CN113406793A - DOE element design method based on joint optimization multi-wavelength beam shaping algorithm - Google Patents

DOE element design method based on joint optimization multi-wavelength beam shaping algorithm Download PDF

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CN113406793A
CN113406793A CN202110666002.4A CN202110666002A CN113406793A CN 113406793 A CN113406793 A CN 113406793A CN 202110666002 A CN202110666002 A CN 202110666002A CN 113406793 A CN113406793 A CN 113406793A
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doe
height
algorithm
wavelength
beam shaping
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CN113406793B (en
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许峰
王霖
陈昱杰
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Suzhou University
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0938—Using specific optical elements
    • G02B27/0944—Diffractive optical elements, e.g. gratings, holograms

Abstract

The application provides a DOE element design method based on a joint optimization multi-wavelength beam shaping algorithm, which comprises the following steps: determining a plurality of central wavelengths of the DOE element to be designed, calculating DOE phases corresponding to the central wavelengths based on a GS algorithm, and converting the calculated DOE phases into heights respectively; performing height superposition on each pixel point in DOE elements with different wavelengths, wherein the superposition is the 2 pi phase delay height corresponding to the designed wavelength each time; and calculating the DOE surface shape height when the weighted average value of the energy utilization rate and the illumination uniformity is maximum based on a PSO algorithm. The DOE element designed by the method can realize beam shaping on plane waves with different wavelengths after being collimated by the LED, the energy utilization rate after shaping can reach more than 70%, and the average illumination uniformity can reach more than 90%.

Description

DOE element design method based on joint optimization multi-wavelength beam shaping algorithm
Technical Field
The application relates to the field of non-imaging optical illumination, in particular to a DOE element design method based on a joint optimization multi-wavelength beam shaping algorithm.
Background
A Diffractive Optical Element (DOE) generally refers to a type of Optical device that obtains an arbitrarily shaped light spot at an output surface by phase-modulating incident light with a surface-remodulating structure. Compared with the traditional geometric optical element, the DOE has high degree of freedom in design and strong wavefront modulation capability, is a common beam shaping device, and can change the shape of a beam and regulate and control the light field distribution through reasonable design.
The DOE design for beam shaping is a process of solving the DOE phase from a known incident light field and target surface intensity distribution. And designing the DOE surface relief pattern according to the obtained phase. Algorithms studied for this purpose include geometric transformation, direct binary search, simulated annealing, iterative fourier transform, GS algorithm (GERCHBERG _ SAXTON algorithm), poplar-considered algorithm, genetic algorithm, particle swarm algorithm (PSO algorithm), and various combinations of these methods. The resulting DOE can simultaneously focus and spatially separate discrete wavelengths. However, as the number of design wavelengths increases, the average energy utilization within the desired region decreases significantly.
Disclosure of Invention
To overcome the drawback of a significant reduction in the average energy utilization in the desired region with an increasing number of design wavelengths, the present application aims at: a design method for solving the problem that when the DOE element is used for multiple wavelengths, the energy utilization rate is reduced along with the increase of the number of the designed wavelengths is provided, and the method can improve the energy utilization rate and reduce the number of used optical elements.
In order to achieve the purpose, the following technical scheme is adopted in the application:
a DOE element design method based on a joint optimization multi-wavelength beam shaping algorithm is characterized by comprising the following steps:
determining a plurality of central wavelengths of the DOE element to be designed, calculating DOE phases corresponding to the central wavelengths based on a GS algorithm, and converting the calculated DOE phases into heights respectively;
height superposition is carried out on each pixel point in DOE elements with different wavelengths, each time superposition is carried out to obtain a 2 pi phase delay height corresponding to a designed wavelength, a group with the minimum height difference in a height range corresponding to a plurality of superposed central wavelengths is selected, and an average height value is obtained and used as a surface shape initial height value optimized by a PSO algorithm;
and calculating the DOE surface shape height when the weighted average value of the energy utilization rate and the illumination uniformity is maximum based on a PSO algorithm.
Preferably, according to the design wavelength, adding a self-adaptive weight coefficient into the GS algorithm, wherein the self-adaptive weight coefficient is a value corresponding to the minimum evaluation function value after the GS algorithm is iterated for a preset number of times, and the evaluation function is the square difference between the target light intensity and the iterated light intensity.
Preferably, the adaptive weight coefficient is added to the GS algorithm, the obtained DOE phase is quantized, and the quantized phase information is converted into corresponding height information.
Preferably, when the PSO algorithm is used, the initial height value of the surface shape is taken as the initial particle of the PSO algorithm,
the search height for each pixel in the DOE element is limited to between the minimum set of height differences corresponding to the different selected wavelengths.
Preferably, the calculated DOE phases are respectively calculated according to the following equations:
Figure BDA0003116840270000021
is converted into a corresponding height, and then,
where h is the height, φ is the phase, n (λ)i) Is the refractive index of the material at different incident wavelengths.
Preferably, the DOE element design method based on the jointly optimized multi-wavelength beam shaping algorithm is characterized by further comprising:
and performing height accumulation on each pixel in the DOE element, wherein the accumulated height is the 2 pi phase delay height corresponding to the design wavelength, and the corresponding height of each pixel after the height accumulation is as follows:
Figure BDA0003116840270000031
where the maximum value of k affects the maximum height of the final DOE profile.
Advantageous effects
Compared with the prior art, the DOE element designed by the method can shape the plane waves with different wavelengths after being collimated by the LED, the energy utilization rate after shaping can reach more than 70%, the average illumination uniformity can reach more than 90%, the DOE element designed by the method can realize a good illumination effect, and compared with a light homogenizing scheme adopted in a traditional illumination system, the DOE element can also simplify a light path structure and reduce the number of used optical elements.
Drawings
FIG. 1 is a flow chart of an algorithm according to an embodiment of the present application;
FIG. 2 is a beam-shaping exemplary optical path diagram of a DOE element according to an embodiment of the present application;
FIG. 3 is an ANSI illuminance uniformity test chart of an embodiment of the present application;
FIG. 4 is a schematic diagram of the design wavelength height matching of an embodiment of the present application;
FIG. 5a is a graph illustrating energy efficiency convergence curves at a design wavelength according to an embodiment of the present application;
FIG. 5b is a graph illustrating the convergence of the illumination uniformity at the design wavelength according to the present embodiment;
FIG. 6 is a grayscale image of a DOE element according to an embodiment of the present application;
FIG. 7a is a graph of energy utilization versus random height error for an embodiment of the present application;
FIG. 7b is a graph of luminance uniformity with random height error for an embodiment of the present application;
FIG. 8a is a graph illustrating a variation of single-pixel energy utilization with a single-pixel size error according to an embodiment of the present disclosure;
FIG. 8b is a graph showing uniformity of illumination per pixel as a function of error per pixel size, according to an embodiment of the present invention.
Detailed Description
The above-described scheme is further illustrated below with reference to specific examples. It should be understood that these examples are for illustrative purposes and are not intended to limit the scope of the present application. The conditions employed in the examples may be further adjusted as determined by the particular manufacturer, and the conditions not specified are typically those used in routine experimentation.
The DOE element designed by the method can keep higher energy utilization rate and illumination uniformity, and can greatly simplify an illumination structure. The method is based on combined optimization of a GS algorithm and a PSO algorithm, is suitable for designing the multi-wavelength beam shaping DOE element, disperses the design size of the DOE element to be composed of single pixel points, and has wide application prospect in the field of non-imaging optical illumination.
The DOE element design method based on the jointly optimized multi-wavelength beam shaping algorithm proposed by the present application is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, fig. 1 shows a flowchart of a DOE (Diffractive Optical Element) design algorithm proposed in the present application.
Referring to fig. 1, the DOE element design method based on the jointly optimized multi-wavelength beam shaping algorithm provided by the present application includes the following steps:
determining multiple center wavelengths (at three design wavelengths λ) of a DOE element to be designed1-λ3For example), and calculates the DOE phase corresponding to each center wavelength by using GS algorithm
Figure BDA0003116840270000041
And converting the DOE phase corresponding to each center wavelength into height (i.e., converting the calculated DOE phase corresponding to the center wavelength into height (e.g., converting the calculated DOE phase corresponding to the center wavelength into height)
Figure BDA0003116840270000042
Corresponds to h1(x，λ1、k1) And so on);
respectively carrying out height superposition on each pixel point in DOE elements with different wavelengths (the height H (x, H) of the multi-wavelength DOE elements1，h2，h3) Each time of superposition is 2 pi phase delay height corresponding to the design wavelength, a group with minimum height difference in the height range corresponding to the multiple superposed central wavelengths is selected, and then average height value, namely the height H (x, H) of the multi-wavelength DOE is obtained1，h2，h3) As an initial height value for PSO algorithm optimization, where x represents a pixel location; then using PSO algorithmOptimizing the DOE surface shape height in one step, and setting a comprehensive evaluation function to be F (x, w)1,λ1,w2,λ2,w3,λ3) Where x represents different pixels, w1,w2,w3The weight values corresponding to different wavelengths, and the specific expression of the evaluation function is described below; the condition of the loop jumping out is that the evaluation function value reaches a set value or the k value reaches a set value (the k value determines the DOE surface shape height), otherwise, the iteration is continuously updated until the condition is met, and the optimal result H (x, lambda) is finally output1，λ2，λ3)。
And calculating the DOE surface shape height when the weighted average value of the energy utilization rate and the illumination uniformity is maximum based on a PSO algorithm (Particle Swarm Optimization). According to the design wavelength, adding a self-adaptive weight coefficient into the GS algorithm to avoid premature convergence of the GS algorithm, wherein the self-adaptive weight coefficient is a corresponding numerical value when the GS algorithm is iterated for a certain number of times to minimize an evaluation function value, and the evaluation function is the square difference between target light intensity and iterative light intensity; and then, quantizing the obtained DOE phase to form a step on the continuous surface, so that the processing is convenient, and the quantized phase information is converted into corresponding height information.
When the PSO algorithm is used, the initial height value of the surface shape is used as an initial particle of the PSO algorithm, the search height of each pixel in the DOE element is limited between the minimum height difference groups corresponding to different selected wavelengths, the evaluation function of the PSO algorithm is the weighted average of the energy utilization rate and the illumination uniformity of each wavelength under the current DOE surface shape, the weight coefficient occupied by each wavelength is continuously updated according to the evaluation function value, the optimization direction is enabled to be carried out towards the balanced position of a plurality of designed central wavelengths, finally, the DOE element with similar beam shaping performance under each designed wavelength is obtained, and meanwhile, the DOE element has the maximum energy utilization rate and the illumination uniformity.
Fig. 2 is a typical optical path diagram of beam shaping of a DOE element according to an embodiment of the present application. In this embodiment, a color LED light source is used to emit time-series multicolor light beams, which are collimated into parallel light by a collimating lens and then modulated by a designed DOE element, so as to finally synthesize a target spot on a target plane. Due to persistence of vision of human eyes, the polychromatic light beams satisfying the time sequence can be synthesized into white light in the human eyes. Whether the synthesized light beam in human eyes has the problems of chromatic aberration and the like is influenced by the modulation and shaping of the DOE element on the light beams with different wavelengths.
Fig. 3 is an ANSI illuminance uniformity test chart for an embodiment of the present application. The illuminance uniformity in the algorithm is calculated by adopting an ANSI illuminance uniformity testing method. As shown in fig. 3, P on the screen1～P13Middle maximum illuminance PmaxAnd P1～P13Average value P of illuminance of each pointaveExpressed in percentage N%, the calculation is as follows:
Figure BDA0003116840270000061
or
Figure BDA0003116840270000062
In addition, in the illumination unit, the energy utilization rate is the ratio of the optical power of the target surface area to the optical power emitted by the light source, and represents the utilization rate of the optical path structure of the illumination unit to the energy. On the premise of finally outputting the same optical power, the higher the energy utilization rate of the lighting unit is, the smaller the power consumption of the whole uniform lighting system is, and the expression of the energy utilization rate is as follows:
Figure BDA0003116840270000063
wherein, ItargetIs the light intensity in the target region, ItotalIs the total intensity of the incident light.
Fig. 4 is a schematic diagram of the design wavelength height matching of the embodiment of the present application.
The optimized design of a single-wavelength DOE is phase-specific, while a multi-wavelength DOE is optimized primarily for height. The obtained DOE phase patterns of the respective wavelengths are converted into height maps by a GS algorithm,
the conversion formula is:
Figure BDA0003116840270000064
where h is the height, φ is the phase, n (λ)i) Is the refractive index of the material at different incident wavelengths. Then, performing height accumulation on each pixel in the DOE element, wherein each time of accumulation is 2 pi phase delay height corresponding to the design wavelength, and the corresponding height of each pixel after the height accumulation is as follows:
Figure BDA0003116840270000065
where the maximum value of k affects the maximum height of the final DOE profile. Consider each wavelength at the corresponding pixel height hi(λi,ki) The group with the smallest height difference within the range is selected, and the selection process is shown in fig. 4. And the final height is the weighted average of the selected set, and this height value is then optimized as the initial height value for the PSO algorithm.
Fig. 5 is a DOE optimization algorithm convergence curve of the embodiment of the present application. The mechanism is that the surface height of the multi-wavelength DOE obtained in the process is used as initial particles of a particle swarm algorithm, the search height of each pixel is limited between the minimum groups of the selected height differences, the evaluation function of the particle swarm algorithm is the weighted average of the energy utilization rate and the illumination uniformity of each wavelength under the current DOE surface, and the comprehensive evaluation function expression is as follows:
G(x,λi)＝wN(x,λi)+(1-w)W(x,λi)
wherein, N (x, λ)i) For incident wave lambdaiUniformity of illumination of target area, W (x, lambda)i) For energy utilization. The final evaluation function is therefore of the form:
F(x,w1,λ1,w2,λ2,w3,λ3)＝w1G(x,λ1)+w2G(x,λ2)+w3G(x,λ3)
fig. 5a is a convergence curve of energy utilization rate at a design wavelength, fig. 5b is a convergence curve of illuminance uniformity at the design wavelength, and it can be seen from fig. 5a/5b that the energy utilization rate of each wavelength tends to be the same after a preset number of iterations (about 8 to 9) of PSO algorithm optimization, and the illuminance uniformity has a smaller change with the number of iterations. Theoretically, the energy utilization rate of each wavelength is higher than 73%, the difference is small, the average illumination uniformity is about 91.2%, and better illumination effect can be achieved overall.
Fig. 6 is a DOE element grayscale image of an embodiment of the present application.
FIG. 7 is a graph of random height error for an embodiment of the present application. The errors of the DOE illumination system designed by the algorithm mainly come from the machining errors of the DOE, and the machining errors are mainly divided into transverse machining errors and longitudinal machining errors. Random height errors of +/-0.05 mu m to +/-1 mu m are added into the DOE designed by the algorithm, the scalar diffraction theory is utilized to simulate the three design wavelengths respectively, variation curves of illuminance uniformity and energy utilization rate along with the random height errors are obtained and are shown in figures 7a and 7b, the energy utilization rate of each wavelength of the DOE element is reduced along with the increase of the random height errors, and when the random height errors are +/-1 mu m, the energy utilization rate of each wavelength tends to be consistent, namely, the DOE loses the beam shaping effect on each wavelength. However, the uniformity of the illuminated surface fluctuates with the increase of the random height error, and it can be considered that the incident light is modulated to a larger range of planes after the random height error is increased, but is still more uniform on the illuminated surface.
Fig. 8a and 8b are graphs of single pixel size error curves for embodiments of the present application. The analysis of the lateral error in the invention focuses on the processing dimension error of each pixel point, and three design wavelengths are respectively simulated by utilizing a scalar diffraction theory, so that the change curves of the illuminance uniformity and the energy utilization rate along with the pixel dimension error are obtained as shown in figures 8a and 8b, the energy utilization rate and the illuminance uniformity of the single pixel processing error of the DOE are reduced along with the deviation of the single pixel point dimension from the design dimension, but the final error can still maintain higher energy utilization rate and illuminance uniformity within the range of +/-0.5 mu m, and the DOE designed by applying the algorithm is not sensitive to the error of the single pixel dimension in the lateral processing error.
The above embodiments are merely illustrative of the technical concepts and features of the present application, and the purpose of the embodiments is to enable those skilled in the art to understand the content of the present application and implement the present application, and not to limit the protection scope of the present application. All equivalent changes and modifications made according to the spirit of the present application are intended to be covered by the scope of the present application.

Claims (7)

1. The DOE element design method based on the joint optimization multi-wavelength beam shaping algorithm is characterized by comprising the following steps of:
determining a plurality of central wavelengths of the DOE element to be designed, calculating DOE phases corresponding to the central wavelengths based on a GS algorithm, and converting the calculated DOE phases into heights respectively;
performing height superposition on each pixel point in DOE elements with different wavelengths, wherein the superposition is the 2 pi phase delay height corresponding to the designed wavelength each time;
and calculating the DOE surface shape height when the weighted average value of the energy utilization rate and the illumination uniformity is maximum based on a PSO algorithm.
2. The DOE element design method based on the joint optimization multi-wavelength beam shaping algorithm according to claim 1,
and selecting a group with the minimum height difference in the height range corresponding to the plurality of superposed central wavelengths, and taking an average height value, wherein the average height value is used as a surface shape initial height value optimized by a PSO algorithm.
3. The DOE element design method based on the joint optimization multi-wavelength beam shaping algorithm according to claim 1,
and adding a self-adaptive weight coefficient into the GS algorithm according to the design wavelength, wherein the self-adaptive weight coefficient is a corresponding numerical value when the evaluation function value is minimum after the GS algorithm is iterated for a preset number of times, and the evaluation function is the square difference between the target light intensity and the iterated light intensity.
4. The DOE element design method based on the joint optimization multi-wavelength beam shaping algorithm according to claim 3,
and after adding the self-adaptive weight coefficient into the GS algorithm, quantizing the obtained DOE phase, and converting the quantized phase information into corresponding height information.
5. The DOE element design method based on the joint optimization multi-wavelength beam shaping algorithm according to claim 1,
when the PSO algorithm is used, the initial height value of the surface shape is taken as the initial particle of the PSO algorithm,
the search height for each pixel in the DOE element is limited to between the minimum set of height differences corresponding to the different selected wavelengths.
6. The DOE element design method based on the joint optimization multi-wavelength beam shaping algorithm according to claim 1,
the calculated DOE phases are respectively calculated according to the following formula:
Figure FDA0003116840260000021
is converted into a corresponding height, and then,
where h is the height, φ is the phase, n (λ)i) Is the refractive index of the material at different incident wavelengths.
7. The DOE element design method based on the joint optimization multi-wavelength beam shaping algorithm according to claim 6, further comprising:
and performing height accumulation on each pixel in the DOE element, wherein the accumulated height is the 2 pi phase delay height corresponding to the design wavelength, and the corresponding height of each pixel after the height accumulation is as follows:
Figure FDA0003116840260000022
where the maximum value of k affects the maximum height of the final DOE profile.
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