Holographic optical system design method and holographic optical system design program

Abstract

To provide a holographic optical system design method that can efficiently design a holographic optical system which can prevent zero-order diffraction light from overlapping with an output surface.SOLUTION: A holographic optical system design method that uses a holographic optical system model 21 comprises: a step of receiving an optical condition 20 (step S1); a step of generating the holographic optical system model 21 (step S2); a step of setting initial phase distribution to each of a plurality of holographic optical elements 44 and 45 (step S3); and a step of performing machine learning of the holographic optical system model 21 (step S4).SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present disclosure relates to a method for designing a holographic optical system and a program for designing a holographic optical system. [Background technology]

[0002] X. Lin, Y. Rivenson, N. T. Hardimci, Y. Luo, M. Jarrahi, and A. Ozcan, "All-optical learning using diffractive deep neural network", Science, 2018, Vol. 361 No. 6406, pp. 1004-1008 (Non-Patent Document 1) describes an optical diffraction deep neural network (D 2 They disclose a method for machine learning the phase distribution of each of multiple diffractive layers using neural network (NN). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] X.Lin, Y.Rivenson, NTYardimci, Y.Luo, M.Jarrahi, and A.Ozcan, “All-optical learning using diffractive deep neural network”, Science, 2018, Vol.361 No.6406, pp.1004-1008 Summary of the Invention [Problem to be solved by the invention]

[0004] However, in Non-Patent Document 1, since multiple diffractive layers are arranged in series on the optical path of straight light, zero-order diffracted light generated in the multiple diffractive layers is superimposed on the output surface. When the zero-order diffractive light is superimposed on the output surface, there is a problem that the signal-to-noise ratio (SN ratio) of the output of the holographic optical system is reduced. An object of the present disclosure is to provide a method for designing a holographic optical system and a program for designing a holographic optical system that can efficiently design a holographic optical system that includes multiple holographic optical elements optically arranged in series and can prevent the zero-order diffracted light generated in the multiple holographic optical elements from superimposing on the output surface. [Means for solving the problem]

[0005] In a method for designing a holographic optical system using a holographic optical system model according to a first aspect of the present disclosure, the holographic optical system model includes an input surface, a plurality of holographic optical elements optically arranged in series, and an output surface. The method for designing a holographic optical system according to the first aspect of the present disclosure includes a step of accepting optical conditions including the number of the plurality of holographic optical elements, the size of each of the plurality of holographic optical elements, an arrangement of the input surface, the plurality of holographic optical elements, and the output surface, and a wavelength of light traveling through the plurality of holographic optical elements, and a step of generating a holographic optical system model that satisfies the number of the plurality of holographic optical elements, the size of each of the plurality of holographic optical elements, and the arrangement of the input surface, the plurality of holographic optical elements, and the output surface, among the optical conditions. The input surface, the plurality of holographic optical elements, and the output surface are arranged such that zero-order diffracted light generated in the plurality of holographic optical elements by light traveling from the input surface to the output surface through the plurality of holographic optical elements does not overlap on the output surface. A method for designing a holographic optical system according to a first aspect of the present disclosure includes the steps of setting an initial phase distribution for each of a plurality of holographic optical elements so that light travels from an input surface through the plurality of holographic optical elements and exits at an output surface, and machine learning a holographic optical system model for which the initial phase distribution has been set by optimizing the phase distribution of each of the plurality of holographic optical elements for the light.

[0006] In a method for designing a holographic optical system using a holographic optical system model according to a second aspect of the present disclosure, the holographic optical system model includes an input surface, a plurality of holographic optical elements optically arranged in series, and an output surface. The method for designing a holographic optical system according to the second aspect of the present disclosure includes a step of receiving optical conditions including the number of the plurality of holographic optical elements, the size of each of the plurality of holographic optical elements, the arrangement of the input surface, the plurality of holographic optical elements, and the output surface, and the wavelengths of the plurality of wavelength components traveling through the plurality of holographic optical elements. The wavelengths of the plurality of wavelength components are different from each other. The method for designing a holographic optical system according to the second aspect of the present disclosure includes a step of generating a plurality of holographic optical system submodels. Each of the plurality of holographic optical system submodels includes an input surface, a plurality of holographic optical elements, and an output surface. Each of the plurality of holographic optical system submodels satisfies the number of the plurality of holographic optical elements, the size of each of the plurality of holographic optical elements, and the arrangement of the input surface, the plurality of holographic optical elements, and the output surface, among the optical conditions. Each of the plurality of holographic optical system submodels is a holographic optical system submodel for a corresponding wavelength component among the plurality of wavelength components. The input surface, the plurality of holographic optical elements and the output surface of each of the plurality of holographic optical system submodels are positioned such that zero order diffracted light generated in the plurality of holographic optical elements of each of the plurality of holographic optical system submodels by corresponding wavelength components traveling through the plurality of holographic optical elements of each of the plurality of holographic optical system submodels from the input surface of each of the plurality of holographic optical system submodels to the output surface of each of the plurality of holographic optical system submodels does not overlap at the output surface of each of the plurality of holographic optical system submodels.A method for designing a holographic optical system according to a second aspect of the present disclosure includes the steps of: setting an initial phase distribution for a wavelength component corresponding to each of a plurality of holographic optical elements of each of a plurality of holographic optical system submodels such that a corresponding wavelength component travels from an input surface of each of the plurality of holographic optical system submodels through a plurality of holographic optical elements of each of the plurality of holographic optical system submodels and exits at an output surface of each of the plurality of holographic optical system submodels; machine learning each of the plurality of holographic optical system submodels for which the initial phase distribution has been set by optimizing the phase distribution for the corresponding wavelength component of each of the plurality of holographic optical system elements of each of the plurality of holographic optical system submodels; and generating a holographic optical system model from the machine-learned plurality of holographic optical system submodels. The input surface, the plurality of holographic optical elements, and the output surface of the holographic optical system model are arranged such that zero-order diffracted light generated in the plurality of holographic optical elements of the holographic optical system model by the plurality of wavelength components traveling from the input surface of the holographic optical system model through the plurality of holographic optical elements of the holographic optical system model toward the output surface of the holographic optical system model does not overlap on the output surface of the holographic optical system model. A method for designing a holographic optical system according to a second aspect of the present disclosure includes machine learning a holographic optical system model by optimizing the phase distribution of each of a plurality of holographic optical elements of the holographic optical system model for multiple wavelength components.

[0007] The holographic optical system design program of the present disclosure causes a processor to execute each step of the holographic optical system design method of the present disclosure. Effect of the Invention

[0008] According to the disclosed holographic optical system design method and the disclosed holographic optical system design program, it is possible to efficiently design a holographic optical system that can prevent zero-order diffracted light generated in multiple holographic optical elements from superimposing on the output surface. [Brief description of the drawings]

[0009] [Figure 1] 1 is a schematic diagram showing an example of a hardware configuration of a holographic optical system design apparatus according to a first embodiment. [Diagram 2] 1 is a schematic diagram showing an example of a functional configuration of a holographic optical system design apparatus according to a first embodiment. [Diagram 3] FIG. 2 is a flowchart showing a method for designing the holographic optical system according to the first embodiment. [Figure 4] 3 is a schematic diagram showing a step of generating a holographic optical system model in the method for designing the holographic optical system according to the first embodiment. FIG. [Diagram 5] 4 is a schematic diagram showing a step of setting initial phase distributions for a plurality of holographic optical elements in the method for designing the holographic optical system according to the first embodiment. FIG. [Figure 6] 4 is a schematic diagram showing a step of setting initial phase distributions for a plurality of holographic optical elements in the method for designing the holographic optical system according to the first embodiment. FIG. [Figure 7] 4 is a schematic diagram showing a step of setting initial phase distributions for a plurality of holographic optical elements in the method for designing the holographic optical system according to the first embodiment. FIG. [Figure 8] 3 is a schematic diagram showing a step of machine learning a holographic optical system model in the method for designing a holographic optical system according to the first embodiment. FIG. [Figure 9] FIG. 2 is a block diagram for explaining the processing contents in a phase distribution machine learning unit in the first embodiment. [Figure 10] FIG. 2 is a flowchart showing steps for machine learning a holographic optical system model according to the first embodiment. [Figure 11] FIG. 4 is a flowchart showing steps for optimizing the phase distribution of a plurality of holographic optical elements in the first embodiment. [Figure 12] FIG. 2 is a schematic diagram showing a holographic optical system model according to a first modified example of the first embodiment. [Figure 13] FIG. 13 is a schematic diagram showing a holographic optical system model according to a second modified example of the first embodiment. [Figure 14] FIG. 13 is a schematic diagram showing a holographic optical system model according to a third modified example of the first embodiment. [Figure 15] FIG. 13 is a schematic diagram showing a step of setting initial phase distributions for a plurality of holographic optical elements in the method for designing the holographic optical system according to the fourth modification of the first embodiment. [Figure 16] FIG. 13 is a schematic diagram showing a step of setting initial phase distributions for a plurality of holographic optical elements in the method for designing the holographic optical system according to the fourth modification of the first embodiment. [Figure 17] FIG. 11 is a schematic diagram showing an example of a hardware configuration of a holographic optical system design apparatus according to a second embodiment. [Figure 18] FIG. 11 is a schematic diagram showing an example of a functional configuration of a holographic optical system design apparatus according to a second embodiment. [Figure 19] FIG. 11 is a flowchart showing a method for designing a holographic optical system according to a second embodiment. [Figure 20] 11 is a schematic diagram showing a step of generating a holographic optical system model in the method for designing the holographic optical system according to the second embodiment. FIG. [Figure 21] 11 is a schematic diagram showing a step of setting initial phase distributions for a plurality of holographic optical elements in the method for designing the holographic optical system according to the second embodiment. FIG. [Figure 22] 11 is a schematic diagram showing a step of machine learning a holographic optical system model in the method for designing a holographic optical system according to the second embodiment. FIG. [Diagram 23] FIG. 11 is a block diagram for explaining the processing contents in a phase distribution machine learning unit of the second embodiment. [Figure 24] FIG. 11 is a flowchart showing steps for machine learning a holographic optical system model in the second embodiment. [Diagram 25] FIG. 11 is a flowchart showing steps for optimizing the phase distribution of a plurality of holographic optical elements in the second embodiment. [Figure 26] FIG. 11 is a flowchart showing steps for optimizing the phase distribution of a plurality of holographic optical elements in the second embodiment. [Figure 27] FIG. 11 is a schematic diagram showing an example of a hardware configuration of a holographic optical system design apparatus according to a third embodiment. [Figure 28] FIG. 11 is a schematic diagram showing an example of a functional configuration of a holographic optical system design apparatus according to a third embodiment. [Figure 29] FIG. 11 is a flowchart showing a method for designing a holographic optical system according to a third embodiment. [Diagram 30] FIG. 13 is a block diagram for explaining the processing contents in a phase distribution machine learning unit of the third embodiment. [Diagram 31] FIG. 13 is a block diagram for explaining the processing contents in a phase distribution machine learning unit of the third embodiment. [Diagram 32] FIG. 13 is a block diagram for explaining the processing contents in a phase distribution machine learning unit of the third embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Hereinafter, an embodiment will be described, in which the same reference numerals are used to refer to the same components, and the description thereof will not be repeated.

[0011] (Embodiment 1)

[0012] <Hardware configuration>

[0013] The hardware configuration of a holographic optical system design device 1 will be described with reference to Fig. 1. The holographic optical system design device 1 is a computer for designing a holographic optical system using a holographic optical system model 21 (see Fig. 1 and Figs. 4 to 9, etc.). The holographic optical system is applicable to, for example, off-axis imaging optical systems such as image transmission optical systems, character recognition optical systems such as optical systems for recognizing handwritten characters, optical systems for sorting data, optical systems for reducing noise contained in an image to improve the signal-to-noise ratio (SN ratio) of the image, imaging optical systems, displays, etc.

[0014] The holographic optical system design device 1 includes, as main hardware elements, an input device 11, a processor 12, a memory 13, a display 14, a network controller 16, a storage medium drive 17, and storage 19.

[0015] The input device 11 accepts various input operations and is, for example, a keyboard, a mouse, a touch panel, or a pen.

[0016] The display 14 displays information necessary for processing in the holographic optical system design apparatus 1. The display 14 displays, for example, optical conditions 20 described below and the phase distribution of each of the multiple holographic optical elements 44, 45 (see FIGS. 4, 5, and 8) of the holographic optical system model 21. In this specification, a holographic optical element (HOE) does not mean a relief-type diffractive optical element, but a refractive index modulation-type diffractive optical element. The display 14 is, for example, an LCD (Liquid Crystal Display) or an organic EL (Electroluminescence) display.

[0017] The processor 12 is a computing entity that executes various programs including the holographic optical system design program 60, thereby executing processes required to realize the functions of the holographic optical system design apparatus 1. The processor 12 is configured, for example, with a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit).

[0018] The memory 13 provides a storage area for temporarily storing program code, a work memory, etc., when the processor 12 executes a program. The memory 13 is, for example, a volatile memory device such as a dynamic random access memory (DRAM) or a static random access memory (SRAM).

[0019] The network controller 16 transmits and receives programs or data (e.g., the optical conditions 20, the training data set 24, the initial phase distribution of the multiple holographic optical elements 44, 45, and the optimized phase distribution of the multiple holographic optical elements 44, 45) to and from an external device (not shown) via a communication network (not shown). The network controller 16 supports any communication method, such as Ethernet (registered trademark), wireless LAN (Local Area Network), or Bluetooth (registered trademark).

[0020] The storage medium drive 17 reads out a program or data stored in the storage medium 18. The storage medium drive 17 may further write the program or data to the storage medium 18. The storage medium 18 is a non-transitory storage medium, and stores the program or data in a non-volatile manner. The storage medium 18 is, for example, an optical storage medium such as an optical disk (for example, a CD-ROM (Compact Disc Read Only Memory) or a DVD (Digital Versatile Disc)), a semiconductor storage medium such as a flash memory or a USB memory, a magnetic storage medium such as a hard disk, a floppy disk (FD) or a storage 19 tape, or a magneto-optical storage medium such as a magneto-optical (MO) disk.

[0021] The storage 19 stores optical conditions 20, a holographic optical system model 21, a training data set 24, and various programs (including a holographic optical system design program 60) executed by the processor 12. The storage 19 is, for example, a non-volatile memory device such as a hard disk or an SSD (Solid State Drive).

[0022] The holographic optical system model 21 is generated on a computer (holographic optical system design device 1). As shown in Figs. 4 to 8, the holographic optical system model 21 includes an input surface 41, a plurality of holographic optical elements 44, 45, and an output surface 42. The holographic optical system model 21 of this embodiment is a holographic optical system model for light 50 that can impart a phase distribution for the light 50 to each of the plurality of holographic optical elements 44, 45. In this embodiment, the light 50 has a single wavelength component, and the holographic optical system model 21 is a holographic optical system model for a single wavelength component.

[0023] The optical conditions 20 include, for example, the number of the plurality of holographic optical elements 44, 45, the size of each of the plurality of holographic optical elements 44, 45, the arrangement of the input surface 41, the plurality of holographic optical elements 44, 45, and the output surface 42, and the wavelength of the light 50 traveling through the plurality of holographic optical elements 44, 45. As shown in Figures 4 to 8, in one example of this embodiment, the number of the plurality of holographic optical elements 44, 45 is two, and the plurality of holographic optical elements 44, 45 are all transmission type holographic optical elements. Also, the light 50 has a single wavelength component.

[0024] The size of each of the plurality of holographic optical elements 44, 45 is the size of an area in which pixels are two-dimensionally arranged. For example, the size of the holographic optical element 44 is the size of an area in which pixels 44p (see FIG. 4, FIG. 5, and FIG. 8) are two-dimensionally arranged. The size of the holographic optical element 45 is the size of an area in which pixels 45p are two-dimensionally arranged. The pixels 44p, 45p are the smallest units that define the phase distribution of each of the plurality of holographic optical elements 44, 45 on a computer (holographic optical system design device 1). The size of each of the plurality of holographic optical elements 44, 45 is the size of an area in which the phase distribution of each of the plurality of holographic optical elements 44, 45 is calculated on the holographic optical system design device 1 (computer).

[0025] The training data set 24 is a training data set for the light 50, and includes a plurality of training data 24a (see FIG. 9). Each of the plurality of training data 24a includes input training data 24b (see FIG. 9) and output training data 24c (see FIG. 9) corresponding to the input training data 24b.

[0026] A program for realizing the functions of the holographic optical system design device 1, such as the holographic optical system design program 60, may be stored in a storage medium 18 and distributed and installed from the storage medium 18 to the storage 19, or may be downloaded to the holographic optical system design device 1 via the Internet or an intranet.

[0027] In this embodiment, an example is shown in which a general-purpose computer (processor 12) executes a program to realize the functions of the holographic optical system design apparatus 1. All or part of the functions of the holographic optical system design apparatus 1 may be realized using a hard-wired circuit such as an integrated circuit. For example, all or part of the functions of the holographic optical system design apparatus 1 may be realized using an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array), etc.

[0028] <Functional configuration>

[0029] An example of a functional configuration of the holographic optical system design device 1 will be described with reference to Fig. 2. The holographic optical system design device 1 of this embodiment includes an optical condition receiving unit 30, a holographic optical system model generating unit 31, an initial phase distribution setting unit 32, and a phase distribution machine learning unit 33.

[0030] 2, the optical condition receiving unit 30 receives the optical conditions 20 from an operator of the holographic optical system design apparatus 1 or the like. The optical condition receiving unit 30 outputs the optical conditions 20 to the storage 19. The optical conditions 20 are stored in the storage 19 (see FIG. 1). The optical conditions 20 may be stored in the storage medium 18 (see FIG. 1).

[0031] Referring to Figure 2, the holographic optical system model generation unit 31 generates a holographic optical system model 21 on a computer (holographic optical system design device 1) in accordance with the optical conditions 20, such as the number of holographic optical elements 44, 45, the size of each of the holographic optical elements 44, 45, and the arrangement of the input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42.

[0032] As shown in Fig. 4, the multiple holographic optical elements 44, 45 are arranged with an axis offset from each other. When the light 50 travels through the multiple holographic optical elements 44, 45 from the input surface 41 toward the output surface 42, zero-order diffracted light 53, 55 is generated in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 are arranged so that the zero-order diffracted light 53, 55 do not overlap on the output surface 42. In this specification, when the holographic optical element is a transmission type holographic optical element, the light 50 traveling through the holographic optical element means that the light 50 passes through the holographic optical element, and when the holographic optical element is a reflection type holographic optical element, the light 50 is reflected at the holographic optical element.

[0033] 2, the initial phase distribution setting unit 32 generates the holographic optical system model 21 in which the initial phase distribution is set from the holographic optical system model 21 generated by the holographic optical system model generation unit 31. For example, an operator inputs the initial phase distribution of each of the multiple holographic optical elements 44, 45 to the holographic optical system design device 1 (see FIG. 1) using the input device 11 (see FIG. 1). The initial phase distribution setting unit 32 accepts the initial phase distribution input by the operator. The initial phase distribution setting unit 32 sets an initial phase distribution for each of the multiple holographic optical elements 44, 45 of the holographic optical system model 21. In this way, the holographic optical system model 21 in which the initial phase distribution is set is generated.

[0034] The initial phase distribution setting unit 32 sets an initial phase distribution for each of the multiple holographic optical elements 44, 45 so that the light 50 travels from the input surface 41 through the multiple holographic optical elements 44, 45 and is output to the output surface 42. When the light 50 travels through each of the multiple holographic optical elements 44, 45, the wavefront of the light 50 changes depending on the initial phase distribution of each of the multiple holographic optical elements 44, 45. The light 50 is diffracted at each of the multiple holographic optical elements 44, 45. The light 50 travels through the multiple holographic optical elements 44, 45 as non-zero order diffracted light (e.g., first order diffracted light) at each of the multiple holographic optical elements 44, 45.

[0035] In each of the multiple holographic optical elements 44, 45, the difference between the maximum phase of the initial phase distribution and the minimum phase of the initial phase distribution for the light 50 is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45, zero-order diffracted light 53, 55 is generated from the light 50.

[0036] The wider the irradiation area of ​​the light 50 on each of the multiple holographic optical elements 44, 45, the more pixels 44p, 45p of each of the multiple holographic optical elements 44, 45 the light 50 is affected by. Therefore, the wider the irradiation area of ​​the light 50 on each of the multiple holographic optical elements 44, 45, the better each of the multiple holographic optical elements 44, 45 can exhibit the designed performance.

[0037] Therefore, the initial phase distribution setting unit 32 sets an initial phase distribution for each of the plurality of holographic optical elements 44, 45 so that the light 50 irradiates a wide area of ​​each of the plurality of holographic optical elements 44, 45. For example, the initial phase distribution for each of the plurality of holographic optical elements 44, 45 is set so that the light 50 irradiates 80% or more of the size of each of the plurality of holographic optical elements 44, 45 in each of the plurality of holographic optical elements 44, 45. More preferably, the initial phase distribution for each of the plurality of holographic optical elements 44, 45 is set so that the light 50 irradiates the entire size of each of the plurality of holographic optical elements 44, 45 in each of the plurality of holographic optical elements 44, 45.

[0038] 2, the phase distribution machine learning unit 33 performs machine learning on the holographic optical system model 21 in which an initial phase distribution is set. The phase distribution machine learning unit 33 optimizes the phase distribution of each of the multiple holographic optical elements 44, 45 for the light 50 by machine learning so that the functions of the holographic optical system (e.g., image transmission, character recognition, data sorting, improvement of the image SNR, etc.) can be realized with higher accuracy. The phase distribution machine learning unit 33 outputs the holographic optical system model 21 including the optimized phase distribution.

[0039] As the light 50 travels through each of the plurality of holographic optical elements 44, 45, the wavefront of the light 50 is changed by the optimized phase distribution of each of the plurality of holographic optical elements 44, 45. The light 50 is diffracted at each of the plurality of holographic optical elements 44, 45. The light 50 travels through the plurality of holographic optical elements 44, 45 as a non-zero order diffracted light (e.g., a first order diffracted light) at each of the plurality of holographic optical elements 44, 45.

[0040] In each of the multiple holographic optical elements 44, 45, the difference between the maximum phase of the optimized phase distribution and the minimum phase of the optimized phase distribution for the light 50 is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45, zero-order diffracted light 53, 55 is generated from the light 50.

[0041] <How to design a holographic optical system>

[0042] A method for designing a holographic optical system using holographic optical system model 21 of this embodiment will be described with reference to Figures 3 to 11. The method for designing a holographic optical system of this embodiment is executed on a computer (holographic optical system design device 1) by processor 12 executing holographic optical system design program 60 (see Figure 1).

[0043] Referring to FIG. 3, the method for designing a holographic optical system of this embodiment includes a step of accepting optical conditions 20 (step S1), a step of generating a holographic optical system model 21 (step S2), a step of setting an initial phase distribution for multiple holographic optical elements 44, 45 of the holographic optical system model 21 (step S3), and a step of machine learning the holographic optical system model 21 with the initial phase distribution set (step S4).

[0044] The step of accepting the optical conditions 20 (step S1) is executed by the optical condition accepting unit 30 (see FIG. 2). An operator inputs the optical conditions 20 to the holographic optical system design apparatus 1 using the input device 11 (see FIG. 1). In step S1, the optical condition accepting unit 30 accepts the optical conditions 20. The optical condition accepting unit 30 outputs the optical conditions 20 to the storage 19. The optical conditions 20 are stored in the storage 19. The optical conditions 20 may be stored in the storage 19 from outside the holographic optical system design apparatus 1 via the network controller 16. The optical conditions 20 may be stored in the storage medium 18 (see FIG. 1).

[0045] 3 and 4, the step of generating the holographic optical system model 21 (step S2) is executed by the holographic optical system model generating unit 31 (see FIG. 2). In step S2, the holographic optical system model generating unit 31 reads out the optical conditions 20 from the storage 19 or the like. The holographic optical system model generating unit 31 generates the holographic optical system model 21 on a computer (holographic optical system design device 1) according to the number of the plurality of holographic optical elements 44, 45, the size of each of the plurality of holographic optical elements 44, 45, and the arrangement of the input surface 41, the plurality of holographic optical elements 44, 45, and the output surface 42, among the optical conditions 20. The holographic optical system model 21 includes the input surface 41, the plurality of holographic optical elements 44, 45, and the output surface 42.

[0046] 4, the multiple holographic optical elements 44, 45 are arranged offset from each other on the axis. When light 50 travels through the multiple holographic optical elements 44, 45 from the input surface 41 to the output surface 42, zero-order diffracted light 53, 55 is generated in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 are arranged so that the zero-order diffracted light 53, 55 do not overlap on the output surface 42.

[0047] Zero-order diffracted light 53 is generated by light 50 being incident on holographic optical element 44. Zero-order diffracted light 53 follows optical path 52 extending from input surface 41 to holographic optical element 44, and then a further optical path extending from holographic optical element 44. Zero-order diffracted light 55 is generated by light 50 being incident on holographic optical element 45. Zero-order diffracted light 55 follows optical path 54 extending from holographic optical element 44 to holographic optical element 45, and then a further optical path extending from holographic optical element 45.

[0048] 3 and 5, the step (step S3) of setting an initial phase distribution to the multiple holographic optical elements 44, 45 of the holographic optical system model 21 is executed by the initial phase distribution setting unit 32 (see FIG. 2). In step S3, an operator uses the input device 11 (see FIG. 1) to input the initial phase distribution of each of the multiple holographic optical elements 44, 45 to the holographic optical system design device 1 (see FIG. 1). The initial phase distribution setting unit 32 accepts the initial phase distribution input by the operator. The initial phase distribution setting unit 32 inputs the initial phase distribution to each of the multiple holographic optical elements 44, 45 of the holographic optical system model 21 generated by the holographic optical system model generation unit 31. In this way, the holographic optical system model 21 in which the initial phase distribution is set is generated.

[0049] The initial phase distribution setting unit 32 sets an initial phase distribution for each of the multiple holographic optical elements 44, 45 so that the light 50 travels from the input surface 41 through the multiple holographic optical elements 44, 45 and is output to the output surface 42. When the light 50 travels through each of the multiple holographic optical elements 44, 45, the wavefront of the light 50 changes depending on the initial phase distribution of each of the multiple holographic optical elements 44, 45. The light 50 is diffracted at each of the multiple holographic optical elements 44, 45. The light 50 travels through the multiple holographic optical elements 44, 45 as non-zero order diffracted light (e.g., first order diffracted light) at each of the multiple holographic optical elements 44, 45.

[0050] In each of the multiple holographic optical elements 44, 45, the difference between the maximum phase of the initial phase distribution and the minimum phase of the initial phase distribution for the light 50 is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45, zero-order diffracted light 53, 55 is generated from the light 50.

[0051] The wider the irradiation area of ​​the light 50 on each of the multiple holographic optical elements 44, 45, the more pixels 44p, 45p of each of the multiple holographic optical elements 44, 45 the light 50 is affected by. Therefore, the wider the irradiation area of ​​the light 50 on each of the multiple holographic optical elements 44, 45, the better each of the multiple holographic optical elements 44, 45 can exhibit the designed performance.

[0052] Therefore, in step S3, the initial phase distribution setting unit 32 (see FIG. 2) sets an initial phase distribution for each of the plurality of holographic optical elements 44, 45 so that the light 50 irradiates a wide area of ​​each of the plurality of holographic optical elements 44, 45. For example, the initial phase distribution for each of the plurality of holographic optical elements 44, 45 is set so that the light 50 irradiates 80% or more of the size of each of the plurality of holographic optical elements 44, 45 in each of the plurality of holographic optical elements 44, 45. More preferably, the initial phase distribution for each of the plurality of holographic optical elements 44, 45 is set so that the light 50 irradiates the entire size of each of the plurality of holographic optical elements 44, 45 in each of the plurality of holographic optical elements 44, 45.

[0053] Specifically, when multiple holographic optical elements are the same size as each other as shown in FIG. 6 and FIG. 7, the nth holographic optical element L n The initial phase distribution Φ n (x, y) is given by the following equation (1). Φ in represents a constant less than or equal to 2π. k represents the wave number of the light 50. The x-axis and y-axis represent the n-th holographic optical element L n The z-axis is an axis perpendicular to the x-axis and y-axis.

number

[0054] θ x is given by equation (2).x,n is the distance of the n-th holographic optical element L when viewed from a direction perpendicular to the xz plane. n and the center of the n+1th holographic optical element L n+1 θ represents the angle between the optical axis 57 connecting the center of the x,n-1 is the n-1th holographic optical element L when viewed from a direction perpendicular to the xz plane. n-1 and the nth holographic optical element L n θ represents the angle between the optical axis 56 connecting the center of the x,n and θ x,n-1 In the z-axis, angles in the clockwise direction are positive angles, and angles in the counterclockwise direction are negative angles. For example, in Figure 6, θ x,n is a positive angle, and θ x,n-1 is a negative angle. θ x =θ x,n -θ x,n-1 (2)

[0055] θ y is given by equation (3). y,n is the distance of the n-th holographic optical element L when viewed from a direction perpendicular to the yz plane. n and the center of the n+1th holographic optical element L n+1 θ represents the angle between the optical axis 57 connecting the center of the y,n-1 is the n-1th holographic optical element L when viewed from a direction perpendicular to the yz plane. n-1 and the nth holographic optical element L n θ represents the angle between the optical axis 56 connecting the center of the y,n and θ y,n-1 In the z-axis, angles in the clockwise direction are positive angles, and angles in the counterclockwise direction are negative angles. For example, in FIG. 7, θ y,n is a positive angle, and θ y,n-1 is a negative angle. θ y =θ y,n -θ y,n-1 (3)

[0056] The nth holographic optical element Ln means the n-th holographic optical element counted from the input surface 41 when viewed along the optical path (optical path of the light 50) of the holographic optical system model 21. When n=1, the n-1th holographic optical element L n-1 is replaced with the input surface 41. In addition, the n-th holographic optical element L n is the last holographic optical element, then the n+1th holographic optical element L n+1 should be read as output surface 42. The last holographic optical element means the holographic optical element that is closest to output surface 42 when viewed along the optical path (optical path of light 50) of holographic optical system model 21. For example, in Figures 4 to 8, holographic optical element 44 is the first holographic optical element, and holographic optical element 45 is the second holographic optical element and the last holographic optical element.

[0057] 3 and 8 to 11, a step (step S4) of machine learning the holographic optical system model 21 in which the initial phase distribution is set is performed by the phase distribution machine learning unit 33. In step S4, the phase distribution machine learning unit 33 optimizes the phase distribution of the multiple holographic optical elements 44, 45 with respect to the light 50 so that the functions of the holographic optical system (e.g., image transmission, character recognition, data sorting, improvement of the image SNR, etc.) can be realized with higher accuracy. The phase distribution machine learning unit 33 outputs the holographic optical system model 21 including the optimized phase distribution.

[0058] As the light 50 travels through each of the plurality of holographic optical elements 44, 45, the wavefront of the light 50 is changed by the optimized phase distribution of each of the plurality of holographic optical elements 44, 45. The light 50 is diffracted at each of the plurality of holographic optical elements 44, 45. The light 50 travels through the plurality of holographic optical elements 44, 45 as a non-zero order diffracted light (e.g., a first order diffracted light) at each of the plurality of holographic optical elements 44, 45.

[0059] In each of the multiple holographic optical elements 44, 45, the difference between the maximum phase of the optimized phase distribution and the minimum phase of the optimized phase distribution for the light 50 is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45, zero-order diffracted light 53, 55 is generated from the light 50.

[0060] Machine learning of the holographic optical system model 21 is, for example, a deep neural network (D 2 This is done using the NN method and light wave diffraction calculations such as the shifted angular spectrum method and the shifted Fresnel diffraction method.

[0061] Optical Diffraction Deep Neural Network (D 2 The optical diffraction deep neural network (DNN) expresses the diffraction of light 50 at the input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42, the propagation of light 50 between the input surface 41 and the holographic optical element (the holographic optical element 44 in Figs. 4 to 6) among the multiple holographic optical elements 44, 45 that is closest to the input surface 41, the propagation of light 50 between the multiple holographic optical elements 44, 45, and the propagation of light 50 between the output surface 42 and the holographic optical element (the holographic optical element 45 in Figs. 4 to 6) among the multiple holographic optical elements 44, 45 that is closest to the output surface 42, by using weight multiplication and bias addition in a deep neural network. 2 NN) is disclosed in, for example, Non-Patent Document 1.

[0062] The light wave diffraction calculation performed in this embodiment is a calculation of the diffraction of light waves between optical layers arranged off-axis (for example, the input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42). The shifted angular spectrum method is disclosed, for example, in K. Matsushima, "Shifted angular spectrum method for off-axis numerical propagation", Optics Express, 2010, Vol.18 No.17, pp.18453-18463. The shifted Fresnel diffraction method is disclosed, for example, in Richard P. Muffoletto, John M. Tyler, and Joel E. Tohline, "Shifted Fresnel diffraction for computational holography", Optics Express, 2007, Vol.15 No.9, pp.5631-5640.

[0063] The processing contents in the phase distribution machine learning unit 33 will be described with reference to FIG.

[0064] The phase distribution machine learning unit 33 includes a phase distribution optimization module 61. The phase distribution optimization module 61 generates the holographic optical system model 21 including an optimized phase distribution by optimizing the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system model 21 in which an initial phase is set.

[0065] The phase distribution optimization module 61 optimizes the phase distribution of the multiple holographic optical elements 44, 45 using the training data set 24. Specifically, the phase distribution optimization module 61 selects one training data 24a from the multiple training data 24a included in the training data set 24. The phase distribution optimization module 61 inputs the input training data 24b included in the selected training data 24a to the input surface 41 of the holographic optical system model 21. A complex amplitude distribution is output to the output surface 42 of the holographic optical system model 21. The phase distribution optimization module 61 calculates an error between the complex amplitude distribution and the output training data 24c.

[0066] The phase distribution optimization module 61 updates (optimizes) the phase distribution of the multiple holographic optical elements 44, 45 so as to reduce the error. Any optimization algorithm may be used when the phase distribution optimization module 61 updates (optimizes) the phase distribution of the multiple holographic optical elements 44, 45. As the optimization algorithm, for example, a gradient method such as SGD (Stochastic Gradient Descent), Momentum SGD (SGD with inertia term added), AdaGrad, RMSprop, AdaDelta, or Adam (Adaptive moment estimation) may be used.

[0067] In a similar manner, the phase distribution optimization module 61 iteratively optimizes the phase distributions of the multiple holographic optical elements 44, 45 of the holographic optical system model 21 based on each training data 24a included in the training data set 24. In this manner, the phase distribution optimization module 61 generates the holographic optical system model 21 including an optimized phase distribution.

[0068] The phase distribution machine learning unit 33 outputs the holographic optical system model 21 including the optimized phase distribution to, for example, the storage 19 (see FIG. 1). The holographic optical system model 21 including the optimized phase distribution is stored in the storage 19. The holographic optical system model 21 including the optimized phase distribution may be output to a storage medium 18 (see FIG. 1).

[0069] An example of the step (step S4) of machine learning the holographic optical system model 21 in which the initial phase distribution is set will be described with reference to FIG.

[0070] 10, in step S5, an operator uses input device 11 (see FIG. 1) to input the number of epochs to holographic optical system design device 1. The number of epochs is the number of times machine learning is repeated, and is stored in storage 19.

[0071] In step S6, the phase distribution of the multiple holographic optical elements 44, 45 is optimized. In step S7, the phase distribution machine learning unit 33 reads the number of epochs stored in the storage 19. The phase distribution machine learning unit 33 determines whether the number of repetitions of step S6 has reached the number of epochs. If the number of repetitions of step S6 has not reached the number of epochs, step S6 is repeatedly performed until the number of repetitions of step S6 reaches the number of epochs.

[0072] When the number of repetitions of step S6 reaches the number of epochs, the phase distribution machine learning unit 33 ends the machine learning of the holographic optical system model 21. The phase distribution machine learning unit 33 generates the holographic optical system model 21 including an optimized phase distribution. The phase distribution machine learning unit 33 outputs the holographic optical system model 21 including the optimized phase distribution to, for example, the storage 19 (see FIG. 1). The holographic optical system model 21 including the optimized phase distribution is stored in the storage 19. The holographic optical system model 21 including the optimized phase distribution may be output to a storage medium 18 (see FIG. 1).

[0073] An example of the step of optimizing the phase distribution of the plurality of holographic optical elements 44, 45 (step S6) will be described with reference to FIG.

[0074] In step S10, one piece of training data 24a is selected from the training data set 24 stored in the storage 19. More specifically, one piece of training data 24a for which steps S12 to S17 described below have not been executed is selected from the training data set 24. As shown in Fig. 9, each piece of training data 24a includes input training data 24b and output training data 24c corresponding to the input training data 24b. In step S11, the input training data 24b of the training data 24a selected in step S10 is converted into a complex amplitude distribution on the input surface 41 and input to the input surface 41.

[0075] In step S12, a complex amplitude distribution of light 50 when light 50 is incident on the nth holographic optical element is calculated from the complex amplitude distribution of light 50 when light 50 is emitted from the n-1th holographic optical element and the arrangement of the nth holographic optical element with respect to the n-1th holographic optical element, by using light wave diffraction calculations such as the shifted angular spectrum method and the shifted Fresnel diffraction method. When n=1, the n-1th holographic optical element is replaced with input surface 41, and the arrangement of the first holographic optical element with respect to input surface 41 is used among the optical conditions 20 received in step S1.

[0076] When the shift angle spectrum method is used to calculate the diffraction of light waves, the complex amplitude distribution G(x-x0, y-y0, z0) of the light 50 when it enters the n-th holographic optical element is calculated from the complex amplitude distribution g(x, y, 0) of the light 50 when it leaves the n-1th holographic optical element by the following formula (4). H(u, v, x0, y0, z0) in formula (4) is given by formula (5). (x0, y0, z0) represent the coordinates of the n-1th holographic optical element. λ represents the wavelength of the light 50 received in step S1. (x, y) represent the coordinates of the n-1th holographic optical element. (u, v) represent the Fourier frequency corresponding to (x, y). FT represents the Fourier transform. FT -1 represents the inverse Fourier transform.

number

number

[0077] In step S13, the complex amplitude distribution of the light 50 when it is emitted from the nth holographic optical element is calculated. As shown in the following formula (6), the complex amplitude distribution G'(x, y) of the light 50 when it is emitted from the nth holographic optical element is calculated by the complex amplitude distribution G(x, y) of the light 50 when it is incident on the nth holographic optical element and the phase distribution Φ n It is given as the product of (x, y). In equation (6), the coordinate of the nth holographic optical element in the z-axis direction is set to 0.

number

[0078] In step S14, it is determined whether the n-th holographic optical element is the last holographic optical element. The last holographic optical element means the holographic optical element that is closest to the output surface 42 when viewed along the optical path (optical path of the light 50) of the holographic optical system model 21. For example, in the holographic optical systems shown in Figures 4 to 8, the holographic optical element 45 is the last holographic optical element.

[0079] If the nth holographic optical element is not the last holographic optical element, steps S12 and S13 are executed for the n+1th holographic optical element. In step S12, the arrangement of the n+1th holographic optical element with respect to the nth holographic optical element is used from the optical conditions 20 accepted in step S1.

[0080] If the n-th holographic optical element is the last holographic optical element, the process proceeds to step S15. In step S15, the complex amplitude distribution of the light 50 on the output surface 42 is calculated from the complex amplitude distribution of the light 50 when it is emitted from the last holographic optical element and the arrangement of the output surface 42 with respect to the last holographic optical element by light wave diffraction calculation such as the shifted angular spectrum method and the shifted Fresnel diffraction method. In step S15, the arrangement of the output surface 42 with respect to the last holographic optical element is used from among the optical conditions 20 accepted in step S1.

[0081] In step S16, an error is calculated between the complex amplitude distribution of the light 50 on the output surface 42 calculated in step S15 and the output training data 24c of the training data 24a selected in step S10. For example, the output training data 24c of the training data 24a selected in step S10 is converted into a complex amplitude distribution on the output surface 42. An error is calculated between the complex amplitude distribution of the light 50 on the output surface 42 calculated in step S15 and the complex amplitude distribution on the output surface 42 of the output training data 24c of the training data 24a selected in step S10.

[0082] In step S17, the phase distribution of the multiple holographic optical elements 44, 45 is updated (optimized) so as to reduce the error calculated in step S16. As an optimization algorithm for the phase distribution of the multiple holographic optical elements 44, 45, for example, a gradient method such as SGD (Stochastic Gradient Descent), Momentum SGD (SGD with inertia term added), AdaGrad, RMSprop, AdaDelta, or Adam (Adaptive moment estimation) can be used.

[0083] In step S18, it is determined whether all the training data 24a have been used to update (optimize) the phase distribution of the multiple holographic optical elements 44, 45. If all the training data 24a have not been used, the process returns to step S10 to newly select one of the unused training data 24a, and steps S11 to S17 are executed for the newly selected training data 24a. If all the training data 24a have been used to update (optimize) the phase distribution of the multiple holographic optical elements 44, 45, the step of optimizing the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system model 21 (step S6) is terminated.

[0084] (Modification)

[0085] 12 to 14, the number of the plurality of holographic optical elements 44, 45, 46, and 47 is not limited to two and may be three or more. The plurality of holographic optical elements 44, 45, 46, and 47 may include a plurality of reflective holographic optical elements that form a folded optical path.

[0086] For example, in a first modification of the present embodiment shown in Fig. 12, the plurality of holographic optical elements 44, 45, 46, 47 include holographic optical elements 44, 47 which are transmission type holographic optical elements, and holographic optical elements 45, 46 which are reflection type holographic optical elements. In a second modification of the present embodiment shown in Fig. 13, the plurality of holographic optical elements 44, 45, 46, 47 include holographic optical element 44 which is a transmission type holographic optical element, and holographic optical elements 45, 46, 47 which are reflection type holographic optical elements. In a third modification of the present embodiment shown in Fig. 14, the plurality of holographic optical elements 44, 45, 46, 47 are all reflection type holographic optical elements.

[0087] As shown in Figures 15 and 16, in a fourth modification of this embodiment, the holographic optical elements may differ from each other in size. For example, as shown in Figures 15 and 16, when the size of the holographic optical elements gradually increases from the input surface 41 to the output surface 42, the nth holographic optical element L is arranged so that the light 50 illuminates a wide area of ​​each of the holographic optical elements. n The initial phase distribution Φ n (x, y) is given, for example, by the following formula (7): n The z-axis coordinate is set to 0.

number

[0088] Psi n (x, y) is the nth holographic optical element L n This light 50 is incident on the (n+1)th holographic optical element L n+1 Irradiate a wide area of ​​Ψ n-1 (x, y) is the nth holographic optical element L nrepresents a phase distribution of light 50 when the light 50 is incident on the n-th holographic optical element L n Irradiate a wide area of ​​Ψ n (x, y) is the x-axis component Ψ as shown in the following equation (8). x,n (x,y) and y-axis component Ψ y,n It is decomposed into (x,y). n-1 (x, y) is the x-axis component Ψ as shown in the following equation (9). x,n-1 (x,y) and y-axis component Ψ y,n-1 It is decomposed into (x,y).

number

number

[0089] As shown in FIG. 15, the n-th holographic optical element L n The aperture end in the x-axis direction of the (n+1)th holographic optical element L n+1 The intersection point of the straight lines 63a and 63b connecting the opening end in the x-axis direction of the point OX is defined as point OX, and the coordinates of point OX are (x OX ,0,z OX ) The n-th holographic optical element L n The aperture end in the x-axis direction of the n-th holographic optical element L n-1 The intersection point of the straight lines 64a and 64b connecting the opening end in the x-axis direction of the point PX is defined as point PX. The coordinates of point PX are (x PX ,0,z PX ) As shown in FIG. 16, the n-th holographic optical element L n The opening end in the y-axis direction of the (n+1)th holographic optical element L n+1 The intersection of the straight lines 65a and 65b connecting the opening end in the y-axis direction of the point OY is defined as point OY. The coordinates of the point OY are (0, y OY ,z OY ) The n-th holographic optical element L n The open end in the y-axis direction of the n-th holographic optical element L n-1The intersection of the straight lines 66a and 66b connecting the opening end in the y-axis direction of the point PY is defined as point PY. The coordinates of the point PY are (0, y PY ,z PY )

[0090] Ψ in Eq. (8) x,n (x,y) and Ψ y,n (x, y) and Ψ in equation (9) x,n-1 (x,y) and Ψ y,n-1 (x, y) is given by the following equations (10) to (13). Φ x,n,in、 Φ y,n,in , Φ x,n―1,in、 and Φ y,n―1,in Each represents a constant less than or equal to 2π.

number

number

number

number

[0091] <Holographic Optical System Design Program 60>

[0092] A holographic optical system design program 60 (see FIG. 1) causes the processor 12 (see FIG. 1) to execute the holographic optical system design method of the present embodiment. A program such as the holographic optical system design program 60 may be recorded in a computer-readable recording medium (a non-transitory computer-readable recording medium, for example, the storage medium 18) of the present embodiment.

[0093] The effects of the holographic optical system design method and the holographic optical system design program 60 according to this embodiment will be described.

[0094] In a method for designing a holographic optical system using the holographic optical system model 21 of the present embodiment, the holographic optical system model 21 includes an input surface 41, a plurality of holographic optical elements 44, 45 optically arranged in series, and an output surface 42. The method for designing a holographic optical system of the present embodiment includes a step (step S1) of accepting optical conditions 20 including the number of the plurality of holographic optical elements 44, 45, the size of each of the plurality of holographic optical elements 44, 45, the arrangement of the input surface 41, the plurality of holographic optical elements 44, 45, and the output surface 42, and the wavelength of light 50 traveling through the plurality of holographic optical elements 44, 45, and a step (step S2) of generating a holographic optical system model 21 that satisfies the number of the plurality of holographic optical elements, the size of each of the plurality of holographic optical elements, and the arrangement of the input surface, the plurality of holographic optical elements, and the output surface, among the optical conditions 20. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 are arranged so that zero-order diffracted light 53, 55 generated in the multiple holographic optical elements 44, 45 by the light 50 traveling from the input surface 41 to the output surface 42 through the multiple holographic optical elements 44, 45 is not superimposed on the output surface 42. The design method of the holographic optical system of the present embodiment includes a step (step S3) of setting an initial phase distribution for each of the multiple holographic optical elements 44, 45 so that the light 50 travels from the input surface 41 through the multiple holographic optical elements 44, 45 and is output to the output surface 42, and a step (step S4) of machine learning the holographic optical system model 21 in which the initial phase distribution is set by optimizing the phase distribution of each of the multiple holographic optical elements 44, 45 for the light 50.

[0095] In the design method of the holographic optical system of this embodiment, the input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 are arranged so that the zero-order diffracted light 53, 55 generated in the multiple holographic optical elements 44, 45 by the light 50 traveling from the input surface 41 to the output surface 42 through the multiple holographic optical elements 44, 45 is not superimposed on the output surface 42. Therefore, it is possible to design a holographic optical system in which the zero-order diffracted light 53, 55 is prevented from superimposing on the output surface 42. Furthermore, in the design method of the holographic optical system of this embodiment, an initial phase distribution is set for each of the multiple holographic optical elements 44, 45 so that the light 50 travels from the input surface 41 through the multiple holographic optical elements 44, 45 and is output to the output surface 42. Therefore, the function of the holographic optical system can be realized with higher accuracy. It is possible to obtain an optimized phase distribution of the multiple holographic optical elements 44, 45 that can realize an optical path of the light 50 from the input surface 41 through the multiple holographic optical elements 44, 45 to the output surface 42 more reliably, with less calculation amount, and in a shorter time. A holographic optical system in which the zero-order diffracted light 53, 55 is prevented from superimposing on the output surface 42 can be designed more efficiently.

[0096] The design method for the holographic optical system of the present embodiment includes a step (step S4) of machine learning the holographic optical system model 21. Therefore, even if the number of holographic optical elements is increased to improve or expand the optical function of the holographic optical system, a significant increase in the amount of calculation can be suppressed. In designing the holographic optical system, it becomes possible to treat the light 50 as a wavefront and to more accurately reflect the diffraction phenomenon of the light 50 in the holographic optical system. The holographic optical system can be simulated more accurately and in a shorter time.

[0097] In the design method of the holographic optical system of the present embodiment, the multiple holographic optical elements 44, 45 include a first holographic optical element (e.g., holographic optical element 44) having a first size and a second holographic optical element (e.g., holographic optical element 45) having a second size different from the first size. In the step of setting an initial phase distribution for each of the multiple holographic optical elements 44, 45, the initial phase distribution is set for each of the multiple holographic optical elements 44, 45 so that the light 50 irradiates 80% or more of the first size and 80% or more of the second size.

[0098] Therefore, the wavefront of the light 50 is affected by many pixels 44p, 45p of the multiple holographic optical elements 44, 45. The multiple holographic optical elements 44, 45 can better exert the designed performance on the light 50. A holographic optical system with higher performance can be designed more efficiently.

[0099] In the design method of the holographic optical system of the present embodiment, the multiple holographic optical elements 44 and 45 include multiple reflective holographic optical elements that form a folded optical path, so that a compact holographic optical system can be designed more efficiently.

[0100] The holographic optical system design program 60 of the present embodiment causes the processor 12 to execute each step of the holographic optical system design method of the present embodiment. Therefore, a holographic optical system in which the zero-order diffracted light beams 53 and 55 are prevented from overlapping on the output surface 42 can be efficiently designed.

[0101] (Embodiment 2)

[0102] The holographic optical system design apparatus 1 of the second embodiment will be described with reference to Figures 17 and 18. The holographic optical system design apparatus 1 of the present embodiment is similar to the holographic optical system design apparatus 1 of the first embodiment, but differs from the holographic optical system design apparatus 1 of the first embodiment mainly in the following points due to the fact that light 50 includes multiple wavelength components 50a, 50b, and 50c (see Figures 20 to 22).

[0103] <Hardware configuration>

[0104] As shown in Figs. 20 to 22, in this embodiment, light 50 includes multiple wavelength components 50a, 50b, and 50c. The wavelengths of the multiple wavelength components 50a, 50b, and 50c are different from each other. In one example of this embodiment, light 50 includes three wavelength components 50a, 50b, and 50c. The wavelength component 50a is, for example, red light. The wavelength component 50b is, for example, green light. The wavelength component 50c is, for example, blue light.

[0105] Referring to FIG. 17, the holographic optical system model 22 of the present embodiment is a holographic optical system model for multiple wavelength components 50a, 50b, 50c that is capable of imparting a phase distribution for each of the multiple wavelength components 50a, 50b, 50c to each of the multiple holographic optical elements 44, 45.

[0106] 17, in this embodiment, a training data set 25 is stored in the storage 19 instead of the training data set 24 (see FIG. 1). The training data set 25 in this embodiment is a training data set for multiple wavelength components 50a, 50b, and 50c, and includes multiple training data 25a (see FIG. 23). Each of the multiple training data 25a includes input training data 25b (see FIG. 23) and output training data 25c (see FIG. 23) corresponding to the input training data 25b. The input training data 25b and the output training data 25c include the multiple wavelength components 50a, 50b, and 50c, respectively. The input training data 25b and the output training data 25c are, for example, color images.

[0107] <Functional configuration>

[0108] 18, the optical condition receiving unit 30 receives the optical conditions 20 from an operator of the holographic optical system design apparatus 1 or the like. In the present embodiment, the optical condition receiving unit 30 receives the wavelengths of the multiple wavelength components 50a, 50b, and 50c as the wavelength of the light 50. The wavelengths of the multiple wavelength components 50a, 50b, and 50c are different from each other.

[0109] 18, the holographic optical system model generating unit 31 generates the holographic optical system model 22 in the same manner as in the first embodiment. The holographic optical system model 22 is a holographic optical system model for the multiple wavelength components 50a, 50b, and 50c. As shown in FIG. 20, the multiple wavelength components 50a, 50b, and 50c travel through the multiple holographic optical elements 44 and 45 from the input surface 41 toward the output surface 42, and thus zero-order diffracted light 53 and 55 are generated in the multiple holographic optical elements 44 and 45. The input surface 41, the multiple holographic optical elements 44 and 45, and the output surface 42 are arranged so that the zero-order diffracted light 53 and 55 do not overlap on the output surface 42.

[0110] In this embodiment, the zero-order diffracted light 53 includes zero-order diffracted light 53a, zero-order diffracted light 53b, and zero-order diffracted light 53c. The zero-order diffracted light 53a is generated in the holographic optical element 44 by the wavelength component 50a traveling through the holographic optical element 44 from the input surface 41 to the output surface 42. The zero-order diffracted light 53b is generated in the holographic optical element 44 by the wavelength component 50b traveling through the holographic optical element 44 from the input surface 41 to the output surface 42. The zero-order diffracted light 53c is generated in the holographic optical element 44 by the wavelength component 50c traveling through the holographic optical element 44 from the input surface 41 to the output surface 42.

[0111] In this embodiment, the zero-order diffracted light 55 includes zero-order diffracted light 55a, zero-order diffracted light 55b, and zero-order diffracted light 55c. The zero-order diffracted light 55a is generated in the holographic optical element 45 by the wavelength component 50a traveling through the holographic optical element 45 from the input surface 41 to the output surface 42. The zero-order diffracted light 55b is generated in the holographic optical element 45 by the wavelength component 50b traveling through the holographic optical element 45 from the input surface 41 to the output surface 42. The zero-order diffracted light 55c is generated in the holographic optical element 45 by the wavelength component 50c traveling through the holographic optical element 45 from the input surface 41 to the output surface 42.

[0112] With reference to FIG. 18, the initial phase distribution setting unit 32 generates the holographic optical system model 22 in which the initial phase distribution is set from the holographic optical system model 22 generated by the holographic optical system model generation unit 31. For example, an operator inputs the initial phase distribution of each of the multiple holographic optical elements 44, 45 to the holographic optical system design device 1 (see FIG. 17) using the input device 11 (see FIG. 17). The initial phase distribution setting unit 32 accepts the initial phase distribution input by the operator. The initial phase distribution setting unit 32 sets an initial phase distribution for each of the multiple holographic optical elements 44, 45 of the holographic optical system model 22 generated by the holographic optical system model generation unit 31. In this way, the initial phase distribution setting unit 32 generates the holographic optical system model 22 in which the initial phase distribution is set.

[0113] The initial phase distribution setting unit 32 sets an initial phase distribution for each of the multiple wavelength components 50a, 50b, 50c so that the multiple wavelength components 50a, 50b, 50c travel from the input surface 41 through the multiple holographic optical elements 44, 45 and are output to the output surface 42. When the multiple wavelength components 50a, 50b, 50c travel through the multiple holographic optical elements 44, 45, the wavefronts of the multiple wavelength components 50a, 50b, 50c change depending on the initial phase distribution for each of the multiple wavelength components 50a, 50b, 50c of each of the multiple holographic optical elements 44, 45. Each of the multiple wavelength components 50a, 50b, 50c is diffracted in each of the multiple holographic optical elements 44, 45.

[0114] Specifically, when the wavelength component 50a travels through the plurality of holographic optical elements 44, 45, the wavefront of the wavelength component 50a is changed by the initial phase distribution for the wavelength component 50a of each of the plurality of holographic optical elements 44, 45. The wavelength component 50a is diffracted at each of the plurality of holographic optical elements 44, 45. When the wavelength component 50b travels through the plurality of holographic optical elements 44, 45, the wavefront of the wavelength component 50b is changed by the initial phase distribution for the wavelength component 50b of each of the plurality of holographic optical elements 44, 45. The wavelength component 50b is diffracted at each of the plurality of holographic optical elements 44, 45. When the wavelength component 50c travels through the plurality of holographic optical elements 44, 45, the wavefront of the wavelength component 50c is changed by the initial phase distribution for the wavelength component 50c of each of the plurality of holographic optical elements 44, 45. The wavelength component 50c is diffracted at each of the plurality of holographic optical elements 44, 45.

[0115] Each of the multiple wavelength components 50a, 50b, 50c travels through the multiple holographic optical elements 44, 45 as non-zero order diffracted light (e.g., first order diffracted light) in each of the multiple holographic optical elements 44, 45. The initial phase distribution setting unit 32 outputs the holographic optical system model 22 in which the initial phase distribution is set.

[0116] In each of the multiple holographic optical elements 44, 45, the difference between the maximum phase of the initial phase distribution and the minimum phase of the initial phase distribution for each of the multiple wavelength components 50a, 50b, 50c is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45, zero-order diffracted light 53, 55 is generated from the multiple wavelength components 50a, 50b, 50c. The zero-order diffracted light 53 includes a zero-order diffracted light 53a, a zero-order diffracted light 53b, and a zero-order diffracted light 53c. The zero-order diffracted light 55 includes a zero-order diffracted light 55a, a zero-order diffracted light 55b, and a zero-order diffracted light 55c.

[0117] The wider the irradiation area of ​​each of the multiple wavelength components 50a, 50b, 50c in each of the multiple holographic optical elements 44, 45, the more pixels 44p, 45p each of the multiple wavelength components 50a, 50b, 50c is affected by in each of the multiple holographic optical elements 44, 45. Therefore, the wider the irradiation area of ​​each of the multiple wavelength components 50a, 50b, 50c in each of the multiple holographic optical elements 44, 45, the better each of the multiple holographic optical elements 44, 45 can exhibit the designed performance.

[0118] Therefore, the initial phase distribution setting unit 32 (see FIG. 18) sets an initial phase distribution for each of the multiple holographic optical elements 44, 45 so that each of the multiple wavelength components 50a, 50b, 50c irradiates a wide area of ​​each of the multiple holographic optical elements 44, 45. For example, the initial phase distribution for each of the multiple holographic optical elements 44, 45 is set so that each of the multiple wavelength components 50a, 50b, 50c irradiates 80% or more of the size of each of the multiple holographic optical elements 44, 45 in each of the multiple holographic optical elements 44, 45. More preferably, the initial phase distribution for each of the multiple holographic optical elements 44, 45 is set so that each of the multiple wavelength components 50a, 50b, 50c irradiates the entire size of each of the multiple holographic optical elements 44, 45 in each of the multiple holographic optical elements 44, 45.

[0119] 18, the phase distribution machine learning unit 33 performs machine learning on the holographic optical system model 22 in which an initial phase distribution is set. The phase distribution machine learning unit 33 optimizes the phase distribution of each of the multiple holographic optical elements 44, 45 for each of the multiple wavelength components 50a, 50b, 50c by machine learning so that the function of the holographic optical system can be realized with higher accuracy. The phase distribution machine learning unit 33 provides each of the multiple holographic optical elements 44, 45 with an optimized phase distribution for each of the multiple wavelength components 50a, 50b, 50c.

[0120] As the multiple wavelength components 50a, 50b, 50c travel through the plurality of holographic optical elements 44, 45, the wavefront of each of the multiple wavelength components 50a, 50b, 50c is changed according to the optimized phase distribution for each of the multiple wavelength components 50a, 50b, 50c of each of the plurality of holographic optical elements 44, 45. Each of the multiple wavelength components 50a, 50b, 50c is diffracted at each of the plurality of holographic optical elements 44, 45.

[0121] Specifically, when the wavelength component 50a travels through the plurality of holographic optical elements 44, 45, the wavefront of the wavelength component 50a is changed by the optimized phase distribution for the wavelength component 50a of each of the plurality of holographic optical elements 44, 45. The wavelength component 50a is diffracted at the plurality of holographic optical elements 44, 45. When the wavelength component 50b travels through the plurality of holographic optical elements 44, 45, the wavefront of the wavelength component 50b is changed by the optimized phase distribution for the wavelength component 50b of each of the plurality of holographic optical elements 44, 45. The wavelength component 50b is diffracted at the plurality of holographic optical elements 44, 45. When the wavelength component 50c travels through the plurality of holographic optical elements 44, 45, the wavefront of the wavelength component 50c is changed by the optimized phase distribution for the wavelength component 50c of each of the plurality of holographic optical elements 44, 45. The wavelength component 50c is diffracted at the plurality of holographic optical elements 44, 45.

[0122] Each of the multiple wavelength components 50a, 50b, 50c travels through the multiple holographic optical elements 44, 45 as non-zero order diffracted light (e.g., first order diffracted light, etc.) at each of the multiple holographic optical elements 44, 45. The phase distribution machine learning unit 33 outputs the holographic optical system model 22 including the optimized phase distribution.

[0123] In each of the multiple holographic optical elements 44, 45, the difference between the maximum phase of the optimized phase distribution and the minimum phase of the optimized phase distribution for each of the multiple wavelength components 50a, 50b, 50c is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45, zero-order diffracted light 53, 55 is generated from the multiple wavelength components 50a, 50b, 50c. The zero-order diffracted light 53 includes a zero-order diffracted light 53a, a zero-order diffracted light 53b, and a zero-order diffracted light 53c. The zero-order diffracted light 55 includes a zero-order diffracted light 55a, a zero-order diffracted light 55b, and a zero-order diffracted light 55c.

[0124] <How to design a holographic optical system>

[0125] A method for designing the holographic optical system of this embodiment will be described with reference to Figures 19 to 26. The method for designing the holographic optical system of this embodiment is similar to the method for designing the holographic optical system of embodiment 1, but differs from the method for designing the holographic optical system of embodiment 1 mainly in the following points due to the fact that light 50 includes multiple wavelength components 50a, 50b, and 50c (see Figures 20 to 22).

[0126] Referring to Figure 19, the design method of the holographic optical system of this embodiment includes a step of accepting optical conditions 20 (step S21), a step of generating a holographic optical system model 22 (step S22), a step of setting an initial phase distribution for multiple holographic optical elements 44, 45 of the holographic optical system model 22 (step S23), and a step of machine learning the holographic optical system model 22 with the initial phase distribution set (step S24).

[0127] 19, the step of accepting optical conditions 20 in this embodiment (step S21) is executed by the optical condition accepting unit 30 (see FIG. 18). Step S21 is similar to step S1 in the first embodiment (see FIG. 3), but in step S21, the optical condition accepting unit 30 accepts the wavelengths of multiple wavelength components 50a, 50b, and 50c as the wavelength of light 50. The wavelengths of the multiple wavelength components 50a, 50b, and 50c are different from one another.

[0128] 19 and 20, a step (step S22) of generating the holographic optical system model 22 of this embodiment is executed by the holographic optical system model generating unit 31 (see FIG. 18). Step S22 is similar to step S2 (see FIG. 3) of the first embodiment, but in step S22, the holographic optical system model generating unit 31 generates the holographic optical system model 22 on a computer (holographic optical system design device 1) according to the number of the plurality of holographic optical elements 44, 45, the size of each of the plurality of holographic optical elements 44, 45, and the arrangement of the input surface 41, the plurality of holographic optical elements 44, 45, and the output surface 42, among the optical conditions 20. The holographic optical system model 22 is a holographic optical system model for the plurality of wavelength components 50a, 50b, and 50c.

[0129] The multiple wavelength components 50a, 50b, 50c travel through the multiple holographic optical elements 44, 45 from the input surface 41 to the output surface 42, thereby generating zero-order diffracted light 53, 55 at the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 are arranged such that the zero-order diffracted light 53, 55 do not overlap at the output surface 42. The zero-order diffracted light 53 includes a zero-order diffracted light 53a, a zero-order diffracted light 53b, and a zero-order diffracted light 53c. The zero-order diffracted light 55 includes a zero-order diffracted light 55a, a zero-order diffracted light 55b, and a zero-order diffracted light 55c.

[0130] 19 and 21, the step (step S23) of setting an initial phase distribution for the multiple holographic optical elements 44, 45 of the holographic optical system model 22 of this embodiment is executed by the initial phase distribution setting unit 32 (see FIG. 18). In step S23 of this embodiment, the initial phase distribution setting unit 32 sets an initial phase distribution for each of the multiple holographic optical elements 44, 45 of the holographic optical system model 22 generated by the holographic optical system model generation unit 31.

[0131] Specifically, the initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50a, an initial phase distribution for the wavelength component 50b, and an initial phase distribution for the wavelength component 50c in the holographic optical element 44. The initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50a, an initial phase distribution for the wavelength component 50b, and an initial phase distribution for the wavelength component 50c in the holographic optical element 45. The initial phase distribution for the wavelength component 50a set in the holographic optical element 45 may be the same as or different from the initial phase distribution for the wavelength component 50a set in the holographic optical element 44. The initial phase distribution for the wavelength component 50b set in the holographic optical element 45 may be the same as or different from the initial phase distribution for the wavelength component 50b set in the holographic optical element 44. The initial phase distribution for the wavelength component 50c set in the holographic optical element 45 may be the same as or different from the initial phase distribution for the wavelength component 50c set in the holographic optical element 44.

[0132] In this way, the initial phase distribution setting unit 32 generates the holographic optical system model 22 in which the initial phase distribution is set.

[0133] The initial phase distribution setting unit 32 sets an initial phase distribution for each of the multiple wavelength components 50a, 50b, 50c so that the multiple wavelength components 50a, 50b, 50c travel from the input surface 41 through the multiple holographic optical elements 44, 45 and are output to the output surface 42. When the multiple wavelength components 50a, 50b, 50c travel through the multiple holographic optical elements 44, 45, the wavefronts of the multiple wavelength components 50a, 50b, 50c change depending on the initial phase distributions of the multiple holographic optical elements 44, 45. The multiple wavelength components 50a, 50b, 50c are diffracted in each of the multiple holographic optical elements 44, 45.

[0134] Specifically, the wavefront of the wavelength component 50a is changed by the initial phase distribution for the wavelength component 50a of the holographic optical element 44 and the initial phase distribution for the wavelength component 50a of the holographic optical element 45. The wavelength component 50a is diffracted at the holographic optical elements 44 and 45. The wavefront of the wavelength component 50b is changed by the initial phase distribution for the wavelength component 50b of the holographic optical element 44 and the initial phase distribution for the wavelength component 50b of the holographic optical element 45. The wavelength component 50b is diffracted at the holographic optical elements 44 and 45. The wavefront of the wavelength component 50c is changed by the initial phase distribution for the wavelength component 50c of the holographic optical element 44 and the initial phase distribution for the wavelength component 50c of the holographic optical element 45. The wavelength component 50c is diffracted at the holographic optical elements 44 and 45.

[0135] Each of the multiple wavelength components 50a, 50b, 50c travels through the multiple holographic optical elements 44, 45 as non-zero order diffracted light (e.g., first order diffracted light) in each of the multiple holographic optical elements 44, 45. The initial phase distribution setting unit 32 outputs the holographic optical system model 22 in which the initial phase distribution is set.

[0136] In the initial phase distribution of each of the multiple holographic optical elements 44 and 45, the difference between the maximum phase of the initial phase distribution and the minimum phase of the initial phase distribution for each of the multiple wavelength components 50a, 50b, and 50c is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44 and 45, zero-order diffracted light 53 and 55 are generated from the multiple wavelength components 50a, 50b, and 50c. The zero-order diffracted light 53 includes a zero-order diffracted light 53a, a zero-order diffracted light 53b, and a zero-order diffracted light 53c. The zero-order diffracted light 55 includes a zero-order diffracted light 55a, a zero-order diffracted light 55b, and a zero-order diffracted light 55c.

[0137] The wider the irradiation area of ​​each of the multiple wavelength components 50a, 50b, 50c in each of the multiple holographic optical elements 44, 45, the more pixels 44p, 45p each of the multiple wavelength components 50a, 50b, 50c is affected by in each of the multiple holographic optical elements 44, 45. Therefore, the wider the irradiation area of ​​each of the multiple wavelength components 50a, 50b, 50c in each of the multiple holographic optical elements 44, 45, the better each of the multiple holographic optical elements 44, 45 can exhibit the designed performance.

[0138] Therefore, the initial phase distribution setting unit 32 (see FIG. 18) sets an initial phase distribution for each of the multiple holographic optical elements 44, 45 so that each of the multiple wavelength components 50a, 50b, 50c irradiates a wide area of ​​each of the multiple holographic optical elements 44, 45. For example, the initial phase distribution for each of the multiple holographic optical elements 44, 45 is set so that each of the multiple wavelength components 50a, 50b, 50c irradiates 80% or more of the size of each of the multiple holographic optical elements 44, 45 in each of the multiple holographic optical elements 44, 45. More preferably, the initial phase distribution for each of the multiple holographic optical elements 44, 45 is set so that each of the multiple wavelength components 50a, 50b, 50c irradiates the entire size of each of the multiple holographic optical elements 44, 45 in each of the multiple holographic optical elements 44, 45.

[0139] 19 and 22 to 26, a step (step S24) of machine learning the holographic optical system model 22 in which the initial phase distribution of the present embodiment is set is executed by the phase distribution machine learning unit 33 (see FIG. 18). In step S24, the phase distribution machine learning unit 33 optimizes the phase distribution of the multiple holographic optical elements 44, 45 so that the function of the holographic optical system can be realized with higher accuracy. The phase distribution machine learning unit 33 provides each of the multiple holographic optical elements 44, 45 with an optimized phase distribution for each of the multiple wavelength components 50a, 50b, 50c.

[0140] The phase distribution of each of the multiple holographic optical elements 44 and 45 is optimized according to each of the multiple wavelength components 50a, 50b, and 50c. That is, the optimized phase distribution of the holographic optical element 44 includes an optimized phase distribution for the wavelength component 50a, an optimized phase distribution for the wavelength component 50b, and an optimized phase distribution for the wavelength component 50c. The optimized phase distribution of the holographic optical element 45 includes an optimized phase distribution for the wavelength component 50a, an optimized phase distribution for the wavelength component 50b, and an optimized phase distribution for the wavelength component 50c.

[0141] As the multiple wavelength components 50a, 50b, 50c travel through the plurality of holographic optical elements 44, 45, the wavefront of each of the multiple wavelength components 50a, 50b, 50c is changed according to the optimized phase distribution for each of the multiple wavelength components 50a, 50b, 50c of each of the plurality of holographic optical elements 44, 45. Each of the multiple wavelength components 50a, 50b, 50c is diffracted at each of the plurality of holographic optical elements 44, 45.

[0142] Specifically, the wavefront of wavelength component 50a is changed by the optimized phase distribution for wavelength component 50a of holographic optical element 44 and the optimized phase distribution for wavelength component 50a of holographic optical element 45. Wavelength component 50a is diffracted at holographic optical elements 44 and 45. Wavefront of wavelength component 50b is changed by the optimized phase distribution for wavelength component 50b of holographic optical element 44 and the optimized phase distribution for wavelength component 50b of holographic optical element 45. Wavelength component 50b is diffracted at holographic optical elements 44 and 45. Wavefront of wavelength component 50c is changed by the optimized phase distribution for wavelength component 50c of holographic optical element 44 and the optimized phase distribution for wavelength component 50c of holographic optical element 45. Wavelength component 50c is diffracted at holographic optical elements 44 and 45.

[0143] Each of the multiple wavelength components 50a, 50b, 50c travels through the multiple holographic optical elements 44, 45 as non-zero order diffracted light (e.g., first order diffracted light, etc.) at each of the multiple holographic optical elements 44, 45. The phase distribution machine learning unit 33 outputs the holographic optical system model 22 including the optimized phase distribution.

[0144] In each of the multiple holographic optical elements 44, 45, the difference between the maximum phase of the optimized phase distribution and the minimum phase of the optimized phase distribution for each of the multiple wavelength components 50a, 50b, 50c is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45, zero-order diffracted light 53, 55 is generated from the multiple wavelength components 50a, 50b, 50c. The zero-order diffracted light 53 includes a zero-order diffracted light 53a, a zero-order diffracted light 53b, and a zero-order diffracted light 53c. The zero-order diffracted light 55 includes a zero-order diffracted light 55a, a zero-order diffracted light 55b, and a zero-order diffracted light 55c.

[0145] The machine learning of the holographic optical system model 22 is performed in the same manner as the machine learning of the holographic optical system model 21 of the first embodiment, for example, using a light diffraction deep neural network (D2 This is done using the NN method and light wave diffraction calculations such as the shifted angular spectrum method and the shifted Fresnel diffraction method.

[0146] 23, the processing contents in the phase distribution machine learning unit 33 of this embodiment will be described. The phase distribution machine learning unit 33 includes wavelength component extraction units 71, 72, and 73, and a phase distribution optimization module 61.

[0147] The wavelength component extraction unit 71 extracts training data 25a for wavelength component 50a from training data 25a. Specifically, the wavelength component extraction unit 71 extracts input training data 25b for wavelength component 50a from input training data 25b in training data 25a. The input training data 25b for wavelength component 50a is data from the input training data 25b that has the same wavelength as the wavelength component 50a. The wavelength component extraction unit 71 extracts output training data 25c for wavelength component 50a from output training data 25c in training data 25a. The output training data 25c for wavelength component 50a is data from the output training data 25c that has the same wavelength as the wavelength component 50a.

[0148] The wavelength component extraction unit 72 extracts training data 25a for wavelength component 50b from training data 25a. Specifically, the wavelength component extraction unit 72 extracts input training data 25b for wavelength component 50b from input training data 25b in training data 25a. The input training data 25b for wavelength component 50b is data from the input training data 25b that has the same wavelength as the wavelength component 50b. The wavelength component extraction unit 72 extracts output training data 25c for wavelength component 50b from output training data 25c in training data 25a. The output training data 25c for wavelength component 50b is data from the output training data 25c that has the same wavelength as the wavelength component 50b.

[0149] The wavelength component extraction unit 73 extracts training data 25a for wavelength component 50c from training data 25a. Specifically, the wavelength component extraction unit 73 extracts input training data 25b for wavelength component 50c from input training data 25b in training data 25a. The input training data 25b for wavelength component 50c is data from the input training data 25b that has the same wavelength as the wavelength component 50c. The wavelength component extraction unit 73 extracts output training data 25c for wavelength component 50c from output training data 25c in training data 25a. The output training data 25c for wavelength component 50c is data from the output training data 25c that has the same wavelength as the wavelength component 50c.

[0150] The phase distribution optimization module 61 optimizes the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system model 22, for which an initial phase has been set, using the training data set 25.

[0151] Specifically, the phase distribution optimization module 61 selects one training data 25a from among the multiple training data 25a included in the training data set 25. The phase distribution optimization module 61 inputs the input training data 25b for each of the multiple wavelength components 50a, 50b, and 50c included in the selected training data 25a and extracted by the wavelength component extraction units 71, 72, and 73 to the input surface 41 of the holographic optical system model 22. The complex amplitude distribution of each of the multiple wavelength components 50a, 50b, and 50c is output to the output surface 42 of the holographic optical system model 22. The phase distribution optimization module 61 calculates an error between the complex amplitude distribution of each of the multiple wavelength components 50a, 50b, and 50c on the output surface 42 generated from the input training data 25b of the selected training data 25a and the output training data 25c of each of the multiple wavelength components 50a, 50b, and 50c of the selected training data 25a.

[0152] For example, the phase distribution optimization module 61 calculates an error between the complex amplitude distribution of the wavelength component 50a at the output surface 42 generated from the input training data 25b for the wavelength component 50a included in the selected training data 25a and the output training data 25c for the wavelength component 50a included in the selected training data 25a. The phase distribution optimization module 61 calculates an error between the complex amplitude distribution of the wavelength component 50b at the output surface 42 generated from the input training data 25b for the wavelength component 50b included in the selected training data 25a and the output training data 25c for the wavelength component 50b included in the selected training data 25a. The phase distribution optimization module 61 calculates an error between the complex amplitude distribution of the wavelength component 50c at the output surface 42 generated from the input training data 25b for the wavelength component 50c included in the selected training data 25a and the output training data 25c for the wavelength component 50c included in the selected training data 25a.

[0153] The phase distribution optimization module 61 updates (optimizes) the phase distribution of the multiple holographic optical elements 44, 45 so as to reduce the error. Any optimization algorithm may be used when the phase distribution optimization module 61 updates (optimizes) the phase distribution of the multiple holographic optical elements 44, 45. As the optimization algorithm, for example, a gradient method such as SGD (Stochastic Gradient Descent), Momentum SGD (SGD with inertia term added), AdaGrad, RMSprop, AdaDelta, or Adam (Adaptive moment estimation) may be used.

[0154] Similarly, the phase distribution optimization module 61 iteratively optimizes the phase distribution of multiple holographic optical elements 44, 45 of the holographic optical system model 22 based on each training data 25a (input training data 25b, output training data 25c) included in the training dataset 25.

[0155] The phase distribution machine learning unit 33 outputs the holographic optical system model 22 for the multiple wavelength components 50a, 50b, and 50c including the optimized phase distribution to, for example, the storage 19 (see FIG. 17). The holographic optical system model 22 including the optimized phase distribution is stored in the storage 19. The holographic optical system model 22 including the optimized phase distribution may be output to a storage medium 18 (see FIG. 17).

[0156] An example of a step (step S24) of machine learning the holographic optical system model 22 in which the initial phase distribution is set will be described with reference to Fig. 24. Step S24 in this embodiment is similar to step S4 in the first embodiment, but differs from step S4 in the first embodiment in a step (step S25) of optimizing the phase distribution of the multiple holographic optical elements 44, 45 due to the fact that the light 50 includes multiple wavelength components 50a, 50b, and 50c (see Figs. 20 to 22). An example of step S25 will be described with reference to Figs. 25 and 26.

[0157] With reference to FIG. 25, in step S27, one training data 25a is selected from the training data set 25 stored in the storage 19. More specifically, one training data 25a for which steps S28 to S36 described later have not been executed is selected from the training data set 25. In this embodiment, the training data set 25 is a training data set for multiple wavelength components 50a, 50b, and 50c, and includes multiple training data 25a (see FIG. 23). Each of the multiple training data 25a includes input training data 25b (see FIG. 23) and output training data 25c (see FIG. 23) corresponding to the input training data 25b. The input training data 25b and the output training data 25c each include the multiple wavelength components 50a, 50b, and 50c.

[0158] In step S28, the wavelength component extraction units 71, 72, and 73 extract training data 25a for each of the multiple wavelength components 50a, 50b, and 50c from the training data 25a selected in step S27. Specifically, the wavelength component extraction unit 71 extracts training data 25a for wavelength component 50a from the selected training data 25a. The wavelength component extraction unit 72 extracts training data 25a for wavelength component 50b from the selected training data 25a. The wavelength component extraction unit 73 extracts training data 25a for wavelength component 50c from the selected training data 25a.

[0159] More specifically, the wavelength component extraction unit 71 extracts input training data 25b for wavelength component 50a from input training data 25b of training data 25a selected in step S27. The wavelength component extraction unit 71 extracts output training data 25c for wavelength component 50a from output training data 25c of training data 25a selected in step S27. The wavelength component extraction unit 72 extracts input training data 25b for wavelength component 50b from input training data 25b of training data 25a selected in step S27. The wavelength component extraction unit 72 extracts output training data 25c for wavelength component 50b from output training data 25c of training data 25a selected in step S27. The wavelength component extraction unit 73 extracts input training data 25b for wavelength component 50c from input training data 25b of training data 25a selected in step S27. The wavelength component extraction unit 73 extracts the output training data 25c for the wavelength component 50c from the output training data 25c of the training data 25a selected in step S27.

[0160] In step S29, the input training data 25b for each of the multiple wavelength components 50a, 50b, and 50c extracted in step S28 is input to the input surface 41. For example, the input training data 25b for wavelength component 50a, the input training data 25b for wavelength component 50b, and the input training data 25b for wavelength component 50c are converted into complex amplitude distributions on the input surface 41 and input to the input surface 41.

[0161] In step S30, the complex amplitude distribution of each of the multiple wavelength components 50a, 50b, 50c when each of the multiple wavelength components 50a, 50b, 50c is incident on the nth holographic optical element is calculated from the complex amplitude distribution of each of the multiple wavelength components 50a, 50b, 50c when each of the multiple wavelength components 50a, 50b, 50c is emitted from the n-1th holographic optical element and the arrangement of the nth holographic optical element relative to the n-1th holographic optical element by light wave diffraction calculation such as the shifted angular spectrum method and the shifted Fresnel diffraction method. When n=1, the n-1th holographic optical element is replaced with the input surface 41, and the arrangement of the first holographic optical element relative to the input surface 41 is used among the optical conditions 20 received in step S21.

[0162] In step S31, the complex amplitude distribution of each of the multiple wavelength components 50a, 50b, 50c when each of the multiple wavelength components 50a, 50b, 50c is output from the n-th holographic optical element is calculated. The complex amplitude distribution of each of the multiple wavelength components 50a, 50b, 50c when each of the multiple wavelength components 50a, 50b, 50c is output from the n-th holographic optical element is given as the product of the complex amplitude distribution of each of the multiple wavelength components 50a, 50b, 50c when each of the multiple wavelength components 50a, 50b, 50c is input to the n-th holographic optical element and the phase distribution for each of the multiple wavelength components 50a, 50b, 50c of the n-th holographic optical element.

[0163] In step S32, it is determined whether the n-th holographic optical element is the last holographic optical element. The last holographic optical element means the holographic optical element that is closest to the output surface 42 when viewed along the optical path (optical path of the light 50) of the holographic optical system model 22. For example, in the holographic optical systems shown in Figures 20 to 22, the holographic optical element 45 is the last holographic optical element.

[0164] If the nth holographic optical element is not the last holographic optical element, steps S30 and S31 are executed for the n+1th holographic optical element. In step S30, the arrangement of the n+1th holographic optical element with respect to the nth holographic optical element is used from the optical condition 20 accepted in step S21.

[0165] If the n-th holographic optical element is the last holographic optical element, the process proceeds to step S33. In step S33, the complex amplitude distribution of each of the multiple wavelength components 50a, 50b, and 50c on the output surface 42 is calculated by light wave diffraction calculation such as the shifted angular spectrum method and the shifted Fresnel diffraction method from the complex amplitude distribution of the light 50 when each of the multiple wavelength components 50a, 50b, and 50c is output from the last holographic optical element and the arrangement of the output surface 42 with respect to the last holographic optical element among the optical conditions 20 accepted in step S1.

[0166] In step S34, the output training data 25c for each of the multiple wavelength components 50a, 50b, and 50c extracted in step S28 is input to the phase distribution optimization module 61. Specifically, the output training data 25c for the wavelength component 50a, the output training data 25c for the wavelength component 50b, and the output training data 25c for the wavelength component 50c extracted from the output training data 25c included in the training data 25a selected in step S27 are converted into complex amplitude distributions on the output surface 42 and input to the phase distribution optimization module 61.

[0167] In step S35, an error is calculated between the complex amplitude distribution of each of the multiple wavelength components 50a, 50b, and 50c on the output surface 42 calculated in step S33 and the output training data 25c for each of the multiple wavelength components 50a, 50b, and 50c input to the phase distribution optimization module 61 in step S34. Specifically, an error between the complex amplitude distribution of the wavelength component 50a on the output surface 42 and the output training data 25c for the wavelength component 50a, an error between the complex amplitude distribution of the wavelength component 50b on the output surface 42 and the output training data 25c for the wavelength component 50b, and an error between the complex amplitude distribution of the wavelength component 50c on the output surface 42 and the output training data 25c for the wavelength component 50c are calculated.

[0168] In step S36, the phase distribution of the multiple holographic optical elements 44, 45 is updated (optimized) so that the error calculated in step S35 for each of the multiple wavelength components 50a, 50b, 50c is reduced. As an optimization algorithm for the phase distribution of the multiple holographic optical elements 44, 45, for example, a gradient method such as SGD (Stochastic Gradient Descent), Momentum SGD (SGD with inertia term added), AdaGrad, RMSprop, AdaDelta, or Adam (Adaptive moment estimation) can be used.

[0169] In step S37, it is determined whether all the training data 25a have been used to update (optimize) the phase distribution of the multiple holographic optical elements 44, 45. If all the training data 25a have not been used, the process returns to step S27 to select one of the unused training data 25a, and steps S28 to S36 are executed for the newly selected training data 25a. If all the training data 25a have been used to update (optimize) the phase distribution of the multiple holographic optical elements 44, 45, the step of optimizing the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system model 22 (step S25) is terminated.

[0170] The phase distribution machine learning unit 33 outputs the holographic optical system model 22 for the multiple wavelength components 50a, 50b, and 50c including the optimized phase distribution to, for example, the storage 19 (see FIG. 17). The holographic optical system model 22 for the multiple wavelength components 50a, 50b, and 50c including the optimized phase distribution is stored in the storage 19. The holographic optical system model 22 for the multiple wavelength components 50a, 50b, and 50c including the optimized phase distribution may be output to a storage medium 18 (see FIG. 17).

[0171] <Holographic Optical System Design Program 60>

[0172] A holographic optical system design program 60 (see FIG. 17) causes the processor 12 (see FIG. 17) to execute the holographic optical system design method of this embodiment. A program such as the holographic optical system design program 60 may be recorded in a computer-readable recording medium (a non-transitory computer-readable recording medium, for example, the storage medium 18) of this embodiment.

[0173] (Modification)

[0174] The light 50 may include two wavelength components, or may include four or more wavelength components.

[0175] The method for designing a holographic optical system and the holographic optical system design program 60 of the present embodiment provide the following effects in addition to the effects of the method for designing a holographic optical system and the holographic optical system design program 60 of the first embodiment.

[0176] In the method for designing a holographic optical system according to the present embodiment, light 50 includes multiple wavelength components 50a, 50b, and 50c having mutually different wavelengths.

[0177] Therefore, a holographic optical system for the multiple wavelength components 50a, 50b, and 50c can be efficiently designed in which the zero-order diffracted light beams 53 and 55 are prevented from overlapping on the output surface .

[0178] In the design method of the holographic optical system of the present embodiment, in a step (step S23) of setting an initial phase distribution to the multiple holographic optical elements 44, 45 of the holographic optical system model 22, an initial phase distribution for each of the multiple wavelength components 50a, 50b, 50c is set for each of the multiple holographic optical elements 44, 45 so that each of the multiple wavelength components 50a, 50b, 50c travels from the input surface 41 through the multiple holographic optical elements 44, 45 and is output to the output surface 42. In a step (step S24) of machine learning the holographic optical system model 22 in which the initial phase distribution is set, the phase distribution for each of the multiple wavelength components 50a, 50b, 50c of each of the multiple holographic optical elements 44, 45 is optimized by machine learning.

[0179] Therefore, the function of the holographic optical system for the multiple wavelength components 50a, 50b, 50c can be realized with higher accuracy. An optimized phase distribution of the multiple holographic optical elements 44, 45 that can realize the optical path of the multiple wavelength components 50a, 50b, 50c from the input surface 41 through the multiple holographic optical elements 44, 45 to the output surface 42 can be obtained more reliably, with less calculation, and in a shorter time. A holographic optical system for the multiple wavelength components 50a, 50b, 50c in which the zero-order diffracted light 53, 55 is prevented from superimposing on the output surface 42 can be designed more efficiently.

[0180] The holographic optical system design program 60 of the present embodiment causes the processor 12 to execute each step of the holographic optical system design method of the present embodiment. Therefore, it is possible to efficiently design a holographic optical system for multiple wavelength components 50a, 50b, and 50c in which zero-order diffracted light 53 and 55 are prevented from overlapping on the output surface 42.

[0181] (Embodiment 3)

[0182] 27 and 28, the holographic optical system design apparatus 1 of the third embodiment will be described. The holographic optical system design apparatus 1 of the present embodiment is similar to the holographic optical system design apparatus 1 of the second embodiment, but differs from it mainly in the following points.

[0183] <Hardware configuration>

[0184] Referring to FIG. 27, in this embodiment, in addition to the optical conditions 20, the holographic optical system model 22, the training data set 25 and the holographic optical system design program 60, a plurality of holographic optical system sub-models 23a, 23b, 23c and training data sets 26, 27, 28 are stored in the storage 19.

[0185] The multiple holographic optical system submodels 23a, 23b, and 23c are generated on a computer (holographic optical system design device 1). As shown in Fig. 30 to Fig. 32, each of the multiple holographic optical system submodels 23a, 23b, and 23c includes an input surface 41, multiple holographic optical elements 44 and 45, and an output surface 42. Each of the multiple holographic optical system submodels 23a, 23b, and 23c is a holographic optical system submodel for a single wavelength component, and corresponds to one wavelength component among the multiple wavelength components 50a, 50b, and 50c.

[0186] Specifically, the holographic optical system submodel 23a is a holographic optical system submodel for wavelength component 50a capable of imparting a phase distribution for wavelength component 50a to each of the multiple holographic optical elements 44 and 45. The holographic optical system submodel 23b is a holographic optical system submodel for wavelength component 50b capable of imparting a phase distribution for wavelength component 50b to each of the multiple holographic optical elements 44 and 45. The holographic optical system submodel 23c is a holographic optical system submodel for wavelength component 50c capable of imparting a phase distribution for wavelength component 50c to each of the multiple holographic optical elements 44 and 45.

[0187] With reference to FIG. 27, the training data set 25 of this embodiment is the same as the training data set 25 of the second embodiment. Each of the training data sets 26, 27, and 28 is used to train a corresponding holographic optical system submodel among the multiple holographic optical system submodels 23a, 23b, and 23c. Specifically, the training data set 26 is a training data set for the wavelength component 50a and is used to train the holographic optical system submodel 23a for the wavelength component 50a. The training data set 27 is a training data set for the wavelength component 50b and is used to train the holographic optical system submodel 23b for the wavelength component 50b. The training data set 28 is a training data set for the wavelength component 50c and is used to train the holographic optical system submodel 23c for the wavelength component 50c.

[0188] 30, the training data set 26 includes a plurality of training data 26a. Each of the plurality of training data 26a includes input training data 26b and output training data 26c corresponding to the input training data 26b. The input training data 26b and the output training data 26c are formed of wavelength components 50a. The input training data 26b and the output training data 26c are, for example, red images.

[0189] 31, the training data set 27 includes a plurality of training data 27a. Each of the plurality of training data 27a includes input training data 27b and output training data 27c corresponding to the input training data 27b. The input training data 27b and the output training data 27c are formed of wavelength components 50b. The input training data 27b and the output training data 27c are, for example, green images.

[0190] 32, the training data set 28 includes a plurality of training data 28a. Each of the plurality of training data 28a includes input training data 28b and output training data 28c corresponding to the input training data 28b. The input training data 28b and the output training data 28c are formed of wavelength components 50c. The input training data 28b and the output training data 28c are, for example, blue images.

[0191] <Functional configuration>

[0192] 28, the holographic optical system design device 1 of the present embodiment further includes a holographic optical system sub-model generation unit 35, a holographic optical system sub-model selection unit 36, and a sub-model machine learning termination determination unit 37.

[0193] The holographic optical system sub-model generation unit 35 generates holographic optical system sub-models 23a, 23b, and 23c on a computer (holographic optical system design device 1) in accordance with the optical conditions 20, which include the number of holographic optical elements 44, 45, the size of each of the holographic optical elements 44, 45, and the arrangement of the input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42.

[0194] Each of the holographic optical system submodels 23a, 23b, and 23c is a holographic optical system submodel for a single wavelength component, similar to the holographic optical system model 21 of the first embodiment. Specifically, the holographic optical system submodel 23a is a holographic optical system submodel for wavelength component 50a. The holographic optical system submodel 23b is a holographic optical system submodel for wavelength component 50b. The holographic optical system submodel 23c is a holographic optical system submodel for wavelength component 50c.

[0195] In the holographic optical system submodel 23a, the wavelength component 50a travels through the multiple holographic optical elements 44, 45 from the input surface 41 toward the output surface 42, thereby generating zero-order diffracted light in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 of the holographic optical system submodel 23a are arranged so that this zero-order diffracted light does not overlap on the output surface 42.

[0196] In the holographic optical system submodel 23b, the wavelength component 50b travels through the multiple holographic optical elements 44, 45 from the input surface 41 toward the output surface 42, thereby generating zero-order diffracted light in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 of the holographic optical system submodel 23b are arranged so that this zero-order diffracted light does not overlap on the output surface 42.

[0197] In the holographic optical system submodel 23c, the wavelength component 50c travels through the multiple holographic optical elements 44, 45 from the input surface 41 toward the output surface 42, thereby generating zero-order diffracted light in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 of the holographic optical system submodel 23c are arranged so that this zero-order diffracted light does not overlap on the output surface 42.

[0198] 28, the holographic optical system submodel selection unit 36 ​​selects one of the multiple holographic optical system submodels 23a, 23b, and 23c. More specifically, the holographic optical system submodel selection unit 36 ​​selects one holographic optical system submodel on which machine learning by the phase distribution machine learning unit 33 has not yet been performed, from the multiple holographic optical system submodels 23a, 23b, and 23c.

[0199] 28, similarly to the second embodiment, the initial phase distribution setting unit 32 generates a holographic optical system model 22 in which an initial phase distribution is set from the holographic optical system model 22 generated by the holographic optical system model generation unit 31. The initial phase distribution setting unit 32 further generates a holographic optical system submodel in which an initial phase distribution is set from the holographic optical system submodel selected by the holographic optical system submodel selection unit 36.

[0200] Specifically, an operator inputs an initial phase distribution for each of the multiple wavelength components 50a, 50b, and 50c to the holographic optical system design device 1 (see FIG. 27) using the input device 11 (see FIG. 27). The initial phase distribution setting unit 32 accepts the initial phase distribution for each of the multiple wavelength components 50a, 50b, and 50c. The initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength components corresponding to the holographic optical system submodel selected by the holographic optical system submodel selection unit 36 ​​for each of the multiple holographic optical elements 44 and 45 of the holographic optical system submodel selected by the holographic optical system submodel selection unit 36. In this way, the initial phase distribution setting unit 32 generates each of the holographic optical system submodels 23a, 23b, and 23c in which the initial phase distribution is set.

[0201] For example, when the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23a, the initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50a in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a so that the wavelength component 50a travels from the input surface 41 of the holographic optical system submodel 23a through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a and is output to the output surface 42 of the holographic optical system submodel 23a. The wavelength component 50a travels through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a as non-zero order diffracted light (e.g., first order diffracted light, etc.) in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a.

[0202] When the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23b, the initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50b in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b so that the wavelength component 50b travels from the input surface 41 of the holographic optical system submodel 23b through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b and is output to the output surface 42 of the holographic optical system submodel 23b. The wavelength component 50b travels through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b as non-zero order diffracted light (e.g., first order diffracted light, etc.) in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b.

[0203] When the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23c, the initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50c in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c so that the wavelength component 50c travels from the input surface 41 of the holographic optical system submodel 23c through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c and is output to the output surface 42 of the holographic optical system submodel 23c. The wavelength component 50c travels through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c as non-zero order diffracted light (e.g., first order diffracted light, etc.) in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c.

[0204] In each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected by the holographic optical system submodel selection unit 36, the difference between the maximum phase of the initial phase distribution and the minimum phase of the initial phase distribution for the wavelength component corresponding to the holographic optical system submodel selected by the holographic optical system submodel selection unit 36 ​​is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected by the holographic optical system submodel selection unit 36, zero-order diffracted light is generated from the wavelength component corresponding to the holographic optical system submodel selected by the holographic optical system submodel selection unit 36.

[0205] 28, the phase distribution machine learning unit 33 performs machine learning on the holographic optical system submodel selected by the holographic optical system submodel selection unit 36 ​​and for which an initial phase distribution has been set. The phase distribution machine learning unit 33 optimizes, by machine learning, the phase distributions of the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected by the holographic optical system submodel selection unit 36 ​​and for which an initial phase distribution has been set, so that the function of the holographic optical system can be realized with higher accuracy.

[0206] When the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23a, the phase distribution machine learning unit 33 provides an optimized phase distribution for the wavelength component 50a to each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a. In this manner, the phase distribution machine learning unit 33 outputs the holographic optical system submodel 23a for the wavelength component 50a including the optimized phase distribution.

[0207] When the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23b, the phase distribution machine learning unit 33 provides an optimized phase distribution for the wavelength component 50b to each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b. In this manner, the phase distribution machine learning unit 33 outputs the holographic optical system submodel 23b for the wavelength component 50b including the optimized phase distribution.

[0208] When the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23c, the phase distribution machine learning unit 33 provides an optimized phase distribution for the wavelength component 50c to each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c. Thus, the phase distribution machine learning unit 33 outputs the holographic optical system submodel 23c for the wavelength component 50c including the optimized phase distribution.

[0209] In each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected by the holographic optical system submodel selection unit 36, the difference between the maximum phase of the optimized phase distribution and the minimum phase of the optimized phase distribution for the wavelength component corresponding to the holographic optical system submodel selected by the holographic optical system submodel selection unit 36 ​​is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected by the holographic optical system submodel selection unit 36, zero-order diffracted light is generated from the wavelength component corresponding to the holographic optical system submodel selected by the holographic optical system submodel selection unit 36.

[0210] 28, the sub-model machine learning completion determination unit 37 determines whether the phase distribution machine learning unit 33 has completed machine learning of all of the multiple holographic optical system sub-models 23a, 23b, and 23c.

[0211] 28, in this embodiment, the holographic optical system model generation unit 31 generates the holographic optical system model 22 from the multiple holographic optical system sub-models 23a, 23b, and 23c. For example, the holographic optical system model generation unit 31 generates the holographic optical system model 22 by integrating the multiple holographic optical system sub-models 23a, 23b, and 23c that have been machine-learned by the phase distribution machine learning unit 33.

[0212] <How to design a holographic optical system>

[0213] A method for designing the holographic optical system of this embodiment will be described with reference to Fig. 29. The method for designing the holographic optical system of this embodiment is similar to the method for designing the holographic optical system of embodiment 2, but differs from the method for designing the holographic optical system of embodiment 2 in the following points.

[0214] 29, in addition to steps S21, S22, and S24 (see FIG. 19) of the second embodiment, the design method of the holographic optical system of the present embodiment further includes a step of generating a plurality of holographic optical system submodels 23a, 23b, and 23c (step S40), a step of selecting one of the plurality of holographic optical system submodels 23a, 23b, and 23c (step S41), a step of setting an initial phase distribution to the plurality of holographic optical elements 44 and 45 of the holographic optical system submodel selected in step S41 (step S42), a step of machine learning the holographic optical system submodel selected in step S41 and to which the initial phase distribution is set (step S43), and a step of determining whether the machine learning of all of the plurality of holographic optical system submodels 23a, 23b, and 23c has been completed (step S44). Steps S40 to S44 are executed between steps S21 and S22.

[0215] 29 to 32, the step of generating holographic optical system sub-models 23a, 23b, and 23c of this embodiment (step S40) is executed by holographic optical system sub-model generation unit 35 (see FIG. 28). The step of generating each of holographic optical system sub-models 23a, 23b, and 23c (step S40) is similar to the step of generating holographic optical system model 21 of the first embodiment (step S2).

[0216] Specifically, in step S40, the holographic optical system sub-model generation unit 35 generates a holographic optical system sub-model 23a for wavelength component 50a, a holographic optical system sub-model 23b for wavelength component 50b, and a holographic optical system sub-model 23c for wavelength component 50c on a computer (holographic optical system design device 1) in accordance with the optical conditions 20 received in step S21, including the number of holographic optical elements 44, 45, the size of each of the holographic optical elements 44, 45, and the arrangement of the input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42.

[0217] In the holographic optical system submodel 23a, the wavelength component 50a travels through the multiple holographic optical elements 44, 45 from the input surface 41 toward the output surface 42, thereby generating zero-order diffracted light in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 of the holographic optical system submodel 23a are arranged so that this zero-order diffracted light does not overlap on the output surface 42.

[0218] In the holographic optical system submodel 23b, the wavelength component 50b travels through the multiple holographic optical elements 44, 45 from the input surface 41 toward the output surface 42, thereby generating zero-order diffracted light in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 of the holographic optical system submodel 23b are arranged so that this zero-order diffracted light does not overlap on the output surface 42.

[0219] In the holographic optical system submodel 23c, the wavelength component 50c travels through the multiple holographic optical elements 44, 45 from the input surface 41 toward the output surface 42, thereby generating zero-order diffracted light in the multiple holographic optical elements 44, 45. The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 of the holographic optical system submodel 23c are arranged so that this zero-order diffracted light does not overlap on the output surface 42.

[0220] The step (step S41) of selecting one holographic optical system submodel from the multiple holographic optical system submodels 23a, 23b, 23c generated in step S40 is executed by the holographic optical system submodel selection unit 36 ​​(see FIG. 28). Specifically, the holographic optical system submodel selection unit 36 ​​selects one holographic optical system submodel for which steps S42 and S43 described below have not yet been executed from the multiple holographic optical system submodels 23a, 23b, 23c.

[0221] The step (step S42) of setting an initial phase distribution for the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected in step S41 is executed by the initial phase distribution setting unit 32 (see FIG. 28). Step S42 in this embodiment is similar to step S3 in the first embodiment, but the initial phase distribution in step S42 in this embodiment is an initial phase distribution for wavelength components corresponding to the holographic optical system submodel selected by the holographic optical system submodel selection unit 36.

[0222] Specifically, in step S42, an operator inputs an initial phase distribution for each of the multiple wavelength components 50a, 50b, and 50c to the holographic optical system design device 1 (see FIG. 27) using the input device 11 (see FIG. 27). The initial phase distribution setting unit 32 accepts the initial phase distribution for each of the multiple wavelength components 50a, 50b, and 50c. The initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength components corresponding to the holographic optical system submodel selected by the holographic optical system submodel selection unit 36 ​​for each of the multiple holographic optical elements 44 and 45 of the holographic optical system submodel selected by the holographic optical system submodel selection unit 36. In this way, the initial phase distribution setting unit 32 generates the holographic optical system submodel selected in step S41 and in which the initial phase distribution is set.

[0223] For example, when the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23a in step S41, the initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50a in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a so that the wavelength component 50a travels from the input surface 41 of the holographic optical system submodel 23a through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a and is output to the output surface 42 of the holographic optical system submodel 23a. The wavelength component 50a travels through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a as non-zero order diffracted light (e.g., first order diffracted light, etc.) in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a.

[0224] When the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23b in step S41, the initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50b in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b so that the wavelength component 50b travels from the input surface 41 of the holographic optical system submodel 23b through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b and is output to the output surface 42 of the holographic optical system submodel 23b. The wavelength component 50b travels through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b as non-zero order diffracted light (e.g., first order diffracted light, etc.) in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b.

[0225] When the holographic optical system submodel selection unit 36 ​​selects the holographic optical system submodel 23c in step S41, the initial phase distribution setting unit 32 sets an initial phase distribution for the wavelength component 50c in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c so that the wavelength component 50c travels from the input surface 41 of the holographic optical system submodel 23c through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c and is output to the output surface 42 of the holographic optical system submodel 23c. The wavelength component 50c travels through the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c as non-zero order diffracted light (e.g., first order diffracted light, etc.) in each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c.

[0226] In each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected in step S41, the difference between the maximum phase of the initial phase distribution and the minimum phase of the initial phase distribution for the wavelength component corresponding to the holographic optical system submodel selected in step S41 is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected in step S41, zero-order diffracted light is generated from the wavelength component corresponding to the holographic optical system submodel selected in step S41.

[0227] A step (step S43) of machine learning the holographic optical system sub-model selected in step S41 and for which the initial phase distribution has been set is executed by the phase distribution machine learning unit 33 (see FIG. 28). In step S43, the phase distribution machine learning unit 33 optimizes the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system sub-model selected in step S41 so that the function of the holographic optical system can be realized with higher accuracy. The phase distribution machine learning unit 33 outputs the holographic optical system sub-model including the optimized phase distribution.

[0228] Step S43 is similar to step S4 in embodiment 1, but in step S43, a training data set for the wavelength component corresponding to the holographic optical system sub-model selected in step S41 and for which an initial phase distribution is set is used to machine-learn the holographic optical system sub-model selected in step S41.

[0229] For example, when the holographic optical system submodel 23a is selected in step S41, in step S43, the holographic optical system submodel 23a is machine-learned using the training data set 26 for the wavelength component 50a (see FIG. 30). Specifically, an error is calculated between the complex amplitude distribution of the wavelength component 50a generated on the output surface 42 of the holographic optical system submodel 23a by inputting the input training data 26b for the wavelength component 50a to the input surface 41 of the holographic optical system submodel 23a and the output training data 26c for the wavelength component 50a input to the phase distribution optimization module 61. The phase distribution optimization module 61 updates (optimizes) the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23a so that this error is reduced.

[0230] When the holographic optical system submodel 23b is selected in step S41, in step S43, the holographic optical system submodel 23b is machine-learned using the training data set 27 for the wavelength component 50b (see FIG. 31). Specifically, an error is calculated between the complex amplitude distribution of the wavelength component 50b generated on the output surface 42 of the holographic optical system submodel 23b by inputting the input training data 27b for the wavelength component 50b to the input surface 41 of the holographic optical system submodel 23b and the output training data 27c for the wavelength component 50b input to the phase distribution optimization module 61. The phase distribution optimization module 61 updates (optimizes) the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23b so that this error is reduced.

[0231] When the holographic optical system submodel 23c is selected in step S41, in step S43, the holographic optical system submodel 23c is machine-learned using the training data set 28 for the wavelength component 50c (see FIG. 32). Specifically, an error is calculated between the complex amplitude distribution of the wavelength component 50c generated on the output surface 42 of the holographic optical system submodel 23c by inputting the input training data 28b for the wavelength component 50c to the input surface 41 of the holographic optical system submodel 23c and the output training data 28c for the wavelength component 50c input to the phase distribution optimization module 61. The phase distribution optimization module 61 updates (optimizes) the phase distribution of the multiple holographic optical elements 44, 45 of the holographic optical system submodel 23c so that this error is reduced.

[0232] In each of the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected in step S41, the difference between the maximum phase of the optimized phase distribution and the minimum phase of the optimized phase distribution for the wavelength component corresponding to the holographic optical system submodel selected in step S41 is, for example, less than 2π. Therefore, in the multiple holographic optical elements 44, 45 of the holographic optical system submodel selected in step S41, zero-order diffracted light is generated from the wavelength component corresponding to the holographic optical system submodel selected in step S41.

[0233] The step of determining whether the machine learning of all of the multiple holographic optical system submodels 23a, 23b, and 23c has been completed (step S44) is executed by the submodel machine learning completion determination unit 37 (see FIG. 28). If the machine learning of all of the multiple holographic optical system submodels 23a, 23b, and 23c has not been completed, the process returns to step S41, and one holographic optical system submodel that has not yet been machine-trained is newly selected from the multiple holographic optical system submodels 23a, 23b, and 23c, and steps S42 and S43 are executed for the newly selected holographic optical system submodel.

[0234] When the machine learning of all of the multiple holographic optical system submodels 23a, 23b, and 23c is completed, the process proceeds to a step (step S22) of generating the holographic optical system model 22. Step S22 in this embodiment is executed by the holographic optical system model generation unit 31. In this embodiment, the holographic optical system model generation unit 31 generates the holographic optical system model 22 for the multiple wavelength components 50a, 50b, and 50c from the holographic optical system submodels 23a, 23b, and 23c including the individually optimized phase distributions. For example, the holographic optical system model generation unit 31 integrates the holographic optical system submodels 23a, 23b, and 23c including the individually optimized phase distributions to generate the holographic optical system model 22 for the multiple wavelength components 50a, 50b, and 50c.

[0235] Step S24 of the present embodiment is executed by the phase distribution machine learning unit 33. In step S24 of the present embodiment, similar to step S24 of the second embodiment, the phase distribution machine learning unit 33 optimizes the phase distributions of the multiple holographic optical elements 44, 45 of the holographic optical system model 22 for the multiple wavelength components 50a, 50b, 50c generated in step S22 so that the function of the holographic optical system can be realized with higher accuracy. The phase distribution machine learning unit 33 provides each of the multiple holographic optical elements 44, 45 with an optimized phase distribution for each of the multiple wavelength components 50a, 50b, 50c.

[0236] <Holographic Optical System Design Program 60>

[0237] Holographic optical system design program 60 (see FIG. 27) causes processor 12 (see FIG. 27) to execute the holographic optical system design method of this embodiment. A program such as holographic optical system design program 60 may be recorded in a computer-readable recording medium (a non-transitory computer-readable recording medium, for example storage medium 18) of this embodiment.

[0238] The method for designing a holographic optical system and the holographic optical system design program 60 of the present embodiment provide the following effects in addition to the effects of the method for designing a holographic optical system and the holographic optical system design program 60 of the second embodiment.

[0239] In the design method of the holographic optical system using the holographic optical system model 22 of the present embodiment, the holographic optical system model 22 includes an input surface 41, a plurality of holographic optical elements 44, 45 optically arranged in series, and an output surface 42. The design method of the holographic optical system of the present embodiment includes a step (step S21) of receiving optical conditions 20 including the number of the plurality of holographic optical elements 44, 45, the size of each of the plurality of holographic optical elements 44, 45, the arrangement of the input surface 41, the plurality of holographic optical elements 44, 45, and the output surface 42, and the wavelengths of the plurality of wavelength components 50a, 50b, 50c traveling through the plurality of holographic optical elements 44, 45. The wavelengths of the plurality of wavelength components 50a, 50b, 50c are different from each other. The design method of the holographic optical system of the present embodiment includes a step (step S40) of generating a plurality of holographic optical system submodels 23a, 23b, 23c. Each of the plurality of holographic optical system submodels 23a, 23b, and 23c includes an input surface 41, a plurality of holographic optical elements 44, 45, and an output surface 42. Each of the plurality of holographic optical system submodels 23a, 23b, and 23c satisfies the number of the plurality of holographic optical elements 44, 45, the size of each of the plurality of holographic optical elements 44, 45, and the arrangement of the input surface 41, the plurality of holographic optical elements 44, 45, and the output surface 42, among the optical conditions 20. Each of the plurality of holographic optical system submodels 23a, 23b, and 23c is a holographic optical system submodel for a corresponding wavelength component among the plurality of wavelength components 50a, 50b, and 50c.The input surface 41, the multiple holographic optical elements 44, 45 and the output surface 42 of each of the multiple holographic optical system submodels 23a, 23b, 23c are arranged so that zero-order diffracted light generated in the multiple holographic optical elements 44, 45 of each of the multiple holographic optical system submodels 23a, 23b, 23c by corresponding wavelength components traveling from the input surface 41 of each of the multiple holographic optical system submodels 23a, 23b, 23c through the multiple holographic optical elements 44, 45 of each of the multiple holographic optical system submodels 23a, 23b, 23c toward the output surface 42 of each of the multiple holographic optical system submodels 23a, 23b, 23c does not overlap on the output surface 42 of each of the multiple holographic optical system submodels 23a, 23b, 23c. The method for designing the holographic optical system of the present embodiment includes: inputting an initial phase for a corresponding wavelength component to each of the plurality of holographic optical elements 44, 45 of each of the plurality of holographic optical system submodels 23 a, 23 b, 23 c such that the corresponding wavelength component travels from an input surface 41 of each of the plurality of holographic optical system submodels 23 a, 23 b, 23 c through the plurality of holographic optical elements 44, 45 of each of the plurality of holographic optical system submodels 23 a, 23 b, 23 c and is output to an output surface 42 of each of the plurality of holographic optical system submodels 23 a, 23 b, 23 c. The method includes a step of setting a distribution (step S42), a step of machine learning each of the multiple holographic optical system sub-models 23a, 23b, 23c for which an initial phase distribution has been set by optimizing the phase distribution for the corresponding wavelength component of each of the multiple holographic optical elements 44, 45 of each of the multiple holographic optical system sub-models 23a, 23b, 23c (step S43), and a step of generating a holographic optical system model 22 from the machine-learned multiple holographic optical system sub-models 23a, 23b, 23c (step S22).The input surface 41, the multiple holographic optical elements 44, 45, and the output surface 42 of the holographic optical system model 22 are arranged so that the zero-order diffracted light generated in the multiple holographic optical elements 44, 45 of the holographic optical system model 22 by the multiple wavelength components 50a, 50b, 50c traveling from the input surface 41 of the holographic optical system model 22 toward the output surface 42 of the holographic optical system model 22 is not superimposed on the output surface 42 of the holographic optical system model 22. The holographic optical system design method of the present embodiment includes a step of machine learning the holographic optical system model by optimizing the phase distribution of each of the multiple holographic optical elements 44, 45 of the holographic optical system model 22 for the multiple wavelength components 50a, 50b, 50c (step S24).

[0240] The size of the memory 13 (see FIG. 27) required for the machine learning of each of the multiple holographic optical system submodels 23a, 23b, and 23c can be smaller than the size of the memory 13 required for the machine learning of the holographic optical system model 22. Furthermore, in this embodiment, the holographic optical system model 22 is generated from the multiple holographic optical system submodels 23a, 23b, and 23c that have been individually machine-learned, so the amount of calculations required for the machine learning of the holographic optical system model 22 is reduced. Therefore, a holographic optical system in which zero-order diffracted light is prevented from superimposing on the output surface 42 can be designed more efficiently or more quickly.

[0241] The holographic optical system design program 60 of the present embodiment causes the processor 12 to execute each step of the holographic optical system design method of the present embodiment. Therefore, a holographic optical system in which superposition of zero-order diffracted light on the output surface 42 is prevented can be designed more efficiently or more quickly.

[0242] The first to third embodiments disclosed herein and their modified examples should be considered to be illustrative and not restrictive in all respects. The scope of the present disclosure is indicated by the claims, not the above description, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0243] 1 Holographic optical system design device, 11 Input device, 12 Processor, 13 Memory, 14 Display, 16 Network controller, 17 Storage medium drive, 18 Storage medium, 19 Storage, 20 Optical conditions, 21, 22 Holographic optical system model, 23a, 23b, 23c Holographic optical system sub-model, 24, 25, 26, 27, 28 Training data set, 24a, 25a, 26a, 27a, 28a Training data, 24b, 25b, 26b, 27b, 28b Input training data, 24c, 25c, 26c, 27c, 28c Output training data, 30 Optical condition reception unit, 31 Holographic optical system model generation unit, 32 Initial phase distribution setting unit, 33 Phase distribution machine learning unit, 35 Holographic optical system sub-model generation unit, 36 Holographic optical system sub-model selection unit, 37 Sub-model machine learning termination determination unit, 41 Input surface, 42 Output surface, 44,45,46,47 Holographic optical element, 44p,45p Pixel, 50 Light, 50a,50b,50c Wavelength components, 52,54 Optical path, 53,53a,53b,53c,55,55a,55b,55c Zero-order diffracted light, 56,57 Optical axis, 60 Holographic optical system design program, 61 Phase distribution optimization module, 63a,63b,64a,64b,65a,65b,66a,66b Straight line, 71,72,73 Wavelength component extraction section.

Claims

1. A method for designing a holographic optical system using a holographic optical system model, the holographic optical system model including an input surface, a plurality of holographic optical elements optically arranged in series, and an output surface, the method for designing the holographic optical system comprising the steps of: accepting optical conditions including a number of the plurality of holographic optical elements, a size of each of the plurality of holographic optical elements, an arrangement of the input surface, the plurality of holographic optical elements, and the output surface, and a wavelength of light traveling through the plurality of holographic optical elements; generating the holographic optical system model that satisfies the number of the plurality of holographic optical elements, the size of each of the plurality of holographic optical elements, and the arrangement of the input surface, the plurality of holographic optical elements, and the output surface, among the optical conditions, wherein the input surface, the plurality of holographic optical elements, and the output surface are arranged such that zero-order diffracted light generated in the plurality of holographic optical elements as the light travels from the input surface to the output surface through the plurality of holographic optical elements does not overlap on the output surface, setting an initial phase distribution for each of the plurality of holographic optical elements such that the light travels from the input surface through the plurality of holographic optical elements and exits at the output surface; A method for designing a holographic optical system, comprising a step of machine learning the holographic optical system model in which the initial phase distribution is set, by optimizing the phase distribution of each of the plurality of holographic optical elements for the light.

2. The method for designing a holographic optical system according to claim 1 , wherein the light includes a plurality of wavelength components having mutually different wavelengths.

3. In the step of setting the initial phase distribution, an initial phase distribution for each of the plurality of wavelength components is set for each of the plurality of holographic optical elements so that each of the plurality of wavelength components travels from the input surface through the plurality of holographic optical elements and is output to the output surface; The method for designing a holographic optical system according to claim 2 , wherein in the step of machine learning the holographic optical system model, a phase distribution for each of the multiple wavelength components of each of the multiple holographic optical elements is optimized by machine learning.

4. A method for designing a holographic optical system using a holographic optical system model, the holographic optical system model including an input surface, a plurality of holographic optical elements optically arranged in series, and an output surface, the method for designing the holographic optical system comprising the steps of: receiving optical conditions including a number of the plurality of holographic optical elements, a size of each of the plurality of holographic optical elements, an arrangement of the input surface, the plurality of holographic optical elements and the output surface, and wavelengths of multiple wavelength components traveling through the plurality of holographic optical elements, the wavelengths of the multiple wavelength components being different from one another; generating a plurality of holographic optical system submodels, each of the plurality of holographic optical system submodels including the input surface, the plurality of holographic optical elements, and the output surface, each of the plurality of holographic optical system submodels satisfying the number of the plurality of holographic optical elements, the size of each of the plurality of holographic optical elements, and the arrangement of the input surface, the plurality of holographic optical elements, and the output surface among the optical conditions, each of the plurality of holographic optical system submodels being a holographic optical system submodel for a corresponding wavelength component among the plurality of wavelength components, and the input surface, the plurality of holographic optical elements, and the output surface of each of the plurality of holographic optical system submodels being arranged such that zero-order diffracted light generated in the plurality of holographic optical elements of each of the plurality of holographic optical system submodels by the corresponding wavelength component traveling from the input surface of each of the plurality of holographic optical system submodels to the output surface of each of the plurality of holographic optical system submodels through the plurality of holographic optical elements of each of the plurality of holographic optical system submodels does not overlap on the output surface of each of the plurality of holographic optical system submodels, setting an initial phase distribution for the corresponding wavelength component in each of the plurality of holographic optical elements of each of the plurality of holographic optical system submodels such that the corresponding wavelength component travels from the input surface of each of the plurality of holographic optical system submodels through the plurality of holographic optical elements of each of the plurality of holographic optical system submodels and exits at the output surface of each of the plurality of holographic optical system submodels; machine learning each of the plurality of holographic optical system sub-models with the initial phase distribution set by optimizing a phase distribution for the corresponding wavelength component of each of the plurality of holographic optical elements of each of the plurality of holographic optical system sub-models; generating the holographic optical system model from the machine-learned holographic optical system sub-models, wherein the input surface, the plurality of holographic optical elements, and the output surface of the holographic optical system model are arranged such that zero-order diffracted light generated in the plurality of holographic optical elements of the holographic optical system model by the plurality of wavelength components traveling from the input surface of the holographic optical system model through the plurality of holographic optical elements of the holographic optical system model toward the output surface of the holographic optical system model does not overlap on the output surface of the holographic optical system model; A method for designing a holographic optical system, comprising a step of machine learning the holographic optical system model by optimizing the phase distribution of each of the plurality of holographic optical elements of the holographic optical system model for the multiple wavelength components.

5. the plurality of holographic optical elements includes a first holographic optical element having a first size and a second holographic optical element having a second size different from the first size; 2. The method for designing a holographic optical system according to claim 1, wherein in the step of setting the initial phase distribution for each of the plurality of holographic optical elements, the initial phase distribution is set for each of the plurality of holographic optical elements so that the light irradiates 80% or more of the first size and 80% or more of the second size.

6. The method for designing a holographic optical system according to claim 1 , wherein the plurality of holographic optical elements includes a plurality of reflective holographic optical elements that form a folded optical path.

7. A holographic optical system design program that causes a processor to execute each step of the holographic optical system design method according to any one of claims 1 to 6.

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