A Design Method for the Phase Structure of a Diffractive Optical Element

Abstract

The present invention discloses a design method for the phase structure of a diffractive optical element. The steps of this method are as follows: 1) Establish a functional relationship between the phase structure of the diffractive element, the input conditions, and the output target values according to specific requirements; 2) Given the incident light conditions and the desired output light intensity distribution, give the initial phase structure of the diffractive element; 3) Add a random function to the initial phase structure multiple times, and obtain the light intensity distribution of the corresponding output surface according to the known conditions; 4) Among the obtained multiple light intensity distributions, select the solution closest to the target value as the temporary sub-optimal solution; 5) Around the selected multiple temporary sub-optimal solutions, gradually change the variation value interval of the diffractive element phase structure variables from dense to sparse, calculate the output results one by one, and compare them with the ideal target value; 6) When the gap between the output result and the ideal target value meets the requirements, the iteration is completed.

Description

Technical Field

[0001] The present invention belongs to the technical field of applied optics, and particularly relates to a design method for the phase structure of a diffractive optical element. Background Art

[0002] Diffractive optical elements use diffraction structures on the surface at the micron and nanometer scales to perform phase modulation on incident light waves, thereby achieving arbitrary wavefront transformation functions that are difficult to achieve with traditional optical elements. They can be widely used in fields such as beam shaping, beam splitting, holographic display, and AR, and have the advantages of small volume, light weight, and easy replication.

[0003] However, for the phase structure of diffractive elements, since it is difficult to directly obtain its analytical solution through the diffraction equation, currently, the phase recovery method is mostly used to optimize the design of the diffraction structure. According to the known incident light conditions and the light intensity distribution conditions of the desired output light field, a design objective function is constructed, and one or more optimization algorithms are used to solve the phase structure of the diffractive element. In the process of optimizing the design of the phase structure, some algorithms have high optimization efficiency and local optimization accuracy, but are prone to falling into local extreme points and have low optimization reliability; some algorithms have a mechanism to jump out of local extreme points and can search the entire solution space, but often it is difficult to quickly obtain the global optimal solution. For the design of the phase structure of diffractive elements, the convergence speed and global optimization accuracy are always the pursued goals. Summary of the Invention

[0004] The present invention aims to overcome the problem of the contradiction between the global optimization accuracy and the convergence speed in the process of optimizing the phase structure of diffractive optical elements, and proposes a design method for the phase structure of diffractive optical elements. By setting the search conditions for independent variables, the search range of the global optimal solution is reduced, and the convergence speed of the operation is improved.

[0005] To achieve the above object, the technical solution adopted by the present invention to solve the above technical problem is: A design method for the phase structure of a diffractive optical element, comprising the following steps:

[0006] Step (1), establishing a functional relationship between the phase structure of the diffractive element, the input conditions, and the output target value;

[0007] Step (2), given the incident light conditions and the light intensity distribution on the output surface of the desired diffraction field, giving the initial phase structure of the diffractive element;

[0008] Step (3), adding a random function to the initial phase structure multiple times, and obtaining the corresponding output result for each calculation according to the functional relationship given in step (1);

[0009] Step (4), among the obtained multiple output results, selecting the solution with a relatively small difference from the ideal target value as the temporary sub-optimal solution;

[0010] Step (5): Around the selected multiple temporary sub-optimal solutions, gradually change the variation value interval of the phase structure variables of the diffraction element from dense to sparse, calculate the output results one by one, and compare them with the ideal target value.

[0011] Step (6): When the gap between the output result and the ideal target value meets the requirements, the iteration is completed.

[0012] Further, the functional relationship in the above step (1) is as shown in Equation (1)

[0013]

[0014] Where: Φ(x, y) is the phase structure of the diffraction element, λ is the wavelength of the incident light, A0(x, y) is the amplitude of the incident light, r is the distance from a point on the diffraction plane to a point on the output plane, k = 2π / λ is the wave number, θ is the diffraction angle, and I(ξ, ζ) is the light intensity distribution on the output plane.

[0015] Further, in the above calculation step (5), the variation value interval of the phase structure variables gradually changes from dense to sparse. The specific variation rule is as follows: First, set the variation value interval of the variable to be dense, calculate the output results one by one. When the change in the gap between the output result and the ideal target value tends to a stable state, increase the value interval, continue to observe and compare the gap between the output result and the ideal target value. When it tends to be stable again, further increase the variation value interval of the phase structure variables, and repeat the above calculation process; If a better solution appears in the stage where the variable change interval is sparse than in the dense stage, use this as a new starting point, and gradually change the variable change interval from dense to sparse again according to the above process, compare the output result with the ideal target value, and screen out the better results one by one; During the entire calculation process, if the gap between the output result and the ideal target value meets the design requirements, the calculation is terminated.

[0016] Compared with the prior art, the present invention has the following advantages and effects:

[0017] The method provided by the present invention overcomes the contradiction between the optimization reliability and the optimization efficiency in the optimization design process of the phase structure of the diffractive element. By setting the search conditions for the independent variables, the search range of the global optimal solution is reduced, and the convergence speed of the operation is increased. In the process of searching for the optimal solution of the phase structure, first, a random function is attached to the initial structure multiple times, and the output results of the diffractive field obtained are compared. Its function is to quickly find relatively better solutions globally and use them as important focuses for further optimization. Because near these relatively better solutions, by changing the phase structure and comparing the output results, the probability of finding a better solution is extremely high; immediately around these relatively better solutions, the change interval of the phase structure variables is set from dense to sparse and the output results are further compared. Its function is to adopt as high a sampling accuracy as possible near the optimal solutions and relatively better solutions with high probability, gradually expand the search range, and as the change trend of the output results becomes stable, reduce the amount of numerical calculation as much as possible and at the same time check for omissions. The method provided by the present invention, by reasonably setting the search conditions, not only ensures the sampling accuracy in the phase structure optimization process but also takes into account reducing the amount of numerical calculation, which is conducive to quickly screening out the optimal solution of the phase structure of the diffractive element that meets the requirements of the diffractive field output target. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 FIG. is a schematic diagram of the positional relationship between a diffractive element including a phase structure, incident light, and a target output surface;

[0019] Figure 2 FIG. is a flowchart of the calculation steps for the optimization design of the phase structure of the diffractive element;

[0020] Figure 3 FIG. is a schematic diagram of the phase structure of the diffractive element.

[0021] The description of the reference numerals is as follows:

[0022] 1 - Incident light, 2 - Diffractive element, 3 - Target output surface. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] In order to make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0024] A design method for the phase structure of a diffractive optical element provided by the present invention specifically includes the following steps:

[0025] Step 1: Refer to Figure 1, Incident light (1) irradiates on a diffraction element (2) containing a phase structure under certain determined and known conditions. After being modulated by the phase structure of the diffraction element (2), it continues to propagate, and an output result of the light intensity distribution is obtained on the output plane (3). According to the diffraction integral equation of light, a functional relationship is established among the phase structure of the diffraction element (2), the input conditions of the incident light (1), and the output result of the target output plane (3).

[0026] In this embodiment, the functional relationship refers to Equation (1):

[0027]

[0028] Where: Φ(x, y) is the phase structure of the diffraction element, λ is the wavelength of the incident light, A0(x, y) is the amplitude of the incident light, r is the distance from a point on the diffraction plane to a point on the output plane, k = 2π / λ is the wave number, θ is the diffraction angle, and I(ξ, ζ) is the light intensity distribution on the output plane.

[0029] The relationship between the phase structure Φ(x, y), the wavelength of the incident light, and the output target can also be simplified according to specific requirements.

[0030] Step 2: Given the conditions of the incident light (1) and the desired light intensity distribution on the output plane (3) of the diffraction field, an initial phase structure of the diffraction element (2) is given.

[0031] The initial phase structure can be a phase modulation function given according to the input-output conditions and diffraction theory, or it can be a phase structure distribution that has been preliminarily optimized by other algorithms in advance but still has a gap from the target value and needs further optimization.

[0032] See Figure 3 the schematic diagram of the phase structure. The grid cells in the figure represent the phase structure units of the diffraction element (2). The shade of each cell color represents the magnitude of the phase value of the cell, and the phase value ranges from 0 to 2π.

[0033] Step 3: Add a random function to the initial phase structure of the diffraction element (2) multiple times. According to the functional relationship given in Step 1, the light intensity distribution results of the corresponding output plane (3) are obtained for each calculation.

[0034] Step 4: Among the multiple obtained output results, select the solution with a relatively smaller gap from the ideal target value as a temporary sub-optimal solution.

[0035] Step 5: Around the selected multiple temporary sub-optimal solutions, gradually change the variation value interval of the phase structure variables of the diffraction element (2) from dense to sparse, calculate the light intensity distribution of the output plane (3) one by one, and compare it with the ideal target value.

[0036] The specific method for gradually changing the interval of the change of the phase structure variables from dense to sparse is as follows: first, set the interval of the change of the variables to dense, calculate the output results one by one, and when the difference between the output results and the ideal target values ​​tends to be stable, increase the interval of the value, continue to observe and compare the difference between the output results and the ideal target values, and when it tends to be stable again, further increase the interval of the change of the phase structure variables, and repeat the above calculation process; if a better solution appears in the stage of sparse variable change interval than in the dense stage, then take this as a new starting point, and re-change the interval of the variable change from dense to sparse according to the above process, compare the output results with the ideal target values, and screen for better results one by one.

[0037] Step 6: During the entire calculation process, when the gap between the output result and the ideal target value meets the design requirements, the iteration is completed and the optimal solution is output.

[0038] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention.

Claims

1. A design method for the phase structure of a diffractive optical element, characterized in that, It includes the following steps: Step (1), establishing the functional relationship between the phase structure of the diffraction element, the input conditions, and the output target value; Step (2), given the incident light conditions and the desired light intensity distribution on the output surface of the diffraction field, giving the initial phase structure of the diffraction element; Step (3), adding a random function to the initial phase structure multiple times, and obtaining the corresponding output results for each calculation according to the functional relationship given in Step (1); Step (4), among the obtained multiple output results, selecting the solution with a relatively small difference from the ideal target value as the temporary sub-optimal solution; Step (5), around the selected multiple temporary sub-optimal solutions, gradually changing the variation value interval of the diffraction element phase structure variable from dense to sparse, calculating the output results one by one, and comparing them with the ideal target value; Step (6), when the difference between the output result and the ideal target value meets the requirements, the iteration is completed.

2. The design method of the phase structure of a diffractive optical element according to claim 1, characterized in that: The functional relationship in the above Step (1) is as shown in Equation (1). Where: Φ(x, y) is the phase structure of the diffraction element, λ is the wavelength of the incident light, A0(x, y) is the amplitude of the incident light, r is the distance from a point on the diffraction surface to a point on the output surface, k = 2π / λ is the wave number, θ is the diffraction angle, and I(ξ, ζ) is the light intensity distribution on the output surface.

3. A design method for the phase structure of a diffractive optical element according to claim 1 or 2, characterized in that: In the above Step (5), the variation value interval of the phase structure variable gradually changes from dense to sparse. The specific change rule is that first, the variation value interval of the variable is set to be dense, and the output results are calculated one by one. When the change in the difference between the output result and the ideal target value tends to a stable state, the value interval is increased, and the difference between the output result and the ideal target value is continuously observed and compared. When it tends to be stable again, the variation value interval of the phase structure variable is further increased, and the above calculation process is repeated; If a better solution appears in the sparse stage of the variable change interval than in the dense stage, then taking this as a new starting point, re-gradually changing the variable change interval from dense to sparse according to the above process, comparing the output result with the ideal target value, and screening out the better results one by one; During the entire calculation process, if the difference between the output result and the ideal target value meets the design requirements, the calculation is terminated.

Images