Hologram generation method, hologram generation apparatus, and light irradiation apparatus

Abstract

To provide a method and an apparatus for generating a hologram that make it possible to generate a high-resolution target intensity image with high accuracy.SOLUTION: A hologram generation method includes a pattern setting step S1, an intensity image calculation step S2, an evaluation value calculation step S3, and the like. In step S2, zero-filing is performed on a complex amplitude distribution obtained when a candidate pattern set in step S1 is presented on an input surface, and a candidate intensity image is generated on the basis of a result of propagation calculation of the complex amplitude distribution after the zero-filing. In step S3, an evaluation value is obtained on the basis of intensity correlation between the candidate intensity image and a target intensity image. Using an optimization method, while changing the candidate pattern to be set in step S1, steps S1 to S3 are repeatedly executed, and one of the candidate patterns is selected as a hologram to be presented on the input surface on the basis of the evaluation value.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a hologram generating method, a hologram generating device, and a light irradiation device. [Background technology]

[0002] A known light irradiation device is one that spatially modulates laser light using a hologram presented on a spatial light modulator, and then performs Fourier transform on the modulated laser light using an optical system to irradiate light. In such a light irradiation device, in order to form a target intensity image having a desired intensity distribution by irradiating light, it is important to present a hologram corresponding to the target intensity image on the spatial light modulator.

[0003] The Iterative Fourier Transform Algorithm (IFTA) is known as an algorithm for generating a hologram to form a target intensity image. IFTA generates a hologram corresponding to the target intensity image by repeating the following processes: Fourier transform calculation of the complex amplitude distribution of light after spatial modulation by a hologram, amplitude modification of the complex amplitude distribution obtained by the Fourier transform calculation based on the target intensity image, inverse Fourier transform calculation of the complex amplitude distribution after the amplitude modification, and modification of the hologram based on the complex amplitude distribution obtained by the inverse Fourier transform calculation.

[0004] A technique for generating a hologram for forming a target intensity image is also known, as described in Non-Patent Document 1. This technique calculates a residual sum-of-squares evaluation value between an intensity image obtained by Fourier transform calculation of the complex amplitude distribution of light after spatial modulation by a hologram and a target intensity image, and updates the hologram based on the evaluation value using an optimization method. The residual sum-of-squares evaluation value is an evaluation value based on the sum of the squares of the differences in pixel values ​​for each pixel between the two images. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] T. Harte, GD Bruce, J. Keelingand D. Cassettari, “Conjugate gradient minimization approach to generating holographic traps for ultracold atoms,” Optics Express, 22(22), pp.26548-26558(2014). Summary of the Invention [Problem to be solved by the invention]

[0006] Both IFTA and the technology described in Non-Patent Document 1 have limitations in generating a high-resolution target intensity image with high accuracy. For example, when the target intensity image has multiple light-focusing regions (light-focusing spots), it is difficult to generate a target intensity image with high accuracy at a resolution close to the diffraction limit of light.

[0007] The present invention has been made to solve the above problems, and has as its object to provide a method and apparatus for generating a hologram that enables generation of a high-resolution target intensity image with high accuracy. Another object of the present invention is to provide a light irradiation device that can generate a high-resolution target intensity image with high accuracy. [Means for solving the problem]

[0008] The hologram generation method of the present invention is a method for generating a hologram to be presented at an input surface in order to optically propagate a complex amplitude distribution of light at the input surface to form a target intensity image at the output surface.

[0009] A first aspect of the hologram generation method of the present invention includes: (1) a pattern setting step of setting a candidate pattern to be a hologram candidate; (2) an intensity image calculation step of zero-filling a complex amplitude distribution obtained when the candidate pattern is presented on an input surface and generating a candidate intensity image based on the results of a propagation calculation of the complex amplitude distribution after the zero-filling; and (3) an evaluation value calculation step of calculating an evaluation value based on the intensity correlation between the candidate intensity image and a target intensity image. Then, the pattern setting step, intensity image calculation step, and evaluation value calculation step are repeated while changing the candidate pattern set in the pattern setting step by an optimization method, and one of the candidate patterns is selected as a hologram to be presented on the input surface based on the evaluation value calculated in the evaluation value calculation step.

[0010] In a second aspect of the hologram generating method of the present invention, in addition to the first aspect, in the pattern setting step, a distortion-added pattern is generated by adding a distortion pattern to a candidate pattern; in the intensity image calculation step, zero-filling is performed on the complex amplitude distribution obtained when the distortion-added pattern is presented on the input surface, and a distortion-added intensity image is generated based on the results of the propagation calculation of the complex amplitude distribution after the zero-filling; and in the evaluation value calculation step, an evaluation value is calculated based on the intensity correlation between the candidate intensity image and the target intensity image and the intensity correlation between the distortion-added intensity image and the target intensity image.

[0011] In a third aspect of the hologram generating method of the present invention, in addition to the first or second aspect, the target intensity image is an image having one or more light-collecting regions at the output plane.

[0012] The program of the present invention is for causing a computer to execute each step of the above-described hologram generating method. Also, the recording medium of the present invention is a computer-readable recording medium having the above-described program recorded thereon.

[0013] The hologram generating device of the present invention is a device that generates a hologram to be presented at an input surface in order to optically propagate the complex amplitude distribution of light at the input surface to form a target intensity image at the output surface.

[0014] A first aspect of the hologram generating device of the present invention includes (1) a pattern setting unit that sets candidate patterns to be hologram candidates, (2) an intensity image calculation unit that performs zero-filling on a complex amplitude distribution obtained when the candidate pattern is presented on an input surface and generates a candidate intensity image based on the results of a propagation calculation of the complex amplitude distribution after the zero-filling, and (3) an evaluation value calculation unit that calculates an evaluation value based on the intensity correlation between the candidate intensity image and a target intensity image.The candidate pattern set by the pattern setting unit is changed using an optimization method, while the processes of the pattern setting unit, intensity image calculation unit, and evaluation value calculation unit are repeatedly performed, and one of the candidate patterns is selected as a hologram to be presented on the input surface based on the evaluation value calculated by the evaluation value calculation unit.

[0015] In a second aspect of the hologram generating device of the present invention, in addition to the first aspect, the pattern setting unit generates a distortion-added pattern by adding a distortion pattern to a candidate pattern, the intensity image calculation unit zero-fills the complex amplitude distribution obtained when the distortion-added pattern is presented on the input surface and generates a distortion-added intensity image based on the result of the propagation calculation of the complex amplitude distribution after the zero-filling, and the evaluation value calculation unit calculates an evaluation value based on the intensity correlation between the candidate intensity image and the target intensity image and the intensity correlation between the distortion-added intensity image and the target intensity image.

[0016] In a third aspect of the hologram generating device of the present invention, in addition to the first or second aspect, the target intensity image is an image having one or more light-collecting regions on the output surface.

[0017] The light irradiation device of the present invention includes: (1) the above-described hologram generating device of the present invention; (2) a laser light source that outputs laser light; (3) a spatial light modulator that spatially modulates the laser light output from the laser light source based on a hologram generated by the hologram generating device and outputs the modulated laser light; and (4) an optical system that propagates the complex amplitude distribution of the laser light output from the spatial light modulator to form an image on an output surface. [Effects of the Invention]

[0018] According to the present invention, it is possible to generate a hologram that enables a high-resolution target intensity image to be generated with high precision. [Brief explanation of the drawings]

[0019] [Figure 1] FIG. 1 is a diagram showing an example of the configuration of a light irradiation device 1. As shown in FIG. [Figure 2] FIG. 2 is a diagram showing the configuration of the hologram generating device 13. As shown in FIG. [Figure 3] FIG. 3 is a flowchart of a hologram generation method. [Figure 4] FIG. 4 is a diagram illustrating the contents of the zero-filling process performed in the intensity image calculation step S2. [Figure 5] FIG. 5 is a diagram illustrating the effect of the zero-filling process performed in the intensity image calculation step S2. [Figure 6] Figure 6 shows holograms generated by simulation. Figure 6(a) shows a hologram generated in Comparative Example 1. Figure 6(b) shows a hologram generated in Comparative Example 2. Figure 6(c) shows a hologram generated in the example. [Figure 7] Figure 7 shows images formed on the output surface in a simulation. Figure 7(a) shows an image formed in Comparative Example 1. Figure 7(b) shows an image formed in Comparative Example 2. Figure 7(c) shows an image formed in an example. [Figure 8] FIG. 8 is a diagram showing the experimental optical system 2. As shown in FIG. [Figure 9] 9A and 9B are diagrams showing images formed on the output surface P2 in an experiment. Fig. 9A is a diagram showing an image formed in Comparative Example 1. Fig. 9B is a diagram showing an image formed in Comparative Example 2. Fig. 9C is a diagram showing an image formed in an example. [Figure 10]Fig. 10(a) is a diagram showing an example of a phase distribution due to defocus aberration of the optical system 12. Fig. 10(b) is a diagram showing an example of an intensity image formed on the output plane P2 when the optical system 12 does not have aberration. [Figure 11] 11(a) to 11(c) are diagrams showing examples of intensity images formed on the output plane P2 when the optical system 12 has aberration. [Figure 12] FIG. 12 is a diagram showing an image formed on the output surface in the simulation. DETAILED DESCRIPTION OF THE INVENTION

[0020] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are designated by the same reference numerals, and duplicate explanations will be omitted. The present invention is not limited to these examples, but is defined by the claims, and is intended to include all modifications within the meaning and scope equivalent to the claims.

[0021] FIG. 1 is a diagram showing an example of the configuration of a light irradiation device 1. The light irradiation device 1 includes a laser light source 10, a spatial light modulator 11, an optical system 12, and a hologram generating device 13. The laser light source 10 outputs laser light that illuminates the spatial light modulator 11. The laser light source 10 preferably includes a beam expander that expands the beam diameter of the light to collimate the light, and also preferably includes an aperture that selectively passes and outputs light in a central beam region of the expanded beam diameter. The laser light source 10 may be, for example, any of a solid-state laser light source, a gas laser light source, a fiber laser light source, a semiconductor laser light source, etc.

[0022] Spatial light modulator 11 presents a hologram generated by hologram generator 13 on modulation plane P1, spatially modulates laser light output from laser light source 10 on modulation plane P1, and outputs the modulated laser light to optical system 12. Optical system 12 optically propagates the complex amplitude distribution of the light modulated on modulation plane (input plane) P1 of spatial light modulator 11, and forms an image on output plane P2. Specifically, optical system 12 optically Fourier-transforms the modulated complex amplitude distribution on input plane P1 using a Fourier optical system, or allows it to propagate freely, thereby forming an image on output plane P2.

[0023] The spatial light modulator 11 may spatially modulate both or either one of the amplitude and phase of light. The spatial light modulator 11 may be a transmissive or reflective type. The spatial light modulator 11 may be any of a liquid crystal light modulator, an electro-optical modulator, an acousto-optical modulator, a digital mirror device, etc. The spatial modulation of laser light on a modulation surface P1 of the spatial light modulator 11 is set by an externally applied electrical signal. A hologram is presented on the modulation surface P1 of the spatial light modulator 11. When laser light is illuminated on the modulation surface P1 on which the hologram is presented, a complex amplitude distribution of the modulated light is obtained on the modulation surface P1. The complex amplitude distribution is optically propagated by the optical system 12, and an image is formed on an output surface P2.

[0024] Hologram generating device 13 generates a hologram to be presented on modulation plane P1 of spatial light modulator 11 to form a target intensity image on output plane P2, and causes spatial light modulator 11 to present the generated hologram. Hologram generating device 13 stores a program for executing each step for generating a hologram. Hologram generating device 13 may be configured as a computer having a processing unit such as a CPU or GPU and a storage unit such as RAM, HDD, or SSD. When hologram generating device 13 is configured as a computer, the program for executing each step is read from the storage unit and executed by the processing unit to generate a hologram.

[0025] The program stored in hologram generating device 13 may be stored in a storage unit of hologram generating device 13 when hologram generating device 13 is manufactured or shipped, or may be acquired via a communication line after shipping and stored in the storage unit of hologram generating device 13, or may be recorded on computer-readable recording medium 14 and stored in the storage unit of hologram generating device 13. Recording medium 14 may be any type of storage medium, such as a flexible disk, CD-ROM, DVD-ROM, BD-ROM, or USB memory.

[0026] The target intensity image may be any image, for example, an image having one or more light-focusing regions (light-focusing spots) on the output surface P2. Alternatively, the target intensity image may be an image in which a plurality of light-focusing regions (light-focusing spots) are regularly arranged in a grid pattern on the output surface P2. The light irradiation device 1 is used, for example, for atom trapping, laser processing, and generating fine light patterns for microscopic observation, and generates a target intensity image according to the application.

[0027] FIG. 2 is a diagram showing the configuration of hologram generating device 13. Hologram generating device 13 includes pattern setting unit 21, intensity image calculation unit 22, evaluation value calculation unit 23, update determination unit 24, pattern storage unit 25, and convergence determination unit 26. FIG. 3 is a flowchart of a hologram generation method. The hologram generation method includes pattern setting step S1, intensity image calculation step S2, evaluation value calculation step S3, update determination step S4, pattern storage step S5, and convergence determination step S6. The hologram generation method generates a hologram to be presented on input plane P1 in order to form a target intensity image on output plane P2 in light irradiation device 1, and is executed by hologram generating device 13. The following description will be given assuming that the hologram presented on input plane P1 is a phase hologram.

[0028] In the pattern setting step S1, the pattern setting unit 21 sets a candidate pattern Φ(x, y) that is a candidate for a hologram to be presented on the input surface P1. The candidate pattern that the pattern setting unit 21 initially sets may be a random pattern.

[0029] In the intensity image calculation step S2, the intensity image calculation unit 22 calculates the complex amplitude distribution g(x, y) obtained by laser light illumination when the candidate pattern Φ(x, y) is presented on the input surface P1 (Equation (1) below), and performs zero padding on this complex amplitude distribution g(x, y). Furthermore, the intensity image calculation unit 22 performs a propagation calculation on the complex amplitude distribution g(x, y) after zero padding to obtain the complex amplitude distribution h(p, q) on the output surface P2 (Equation (2) below), and generates a candidate intensity image I(p, q) on the output surface P2 from this (Equation (3) below). Here, i is the imaginary unit. x and y are variables representing the position on the input surface P1. p and q are variables representing the position on the output surface P2. a represents the amplitude distribution due to the light intensity distribution in the beam cross section of the laser light input to the input surface P1.

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[0033] In the evaluation value calculation step S3, the evaluation value calculation unit 23 calculates an evaluation value f based on the intensity correlation between the candidate intensity image I(p,q) and the target intensity image T(p,q) (Equation (4) below). j is the pixel value of the j-th pixel in the candidate intensity image I. T j is the pixel value of the j-th pixel in the target intensity image T. I is the normalization constant of the candidate intensity image I (Equation (5) below). T is a normalization constant of the target intensity image T (Equation (6) below). The evaluation value f can take a value between −1 and 0.

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[0037] In the update determination step S4, in the first case, the update determination unit 24 sets the evaluation value f to the minimum value f min The process proceeds to pattern saving step S5. In the second and subsequent cases, the update decision unit 24 stores the evaluation value f and the smallest value f up to now. min As a result of the comparison, the evaluation value f is the smallest value f min If it is determined that the evaluation value f is smaller than the minimum value f, the update determination unit 24 sets the evaluation value f to a new minimum value f min On the other hand, as a result of the comparison, the evaluation value f is equal to the smallest value f up to now. min If it is determined that the minimum value f min Without updating, the process proceeds to the convergence determination step S6.

[0038] In pattern saving step S5, pattern saving unit 25 saves candidate pattern Φ(x,y). The candidate pattern Φ saved here is the candidate pattern for which the smallest evaluation value f has been obtained so far. After saving the candidate pattern, the process proceeds to convergence determination step S6.

[0039] In the convergence determination step S6, the convergence determination unit 26 determines whether the evaluation value f has converged. If it is determined that the evaluation value f has not converged, the process returns to the pattern setting step S1. If it is determined that the evaluation value f has converged, the process ends.

[0040] Steps S1 to S6 are repeated while changing the candidate pattern Φ(x, y) set in pattern setting step S1 until it is determined in convergence determination step S6 that the evaluation value f has converged.Then, the candidate pattern that has the smallest evaluation value f by the time the process is completed is selected as the hologram to be presented on input surface P1.

[0041] This iterative process uses an optimization method based on a given algorithm, such as the Nelder-Mead algorithm, simulated annealing, genetic algorithms, Newton's method, quasi-Newton's method, steepest descent method, and conjugate gradient method.

[0042] 4 is a diagram illustrating the contents of the zero padding process performed in the intensity image calculation step S2. Zero padding is a process of adding pixels with a pixel value of 0 around the original complex amplitude distribution (the complex amplitude distribution obtained by laser light illumination when the candidate pattern Φ is presented on the input surface P1) to increase the number of pixels in the complex amplitude distribution. When the number of pixels is increased by K×K times by zero padding, it is expected that the resolution of the image formed on the output surface P2 will be improved by K times. K is preferably 10 or more.

[0043] FIG. 5 illustrates the effect of the zero-filling process performed in the intensity image calculation step S2. Here, the target intensity image to be formed on the output surface P2 is an image in which 5 × 5 light-collecting regions are arranged in a square lattice pattern. As shown in FIG. 5(a), when the resolution of the image formed on the output surface P2 is low, each light-collecting region in the image formed on the output surface P2 simply appears as a dot-shaped bright spot. While the intensity of the bright spot can be evaluated, the shape and intensity distribution of the bright spot cannot be evaluated. In contrast, as shown in FIG. 5(b), when the resolution of the image formed on the output surface P2 is high, the shape and intensity distribution of each light-collecting region in the image formed on the output surface P2 can be evaluated. Therefore, it is expected that a more accurate target intensity image can be formed by performing zero-filling on the complex amplitude distribution before propagation calculation to increase the number of pixels.

[0044] Next, the simulation results will be described using Figures 6 and 7. Here, the target intensity image to be formed on the output plane P2 is an image in which 5 x 5 light-collecting regions, each circular, are arranged in a square lattice pattern. The hologram is a phase hologram. Comparative Example 1 is a case in which a hologram is generated using IFTA, Comparative Example 2 is a case in which a hologram is generated using the technology described in Non-Patent Document 1, and Example is a case in which a hologram is generated using the hologram generation method of this embodiment. In Comparative Example 2 and Example, the conjugate gradient method was used as the optimization method.

[0045] FIG. 6 shows holograms generated by simulation. FIG. 6(a) shows a hologram generated in Comparative Example 1. FIG. 6(b) shows a hologram generated in Comparative Example 2. FIG. 6(c) shows a hologram generated in the Example. In these figures, the phase distribution of the phase hologram is shown by shading. Also, in these figures, areas where pixels have been added by zero padding are not shown. As can be seen by comparing these figures, the hologram generated in the Example (FIG. 6(c)) is significantly different from the holograms generated in Comparative Examples 1 and 2 (FIGS. 6(a) and (b)).

[0046] FIG. 7 shows an image formed on the output surface P2 in a simulation. FIG. 7(a) shows an image formed in Comparative Example 1. FIG. 7(b) shows an image formed in Comparative Example 2. FIG. 7(c) shows an image formed in the Example. In these figures, the intensity distribution in the image formed on the output surface P2 is shown by shading. As can be seen by comparing these figures, in the images formed in Comparative Examples 1 and 2 (FIGS. 7(a) and 7(b)), pixels having a certain light intensity exist between adjacent light-collecting regions, causing the adjacent light-collecting regions to connect, and the shape of each light-collecting region is significantly distorted. In contrast, in the image formed in the Example (FIG. 7(c)), each light-collecting region is formed independently of the other, and the distortion of the shape of each light-collecting region is small.

[0047] Next, the experimental results will be described with reference to Figures 8 and 9. Figure 8 is a diagram showing an experimental optical system 2. In this experimental optical system 2, laser light with a wavelength of 820 nm output from a laser diode 31, which is a semiconductor laser light source, was guided by a single-mode optical fiber (optical fiber) 32 and output as diverging light from the output end face of the single-mode optical fiber 32. The output end face of the single-mode optical fiber 32 can be considered a point light source. The laser light output from the output end face was collimated by a lens 33, its intensity was adjusted by an ND filter 34, and the output was input to an aperture 35. Of the laser light input to the aperture 35, light in the beam center region passed through the aperture 35 and input to a polarizing beam splitter 36.

[0048] Of the laser light input from aperture 35 to polarizing beam splitter 36, the P-polarized light component passes through polarizing beam splitter 36, passes through half-wave plate 37, and is input to spatial light modulator 11. Laser light is incident on spatial light modulator 11, on which a hologram generated by hologram generating device 13 is displayed, and is reflected after being spatially modulated by the hologram. In experimental optical system 2, spatial light modulator 11 was a reflective type that spatially modulated the phase of light.

[0049] The laser light spatially phase-modulated by the spatial light modulator 11 was input to the polarizing beam splitter 36 via the half-wave plate 37. The laser light was converted from P-polarized light to S-polarized light by passing through the half-wave plate 37 twice. The S-polarized laser light input to the polarizing beam splitter 36 from the half-wave plate 37 was reflected by the polarizing beam splitter 36 to the lens 41. The laser light reflected by the polarizing beam splitter 36 was relayed by the lenses 41 and 42, reflected by the mirror 43, and input to the objective lens 44. The modulation plane (input plane) P1 of the spatial light modulator 11 and the pupil plane of the objective lens 44 were optically conjugate to each other.

[0050] The laser light input to the objective lens 44 was intensely focused by the objective lens 44 onto the output surface P2, forming an image on the output surface P2. The optical system from the spatial light modulator 11 to the output surface P2 corresponds to the optical system 12 in the configuration of FIG. 1. The image formed on the output surface P2 reached the imaging surface of the camera 53 via the objective lens 51 and the lens 52. The output surface P2 and the imaging surface of the camera 53 are in an optically conjugate relationship, and the image formed on the output surface P2 was captured by the camera 53. The image formed on the output surface P2 by the objective lens 51 and the lens 52 was magnified 60 times and acquired on the imaging surface of the camera 53.

[0051] FIG. 9 shows an image formed on output surface P2 in an experiment. FIG. 9(a) shows an image formed in Comparative Example 1. FIG. 9(b) shows an image formed in Comparative Example 2. FIG. 9(c) shows an image formed in an Example. In Comparative Example 1 (IFTA), the target intensity image to be formed on output surface P2 was an image in which 5 × 5 light-collecting regions, each having a Gaussian distribution shape, were arranged in a square lattice with a pitch of 1.16 μm. In Comparative Example 2 (technology described in Non-Patent Document 1) and the Example, the target intensity image to be formed on output surface P2 was an image in which 5 × 5 light-collecting regions, each having a circular shape, were arranged in a square lattice with a pitch of 0.952 μm.

[0052] As can be seen from comparing these figures, the experimental results also show that in the images formed in Comparative Examples 1 and 2 (FIGS. 9(a) and (b)), pixels with a certain light intensity exist between adjacent light-collecting regions, causing the adjacent light-collecting regions to be connected, and the shape of each light-collecting region is significantly distorted. In contrast, in the image formed in the Example (FIG. 9(c)), the light-collecting regions are formed independently of each other, and the distortion of the shape of each light-collecting region is small. Compared to Comparative Examples 1 and 2, in the Example, the distortion of the shape of each light-collecting region is kept small, and the lattice spacing can be made narrower while keeping the light-collecting regions separated from each other. Thus, it was confirmed that in the Example, it is possible to generate a high-resolution target intensity image close to the diffraction limit of light with high accuracy.

[0053] Next, when generating a hologram based on evaluation values ​​by the optimization method, a comparison will be made between a case where an intensity correlation type evaluation value is used as in this embodiment, a case where an amplitude correlation type evaluation value is used, and a case where a residual sum of squares type evaluation value is used as in the technology described in Non-Patent Document 1. The intensity correlation type evaluation value f is expressed by the above equations (4) to (6). The amplitude correlation type evaluation value f is expressed by the following equations (7) to (9). The residual sum of squares type evaluation value f is expressed by the following equation (10).

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[0058] Correlation-type evaluation values ​​are sometimes used when performing optimization in the fields of physics or optics. However, amplitude correlation-type evaluation values ​​for the amplitude of light (i.e., the square root of intensity) are usually used. Amplitude correlation-type evaluation values ​​are normalized by the square root of the sum of the intensities of each pixel (Equations (8) and (9) above). This physically corresponds to the law of conservation of energy, so amplitude correlation-type evaluation values ​​can be said to be natural evaluation values. However, when optimization is performed using amplitude correlation-type evaluation values, the results are equivalent to when residual sum-of-squares evaluation values ​​are used.

[0059] Until now, in terms of evaluating errors in optimization methods, it has been common to use residual sum-of-squares evaluation values, and this has been considered sufficient. Furthermore, as described above, amplitude correlation evaluation values ​​can be said to be natural evaluation values, whereas the use of intensity correlation evaluation values, as in this embodiment, means normalization by the sum of the squares of the intensities of each pixel (the above equations (5) and (6)). Intensity correlation evaluation values ​​have been considered unnatural in the fields of natural science, particularly physics, and there has been little motivation for their application. The present inventors have conducted extensive research without being bound by the common technical knowledge of those skilled in the art, and have decided to use intensity correlation evaluation values ​​when generating holograms using optimization methods.

[0060] Furthermore, according to the findings of the present inventors, when generating a hologram by the optimization method, the resolution of the formed image is higher when an intensity correlation-based evaluation value is used than when a residual sum-of-squares evaluation value is used (FIGS. 6 to 9), but the light utilization efficiency is lower. The light utilization efficiency is the ratio of the light intensity used at the output surface to the light intensity incident on the hologram, and is calculated as the light intensity of the region of interest / the incident light intensity. For example, when forming an image in which 5 × 5 light-collecting regions are arranged in a square lattice, the light utilization efficiency when using the residual sum-of-squares evaluation value was 0.928 in the simulation and 0.64 in the experiment, whereas the light utilization efficiency when using the intensity correlation-based evaluation value was 0.120 in the simulation and 0.127 in the experiment. This embodiment, which uses an intensity correlation-based evaluation value when generating a hologram by the optimization method, aims to achieve higher image resolution and accuracy at the expense of light utilization efficiency.

[0061] Next, an improvement in the robustness of a hologram will be described. If the optical system 12 between the input surface P1 and the output surface P2 has aberration, a distorted image will be formed on the output surface P2 due to the influence of the aberration. FIG. 10(a) is a diagram showing an example of a phase distribution due to defocus aberration of the optical system 12. FIG. 10(b) is a diagram showing an example of an intensity image formed on the output surface P2 when the optical system 12 has no aberration. FIGS. 11(a) to 11(c) are diagrams showing examples of intensity images formed on the output surface P2 when the optical system 12 has aberration. As shown in these figures, if the optical system 12 has aberration, the image formed on the output surface P2 will be distorted.

[0062] When the image formed on the output plane P2 is distorted due to aberrations in the optical system 12, the robustness of the hologram can be improved as follows. The following describes the differences from the hologram generation method described using Figures 2 and 3.

[0063] In the pattern setting step S1, the pattern setting unit 21 sets a candidate pattern Φ(x,y) that is a candidate for a hologram to be presented on the input surface P1, and also sets a distortion-added pattern Φ(x,y) by adding a distortion pattern ε(x,y) to the candidate pattern Φ(x,y). ε Generate (x, y) (equation (11) below).

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[0065] In the intensity image calculation step S2, the intensity image calculation unit 22 generates a candidate intensity image I(p,q) on the output plane P2 based on the candidate pattern Φ(x,y) (the above equations (1) to (3)), and also performs the following processing. ε When (x, y) is presented on the input plane P1, the complex amplitude distribution g obtained by laser light illumination is ε (x, y) is calculated (Equation (12) below), and the complex amplitude distribution g ε The intensity image calculation unit 22 performs zero padding on (x, y). Then, the intensity image calculation unit 22 calculates the complex amplitude distribution g after the zero padding. ε (x, y) is propagated and the complex amplitude distribution h at the output plane P2 is obtained. ε (p, q) is calculated (Equation (13) below), and the distortion-added intensity image I ε (p, q) is generated (see equation (14) below).

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[0069] In the evaluation value calculation step S3, the evaluation value calculation unit 23 calculates the intensity correlation between the candidate intensity image I(p,q) and the target intensity image T(p,q) and the distortion-added intensity image I ε The evaluation value is calculated based on the intensity correlation between the candidate intensity image I(p,q) and the target intensity image T(p,q). This evaluation value is calculated by multiplying the evaluation value f (the above formula (4)) based on the intensity correlation between the candidate intensity image I(p,q) and the target intensity image T(p,q) by the evaluation value f (the above formula (4)) based on the intensity correlation between the candidate intensity image I(p,q) and the target intensity image T(p,q). ε The evaluation value f based on the intensity correlation between (p, q) and the target intensity image T(p, q) ε The weights w1 and w2 may be equal to each other (see the following equation (15)).

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[0071] Here, the evaluation value is not limited to the intensity correlation type, but may be an amplitude correlation type evaluation value or a residual sum of squares type evaluation value. Also, the distortion pattern ε(x, y) may be one or more.

[0072] The update determination step S4, the pattern storage step S5, and the convergence determination step S6 are the same processes as those in the hologram generation method described with reference to FIGS.

[0073] FIG. 12 shows an image formed on the output surface P2 in a simulation performed to improve robustness. σ in the figure represents the variation (relative standard deviation) in intensity of the light-condensing region (light-condensing spot) on the output surface P2. When the optical system 12 has distortion, the variation σ in intensity of the light-condensing region was improved from 0.140 to 0.104 by taking the distortion pattern ε(x, y) into consideration as described above. [Explanation of symbols]

[0074] 1...light irradiation device, 2...experimental optical system, 10...laser light source, 11...spatial light modulator, 12...optical system, 13...hologram generation device, 21...pattern setting unit, 22...intensity image calculation unit, 23...evaluation value calculation unit, 24...update determination unit, 25...pattern storage unit, 26...convergence determination unit, 31...laser diode, 32...single-mode optical fiber, 33...lens, 34...ND filter, 35...aperture, 36...polarizing beam splitter, 37...half-wave plate, 41, 42...lens, 43...mirror, 44...objective lens, 51...objective lens, 52...lens, 53...camera.

Claims

1. 1. A method for generating a hologram for presentation at an input surface to form a target intensity image at an output surface by optically propagating a complex amplitude distribution of light at said input surface, comprising: a pattern setting step of setting a candidate pattern to be a candidate for the hologram; an intensity image calculation step of performing zero-filling on a complex amplitude distribution obtained when the candidate pattern is presented on the input surface, and generating a candidate intensity image based on a result of a propagation calculation of the complex amplitude distribution after the zero-filling; an evaluation value calculation step of calculating an evaluation value based on the intensity correlation between the candidate intensity image and the target intensity image; Equipped with repeating the pattern setting step, the intensity image calculation step, and the evaluation value calculation step while changing the candidate pattern set in the pattern setting step by using an optimization method, and selecting one of the candidate patterns as a hologram to be presented on the input surface based on the evaluation value calculated in the evaluation value calculation step. Hologram generation method.

2. In the pattern setting step, a distortion pattern is generated by adding a distortion pattern to the candidate pattern; in the intensity image calculation step, zero-filling is performed on a complex amplitude distribution obtained when the distortion-added pattern is presented on the input surface, and a distortion-added intensity image is generated based on a result of a propagation calculation of the complex amplitude distribution after the zero-filling; In the evaluation value calculation step, an evaluation value is calculated based on an intensity correlation between the candidate intensity image and the target intensity image and an intensity correlation between the distorted intensity image and the target intensity image.

10. The method of claim 1.

3. the target intensity image is an image having one or more light collection regions at the output surface; 10. The method of claim 1.

4. A program for causing a computer to execute each step of the hologram generating method according to any one of claims 1 to 3.

5. A computer-readable recording medium on which the program according to claim 4 is recorded.

6. 1. An apparatus for generating a hologram to be presented at an input surface to optically propagate a complex amplitude distribution of light at said input surface to form a target intensity image at an output surface, comprising: a pattern setting unit that sets candidate patterns to be candidates for the hologram; an intensity image calculation unit that performs zero-filling on a complex amplitude distribution obtained when the candidate pattern is presented on the input surface, and generates a candidate intensity image based on a result of a propagation calculation of the complex amplitude distribution after the zero-filling; an evaluation value calculation unit that calculates an evaluation value based on the intensity correlation between the candidate intensity image and the target intensity image; Equipped with repeating the processes of the pattern setting unit, the intensity image calculation unit, and the evaluation value calculation unit while changing the candidate pattern set by the pattern setting unit using an optimization method, and selecting one of the candidate patterns as a hologram to be presented on the input surface based on the evaluation value calculated by the evaluation value calculation unit. Hologram generator.

7. the pattern setting unit generates a distortion-added pattern by adding a distortion pattern to the candidate pattern; the intensity image calculation unit performs zero-padding on a complex amplitude distribution obtained when the distortion-added pattern is presented on the input surface, and generates a distortion-added intensity image based on a result of a propagation calculation of the complex amplitude distribution after the zero-padding; the evaluation value calculation unit calculates an evaluation value based on an intensity correlation between the candidate intensity image and the target intensity image and an intensity correlation between the distortion-added intensity image and the target intensity image.

7. The hologram generating device according to claim 6.

8. the target intensity image is an image having one or more light collection regions at the output surface; 7. The hologram generating device according to claim 6.

9. A hologram generating device according to any one of claims 6 to 8, a laser light source that outputs laser light; a spatial light modulator that spatially modulates the laser light output from the laser light source based on the hologram generated by the hologram generating device and outputs the modulated laser light; an optical system that propagates the complex amplitude distribution of the laser light output from the spatial light modulator to form an image on an output surface; A light irradiation device comprising:

Images