Design method and design device of diffractive optical element

Abstract

The invention provides a diffractive optical element design method and device, and the method comprises the steps: initializing the complex amplitude distribution of an incident light field, the complex amplitude distribution of a target light field, and the geometric structure of a diffractive optical element; based on an incident light field and a target light field, obtaining initial phase modulation distribution of a diffractive optical element through a diffractive optical geometric mapping theory; iteratively solving the phase distribution of the diffractive optical element by adopting a cascade angular spectrum propagation method; calculating a reconstructed light field according to the incident light field and the phase distribution; calculating an evaluation function value of a residual error between the reconstructed light field and the target light field; and when the evaluation function value meets a preset index, outputting the current phase distribution of the diffractive optical element as a final design result. According to the invention, the calculation complexity of the design of the diffractive optical element is reduced, and the design speed is improved.

Description

Technical Field

[0001] This application relates to the field of optical devices, and more specifically, to a design method and design apparatus for a diffractive optical element. Background Technology

[0002] Currently, diffractive optical elements (DOEs), as a novel type of optical element capable of flexibly controlling the wavefront of light fields through micro- and nano-structures, are showing broad application prospects in fields such as laser processing, optical sensing, and virtual reality. Their performance directly depends on the design precision of their surface micro- and nano-structures; therefore, efficient and accurate design methods are crucial for the application of DOEs.

[0003] In existing technologies, to obtain output light fields with high diffraction efficiency and high uniformity, it is usually necessary to establish an extremely large grid system to iteratively reconstruct the phase distribution of the DOE. This global optimization strategy results in huge computational resource consumption, and its computational complexity increases exponentially with the problem size (O(e^(-1 / 2))). n This constitutes a significant computational bottleneck. This bottleneck severely restricts design efficiency, making it difficult to achieve rapid and accurate design for large dimensions (such as centimeters). Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a design method and design apparatus for diffractive optical elements to overcome at least one of the above-mentioned defects.

[0005] In a first aspect, embodiments of this application provide a design method for a diffractive optical element. The method includes: initializing the complex amplitude distribution of the incident light field, the complex amplitude distribution of the target light field, and the geometric structure of the diffractive optical element; obtaining the initial phase modulation distribution of the diffractive optical element based on the incident light field and the target light field using diffractive optical geometry mapping theory; iteratively solving the phase distribution of the diffractive optical element using the cascaded angular spectrum propagation method, wherein, based on the geometric structure of the diffractive optical element, its characteristic distribution is divided into multiple scale levels, and its angular spectrum propagator is calculated for each scale level. Based on the target light field and the angular spectrum propagator of the current level, the phase distribution of that level is solved sequentially from the largest scale level to the smallest scale level; calculating the reconstructed light field according to the incident light field and the phase distribution; calculating the evaluation function value of the residual between the reconstructed light field and the target light field; and outputting the current phase distribution of the diffractive optical element as the final design result of the diffractive optical element when the evaluation function value meets a preset index.

[0006] In one optional embodiment of this application, the geometry of the diffractive optical element is initialized by defining the length and width dimensions, minimum feature size, total height, and number of steps of the diffractive optical element; wherein, the minimum feature size is the minimum processing size of the microstructure on the surface of the diffractive optical element, the total height is the maximum depth of the microstructure on the surface of the diffractive optical element, and the number of steps is the number of phase levels corresponding to the total height.

[0007] In one optional embodiment of this application, the complex amplitude distribution of the incident light field and the complex amplitude distribution of the target light field are initialized in the following manner: a grid corresponding to the geometry of the diffractive optical element is established, and the number of rows and columns of the grid is set; a complex amplitude matrix of the incident light field is defined on the grid to describe the spatial distribution of the amplitude and phase of the incident light; and a complex amplitude matrix of the target light field is defined on the grid to describe the amplitude and phase distribution of the light field to be obtained on the target plane.

[0008] In one optional embodiment of this application, the initial phase modulation distribution of the diffractive optical element is obtained by: based on the complex amplitude distribution of the incident light field and the complex amplitude distribution of the target light field, and based on the physical relationship of light wave propagation, establishing a mapping from the complex amplitude of the light field to the phase distribution through mathematical transformation, and calculating the initial phase distribution of the diffractive optical element as the initial phase modulation distribution of the diffractive optical element.

[0009] In one optional embodiment of this application, the reconstructed light field is calculated as follows: the complex amplitude distribution of the incident light field is multiplied by the total phase distribution of the diffractive optical element obtained by the current iteration to obtain the complex amplitude distribution of the outgoing light field at the exit surface of the diffractive optical element; based on the angular spectrum propagator, the angular spectrum propagation calculation is performed on the complex amplitude distribution of the outgoing light field to obtain the light field distribution on the target plane, which is used as the reconstructed light field.

[0010] In one optional embodiment of this application, the evaluation function value of the residual between the reconstructed light field and the target light field is calculated in the following manner: the light intensity difference between the reconstructed light field and the target light field at corresponding points on the grid is calculated; the root mean square value of the differences at all points is calculated, and the root mean square value is used as the evaluation function value.

[0011] In one optional embodiment of this application, the step of outputting the current phase distribution of the diffractive optical element as the final design result of the diffractive optical element when the evaluation function value meets the preset index includes: comparing the evaluation function value with a preset threshold; if the evaluation function value is less than the threshold, it is determined that the preset index is met, and the current phase distribution of the diffractive optical element is output as the final design result of the diffractive optical element; if the evaluation function value is greater than or equal to the threshold, it is determined that the preset index is not met, and the process returns to the step of iteratively solving the phase distribution of the diffractive optical element using the cascaded angular spectrum propagation method.

[0012] Secondly, embodiments of this application also provide a design apparatus for a diffractive optical element. The apparatus includes: an initialization module for initializing the complex amplitude distribution of the incident light field, the complex amplitude distribution of the target light field, and the geometry of the diffractive optical element; an initial phase modulation distribution acquisition module for obtaining the initial phase modulation distribution of the diffractive optical element based on the incident light field and the target light field, using diffractive optical geometry mapping theory; and a phase distribution solving module for iteratively solving the phase distribution of the diffractive optical element using the cascaded angular spectrum propagation method, wherein, based on the geometry of the diffractive optical element, its characteristic features are... The light field is divided into multiple scale levels. For each scale level, its angular spectrum propagator is calculated. Based on the target light field and the angular spectrum propagator of the current level, the phase distribution of that level is solved sequentially from the largest scale level to the smallest scale level. The reconstructed light field calculation module is used to calculate the reconstructed light field according to the incident light field and the phase distribution. The evaluation function value calculation module is used to calculate the evaluation function value of the residual between the reconstructed light field and the target light field. The final design result output module is used to output the phase distribution of the current diffractive optical element as the final design result of the diffractive optical element when the evaluation function value meets the preset index.

[0013] Thirdly, embodiments of this application also provide an electronic device, including: a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor communicates with the memory via the bus, and when the machine-readable instructions are executed by the processor, the steps of the method described above are performed.

[0014] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the method described above.

[0015] The design method and apparatus for diffractive optical elements provided in this application initialize the complex amplitude distribution of the incident light field, the complex amplitude distribution of the target light field, and the geometry of the diffractive optical element. Based on the incident and target light fields, the initial phase modulation distribution of the diffractive optical element is obtained through diffractive optical geometry mapping theory. The phase distribution of the diffractive optical element is iteratively solved using the cascaded angular spectrum propagation method. The reconstructed light field is calculated based on the incident and phase distributions. The evaluation function value of the residual between the reconstructed and target light fields is calculated. When the evaluation function value meets a preset index, the current phase distribution of the diffractive optical element is output as the final design result. This application reduces the computational complexity of diffractive optical element design and improves the design speed.

[0016] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating the design method of the diffractive optical element provided in the embodiments of this application; Figure 2 A flowchart illustrating the complex amplitude distribution of the initial incident light field and the complex amplitude distribution of the target light field, provided for embodiments of this application; Figure 3 A flowchart illustrating the computational reconstruction of the light field provided in this application embodiment; Figure 4 A flowchart illustrating the evaluation function value for calculating the residual between the reconstructed light field and the target light field, provided in an embodiment of this application. Figure 5 This is a schematic diagram of the design apparatus for the diffractive optical element provided in the embodiments of this application; Figure 6 The present application provides a schematic diagram of the structure of an electronic device. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. Based on the embodiments of this application, every other embodiment obtained by those skilled in the art without inventive effort falls within the scope of protection of this application.

[0020] First, the applicable scenarios for this application will be introduced. This application can be applied to the field of optical devices.

[0021] Research has revealed that to meet the requirements of high diffraction efficiency and high uniformity, the design of diffractive optical elements (DOEs) requires the establishment of a massive mesh system for iterative reconstruction, resulting in enormous computational resource consumption and an exponential increase in algorithm complexity (O(e^(-1 / 2))). n This computational bottleneck severely restricts design efficiency, making it difficult to achieve rapid and accurate design of large-size DOEs.

[0022] Based on this, the embodiments of this application provide a design method and design apparatus for diffractive optical elements. By introducing the cascaded angular spectrum propagation method, the characteristic distribution of the diffractive optical element is divided into multiple scale levels and the phase distribution is solved iteratively at each level. This achieves effective control over computational complexity, thereby reducing the algorithm complexity from exponential to quadratic while ensuring design accuracy, and improving the design speed of large-size diffractive optical elements.

[0023] Please see Figure 1 , Figure 1 A flowchart illustrating the design method of the diffractive optical element provided in the embodiments of this application. Figure 1 As shown in the embodiments of this application, the design method for diffractive optical elements includes: S101. Initialize the complex amplitude distribution of the incident light field, the complex amplitude distribution of the target light field, and the geometry of the diffractive optical element.

[0024] Here, the geometry of the diffractive optical element is initialized in the following manner: Define the length, width, minimum feature size, total height, and number of steps of a diffractive optical element.

[0025] Among them, the minimum feature size is the minimum processing size of the microstructure on the surface of the diffractive optical element, the total height is the maximum depth of the microstructure on the surface of the diffractive optical element, and the number of steps is the number of phase levels corresponding to the realization of the total height.

[0026] The length and width dimensions refer to the overall physical dimensions of the component, such as a circle with a diameter of 20 mm or a square of 10 mm × 10 mm. These dimensions are determined by the final application and system packaging requirements of the diffractive optical element. For example, a DOE used in a laser projector may need to match the size of a DMD chip; therefore, its length and width are predetermined system parameters, directly determining the physical extent of the computational grid. The grid must cover the entire length and width dimensions of the component.

[0027] The minimum feature size refers to the minimum width of the micro / nano structure (such as grating lines or pixel units) on the surface of a device. It is a key parameter determining the optical performance (such as diffraction angle and resolution) of a DOE (Distributed Optical Array). It is determined by the limits of micro / nano fabrication processes (such as the resolution of stepper lithography and electron beam lithography). This is the minimum linewidth that can be achieved through fabrication.

[0028] The minimum feature size determines the accuracy (resolution) of the computational grid; the grid point spacing must be much smaller than the minimum feature size to accurately describe the structure.

[0029] Secondly, in the subsequent cascaded angular spectrum propagation method, it is explicitly defined as the first-order scale, and all coarser scales (the m-th order) are defined by its 2 m Divide by multiples.

[0030] The total height refers to the maximum etching depth of the relief structure on the component surface, calculated using physical formulas based on the operating wavelength and the refractive index of the component material. To achieve complete modulation of the light wave phase from 0 to 2π, the required maximum depth (i.e., the total height h) is given by the formula h = λ / (n...). 1) Determined, where λ is the wavelength and n is the material refractive index. The total height, combined with the number of steps, is used to quantify the calculated continuous phase distribution into a practically machinable discrete surface shape at the end.

[0031] The number of steps refers to the number of levels at which a continuous phase change (0 to 2π) is discretized. For example, 8 steps means that the 2π phase is divided into 8 equal parts, with each step corresponding to a phase change of π / 4.

[0032] The number of steps is determined by the cost and complexity of the chosen manufacturing process. For example, a 4-step structure can be manufactured using a 2-mask process, while a 16-step structure can be manufactured using a 4-mask process. More steps result in more precise phase control, but also higher costs and longer lead times.

[0033] At the end of the design process, the final output continuous phase distribution is rounded down to the nearest discrete level based on the total height and number of steps, thereby generating a processing drawing that can directly drive the lithography machine.

[0034] For further details, please refer to Figure 2 , Figure 2 The flowchart illustrates the complex amplitude distribution of the initial incident light field and the complex amplitude distribution of the target light field, as provided in the embodiments of this application. Figure 2 As shown, the complex amplitude distribution of the incident light field and the complex amplitude distribution of the target light field are initialized in the following manner: S201. Create a grid corresponding to the geometry of the diffractive optical element, and set the number of rows and columns of the grid.

[0035] The physical extent of the computational region is determined based on the length and width dimensions of the diffractive optical element.

[0036] The required spatial resolution is determined based on the minimum feature size of the element. To accurately describe the finest structures, the sampling interval of the grid (i.e., the physical size of a grid point) must be smaller than the minimum feature size (typically requiring the Nyquist sampling theorem to be satisfied).

[0037] Based on the above two points, the required number of grid rows (M) and columns (N) can be calculated. For example, for a square element with a side length of 10 mm, if the minimum feature size is 1 micrometer, the number of grid points M and N may need to reach the order of 10,000 to ensure that each feature structure can be accurately described by multiple grid points.

[0038] Furthermore, this M×N grid serves as the digital stage for the entire design, where all subsequent light field and phase distributions will be defined and calculated.

[0039] This step transforms a continuous physical problem into discrete matrix operations that a computer can process, forming the basis of numerical computation. Furthermore, by binding it to the smallest feature size, it ensures that the design can analyze and control the finest structures, thereby guaranteeing the final diffraction efficiency and pattern fidelity.

[0040] S202. Define the complex amplitude matrix of the incident light field on the grid to describe the spatial distribution of the amplitude and phase of the incident light.

[0041] The incident light field is usually set by the user based on the actual laser source being used.

[0042] First, we need to create an M×N complex matrix.

[0043] For amplitude distribution, if an ideal, uniform parallel laser beam is used, the amplitude value at all grid points is set to 1 (or a constant) to indicate uniform light intensity.

[0044] For phase distribution, for ideal parallel light, the initial phase value at all grid points is set to 0.

[0045] This matrix (denoted as Uin(x,y)) is the complete mathematical description of the incident light field.

[0046] This matrix will be used directly for phase initialization and optical field reconstruction calculations, and is the starting point for light wave propagation.

[0047] This step accurately models the actual light source illuminating the DOE, ensuring consistency between the design and real-world conditions; it uses complex amplitude (containing both amplitude and phase) rather than just light intensity to describe the light field, laying the foundation for subsequent accurate diffraction calculations based on wave optics.

[0048] S203. Define the complex amplitude matrix of the target light field on the grid to describe the amplitude and phase distribution of the light field to be obtained on the target plane.

[0049] The target light field is defined by the user based on the final optical application requirements.

[0050] First, create another M×N complex matrix.

[0051] Amplitude distribution: Set the desired spot pattern on the grid. For example, to generate a uniform circular spot, set the amplitude of grid points within the circular area to 1 and the amplitude outside the area to 0. To generate a multi-point array, set the amplitude value at the corresponding location.

[0052] Phase distribution: Set according to requirements. If only the light intensity distribution needs to be controlled (most imaging and processing applications), set the phase of all points to 0 (plane wavefront).

[0053] This matrix (denoted as Utarget(x,y)) is the target that the design aims to achieve.

[0054] This matrix is ​​used for phase initialization, cascade solution, and evaluation function calculation. It serves as the target and evaluation criterion for the entire optimization process.

[0055] Here, abstract optical requirements are transformed into concrete, quantifiable digital targets. Furthermore, by freely defining this matrix on the grid, arbitrary patterns of light field output can be achieved, expanding the application scope of DOE.

[0056] Mapping the physical world's component size, fabrication capabilities (geometry), and application requirements (target light field) along with the light source characteristics (incident light field) onto discrete grids and matrices in the digital world reduces the computational complexity of diffractive optical component design.

[0057] S102. Based on the incident light field and the target light field, the initial phase modulation distribution of the diffractive optical element is obtained through the diffractive optical geometric mapping theory.

[0058] The theory of geometrical mapping in diffraction optics is a fast approximate estimation method. Its core is to establish a simplified physical model that derives the DOE phase distribution from the target light field. A typical and commonly used method is "back projection" or a simplified formula based on scalar diffraction theory.

[0059] This step provides an initial solution, which can reduce the number of subsequent iterations and prevent the algorithm from "blindly" searching from a completely random phase, thereby accelerating the entire convergence process.

[0060] Specifically, the initial phase modulation distribution of the diffractive optical element is obtained in the following manner: Based on the complex amplitude distribution of the incident light field and the complex amplitude distribution of the target light field, and based on the physical relationship of light wave propagation, a mapping from the complex amplitude of the light field to the phase distribution is established through mathematical transformation. The initial phase distribution of the diffractive optical element is then calculated as the initial phase modulation distribution of the diffractive optical element.

[0061] The complex amplitude distribution of the incident light field is denoted as Uin(x,y)=Ain(x,y)×exp(i in(x,y)), where Ain is the amplitude. in represents the phase (usually 0).

[0062] Complex amplitude distribution of the target light field: Let it be denoted as Utarget(x',y')=Atarget(x',y') ×exp(i target(x',y')), where Atarget is the target amplitude (such as the shape of the light spot). target is the target phase (usually 0).

[0063] Here, if the iteration starts from zero or a random phase, the algorithm would take a long time to "find" the correct direction. This step, however, provides a highly relevant initial solution, allowing subsequent iterations to begin from a region very close to the optimal solution, thus reducing the number of iterations required.

[0064] S103. The phase distribution of the diffractive optical element is solved iteratively using the cascaded angular spectrum propagation method.

[0065] The cascaded angular spectrum propagation iterative solution involves solving the angular spectrum propagator for each level of uniform structural unit (in this scheme, the DOE characteristic size is used as the first-level scale, and the m-th level is the second-order scale of the first-level scale). m times).

[0066] Based on the geometry of the diffractive optical element, its characteristic distribution is divided into multiple scale levels. For each scale level, its angular spectrum propagator is calculated. Based on the target light field and the angular spectrum propagator of the current level, the phase distribution of the current scale level is solved sequentially from the largest scale level to the smallest scale level.

[0067] Based on the geometric structure defined above (especially the feature size), the feature distribution (i.e., phase) of the entire DOE is divided into multiple scales. For example, the first level is the coarsest scale (2 times the feature size). 1 Level 2 is more refined (2 times), Level 2 is more refined (2 times). 2 (multiplied by ), up to the finest m-th level (corresponding to the smallest feature size).

[0068] Calculate the angular spectrum propagator: For each scale level, pre-calculate its corresponding "angular spectrum propagator". This is a mathematical function (based on scalar diffraction theory) that describes how light propagates from the DOE plane to the target plane at that specific scale structure.

[0069] Cascaded solution: Starting from the largest scale (the coarsest profile), using the angular spectral propagator and target light field at that scale, the phase distribution that the DOE should have at that scale is deduced. Then, this result is used as the initial value to proceed to the next smaller scale for refinement. This process is repeated step by step from coarse to fine until the finest phase distribution is obtained.

[0070] This step is to reduce computational complexity (from O(e)). n ) to O(N 2 The key is to decompose the huge and complex global optimization problem into a series of simple local optimization subproblems. Starting from the large scale, the main distribution of light field energy is locked first (the big picture), and then details are added step by step. This effectively avoids the problem that traditional methods are prone to getting stuck in local optima. As a result, the amount of computation at each scale is greatly reduced, and the polynomial complexity increases much slower than the exponential complexity, which reduces the computational complexity of diffractive optical element design and improves the design speed.

[0071] S104. Calculate the reconstructed light field based on the incident light field and phase distribution.

[0072] The complex amplitude of the incident light field is multiplied by the current total phase distribution to obtain the light field at the exit surface of the DOE. Then, the angular spectrum propagation method is used to accurately propagate this exit light field to the target plane, simulating the actual light field that the current DOE design can produce.

[0073] Specifically, please refer to Figure 3 , Figure 3 This is a flowchart illustrating the calculation and reconstruction of the light field provided in an embodiment of this application. Figure 3 As shown, the reconstructed light field is calculated in the following way: S301. Perform a complex multiplication operation between the complex amplitude distribution of the incident light field and the total phase distribution of the diffractive optical element obtained by the current iteration to obtain the complex amplitude distribution of the outgoing light field of the outgoing surface of the diffractive optical element.

[0074] The complex amplitude distribution of the incident light field is a digital matrix initialized at the beginning of the process, representing complete information (intensity and initial wavefront) of the original laser irradiating the DOE.

[0075] The total phase distribution of the DOE is the latest result calculated in the current iteration of the core algorithm (cascaded angular spectrum method) of this application. It represents the DOE design scheme we are currently testing, and is essentially a data matrix that specifies how much delay each point on the DOE should cause to the phase of the light wave.

[0076] A complex multiplication operation is performed between the incident light field matrix and the DOE phase distribution matrix. This operation simulates a real physical process where the wavefront of the incident light is precisely distorted and modulated as it passes through the microstructure of the DOE. The result of the multiplication operation is a new complex matrix, the outgoing light field. It describes the state of the light just as it leaves the DOE surface.

[0077] The calculated outgoing light field serves as the input for the next step, which is a bridge connecting "design" and "effect." Through mathematical calculations, the core "phase modulation" function of DOE is accurately reproduced in the digital world, ensuring the consistency between virtual simulation and real physics.

[0078] S302. Based on the angular spectrum propagator, the complex amplitude distribution of the outgoing light field is calculated by angular spectrum propagation to obtain the light field distribution on the target plane, which is used as the reconstructed light field.

[0079] The angular spectrum propagator is a "propagation model" or "converter" pre-calculated in the core algorithm steps. It encapsulates the physical laws (diffraction effects) that govern the propagation of light from the DOE surface to a distant target plane, and its content depends on fixed parameters such as the wavelength of light and the propagation distance.

[0080] The data of the outgoing light field is input into this angular spectrum propagation sub-model; the model will perform a series of calculations (mainly based on fast Fourier transform) to simulate the changes that occur after light propagates forward a certain distance in free space, including diffraction phenomena such as light diffusion and interference.

[0081] The final output of the calculation is a new complex matrix, which is the reconstructed light field. It is a digital prediction of the actual light spot pattern that the currently designed DOE will produce on the target screen.

[0082] This reconstructed light field will be immediately sent to subsequent steps to be compared with the user's initial ideal target light field, thereby quantifying the merits of the current design.

[0083] This application enables a realistic simulation of diffraction effects, thus ensuring the reliability of the prediction results. The method utilizes the Fast Fourier Transform algorithm, which makes the simulation of such complex physics extremely fast, meeting the needs of rapid iteration.

[0084] S105. Calculate the evaluation function value of the residual between the reconstructed light field and the target light field.

[0085] The reconstructed light field obtained above is compared with the defined target light field. Specifically, the difference in light intensity between the two at each point on an M×N grid is calculated, and then the root mean square (RMS) value of all differences is obtained as the evaluation function value (RMS). This value quantifies the gap between the current design result and the ideal target, thus providing an objective and quantitative evaluation standard. This RMS value is the sole indicator for judging whether the design is successful.

[0086] Specifically, please refer to Figure 4 , Figure 4 This is a flowchart illustrating the evaluation function value for calculating the residual between the reconstructed light field and the target light field, provided in an embodiment of this application. Figure 4 As shown, the evaluation function value of the residual between the reconstructed light field and the target light field is calculated in the following manner: S401. Calculate the light intensity difference between the reconstructed light field and the target light field at corresponding points on the grid.

[0087] Here, the reconstructed light field comes from the output of S302, which is a complex matrix that predicts the actual light field that the current DOE design can produce on the target plane.

[0088] The target light field comes from the complex matrix initially initialized in the process, which defines the user's desired, ideal light field.

[0089] Mesh: The M×N computational mesh initially established based on the DOE geometry.

[0090] First, the two complex matrices, the reconstructed light field and the target light field, are converted into light intensity distribution matrices. Light intensity is the distribution of light energy, which can be directly obtained by calculating the square of the complex amplitude modulus. This step transforms the complex wavefront information into more intuitive brightness information.

[0091] Next, at each corresponding grid point of the two light intensity matrices, a subtraction operation is performed. That is, it compares the difference between the "actual predicted brightness" and the "desired ideal brightness" point by point.

[0092] Finally, this calculation produces a new matrix that records the brightness error of every point on the entire target surface. This data matrix, which contains the errors of all points, is the direct input for the subsequent overall statistical calculation.

[0093] This step transforms the abstract question of whether a design is "good" or "bad" into a precise, quantifiable numerical comparison. This ensures the objectivity and accuracy of the evaluation process; for most DOE applications (such as laser marking and uniform illumination), the accuracy of light intensity (energy) distribution is the primary goal. This step directly evaluates this core indicator, ensuring that the optimization direction is highly consistent with actual application requirements.

[0094] S402. Calculate the root mean square value of all point differences and use the root mean square value as the evaluation function value.

[0095] All point differences are the entire light intensity error matrix calculated above.

[0096] Squaring is performed on all the obtained error values. This serves two purposes: first, to eliminate the possibility of positive and negative errors canceling each other out; and second, to amplify the weight of larger errors, making the algorithm more sensitive to "bad pixels" with poor uniformity.

[0097] Then, calculate the average of all these squared values.

[0098] Finally, the square root of this average is taken to restore its dimensions to their previous level. The final result is the root mean square (RMS) value, which is the evaluation function value for this round.

[0099] This RMS value will be immediately sent to the final decision-making step and compared with a preset indicator (threshold) to determine whether to output the final design or continue iterating.

[0100] We can determine whether the optimization direction is correct by comparing whether the RMS value decreases over multiple consecutive iterations; and we can determine whether the design has been successful by judging whether the RMS value is below a threshold.

[0101] By setting a threshold for the RMS value, the mechanism ensures that the performance of any design in the final output will reach the preset minimum standard, thereby reliably achieving the design goal of high uniformity.

[0102] S106. When the evaluation function value meets the preset index, output the current phase distribution of the diffractive optical element as the final design result of the diffractive optical element.

[0103] In this step, the RMS value is compared with a pre-set threshold (e.g., 0.01).

[0104] If the RMS value is less than the threshold, it means the design result is good enough, the process ends, and the final DOE phase distribution is output, which can be used to guide the manufacturing process.

[0105] If the conditions are not met, return to S103 and start a new round of cascaded iterative optimization based on the phase distribution of the previous round until the target is met.

[0106] Furthermore, the evaluation function value is compared with a preset threshold.

[0107] Preset thresholds are precision standards set by designers before the process begins, based on the performance requirements of the final product. For example, if a light intensity uniformity of 95% is required, a specific RMS threshold (such as 0.05) can be calculated and set accordingly. This threshold serves as an objective benchmark for judging whether the design is "good enough."

[0108] This application compares the evaluation function value with a preset threshold to establish a clear standard, transforming the subjective "whether the design is good or not" into the objective and measurable "whether it is below the threshold", thus giving success a clear definition.

[0109] If the evaluation function value is less than the threshold, it is determined that the preset index is met, and the current phase distribution of the diffractive optical element is output as the final design result of the diffractive optical element.

[0110] If the comparison result is "yes" (i.e., the evaluation function value < preset threshold), then the current design is determined to meet all performance indicators, and the entire iteration cycle is terminated. The phase distribution of the diffractive optical element used in the current iteration is output as the final, qualified design scheme. This phase distribution data can be directly used to generate subsequent micro / nano fabrication drawings.

[0111] The output phase distribution is the final result of the entire design methodology and will be delivered to the manufacturing department for production.

[0112] In this step, by setting thresholds, it is ensured that any output design meets predetermined performance requirements (such as high uniformity). This provides the most fundamental guarantee for the performance of the final product; no manual intervention is required to determine whether the design is qualified.

[0113] If the evaluation function value is greater than or equal to the threshold, it is determined that the preset index is not met, and the process returns to the step of iteratively solving the phase distribution of the diffractive optical element using the cascaded angular spectrum propagation method.

[0114] If the evaluation function value is greater than or equal to the threshold, the current design is determined to be substandard. Instead of outputting a result, the system returns to the core step (S103) with all currently calculated data (especially the current phase distribution).

[0115] Subsequently, in S103, the cascaded angular spectrum propagation method will use the results of the previous iteration as new initial values ​​to start a new round of more refined optimization, thereby producing a theoretically better phase distribution.

[0116] This step connects "evaluation" and "solution" into a loop, allowing the algorithm to continuously improve itself based on each "performance," forming a closed-loop automatic optimization system. This ensures that the quality of the final output will meet the preset accuracy requirements, and the entire process requires no manual intervention, achieving automated design.

[0117] The entire scheme, through the core idea of ​​"cascading," transforms the computational mode from global optimization to progressive optimization from coarse to fine, thereby achieving an order-of-magnitude improvement in computational efficiency while ensuring high diffraction efficiency and high uniformity, and successfully solving the computational bottleneck problem in the design of large-size diffractive optical elements.

[0118] The design method and apparatus for diffractive optical elements provided in this application solve the technical problems of low design efficiency and huge computational resource consumption of large-size diffractive optical elements caused by the exponential growth of computational complexity in the prior art. By introducing the cascaded angular spectrum propagation method to divide the characteristic distribution of diffractive optical elements into multiple scale levels and iteratively solving the phase distribution level step by step, the method and apparatus solve the technical problems of low design efficiency and huge computational resource consumption of large-size diffractive optical elements caused by the exponential growth of computational complexity in the prior art. The method and apparatus solve the technical problems of low design efficiency and huge computational resource consumption ..., while ensuring high diffraction efficiency and high uniformity design accuracy, and reduce the algorithm complexity from exponential to quadratic level, thereby improving the design speed of large-size diffractive optical elements.

[0119] This application targets large-size diffractive optical element (DOE) unit structures. Based on a given target light field, it iterates the DOE phase modulation distribution using the cascaded angular spectrum propagation method, and then approximates the DOE surface height distribution using thin elements. This reduces the complexity of the original algorithm to O(e^(-1 / 2)). n ) transforms into O(N) 2 This ensures both information integrity and rapid reconstruction.

[0120] This application exhibits high diffraction efficiency, high uniformity, and arbitrary patterns because its design method ensures information integrity. Furthermore, the algorithm employed in this application boasts high reconstruction efficiency, reducing the original complexity from O(e^(-1 / 2)) to O(e^(-1 / 2)). n ) transforms into O(N) 2 The design method of this application, due to the use of cascaded angular spectrum reconstruction, can quickly reconstruct large-size structures (above the centimeter level); the design method of this application, due to the use of cascaded angular spectrum reconstruction, can quickly reconstruct DOE structures with large field-of-view diffraction imaging.

[0121] Based on the same inventive concept, this application also provides a design apparatus for diffractive optical elements corresponding to the design method of diffractive optical elements. Since the principle of the apparatus in this application is similar to the design method of diffractive optical elements described above in this application, the implementation of the apparatus can refer to the implementation of the method, and the repeated parts will not be described again.

[0122] Please see Figure 5 , Figure 5 This is a schematic diagram of the design apparatus for the diffractive optical element provided in the embodiments of this application. Figure 5 As shown, the design apparatus 500 for the diffractive optical element includes: Initialization module 501 is used to initialize the complex amplitude distribution of the incident light field, the complex amplitude distribution of the target light field, and the geometry of the diffractive optical element; The initial phase modulation distribution acquisition module 502 is used to obtain the initial phase modulation distribution of the diffractive optical element based on the incident light field and the target light field, through the diffractive optical geometry mapping theory. The phase distribution solution module 503 is used to iteratively solve the phase distribution of the diffractive optical element using the cascaded angular spectrum propagation method. Based on the geometric structure of the diffractive optical element, its characteristic distribution is divided into multiple scale levels. For each scale level, its angular spectrum propagator is calculated. Based on the target light field and the angular spectrum propagator of the current level, the phase distribution of that level is solved sequentially from the largest scale level to the smallest scale level. The reconstructed light field calculation module 504 is used to calculate the reconstructed light field based on the incident light field and the phase distribution; The evaluation function value calculation module 505 is used to calculate the evaluation function value of the residual between the reconstructed light field and the target light field; The final design result output module 506 is used to output the phase distribution of the current diffractive optical element as the final design result of the diffractive optical element when the evaluation function value meets the preset index.

[0123] Please see Figure 6 , Figure 6 This is a schematic diagram of the structure of the electronic device provided in an embodiment of this application. Figure 6 As shown, the electronic device 600 includes a processor 610, a memory 620, and a bus 630.

[0124] The memory 620 stores machine-readable instructions executable by the processor 610. When the electronic device 600 is running, the processor 610 and the memory 620 communicate via the bus 630. When the machine-readable instructions are executed by the processor 610, they can perform the operations described above. Figure 1The steps of the design method for the diffractive optical element in the method embodiment shown are described in detail in the method embodiment, and will not be repeated here.

[0125] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can perform the above-described actions. Figure 1 The steps of the design method for the diffractive optical element in the method embodiment shown are described in detail in the method embodiment, and will not be repeated here.

[0126] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0127] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0128] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0129] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0130] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0131] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The scope of protection of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for designing a diffractive optical element, characterized in that, include: Initialize the complex amplitude distribution of the incident light field, the complex amplitude distribution of the target light field, and the geometry of the diffractive optical element; Based on the incident light field and the target light field, the initial phase modulation distribution of the diffractive optical element is obtained through the diffractive optical geometry mapping theory; The phase distribution of the diffractive optical element is solved iteratively using the cascaded angular spectrum propagation method. Based on the geometric structure of the diffractive optical element, its characteristic distribution is divided into multiple scale levels. For each scale level, its angular spectrum propagator is calculated. Based on the target light field and the angular spectrum propagator of the current level, the phase distribution of that level is solved sequentially from the largest scale level to the smallest scale level. The reconstructed light field is calculated based on the incident light field and the phase distribution; Calculate the evaluation function value of the residual between the reconstructed light field and the target light field; When the evaluation function value meets the preset index, the current phase distribution of the diffractive optical element is output as the final design result of the diffractive optical element.

2. The method according to claim 1, characterized in that, The geometry of the diffractive optical element is initialized in the following manner: Define the length, width, minimum feature size, total height, and number of steps of the diffractive optical element; Wherein, the minimum feature size is the minimum processing size of the microstructure on the surface of the diffractive optical element, the total height is the maximum depth of the microstructure on the surface of the diffractive optical element, and the number of steps is the number of phase levels corresponding to the total height.

3. The method according to claim 2, characterized in that, The complex amplitude distributions of the incident light field and the target light field are initialized in the following manner: Establish a grid corresponding to the geometry of the diffractive optical element, and set the number of rows and columns of the grid; A complex amplitude matrix of the incident light field is defined on the grid to describe the spatial distribution of the amplitude and phase of the incident light. A complex amplitude matrix of the target light field is defined on the grid to describe the amplitude and phase distribution of the light field to be obtained on the target plane.

4. The method according to claim 1, characterized in that, The initial phase modulation distribution of the diffractive optical element is obtained in the following manner: Based on the complex amplitude distribution of the incident light field and the complex amplitude distribution of the target light field, and based on the physical relationship of light wave propagation, a mapping from the complex amplitude of the light field to the phase distribution is established through mathematical transformation. The initial phase distribution of the diffractive optical element is then calculated as the initial phase modulation distribution of the diffractive optical element.

5. The method according to claim 1, characterized in that, The reconstructed light field is calculated using the following method: The complex amplitude distribution of the incident light field is multiplied by the total phase distribution of the diffractive optical element obtained by the current iteration to obtain the complex amplitude distribution of the outgoing light field at the exit surface of the diffractive optical element. Based on the angular spectrum propagator, the complex amplitude distribution of the outgoing light field is calculated by angular spectrum propagation to obtain the light field distribution on the target plane, which is used as the reconstructed light field.

6. The method according to claim 3, characterized in that, The evaluation function value of the residual between the reconstructed light field and the target light field is calculated using the following method: Calculate the light intensity difference between the reconstructed light field and the target light field at corresponding points on the grid; Calculate the root mean square value of all point differences and use this root mean square value as the evaluation function value.

7. The method according to claim 6, characterized in that, When the evaluation function value meets the preset index, the current phase distribution of the diffractive optical element is output as the final design result of the diffractive optical element, including: The evaluation function value is compared with a preset threshold. If the evaluation function value is less than the threshold, it is determined that the preset index is met, and the current phase distribution of the diffractive optical element is output as the final design result of the diffractive optical element. If the evaluation function value is greater than or equal to the threshold, it is determined that the preset index is not met, and the process returns to the step of iteratively solving the phase distribution of the diffractive optical element using the cascaded angular spectrum propagation method.

8. A design apparatus for a diffractive optical element, characterized in that, include: The initialization module is used to initialize the complex amplitude distribution of the incident light field, the complex amplitude distribution of the target light field, and the geometry of the diffractive optical elements. The initial phase modulation distribution acquisition module is used to obtain the initial phase modulation distribution of the diffractive optical element based on the incident light field and the target light field, through the diffractive optical geometry mapping theory. The phase distribution solution module is used to iteratively solve the phase distribution of the diffractive optical element using the cascaded angular spectrum propagation method. Based on the geometric structure of the diffractive optical element, its characteristic distribution is divided into multiple scale levels. For each scale level, its angular spectrum propagator is calculated. Based on the target light field and the angular spectrum propagator of the current level, the phase distribution of that level is solved sequentially from the largest scale level to the smallest scale level. The reconstructed light field calculation module is used to calculate the reconstructed light field based on the incident light field and the phase distribution; The evaluation function value calculation module is used to calculate the evaluation function value of the residual between the reconstructed light field and the target light field; The final design result output module is used to output the phase distribution of the current diffractive optical element as the final design result of the diffractive optical element when the evaluation function value meets the preset index.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is in operation, the processor communicates with the memory via the bus, and the processor executes the machine-readable instructions to perform the steps of the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the method as described in any one of claims 1 to 7.

Images