CN110596894A - Method and system for designing diffractive optical element - Google Patents

Method and system for designing diffractive optical element Download PDF

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Publication number
CN110596894A
CN110596894A CN201911021030.XA CN201911021030A CN110596894A CN 110596894 A CN110596894 A CN 110596894A CN 201911021030 A CN201911021030 A CN 201911021030A CN 110596894 A CN110596894 A CN 110596894A
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particle
temperature
phase distribution
distribution
complex amplitude
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苏萍
蔡超
宋昱铭
谭峭峰
马建设
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Shenzhen International Graduate School of Tsinghua University
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Shenzhen International Graduate School of Tsinghua 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
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4205—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive optical element [DOE] contributing to image formation, e.g. whereby modulation transfer function MTF or optical aberrations are relevant
    • 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
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4233—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive element [DOE] contributing to a non-imaging application

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  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Diffracting Gratings Or Hologram Optical Elements (AREA)

Abstract

The present invention provides a method and system for diffractive optical element design. The method comprises the following steps: randomly disturbing the phase distribution i of the optical diffraction element at the temperature t in the temperature range to generate n particle swarms; at the temperature t, for each particle in the particle swarm, calculating the fitness of the particle by comparing the complex amplitude distribution of the diffraction pattern with the complex amplitude distribution of the target pattern, and carrying out particle swarm evolution to obtain the globally optimal fitness and the globally optimal solution j of the phase distribution of the corresponding optical diffraction elementk(ii) a Global optimal solution j for phase distribution at temperature tkThe corresponding phase distribution j is obtained by random perturbationmComparison jkAnd jmAnd obtaining the optimal solution of the phase distribution of the optical diffraction element at the temperature t according to the corresponding complex amplitude distribution of the diffraction pattern and the target complex amplitude distribution. The invention can provide diffracted light with good convergence rate and search resultDesigning a design scheme of the optical element.

Description

Method and system for designing diffractive optical element
Technical Field
The present invention relates to the field of optical design technologies, and in particular, to a method and a system for designing a diffractive optical element.
Background
A DOE (diffractive optical element) element is a transmissive optical phase modulation device, and a diffraction field pattern of an arbitrary shape can be obtained by changing the phase distribution of the DOE surface (i.e., the stepped surface shape of the DOE). The design principle of DOE is fresnel diffraction integral formula, with which fourier variation (see formula 3 below) cannot be known in U0(x1, y1) and UxIn the case of (x, y), since an analytical expression of P (x1, y1) is solved, it is necessary to design an efficient numerical algorithm. Currently, the commonly used DOE design algorithms include an iterative GS algorithm, a search-type simulated annealing algorithm, a particle swarm algorithm and the like.
The GS algorithm has the characteristics that the iterative process is fast in convergence, the algorithm is easy to realize, but the algorithm is easy to fall into a local optimal solution; the simulated annealing algorithm can effectively jump out of a local optimal solution, but the annealing process is long, and the time consumption of the algorithm is high; the particle swarm optimization has high convergence speed and wide search range, but still can possibly fall into a local optimal solution.
Therefore, there is a need for improvement of the prior art to provide a design method of diffractive optical element with good convergence speed and search results.
Disclosure of Invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and to provide a method and a system for designing a diffractive optical element by combining an annealing algorithm and a particle swarm algorithm.
According to a first aspect of the present invention, a method for optical diffraction element design is provided. The method comprises the following steps:
step S1: randomly disturbing the phase distribution i of the optical diffraction element at the temperature t in the temperature range to generate n particle swarms;
step S2: at a temperature t, for each particle in the population, calculating the particle by comparing its diffraction pattern complex amplitude distribution with a target pattern complex amplitude distributionThe fitness of the son is calculated, and the particle swarm evolution is carried out to obtain the global optimal fitness and the corresponding phase distribution global optimal solution j of the optical diffraction elementk；
Step S3: global optimal solution j for phase distribution at temperature tkThe corresponding phase distribution j is obtained by random perturbationmComparison jkAnd jmAnd obtaining the optimal solution of the phase distribution of the optical diffraction element at the temperature t according to the corresponding complex amplitude distribution of the diffraction pattern and the target complex amplitude distribution.
In one embodiment, step S1 includes:
setting initial phase distribution solution i-P (x1, y1) of the optical diffraction element at the temperature t;
at the temperature t, randomly disturbing the phase distribution i for n times to obtain the phase distribution inThe term "x 1, y1) +6(x1, y1), where δ (x1, y1) is a random perturbation factor, and ranges from-pi to pi, and x1 and y1 represent two perpendicular direction coordinates in the plane of the optical diffraction element, respectively.
In one embodiment, the particle swarm evolution formula is represented as:
Vn(m+1)＝ωVn(m)+C1×φ1×(Pni-Xn(m))+C2×φ2×(Png-Xn(m))
Xn(m+1)＝Xn(m)+Vn(m+1)
wherein m and m +1 represent the first generation of particle swarm evolution, VnDenotes the velocity, X, of each particlenDenotes the position, ω, C, of each particle1、C2Represents a weight parameter, phi1And phi2Represents that the value of the random number is 0-1, PniRepresents the phase distribution, P, of the individual best optical diffraction element searched for each individual particlengThe phase distribution of the optical diffraction element having the best population searched for in the particle group is shown.
In one embodiment, the weight parameter ω is set to 0.9, C1Is set to 1.5, C2Set to 1.8.
In one embodiment, the fitness of the particle is calculated based on the following loss function:
wherein, Ux(x, y) is the complex amplitude distribution of the diffraction pattern calculated, Ux，ex(x, y) is the target pattern complex amplitude distribution, x and y respectively represent two perpendicular direction coordinates within the imaging plane.
In one embodiment, step S3 includes the following sub-steps:
at temperature t, randomly perturb once jkTo obtain jmCalculating and comparing f (j)m) And f (j)k)；
If f (j)m)≤f(jk) Then use jmReplacing i as an optimal solution of the phase distribution at the temperature, and otherwise, calculating the receiving probability Pr;
if Pr is greater than or equal to r, use jmTo replace i, otherwise with jkReplacing i with the phase distribution optimization solution at the temperature;
where r is a random number, the probability of reception is expressed as:
according to a second aspect of the invention, a system for optical diffraction element design is provided. The system comprises:
a particle group generation unit: randomly perturbing the phase distribution i of the optical diffraction element at a temperature t within a temperature range to generate n particle groups;
a particle swarm evolution unit: for each particle in the particle swarm, calculating the fitness of the particle by comparing the complex amplitude distribution of the diffraction pattern with the complex amplitude distribution of the target pattern at the temperature t, and carrying out particle swarm evolution to obtain the globally optimal fitness and the globally optimal solution j of the phase distribution of the corresponding optical diffraction elementk；
Simulated annealing sheetElement: for a global optimal solution j for the phase distribution at temperature tkThe corresponding phase distribution j is obtained by random perturbationmComparison jkAnd jmAnd obtaining the optimal solution of the phase distribution of the optical diffraction element at the temperature t according to the corresponding complex amplitude distribution of the diffraction pattern and the target complex amplitude distribution.
Compared with the prior art, the invention has the advantages that: the particle swarm algorithm is embedded in the simulated annealing algorithm, and global particle swarm search is carried out after each annealing, so that the method is high in convergence speed and capable of effectively jumping out local extreme points.
Drawings
The invention is illustrated and described only by way of example and not by way of limitation in the scope of the invention as set forth in the following drawings, in which:
FIG. 1 is a flow chart of a method for diffractive optical element design according to one embodiment of the present invention;
FIG. 2 is a flow chart of a method for diffractive optical element design according to one embodiment of the present invention;
FIG. 3 is a schematic diagram of effect verification according to one embodiment of the present invention;
FIG. 4 is a target diffraction pattern according to one embodiment of the present invention;
FIG. 5 is a graph of diffraction effects according to one embodiment of the present invention;
fig. 6 is a diagram of diffraction effects in the prior art.
Detailed Description
In order to make the objects, technical solutions, design methods, and advantages of the present invention more apparent, the present invention will be further described in detail by specific embodiments with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not as a limitation. Thus, other examples of the exemplary embodiments may have different values.
Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate.
According to one embodiment of the present invention, there is provided a method for diffractive optical element design, briefly (referred to herein as the SA-PSO method), as illustrated in connection with fig. 1 and 2, the method comprising the steps of:
step S110, a correlation function of the initial parameters and the design of the diffractive optical element is determined.
For example, the set parameters include: the light source is a plane light wave with the wavelength of lambda, the initial phase distribution solution i of the DOE element is P (x1, y1), the loss function f, the receiving probability Pr (or expressed as Pt), and the random number r, wherein the user (x, y) is a binary discrete function, the range of the function value is-pi to pi, x1 and y1 respectively express two vertical direction coordinates in the DOE plane, and the calculation formula of the receiving probability Pr meets the Metropolis criterion and is expressed as:
the expression of the loss function f is as follows
Wherein U isx(x, y) is the calculated complex amplitude distribution of the diffraction pattern, Ux，ex(x, y) is the target pattern complex amplitude distribution (which can be preset), x and y represent two perpendicular coordinates in the imaging plane, t represents temperature, j representskRepresents the DOE phase distribution optimal solution, j, obtained by particle swarm evolutionmRepresenting perturbations j in the simulated annealing processkCorresponding DOE phase distribution solution.
The loss function is not limited to the formula (2), and other types of loss functions may be used, for example, the calculated diffraction pattern complex amplitude distribution and the target pattern complex amplitude distribution may be weighted to adjust the ratio of the both in the loss function.
In this step S110, the initialization includes an initial phase distribution i of the given DOE element being P (x1, y1), for example, the initial phase distribution i may be a rough solution obtained by using other conventional algorithms, such as the GS algorithm, or an arbitrarily set initial phase distribution, and a start temperature Ts and an end temperature Td of the simulated annealing are set, in this embodiment, the set Ts is greater than Td.
In step S120, the phase distribution of the diffractive optical element is evaluated by using the loss function.
Evaluating the current phase distribution solution i of the DOE element, e.g., using a fourier transform form of the fresnel diffraction integral equation, expressed as:
wherein, in the formula (3), j is an imaginary unit, k is a wave number, λ is a wavelength, z1Represents the diffraction distance.
In calculating Ux(x, y) then the value of the loss function f is calculated using equation (2), where U0(x1, y1) is the complex amplitude distribution of light waves, generally considered to be uniformly distributed plane waves.
And step S130, performing particle swarm evolution at a certain temperature t to obtain the global optimal fitness and the global phase distribution optimal solution of the corresponding diffractive optical element.
Specifically, a particle population is generated: at a temperature t, randomly disturbing the DOE phase distribution i n times, namely changing the phase distribution into inP (x1, y1) + δ (x1, y1), whereby a number n of particle groups are generated at temperature t, where δ (x1, y1) is a random perturbation factor, which is larger at higher temperatures t and smaller at lower temperatures t, which can be implemented using a linearly decreasing manner and whose value distribution ranges from-pi to pi.
Evolving a particle swarm: still continuing at this temperature t, for the above-described generated particle population, the values of the loss function per particle, also referred to as the fitness of the particle, are calculated using equations (2), (3), in this example, the smaller the fitness value the better.
In one embodiment, evolving a population of particles is represented as:
Vn(m+1)＝ωVn(m)+C1×φ1×(Pni-Xn(m))+C2×φ2×(Png-Xn(m)) (4)
Xn(m+1)＝Xn(m)+Vn(m+1) (5)
wherein m and m +1 represent the first generation of the particle swarm evolution, VnDenotes the velocity, X, of each particlenDenotes the position, ω, C, of each particle1、C2Represents a weight parameter, phi1And phi2Represents a random number with a value of 0-1, PniRepresenting the individual best position (i.e. the individual best DOE phase distribution), P, searched for each individual particlengRepresenting the global optimum position searched for the particle swarm (i.e. the best-swarm DOE phase distribution, i.e. the global optimum with respect to the particle swarm). After M generations of evolution, the global optimal fitness and the corresponding optimal DOE phase distribution solution are obtained and are marked as jk。
In particle swarm evolution, the weight parameter ω is a number between 0 and 1, for example, the value C is 0.91、C2Taking a number between 1 and 2, e.g. C1Is set to 1.5, C2Set to 1.8.
Step S140, performing simulated annealing to obtain an optimized solution of phase distribution at the temperature t.
In this step, a simulated annealing is performed, for example, at a temperature t, for N cycles: random perturbation once jkTo obtain jmCalculating f (j)m) And f (j)k) If f (j)m)≤f(jk) Then use jmReplacing i with the optimal solution; otherwise, the receiving probability Pr is calculated by using the formula (1), and if Pr is larger than or equal to r, j is usedmTo replace the original solution i, otherwise to use jkInstead of the original solution i.
And step S150, repeating the steps S120 to S140, and obtaining the phase distribution of the diffraction optical element at each temperature in the temperature range.
After obtaining the optimal solution of the phase distribution at the temperature t, the temperature t is decreased, for example, by one step, and steps S120 to S140 are repeated until all calculations are finished after the temperature is decreased to Td.
It should be noted that, in the first cycle (i.e., at the time of initialization), the phase distribution initial solution i is evaluated by using the loss function in step S120, and after step S140 is executed, the phase distribution optimal solution i obtained after particle swarm evolution and simulated annealing is evaluated, and the optimal solution i continuously changes along with the annealing process. When the temperature Td is reduced to be the temperature Td, the calculation is finished, and besides the optimal solution at each temperature t, the optimal solution with the minimum fitness can be finally obtained to serve as the optimal solution of the invention.
In accordance with the above method, embodiments of the present invention also provide a system for designing a diffractive optical element, for implementing one or more aspects of the above method, for example, the system includes: a particle group generation unit for randomly disturbing a phase distribution i of the optical diffraction element at a temperature t within a temperature range to generate n number of particle groups; a particle swarm evolution unit for calculating the fitness of each particle in the particle swarm by comparing the complex amplitude distribution of the diffraction pattern with the complex amplitude distribution of the target pattern at the temperature t, and performing particle swarm evolution to obtain the global optimal fitness and the phase distribution global optimal solution j of the corresponding optical diffraction elementk(ii) a A simulated annealing unit for globally optimal solution j for phase distribution at temperature tkThe corresponding phase distribution j is obtained by random perturbationmComparison jkAnd jmAnd obtaining the optimal solution of the phase distribution of the optical diffraction element at the temperature t according to the corresponding complex amplitude distribution of the diffraction pattern and the target complex amplitude distribution.
In order to verify the effect of the invention, the SA-PSO algorithm of the embodiment of the invention is used for carrying out phase modulation on the plane wave to obtain the target pattern. Experimental light path as shown in fig. 3, comprising laser, pinhole filter, collimating lens, LCOS, photodetector, where the diffraction distance is 45cm, the DOE element is equivalently simulated by reflective LCOS. The DOE phase distribution obtained in the above embodiment is loaded on the spatial light modulator LCOS, and the laser is turned on to obtain a diffraction pattern. When the target pattern is fig. 4, the simulation result of the resulting pattern is fig. 5(a), and the actual experiment result is fig. 5(b) (a part is cut out). For comparative illustration of the advantages of the SA-PSO algorithm of the present invention, the results obtained by the existing GS algorithm are shown in fig. 6. After comparing the two groups of results, it can be seen that the result of the SA-PSO algorithm of the embodiment of the present invention is closer to the target pattern, and is more excellent in the high brightness part. Experiments show that the method has higher design precision and accuracy.
It should be noted that, although the steps are described in a specific order, the steps are not necessarily performed in the specific order, and in fact, some of the steps may be performed concurrently or even in a changed order as long as the required functions are achieved.
The present invention may be a system, method and/or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions embodied therewith for causing a processor to implement various aspects of the present invention.
The computer readable storage medium may be a tangible device that retains and stores instructions for use by an instruction execution device. The computer readable storage medium may include, for example, but is not limited to, an electronic memory device, a magnetic memory device, an optical memory device, an electromagnetic memory device, a semiconductor memory device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a Static Random Access Memory (SRAM), a portable compact disc read-only memory (CD-ROM), a Digital Versatile Disc (DVD), a memory stick, a floppy disk, a mechanical coding device, such as punch cards or in-groove projection structures having instructions stored thereon, and any suitable combination of the foregoing.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen in order to best explain the principles of the embodiments, the practical application, or improvements made to the technology in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

Claims (8)

1. A method for optical diffraction element design, comprising the steps of:
step S1: randomly disturbing the phase distribution i of the optical diffraction element at the temperature t in the temperature range to generate n particle swarms;
step S2: at the temperature t, for each particle in the particle swarm, calculating the fitness of the particle by comparing the complex amplitude distribution of the diffraction pattern with the complex amplitude distribution of the target pattern, and carrying out particle swarm evolution to obtain the globally optimal fitness and the globally optimal solution j of the phase distribution of the corresponding optical diffraction elementk；
Step S3: global optimal solution j for phase distribution at temperature tkThe corresponding phase distribution j is obtained by random perturbationmComparison jkAnd jmAnd obtaining the optimal solution of the phase distribution of the optical diffraction element at the temperature t according to the corresponding complex amplitude distribution of the diffraction pattern and the target complex amplitude distribution.
2. The method according to claim 1, wherein step S1 includes:
setting initial phase distribution solution i-P (x1, y1) of the optical diffraction element at the temperature t;
at the temperature t, randomly disturbing the phase distribution i for n times to obtain the phase distribution inP (x1, y1) + δ (x1, y1), where δ (x1, y1) is a random perturbation factor, and ranges from-pi to pi, and x1 and y1 represent two perpendicular direction coordinates in the plane of the optical diffraction element, respectively.
3. The method of claim 1, wherein the particle swarm evolution formula is expressed as:
Vn(m+1)＝ωVn(m)+C1×φ1×(Pni-Xn(m))+C2×φ2×(Png-Xn(m))
Xn(m+1)＝Xn(m)+Vn(m+1)
wherein m and m +1 represent the first generation of particle swarm evolution, VnDenotes the velocity, X, of each particlenDenotes the position, ω, C, of each particle1、C2Represents a weight parameter, phi1And phi2Represents that the value of the random number is 0-1, PniRepresents the phase distribution, P, of the individual best optical diffraction element searched for each individual particlengThe phase distribution of the optical diffraction element having the best population searched for in the particle group is shown.
4. A method according to claim 3, characterized in that the weight parameter ω is set to 0.9, C1Is set to 1.5, C2Set to 1.8.
5. The method of claim 1, wherein the fitness for the particle is calculated based on the following loss function:
wherein, Ux(x, y) is the complex amplitude distribution of the diffraction pattern calculated, Ux，ex(x, y) is the target pattern complex amplitude distribution, x and y respectively represent two perpendicular direction coordinates within the imaging plane.
6. The method according to claim 5, wherein step S3 includes the sub-steps of:
at temperature t, randomly perturb once jkTo obtain jmCalculating and comparing f (j)m) And f (j)k)；
If f (j)m)≤f(jk) Then use jmReplacing i as an optimal solution of the phase distribution at the temperature, and otherwise, calculating the receiving probability Pr;
if Pr is greater than or equal to r, use jmTo replace i, otherwise with jkReplacing i with the phase distribution optimization solution at the temperature;
where r is a random number, the probability of reception is expressed as:
7. a system for optical diffraction element design, comprising:
a particle group generation unit: randomly perturbing the phase distribution i of the optical diffraction element at a temperature t within a temperature range to generate n particle groups;
a particle swarm evolution unit: for each particle in the particle swarm, calculating the fitness of the particle by comparing the complex amplitude distribution of the diffraction pattern with the complex amplitude distribution of the target pattern at the temperature t, and carrying out particle swarm evolution to obtain the globally optimal fitness and the globally optimal solution j of the phase distribution of the corresponding optical diffraction elementk；
A simulated annealing unit: for a global optimal solution j for the phase distribution at temperature tkThe corresponding phase distribution j is obtained by random perturbationmComparison jkAnd jmAnd obtaining the optimal solution of the phase distribution of the optical diffraction element at the temperature t according to the corresponding complex amplitude distribution of the diffraction pattern and the target complex amplitude distribution.
8. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 6.
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CN114019597A (en) * 2021-11-12 2022-02-08 深圳市安思疆科技有限公司 Method for designing diffractive optical element, and structured light projector

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Application publication date: 20191220