Pure phase hologram optimization method based on combination of non-iterative algorithm and simulated annealing algorithm

Abstract

The invention discloses a method for efficiently optimizing an optical pure phase hologram, and belongs to the field of optics, and the optimized pure phase hologram can accurately and efficiently modulate an ideal light field or pattern. According to the invention, a non-iterative optimization algorithm and an iterative optimization algorithm are combined, and then a chromatographic measurement technology is used to check whether a modulated light field accords with theoretical calculation. The optimization and tomographic measurement mainly comprises the following steps: optimizing a pure phase hologram by using a non-iterative algorithm to obtain a pure phase hologram 1, loading the pure phase hologram 1 to a spatial light modulator to modulate a light field, and dynamically optimizing the pure phase hologram by using a simulated annealing algorithm in an iterative optimization algorithm. And after the optimization is finished by utilizing the simulated annealing algorithm, analyzing the optimized light field by utilizing a technical means of chromatographic measurement so as to ensure that an optimization result accords with a theoretical calculation result.

Description

Technical Field

[0001] The invention belongs to the field of optics, and in particular to a method for efficiently and accurately optimizing a pure phase hologram. Background Art

[0002] A pure phase hologram is an optical element used to record the phase information of an object. When the pure phase hologram carrying the phase information of the object is loaded onto a phase-type spatial light modulator, the original object can be reconstructed on the reconstruction plane. However, due to air turbulence, lens aberrations and other reasons, the reconstruction results are often biased. Therefore, how to effectively optimize under these objective conditions has become a key issue in current research. At present, the optimization methods are mainly divided into non-iterative optimization algorithms and iterative optimization algorithms. However, non-iterative optimization algorithms cannot obtain an exact solution, but only an approximate solution, and cannot eliminate the influence of objective conditions. Among the iterative algorithms, the Gerchberg-Saxton (GS) algorithm is a more representative algorithm with the advantage of fast convergence. However, the GS algorithm is prone to fall into the local optimum and cannot obtain the global optimal solution. Another iterative algorithm is the simulated annealing (SA) algorithm, which can jump out of the local optimum and find the global optimal solution. However, the SA algorithm has high requirements for the accuracy of setting parameters and a slow convergence process. In order to overcome the above problems, the present invention proposes a method of combining a non-iterative optimization algorithm with a simulated annealing algorithm, using the non-iterative optimization algorithm to provide an initial solution, providing a high-quality initial value for the simulated annealing algorithm, and at the same time improving the optimization efficiency, ensuring that the final result is more accurate, and has broad application prospects. Summary of the invention

[0003] The present invention provides an efficient and accurate method for optimizing pure phase holograms. The method combines the advantages of non-iterative optimization algorithms and simulated annealing algorithms, and can not only quickly provide approximate solutions, but also further optimize through simulated annealing algorithms to ensure the reconstruction of ideal light fields or patterns. Through this method, the optimization efficiency is significantly improved, and the limitations of a single algorithm in processing complex objects are overcome. It is particularly suitable for complex light field reconstruction tasks, such as light field transmission, holographic imaging, and optical communications. By optimizing the operating procedures of the optical system, the method enables the technology to efficiently and accurately complete tasks in practical applications, and has high reliability.

[0004] To achieve the above objectives, the present invention adopts the following technical solutions:

[0005] When the incident light field is:

[0006] The modulated light field is:

[0007] The phase information recorded by the pure phase hologram is: H(x,y)=Φout (x,y)-Φ in (x,y), H(x,y) needs to be optimized;

[0008] An optimization method combining a non-iterative optimization algorithm and a simulated annealing algorithm comprises the following steps:

[0009] (1) Use a non-iterative algorithm to optimize H(x,y), that is, Where A(x,y)=E out (x,y) / E in (x,y),Φ(x,y)=Φ out (x,y)-Φ in (x, y), sinc(a) = sina / a;

[0010] (2) The pure phase hologram obtained by the non-iterative algorithm in step (1) is used as the initial value of simulated annealing, and the hologram is optimized twice on the optical path by using a feedback system. The optimization result is the result of the combination of non-iterative optimization and simulated annealing.

[0011] (3) The light field obtained after optimization by combining the non-iterative optimization algorithm and the simulated annealing algorithm in (2) is subjected to tomographic measurement to ensure that the optimization result is consistent with the theoretical calculation.

[0012] In the above steps, the optimization of the pure phase hologram using a non-iterative algorithm in step (1) is completed on a computer.

[0013] In step (2), the secondary optimization using the simulated annealing algorithm is performed in the optical path.

[0014] The tomographic measurement in step (3) is to project the complex light field (U(x,y)) to be measured onto a set of complete orthogonal bases, that is, Here LG is Laguerre-Gaussian mode light.

[0015] Beneficial effects: The optimization method proposed in the present invention combines the non-iterative optimization algorithm and the simulated annealing algorithm, which significantly improves the optimization efficiency and accuracy of the pure phase hologram. Compared with the existing single algorithm, the present invention overcomes the shortcomings of non-iterative optimization that cannot obtain an exact solution and the slow convergence speed of the simulated annealing algorithm. By introducing tomography measurement technology, the present invention can accurately evaluate the optimization results. Test results show that the fidelity of the optimized light field reaches an average of more than 99%, ensuring a high degree of consistency between the optimized light field and theoretical expectations, and has extremely high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1It is a schematic diagram of the optical path configuration during the implementation of the present invention, showing the optical transmission path between the laser source, the spatial light modulator, the lens group, the light field reconstruction plane and the measurement device. The optical path design ensures the accurate modulation and measurement of the optimized light field;

[0017] Figure 2 is the theoretical light field of the light field reconstructed by the present invention;

[0018] Figure 3 It is the light field reconstructed by the present invention using the non-iterative optimization algorithm;

[0019] Figure 4 The present invention implements a non-iterative optimization algorithm and a simulated annealing algorithm to optimize the hologram and reconstruct the light field;

[0020] Figure 5 is a light path diagram for tomographic measurement of the present invention;

[0021] Figure 6 This is a result diagram of tomographic measurement of the light field optimized by the present invention;

[0022] Figure 7 It is a quantitative calculation diagram of the tomographic measurement results of the light field optimized by the present invention. DETAILED DESCRIPTION

[0023] The present invention is described in detail below with reference to the accompanying drawings and specific implementations:

[0024] Figure 1 The figure shows the optical path diagram for optimizing the pure phase hologram. The laser (Laser, Thorlabs S1FC660) is used as the light source. Through the beam expander composed of the lens group (L1, L2), the light is approximately a plane wave and irradiated on the reflective spatial light modulator (SLM, MeadowlarkOptics, P1920-400 800-HDMI). The pure phase hologram optimized by the non-iterative algorithm is loaded on the spatial light modulator to modulate the light. The modulated light passes through a 4f system composed of lenses (L3, L4) and a spatial filter (SF) to select the diffracted light of the positive first order.

[0025] Figure 2 shows the theoretical pattern of the complex light field that needs to be optimized and is also the target light field to be obtained, which are Laguerre-Gaussian light (LG 11 LG 22 ) and Hermite-Gaussian light (HG 11 , HG 22 ).

[0026] The pure phase hologram is optimized by combining the non-iterative algorithm and the simulated annealing algorithm, including the following steps:

[0027] (1) Calculate LG using the non-iterative method 11 LG 22 , HG 11 , HG 22 Pure phase holograms of four light fields. The results of reconstructing the light fields are shown in Figure 3 ;

[0028] (2) The pure phase hologram obtained by the non-iterative optimization algorithm in step (1) is used as the initial value and loaded onto the spatial light modulator, and then a secondary optimization is performed using the simulation algorithm;

[0029] (3) The optimization process of the simulated annealing algorithm consists of two parts: the outer loop and the inner loop. The outer loop is responsible for controlling the change of the global temperature and setting the initial temperature; the inner loop performs multiple local optimizations at a given temperature, controls the number of optimizations in each round (i.e., the length of the Markov chain), and continuously adjusts the temperature and local disturbances so that the hologram gradually approaches the optimal solution.

[0030] (4) At the set initial temperature, the simulated annealing algorithm starts the inner loop. In the first inner loop, the optimized initial hologram is first loaded onto the spatial light modulator, the modulated light is transmitted to the reconstruction plane through the optical system, the camera captures the reconstructed light field, and the image is fed back to the computer for processing, and the correlation coefficient β1 between the light field and the target light field is calculated. The specific formula is: The reconstructed light field is R(x,y), the target light field is T(x,y), and the integration area is A;

[0031] (5) Since the simulated annealing algorithm simulates the cooling process of an object, the value function is set to g = 1-β, and then step (4) calculates g1, which is temporarily stored in the memory;

[0032] (6) Then, the computer will give the hologram Figure 1 A perturbation is performed, and the hologram with the perturbation is loaded onto the spatial modulator as a new hologram. At the end of the optical path, a camera is used to take a picture of the newly modulated light field, and the picture is sent back to the computer to calculate the correlation coefficient g2.

[0033] (7) If g2 is less than g1, the new hologram will definitely be accepted. Otherwise, it will be accepted with a certain probability, which is:

[0034] (8) The inner loop is analogous to this, and the number of loops is the length of the Markov chain set at the beginning;

[0035] (9) When the internal circulation is completed, the initial temperature begins to cool down. The cooling principle is: T k =α kT0(T0>0,0<α<1,k=1,2,3,...)

[0036] (10) After the temperature drops, a new internal cycle begins, and so on, until the temperature drops to the set threshold, ending the cycle.

[0037] Picture 4 is the pure phase hologram and reconstructed light field image optimized by combining the non-iterative optimization algorithm and the simulated annealing algorithm;

[0038] Then the modulated light field is measured using the tomography measurement technique. Figure 5 , including the following steps:

[0039] (1) Place the second reflective spatial light modulator (SLM, Hamatsu LCOS-SLM, X15213) at the position of light field reconstruction;

[0040] (2) Loading a set of pure phase holograms of a complete orthogonal basis after LG mode optimization onto the second spatial light modulator;

[0041] (3) placing a lens on the reflected light path of the second spatial light modulator;

[0042] (4) Take a picture with a camera on the back focal plane of the lens and read the number of photons, then reconstruct the density matrix and calculate the fidelity.

[0043] The results of the above chromatography are shown in Figure 6 The quantitative calculation results are shown in Figure 7 , LG 11 LG 22 , HG 11 , HG 22 The fidelity is 0.995, 0.987, 0.992, and 0.981, respectively, proving the success of this method.

[0044] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. An optimization algorithm that combines a non-iterative optimization algorithm with a simulated annealing algorithm to optimize pure phase holograms.

2. The optimization algorithm combining the non-iterative optimization algorithm and the simulated annealing algorithm according to claim 1, characterized in that: The results obtained by the non-iterative optimization algorithm are used as the initial values ​​of simulated annealing.

3. An optimization algorithm for optimizing pure phase holograms by combining a non-iterative optimization algorithm with a simulated annealing algorithm, characterized in that: The following steps are involved: (1) Optimize the pure phase hologram using a non-iterative optimization algorithm; (2) The method used in step (1) is (3) the optimized pure phase hologram obtained in step (2) is used as the initial phase of the simulated annealing algorithm; (4) Using the simulated annealing algorithm to dynamically perform secondary optimization on the results obtained by the non-iterative optimization algorithm; (5) Perform tomographic measurements on the results obtained by combining the non-iterative optimization algorithm with the simulated annealing algorithm.

4. The optimization algorithm for optimizing pure phase holograms by combining a non-iterative optimization algorithm with a simulated annealing algorithm according to claim 3 is characterized in that: In step (3), the solution obtained by the non-iterative optimization algorithm is used as the initial solution of simulated annealing.

5. The optimization algorithm for optimizing pure phase holograms by combining a non-iterative optimization algorithm with a simulated annealing algorithm according to claim 3, characterized in that: The cost function g in step (4) is g = 1-β.

6. The optimization algorithm for optimizing pure phase holograms by combining a non-iterative optimization algorithm with a simulated annealing algorithm according to claim 3, characterized in that: The optical system optimized using the simulated annealing algorithm in step (4) is a feedback system.

7. The optimization algorithm for optimizing pure phase holograms by combining a non-iterative optimization algorithm with a simulated annealing algorithm according to claim 3 is characterized in that: In step (5), the measurement light field is projected onto the orthogonal basis of the LP mode for measurement.

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