CN117555133A - White light diffraction optical element and design method thereof - Google Patents
White light diffraction optical element and design method thereof Download PDFInfo
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- CN117555133A CN117555133A CN202311464327.XA CN202311464327A CN117555133A CN 117555133 A CN117555133 A CN 117555133A CN 202311464327 A CN202311464327 A CN 202311464327A CN 117555133 A CN117555133 A CN 117555133A
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- G—PHYSICS
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- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- F21V9/00—Elements for modifying spectral properties, polarisation or intensity of the light emitted, e.g. filters
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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Abstract
The invention discloses a white light diffraction optical element and a design method thereof. Determining input plane parameters of a diffraction optical element according to the incident light caliber of spherical waves by adopting a laser LD white light source, taking a certain distance of the diffraction optical element as an output plane, and defining an output plane target image; the laser LD white light source irradiates on a DOE input plane, the DOE surface phase surface carries out uniform light shaping on incident light, and a target image is obtained on an output plane; preliminary optimization is carried out on the DOE surface shape by adopting a GS/smooth optimization algorithm, and the phase surface shape of the diffraction element during single-wavelength incidence is obtained through iterative calculation; and converting the obtained phase surface into a height value, adding a multi-wavelength incidence condition, and optimizing the height value by using a global optimization algorithm to obtain different height distribution of each pixel point of the diffraction optical element, thereby obtaining the DOE surface type matched with the input and output images. The white light diffraction optical element provided by the invention can effectively improve the diffraction efficiency in the whole wave band and the incident angle range.
Description
Technical Field
The invention relates to a white light diffraction optical element and a design method thereof, belonging to the technical field of optical design.
Background
The laser illumination light source has the characteristics of high power, good monochromaticity, high brightness, small light emitting area, compact structure, strong collimation, long irradiation distance and the like. As a new generation light source, the laser diode has a longer irradiation distance, higher brightness and higher photoelectric conversion efficiency than the LED light source, and the extremely small element size greatly facilitates the design of the external shape. It is believed that as technology advances and matures, laser diodes, with their superior performance, will gradually replace LEDs in the future, becoming the dominant illumination source.
The laser diode is used as a monochromatic light source, white light can be generated by exciting fluorescent powder through blue light or synthesizing three primary colors, and the white light generated by the method is uneven in distribution, and the integral light type cannot meet the illumination requirement, so that the laser diode is required to be matched with an optical system. For conventional optical designs, the laser beam synthesis is shaped by using relay lenses, and various reflective, refractive or array structures are currently used to shape the optical system. The reflection, refraction or array structure optical system based on the law of refraction and reflection is complex, has large volume and heavy weight, and is difficult to realize beam shaping of any shape. Compared with the traditional geometrical optical element, the optical element adopting the diffraction structure has two greatest advantages, namely small volume and light weight, the diffraction structure directly regulates and controls the light field through the surface microstructure, and multiple purposes can be realized through one surface. The second advantage is that the design freedom is large and the use is more. The diffraction optical element can adjust complex parameters such as polarization, directional intensity and the like according to requirements by controlling the size of each micro unit on the surface of the diffraction structure, so as to realize fine control on the light beam.
A Diffractive Optical Element (DOE) generates different diffraction patterns for different wavelengths of light waves, and a conventional diffractive optical element can only satisfy high diffraction efficiency at a designed wavelength, and is difficult to maintain for a broadband beam shaping effect. The DOE therefore works mostly under monochromatic light illumination. The document [ design two-dimensional diffractive optical elements forbeam shaping ofmulticolor light-grouping diodes, appl. Opt,2018,57 (10): 2653-2658] proposes a DOE design algorithm for multi-wavelength light beams based on RGB three wavelength designs, but under white LED illumination, the diffraction spots have a certain chromatic aberration. The broadband DOE design algorithm proposed in document [ Diffractive optical element optimizationunderwide incident angle andwaveband settings, opt. Communications,2020,458:124762] can improve diffraction efficiency over the whole band and range of angles of incidence, but the method is only for the infrared band and cannot be applied to the white light band. The design method of the white light LD diffraction optical element has important practical significance in practical application, but related technical schemes and products are not reported at present.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a white light LD diffraction optical element capable of effectively improving diffraction efficiency in the whole wave band and the incident angle range and a design method thereof.
The technical scheme for realizing the purpose of the invention is to provide a design method of a white light diffraction optical element, which comprises the following steps:
step one, preliminary design of a DOE of a diffractive optical element
(1) Setting input face parameters of DOE, including diffractive optical element size D x 、D y The method comprises the steps of inputting sampling points M, N corresponding to a plane in the x and y directions, and determining an incident pattern with the sampling points of MxN according to initial incident light intensity distribution of a diffraction optical element;
(2) Setting the output face parameters of the DOE, including the diffraction distance z, the desired diffraction output face dimension D X 、D Y The method comprises the steps of carrying out a first treatment on the surface of the The output plane is K, L in the X, Y direction, and the sampling point is K×L diffraction pattern;
(3) Preliminary optimization of DOE phase plane by adopting GS/smooth optimization algorithm
By the ratio of the total intensity of the diffraction pattern expected from the output surface to the total intensity in the input plane
Is the light energy utilization rate evaluation index of DOE, wherein I mn For input ofThe light intensity of the (m, n) th sampling point in the plane; i kl The intensity of the (k, l) th sampling point in the diffraction pattern desired for the output facet;
to output the unevenness of the light intensity in the diffraction pattern area expected by the surface
Is used as the light intensity uniformity evaluation index of DOE, wherein +.>Is the average light intensity within the region;
in the fresnel diffraction region, the forward/reverse diffraction formula according to the scalar diffraction formula:
taking the light energy utilization rate and the light intensity uniformity as evaluation indexes, carrying out Fourier iteration in the forward/reverse direction, and outputting a phase distribution result phi (x, y); wherein i is imaginary unit, λ is wavelength of incident light, and k=2pi/λ is wave number;
according to phi (x, y) -phi 0 (x, y) obtaining a preliminary phase distribution of the designed DOE under incident light single-wavelength conditions, wherein φ 0 (x, y) is the phase distribution of the initial incident light.
Step two: highly optimizing DOE obtained by preliminary design by adopting global optimization algorithm
(1) Converting the DOE preliminary phase distribution obtained in the step one into a height distribution;
(2) Weighted average of energy utilization and light intensity uniformity at different wavelengths at the current DOE profile:
G(ω 1 ,λ 1 ,ω 2 ,λ 2 ,…,ω n ,λ n ,)＝(1-ω 1 )η 1 +ω 1 rms I +(1-ω 2 )η 2 +ω 2 rms I +…+(1-ω n )η n +ω n rms I
the method is an evaluation function of a global optimization algorithm, wherein omega is weight corresponding to different wavelengths;
under the multi-wavelength condition, performing iterative optimization by adopting a global optimization algorithm to obtain the plane parameters of the DOE of the diffraction optical element.
The global optimization algorithm comprises a particle swarm algorithm, a simulated annealing algorithm and a genetic algorithm.
In the first step of the technical scheme of the invention, the forward/inverse direction Fourier iteration is performed, the energy utilization rate and the light intensity uniformity of the output result of each iteration are judged, the next iteration process is GS algorithm optimization when the energy utilization rate is lower, and the next iteration process is smooth optimization algorithm optimization when the light intensity uniformity is lower.
The technical scheme of the invention also comprises a white light diffraction optical element, wherein the plane type parameters of the DOE of the diffraction optical element are obtained by adopting a laser direct writing process according to the design method, and the surface of the photoresist is processed to obtain the white light diffraction optical element.
Compared with the prior art, the invention has the beneficial effects that:
1. the diffraction structure provided by the invention can directly regulate and control the light field through the surface microstructure, has small volume, light weight and large degree of freedom, and can realize multiple purposes through one surface.
2. The broadband DOE design algorithm is not limited to a single wavelength condition, and can effectively improve diffraction efficiency in the whole wave band and the incident angle range.
Drawings
FIG. 1 is an algorithm flow chart of a method for designing a white light diffractive optical element according to the present invention.
FIG. 2 is a schematic diagram of a white light diffraction optical element for shaping Gaussian intensity output light into a flat-top beam according to an embodiment of the present invention;
in the figure, a 1.Ld white light source; 2. a collimating lens; doe;4. diffracting the target surface.
Fig. 3 is a gaussian beam intensity distribution pattern according to an embodiment of the present invention.
Fig. 4 shows a diffraction pattern of the intensity distribution of Gao Jiechao gaussian beams in a desired area provided by an embodiment of the present invention.
Fig. 5 is a phase distribution diagram obtained by the design method of the white light diffraction optical element according to the embodiment of the invention.
Fig. 6 shows simulation results of three kinds of LD diffraction patterns of RGB obtained by the design method of the white light diffraction optical element according to the embodiment of the present invention.
Fig. 7 is a simulation result of a white light LD diffraction pattern obtained by the design method of the white light diffraction optical element according to the embodiment of the present invention.
Fig. 8 is a schematic diagram of DOE morphology obtained by the design method of the white light diffraction optical element according to the embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
Example 1
The LD light source generally uses three primary colors synthesis or blue light to excite yellow phosphor and other technologies to generate white light, and the light intensity distribution on the emergent surface is Gaussian distribution or cosine distribution (lambertian light source).
Referring to fig. 1, a flow chart of a method for designing a white light diffraction optical element according to the present embodiment is provided; the method comprises the following steps:
step one, preliminary design of a DOE of a diffraction optical element:
1. setting DOE input plane parameters
Determining the size D of the diffraction optical element according to the caliber of the incident light of the spherical wave x 、D y Determining the sampling point number M, N of the input plane of the diffraction optical element in the x and y directions according to a sampling principle of fine design, and determining the incident pattern with the sampling point number of MXN according to the initial incident light intensity distribution of the diffraction optical element;
2. setting DOE output face parameters
Determining the diffraction distance z, the desired diffraction output face dimension D X 、D Y The method comprises the steps of carrying out a first treatment on the surface of the The output plane is K, L in the X, Y direction, and the sampling point is K×L diffraction pattern;
3. preliminary optimization of DOE phase plane by adopting GS/smooth optimization algorithm
In the fresnel diffraction region, scalar diffraction/inverse diffraction formula can be known
Wherein: i is an imaginary unit, λ is the wavelength of incident light, k=2pi/λ is the wavenumber, exp is an exponential function.
The positive/negative diffraction formula of scalar diffraction is the positive/negative direction Fourier iterative calculation process in the optimization algorithm;
defining the light energy utilization of the DOE as the ratio of the total intensity of the output diffraction pattern to the total intensity in the input plane, i.e
Wherein: i mn Light intensity for the (m, n) th sampling point in the input plane; i kl Is the light intensity of the (k, l) th sampling point in the output plane.
For the output diffraction pattern uniformity evaluation index, intensity non-uniformity is defined as the square root of the intensity of light in the output diffraction pattern region
Wherein:is the average light intensity in the area where the light intensity is uniformly distributed.
Judging according to the energy utilization rate and the light intensity uniformity of the output result of each iteration, wherein the GS algorithm is optimized in the next iteration process when the energy utilization rate is lower, and the smooth optimization algorithm is optimized in the next iteration process when the uniformity is lower until the output condition is met, so that the final output result phi (x, y) is obtained.
After phi (x, y) is found, phi 0 (x, y) is the phase of the incident light, φ (x, y) - φ 0 (x, y) is the preliminary phase distribution of the designed DOE.
Step two, adopting a global optimization algorithm to perform high optimization
The DOE phase distribution obtained in the first step is only the phase distribution under a single-wavelength condition, a global optimization algorithm (a particle swarm algorithm, simulated annealing, a genetic algorithm and the like) is used, the obtained DOE phase is used as an initial value of global optimization, and a multi-wavelength condition is added for iterative optimization, so that an optimal solution in a wide-band range is sought.
According to the phase-height conversion formula, the DOE preliminary phase distribution obtained in the step one is converted into height distribution, and then different height values of each sampling point are used as optimization variables, and the variable range is set for global optimization calculation.
The evaluation function of the global optimization algorithm is a weighted average of the energy utilization rate and the light intensity uniformity of different wavelengths under the current DOE surface type, and the final evaluation function is as follows:
G(ω 1 ,λ 1 ,ω 2 ,λ 2 ,…,ω n ,λ n ,)
＝(1-ω 1 )η 1 +ω 1 rms I +(1-ω 2 )ω 2 +ω 2 rms I +…+(1-ω n )η n +ω n rms I
wherein ω is the weight corresponding to different wavelengths.
The goal of the global optimization algorithm is to find the evaluation function G (ω 1 ,λ 1 ,ω 2 ,λ 2 ,…,ω n ,λ n (ii) the final output result is the designed DOE's face shape.
Example 2
Referring to fig. 2, a schematic optical path diagram of a design method of a white light diffraction optical element for shaping gaussian intensity outgoing light into a flat-top beam is provided in this embodiment. After passing through the collimating lens 2, the incident light emitted by the LD white light source 1 is incident to the input plane of the DOE 3, the incident light is uniformly shaped by the phase surface of the DOE surface, and a target image is obtained on the diffraction target surface 4 of the output plane.
According to the technical scheme provided in embodiment 1, in the white light diffraction optical element for shaping the gaussian intensity outgoing light into the flat-top beam in this embodiment, the ultra-gaussian distribution can be expressed as:
wherein R is SG And p represents the beam waist radius and the order of the ultra-high-si beam, I 0 Representing the normalized light field intensity. When the order p=2 of the super gaussian beam, the light field distribution of the super gaussian beam is a gaussian beam, and as the order increases gradually, the super gaussian beam gradually approaches a flat top beam, and when the order is 12, the light field distribution of the super gaussian beam is a near flat top beam. Thus, for the DOE input plane, the initial incident light intensity distribution is gaussian, and for the desired region of the output plane, the design objective is a higher order super gaussian beam.
Referring to fig. 3, a gaussian intensity outgoing light intensity distribution pattern is provided for the present embodiment.
It is required to obtain the maximum dimension D at the diffraction distance z=100 mm X ×D Y Diffraction pattern of 12.4mm×12.4mm, the number of sampling points of the diffraction pattern is k=l=1080.
Referring to fig. 4, a Gao Jiechao gaussian beam intensity distribution diffraction pattern is provided in the desired area for this embodiment.
In this embodiment, assuming that the aperture of the incident light is 8.64mm×8.64mm, the parameters of the diffractive optical element are: dimension D x ×D y 8.64mm×8.64mm, and the number of sampling points is m=n=1080.
Based on
And (d) the
G(ω 1 ,λ 1 ,ω 2 ,λ 2 ,…,ω n ,λ n ,)
＝ω 1 η 1 +(1-ω 1 )rms I +ω 2 η 2 +(1-ω 2 )rms I +…+ω n η n +(1-ω n )rms I
According to the optimization algorithm provided by the embodiment, the designed phase distribution is shown in a graph of fig. 5a, and a graph b is an enlarged view of a phase part area in the graph a.
Referring to fig. 6, simulation results of LD diffraction patterns of three wavelengths of red, green and blue are shown; graph a shows the diffraction pattern when the light source wavelength 455nm (blue light) is incident; b is the diffraction pattern when the light source wavelength 532nm (green light) is incident; and c is the diffraction pattern at 633nm (red) incidence.
Referring to fig. 7, simulation results of a white LED diffraction pattern are shown.
Referring to fig. 8, a schematic diagram of DOE morphology obtained by the design method of the white light diffraction optical element provided in this embodiment is shown.
According to the DOE morphological structure parameter provided by the embodiment, the laser direct writing is adopted to process the photoresist surface, so that the white light diffraction optical element is obtained.
Claims (4)
1. A method of designing a white light diffracting optical element, comprising the steps of:
step one, preliminary design of a DOE of a diffractive optical element
(1) Setting input face parameters of DOE, including diffractive optical element size D x 、D y The method comprises the steps of inputting sampling points M, N corresponding to a plane in the x and y directions, and determining an incident pattern with the sampling points of MxN according to initial incident light intensity distribution of a diffraction optical element;
(2) Setting the output face parameters of the DOE, including the diffraction distance z, the desired diffraction output face dimension D X 、D Y The method comprises the steps of carrying out a first treatment on the surface of the The output plane is K, L in the X, Y direction, and the sampling point is K×L diffraction pattern;
(3) Preliminary optimization of DOE phase plane by adopting GS/smooth optimization algorithm
By the ratio of the total intensity of the diffraction pattern expected from the output surface to the total intensity in the input planeIs the light energy utilization rate evaluation index of DOE, wherein I mn Light intensity for the (m, n) th sampling point in the input plane; i kl The intensity of the (k, l) th sampling point in the diffraction pattern desired for the output facet;
to output the unevenness of the light intensity in the diffraction pattern area expected by the surfaceIs used as the light intensity uniformity evaluation index of DOE, wherein +.>Is the average light intensity within the region;
in the fresnel diffraction region, the forward/reverse diffraction formula according to the scalar diffraction formula:
taking the light energy utilization rate and the light intensity uniformity as evaluation indexes, carrying out Fourier iteration in the forward/reverse direction, and outputting a phase distribution result phi (x, y); wherein i is imaginary unit, λ is wavelength of incident light, and k=2pi/λ is wave number;
according to phi (x, y) -phi 0 (x, y) obtaining a preliminary phase distribution of the designed DOE under incident light single-wavelength conditions, wherein φ 0 (x, y) is the phase distribution of the initial incident light;
step two: highly optimizing DOE obtained by preliminary design by adopting global optimization algorithm
(1) Converting the DOE preliminary phase distribution obtained in the step one into a height distribution;
(2) Weighted average of energy utilization and light intensity uniformity at different wavelengths at the current DOE profile:
G(ω 1 ，λ 1 ，ω 2 ，λ 2 ，...，ω n ，λ n ，)＝(1-ω 1 )η 1 +ψ 1 rms I +(1-ω 2 )η 2 +ω 2 rms I +...+(1-ω n )η n +ω n rms I
the method is an evaluation function of a global optimization algorithm, wherein omega is weight corresponding to different wavelengths;
under the multi-wavelength condition, performing iterative optimization by adopting a global optimization algorithm to obtain the plane parameters of the DOE of the diffraction optical element.
2. The method of designing a white light diffracting optical element according to claim 1, wherein: the global optimization algorithm comprises a particle swarm algorithm, a simulated annealing algorithm and a genetic algorithm.
3. The method of designing a white light diffracting optical element according to claim 1, wherein: and (3) carrying out Fourier iteration in the forward/reverse direction, wherein the energy utilization rate and the light intensity uniformity of the output result of each iteration are judged, the next iteration process is GS algorithm optimization when the energy utilization rate is lower, and the next iteration process is smooth optimization algorithm optimization when the light intensity uniformity is lower.
4. A white light diffracting optical element, characterized by: the surface of the photoresist is processed by adopting a laser direct writing process to obtain the plane type parameters of the DOE of the diffraction optical element according to the design method of claim 1, so as to obtain the white light diffraction optical element.
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