. BRIEF DESCRIPTION OF DRAWINGS
[0015] Figure 1 The schematic diagram of the core principle of the method of the present application.
[0016] Figure 2 The schematic diagram of the flow of the additive manufacturing refraction correction reverse ray tracing method of the present application.
[0017] Figure 3 The schematic diagram of the refraction parameter involved in the present application.
[0018] Figure 4 The comparative image of the traditional method and the refraction correction method in different manufacturing process links.
[0019] Figure 5 The comparative effect diagram of the real printing task. DETAILED DESCRIPTION
[0020] The purpose and effect of the present application will become more apparent from the following detailed description of the preferred embodiments with reference to the accompanying drawings, and it should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.
[0021] As shown in Figure 1 , the light of the traditional additive manufacturing volume printing enters the resin medium from the air medium, and according to Snell's law, refraction phenomenon occurs at the container wall interface, so that the geometric correspondence relationship between the severely distorted projection image and the target three-dimensional model in the resin is seriously distorted, and finally the spatial distortion problem of the formed structure occurs. The present application uses the reverse ray tracing method, assumes that the resin vial is parallel light, so that the refracted line of the parallel light is used as the actual projection line, and the real projection image is recombined, so as to ensure that the light in the resin vial is parallel line, and the correction of the refraction effect is completed.
[0022] As shown in Figure 2 , the additive manufacturing refraction correction reverse ray tracing method of the present application comprises the following steps: Step 1: receiving the STL model to be printed, calculating the rectangular envelope box of the STL model; receiving the number of voxels res in the longitudinal direction and the number of forward projection frames in the resolution input by the user n , calculating the voxel size according to the number of voxels res, and calculating the angle interval θ n between different frames according to the number of forward projection frames step .
[0023] The minimum point of the rectangular envelope box is represented as min 3 D (Xmin Y min Z min , the maximum point is represented as max3D(X max Y max Z max ), wherein X min , Y min , Z min , X max , Y max , Z max represent the minimum and maximum values of the rectangular envelope box in three directions, respectively.
[0024] The voxel size v l = (Z max - Z min ) / res.
[0025] The angular interval θ step between different frames = 360 / n.
[0026] Step two: calculate the volume additive manufacturing forward projection data prog ori , step two includes the following sub-steps: S2.1: divide the regular voxel grid in the rectangular envelope box with the number of x-direction grid N x , the number of y-direction grid N y , and the number of z-direction grid N z , wherein: N z = res; N x = (X max - X min ) / v l ; N y = (Y max - Y min ) / v l ; S2.2: in the regular voxel grid, construct the voxel model based on the STL model target geo according to the STL model to be printed, and assign the voxel in the internal region of the STL model as 1 and the voxel in the external region as 0.
[0027] S2.3: use Radon transform to perform forward projection on the voxel model target geo , and obtain the forward projection data prog_ori(n h , n i , n j ), wherein n h represents the number of image frames when the resin bottle rotates one circle, n in represents the number of voxels in the x direction of the two-dimensional projection plane j n represents the number of voxels in the y direction of the two-dimensional projection plane; wherein, n i = n j = n r , n r represents half of the number of voxels in a single direction on the two-dimensional square projection plane, when N x > n y , n r = N x / 2; otherwise, n r = N y / 2.
[0028] n h may be equal to the number of forward projection frames n , or a multiple of n .
[0029] Step three: receiving the refractive coefficient k input by the user, the radius R of the resin vial containing the additive manufacturing resin material, first calculating the maximum distance of the incident parallel light from the center of the corresponding projection plane and the number of voxels in the Y direction required by the real projection plane considering the refraction effect, and calculating the exit light Y coordinate of each voxel on the real projection plane and the corresponding rotation angle, and generating a refraction sequence set, each element in the refraction sequence set is a two-tuple composed of the rotation angle and the exit light Y coordinate of each voxel.
[0030] As shown in Figure 3 , place the container containing the additive manufacturing resin material at the origin of the coordinate axis, and the radius of the transverse cross section of the container is R; for any parallel light in the container, the y coordinate of the light is represented as p y , the coordinates of the intersection of the parallel light and the interface of the resin vial p(p x , p y ) can be obtained by the circular formula, and the incident angle theta in and the exit angle theta out when the parallel light is the exit relationship: p y - sqrt (R 2 -p y 2 ); theta out = arcsin(p y / R); theta in = arcsin(n2×sin thetaout / n1); The present application sets the light ray emitted by the light machine as collimated light, i.e. the emitted light is parallel light. According to the obtained incident angle theta in and the exit angle theta out , the real projection plane and the Y direction position of the light ray on the real projection plane can be obtained. As shown in the figure, the gray and blue color in the figure is the real projection plane. Figure 3
[0031] In order to obtain the projection data without the stripe phenomenon, step three includes the following sub-steps: S3.1: Calculate the horizontal and vertical coordinates (p Max , p Max.x ) of the intersection point p Max.y of the maximum refracted parallel light and the container; p Max.y = v l × n r ; p Max.x = ; S3.2: According to the law of refraction of light, calculate the exit angle theta out corresponding to the maximum refracted parallel light and the incident angle theta in : theta out = arcsin(p Max.y / R) ; theta in = arcsin(k × sin theta out ) ; wherein k is the refractive coefficient input by the user, and R is the radius of the resin vial containing the additive manufacturing resin material.
[0032] S3.3: Calculate the maximum refractive distance refMax.y of the real projection plane: refMax.y = R × sin theta in ; Since the parallel light is specified in the present application, the light indicated by the incident angle theta in has the characteristic of being perpendicular to the projection plane, and the maximum refractive distance refMax.y of the real projection plane can be calculated according to the formula of S3.3.
[0033] S3.4: Calculate the number of voxels in the Y direction refMax.n required to divide the real projection surface into the number of vertical grids according to the voxel size after considering the refraction effect: refMax.n=ceil((reMax.y) / v l )×2+1; Among them, ceil() represents the rounding up operation; S3.5: Calculate the Y coordinate p_in of the incident light corresponding to each voxel in refMax.n voxels i .y, outgoing ray Y coordinate p_out i .y and the corresponding rotation angle theta rotate,i , and generates a refraction sequence set refPairs, each element of which is a tuple of each voxel ( theta rotate,i , p_in i .y): p_in i .y=i×v l -refMax.y; p_out i .y = p_in i .y×n1 / n2; theta out,i =arcsin(p_out i .y / R); theta in,i = arcsin(k×sin theta out,i ); theta rotate,i = theta in,i - theta out,i ; Where i represents the voxel number, ranging from 0 to refMax.n-1. theta out,i and theta in,i They represent the incident angle and the exit angle corresponding to the i-th voxel respectively.
[0034] Here we calculate the Y coordinate of the outgoing light of each voxel p_out i .y, uses an approximate calculation based on the scaling principle of the refractive index.
[0035] Step 4: Calculate updated forward projection data based on the refraction sequence set and the forward projection data.
[0036] Step four includes the following sub-steps: S4.1: According to the refraction sequence set refPairs obtained in step three and the forward projection data prog ori(n h , n i , n j ) obtained in step two, calculate the updated forward projection data proj update(n h , updata_n i , n j ), wherein updata_n i represents the number of voxels in the x direction of the two-dimensional projection plane, and its value is equal to refMax.n.
[0037] The update of the number of voxels in the x direction of the two-dimensional projection plane here is to correct the distortion caused by the refraction effect.
[0038] S4.2: Perform triple loop traversal on the updated forward projection data proj update(n h , updata_n i , n j ), that is, traverse from 0~ n h , 0~updata_n i , 0~ n j in three dimensions respectively, and perform the following mapping operation for each element position: (1) Calculate the Y direction position of the projection light in the container corresponding to each element: ori_i.y =[(i -refMax.n / 2) / k + n r ]; Wherein, [ ] represents the rounding operation; (2) Calculate the light intensity resinValue after the light intensity is reduced due to the change caused by the increase in the number of voxels: resinValue=proj_ori(h.ori_i.y,j) / k; Wherein, proj_ori(h.ori_i.y,j) represents the original light intensity of the voxel position ori_i.y; (3) Calculate the corrected rotation angle : =[ theta rotate,i + θ step × h) % 360]; θ step =360 / n; Wherein,Figure 5 rotate,i θori(i) represents the original rotation angle of the i-th voxel step represents the angle interval between different frames; represents the remainder function, [ ] represents the rounding operation; h represents the forward projection of the specified position image frame number, which ranges from 0 to n h .
[0039] (4) Calculate the real rotation projection Y coordinate: proj(,h i,j).y= p_in i .y + n j ; (5) Accumulate and update the target light intensity: proj_update[ , proj(h,i,j).y,j]+= resinValue。
[0040] A specific implementation case is given below to prove the effect of the method of the application.
[0041] 1. Take the three-dimensional model to be printed as shown in Figure 4 (a), the model size is 6mm x 1mm x 6mm; 2. According to the STL file of the model, perform voxelization operation, set the resolution to 200, and construct the voxelized model; 3. Set the frame number to n=360, perform forward projection calculation according to the voxelized model, and obtain the forward projection set prog_ori(n, n r , n r ).
[0042] 4. Set the radius R of the small bottle containing resin to 5mm, set the refractive index k=1.53, and calculate the refraction sequence set refPairs.
[0043] 5. Through reverse ray tracing recombination, the real target projection data is established and updated, and the real target projection data with complete additive manufacturing information is obtained. As shown in Figure 4 , the inverse process of the correction process, Figure 4 (b) to Figure 4 (a), after reversing the normal image in the small bottle to the real projection, the real projection result shows the effect of elongation.
[0044] 6. Convert the real target projection data to mp4 format through opencv, and after adapting to the volume additive manufacturing equipment, the manufacturing task can be completed.
[0045] As shown in Figure 4As shown, the implementation of the present invention mainly involves three key links: the real projection image, the projection image inside the container, and the final reconstructed three-dimensional model effect. In the traditional process (corresponding to Figure 4 (Left side, traditional process) The actual projected image itself is normal and undistorted; however, when the pattern light enters the resin vial, the refraction effect causes the projected image inside the vial to be lateral distorted, and the aspect ratio changes; although the cured cross section of the model is still clear ( Figure 4 (c) 2D image), but the reconstructed model is narrowed and distorted. Figure 5 (Third row refraction correction process) The actual projected image is actively designed to be laterally elongated and visually free of noticeable streaking effects. After the pattern is refracted through the vial, the distortion is compensated, and the projected image inside the vial becomes normally proportioned and free of noticeable distortion. The final reconstructed model displays clear solidified boundaries, and the model size is consistent with expectations, effectively correcting the distortion caused by refraction.
[0046] A test case of a model being printed in actual volume is presented, and the results are consistent with the above analysis. Without the refraction correction scheme of the present invention, the printed model exhibits significant distortion. However, with this scheme, the printed model maintains normal dimensions, significantly correcting the distortion.
[0047] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art will still be able to modify the technical solutions described in the foregoing examples or substitute equivalents for some of the technical features therein. Any modifications, equivalent substitutions, etc. made within the spirit and principles of the invention shall be included within the scope of protection of the invention.
Claims
1. A refraction-corrected reverse ray tracing method for additive manufacturing, characterized in that: The following steps are involved: Step 1: Receive the STL model to be printed and calculate the rectangular envelope of the STL model; Receive the vertical voxel number res in the resolution input by the user to determine the voxel size; receive the forward projection frame number input by the user n , calculate the angular interval θ between different frames step ; Step 2: Calculate volumetric additive manufacturing forward projection data; Step 3: Receive the refractive index and the radius of the container containing the additive manufacturing resin material input by the user, first calculate the maximum distance between the incident parallel light and the center of the corresponding projection plane and the number of voxels in the Y direction required for the real projection plane after considering the refraction effect, and calculate the Y coordinate of the outgoing light and the corresponding rotation angle of each voxel on the real projection plane, and generate a refraction sequence set, where each element of the refraction sequence set is a two-tuple consisting of the rotation angle of each voxel and the Y coordinate of the outgoing light; Step 4: Calculate updated forward projection data based on the refraction sequence set and the forward projection data.
2. The additive manufacturing refraction-corrected reverse ray tracing method according to claim 1, characterized in that: In step 1, the minimum point of the rectangular envelope is expressed as min 3 D (X min ,Y min ,Z min ), the maximum value point is expressed as max3D(X max ,Y max ,Z max ), where X min 、Y min , Z min 、X max 、Y max , Z max Represents the minimum and maximum values of the rectangular envelope in three directions respectively; the voxel size v l =(Z max -Z min ) / res.
3. The additive manufacturing refraction-corrected reverse ray tracing method according to claim 2, characterized in that: The second step includes the following sub-steps: S2.1: Divide the x-direction grids into N within the rectangular envelope. x , the number of grids in the y direction is N y , the number of grids in the z direction is N z A regular voxel grid where: N z =res; N x =(X max -X min ) / v l ; N y =(And max -AND min ) / v l ; S2.2: In the regular voxel grid, construct a voxel model target based on the STL model to be printed geo , and assign the voxels in the inner area of the STL model to 1, and the voxels in the outer area to 0; S2.3: Using Radon transform, the voxel model target geo Perform forward projection to obtain the forward projection data prog_ori(n h , n i , n j ), where n h Indicates the number of image frames for one rotation of the container, n i Represents the number of voxels in the x direction of the two-dimensional projection plane, n j Represents the number of voxels in the y direction of the two-dimensional projection plane; where n i =n j =n r , n r Represents half of the number of voxels in a single direction on a two-dimensional square projection plane. When N x >N y When n r = N x / 2; otherwise, n r = N y / 2.
4. The additive manufacturing refraction-corrected reverse ray tracing method according to claim 3, characterized in that: The step three includes the following sub-steps: S3.1: Calculate the intersection point p of the parallel ray of maximum refraction with the container Max The horizontal and vertical coordinates (p Max.x , p Max.y ); p Max.y =v l ×n r ; p Max.x = ； S3.2: Based on the law of light refraction, calculate the angle of incidence corresponding to the maximum refracted parallel light θ out and the angle of incidence θ in : θ out =arcsin(p Max.y / R) ; θ in = arcsin(k×sin θ out ) ; Where k is the refractive index input by the user, and R is the radius of the container containing the additive manufacturing resin material; S3.3: Calculate the maximum refraction distance refMax.y of the real projection surface: refMax.y=R×sin θ in ; S3.4: Calculate the number of voxels in the Y direction refMax.n required to divide the real projection surface into the number of vertical grids according to the voxel size after considering the refraction effect: refMax.n=ceil((reMax.y) / v l )×2+1; Among them, ceil() represents the rounding up operation; S3.5: Calculate the Y coordinate p_in of the incident light corresponding to each voxel in refMax.n voxels i .y, outgoing ray Y coordinate p_out i .y and the corresponding rotation angle θ rotate,i , and generates a refraction sequence set refPairs, each element of which is a tuple of each voxel ( θ rotate,i , p_in i .y): p_in i .y=i×v l -refMax.y; p_out i .y= p_in i .y×n1 / n2; θ out,i =arcsin(p_out i .y / R) ; θ in,i = arcsin(k×sin θ out,i ) ; θ rotate,i = θ in,i - θ out,i ； Where i represents the voxel number, ranging from 0 to refMax.n-1. θ out,i and θ in,i They represent the incident angle and the exit angle corresponding to the i-th voxel respectively.
5. The additive manufacturing refraction-corrected reverse ray tracing method according to claim 4, characterized in that: The step 4 includes the following sub-steps: S4.1: Obtain forward projection data prog_ori (n according to the refraction sequence set refPairs and step 2 h , n i ,n j ), calculate the updated forward projection data proj_update(n h ,updata_n i ,n j ), where update_n i Indicates the number of voxels in the x direction of the two-dimensional projection plane, and its value is equal to refMax.n; S4.2: Update the forward projection data proj_update(n h ,updata_n i ,n j ) performs a triple loop traversal and performs the following mapping operation for each element position: (1) Calculate the Y position of the projection light in the container corresponding to each element: ori_i.y =[(i -refMax.n / 2) / k + n r ]; Among them, [ ] represents the rounding operation; (2) Calculate the light intensity resinValue after the light intensity decreases due to the increase in the number of voxels: resinValue=proj_ori(h.ori_i.y,j) / k; Among them, proj_ori(h.ori_i.y,j) represents the original light intensity of the voxel position ori_i.y; (3) Calculate the corrected rotation angle : =[ θ rotate,i + θ step × h) % 360]; i step =360 / n; in, θ rotate,i represents the original rotation angle of the i-th voxel, θ step Indicates the angle interval between different frames; % indicates the remainder function, [ ] indicates the rounding operation; h indicates the image frame number at the specified position of the forward projection, and its value range is 0~n h ; (4) Calculate the true rotation projection Y coordinate: proj(h,i,j).y= p_in i .y + n j ; (5) Accumulate and update the target light intensity: proj_update[ , proj(h,i,j).y,j]+= resinValue。