Optical device and variable optical apparatus

Abstract

To provide an optical device and a variable optical device that have an arrangement distance less restricted and an optical characteristic variable with a high degree of freedom.SOLUTION: An optical device comprises: a first optical element 10; and a second optical element 20 which is arranged in parallel at a distance z from the first optical element with an optical element center aligned with that of the first optical element. The first optical element and the second optical element are configured so that modulation regions thereof subjected to complex amplitude modulation with previously set complex amplitude distribution are arranged at positions opposite to each other, and that a relative angle between the first optical element or second optical element are varied around an optical center of one of the first optical element or the second optical element as a center of an axis of rotation so as to dynamically vary optical characteristics of a phase of a light wave having symmetry of rotation.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to optical elements, particularly optical devices such as computer-generated holograms, metasurfaces, lenses, variable-focus lenses, axicon lenses, helical phase plates, and phase-shift elements, and variable optical apparatuses configured using optical devices. [Background technology]

[0002] Lenses are an essential optical element for controlling light and are found in a wide variety of optical devices, including cameras, microscopes, telescopes, measuring instruments, projectors, and laser processing equipment. Lenses are typically made from glass or polymer materials, and their optical characteristics, i.e., focal length, are fixed. However, if the focal length of a lens could be varied, the functionality of the optical elements or optical devices described above could be expanded in a variety of ways. Therefore, there is a demand for variable-focus lenses, which allow for arbitrary adjustment of focal length. In addition to lenses, optical elements that can generate special beam shapes, such as axicon lenses that impart an axicon phase to light waves and helical phase plates that impart a helical phase to light waves, are finding increasing application value in the fields of microscopes, optical communications, and laser processing, and there is a demand for the optical properties of each to be variable. Furthermore, in the fields of interferometry, digital holography, and incoherent digital holography, accurate measurement of phase information requires a phase-shifting element that uniformly changes the phase distribution of light waves, and a variable optical device that can sequentially impart any phase to light waves is required.

[0003] Liquid crystal devices are an example of optical devices that can change the optical properties of the lenses, axicon lenses, helical phase plates, or phase shift elements mentioned above. For example, a liquid crystal variable-focus lens can be realized by applying an appropriate voltage to liquid crystal molecules using multiple annular electrodes (see Patent Document 1). Based on a similar concept, axicon lenses, helical phase plates, or phase shift elements with variable optical properties can be realized by appropriately designing the electrode pattern and applied voltage. However, in the case of liquid crystal elements, the phase generated by the difference in the inclination of the elliptical, rod-shaped liquid crystal molecules with birefringence is typically imparted to light waves, and the direction of the long axis of the liquid crystal molecules must always match the direction of the incident polarized light.

[0004] In response to this, a moiré lens has been proposed in the past, which uses two diffractive optical elements made of a material with an isotropic refractive index greater than 1 as a pair of optical devices, and changes the optical characteristics by changing the relative angle between these two diffractive optical elements (Patent Document 2, Non-Patent Document 1). In this conventional technology, the material constituting the diffractive optical elements does not have birefringence, so in principle, there are no restrictions on the polarization state of incident light. Furthermore, changing the optical characteristics requires only rotating at least one of the two diffractive optical elements, making the optical system smaller and simpler in configuration than a zoom lens system. Furthermore, unlike a zoom lens system, the principal plane does not change even when the focal length changes. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent No. 5328315 [Patent Document 2] Patent No. 5622571 [Non-patent literature]

[0006] [Non-Patent Document 1] S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive Moire-lenses,” Optics Express Vol. 21, No. 6 6955-6966 (2013). Summary of the Invention [Problem to be solved by the invention]

[0007] However, the principle of the above-mentioned conventional technology requires that the two diffractive optical elements be placed sufficiently close to each other, with a distance of 0 μm or less. Therefore, if the placement distance is too large, the wavefront of the light immediately after exiting the second diffractive optical element becomes significantly distorted, making it impossible to obtain the desired optical characteristics. Furthermore, if the two diffractive optical elements are placed in contact with each other, they may interfere with each other and be damaged when one of the elements is rotated. Therefore, it is extremely difficult to place the two diffractive optical elements in contact with each other in practice. Furthermore, introducing a rotation mechanism while the two elements are placed in close proximity limits the degree of freedom in the mechanical design and makes processing and manufacturing difficult. Furthermore, in this conventional technology, the physical quantity of light modulated by the two diffractive optical elements is limited to the phase, limiting the functionality that can be achieved as an optical device. The present invention has been devised in view of the above-mentioned circumstances, and an object of the present invention is to provide an optical element and a variable optical device that have few restrictions on the placement distance and whose optical characteristics can be varied with a high degree of freedom. [Means for solving the problem]

[0008] In order to solve the above problem, the optical device of the present invention is an optical device comprising a first optical element and a second optical element arranged parallel to the first optical element and spaced a distance z from the first optical element with the optical element center aligned, wherein the first optical element and the second optical element have modulation regions that are complex amplitude modulated with a predetermined complex amplitude distribution at positions facing each other, and the first optical element is configured to apply a diffraction integral calculation to the complex amplitude distribution of the modulation region of the first optical element so as to generate a phase distribution that has the same shape as the modulation region of the second optical element and is the sum of a phase distribution that varies in the radial direction and a phase distribution that varies in the circumferential direction, and to impart the complex amplitude distribution to the modulation region of the first optical element by applying an operation of backpropagating a distance of -z with respect to the distance z, and to change the relative angle between the first optical element and the second optical element with the optical element center of one of the first optical element or the second optical element as the center of a rotation axis.

[0009] In order to solve the above-mentioned problems, an optical device according to the present invention is an optical device including a first optical element and a second optical element arranged parallel to the first optical element at a distance z from the first optical element with the optical element center aligned with the first optical element, wherein the first optical element and the second optical element have modulation regions that are complex amplitude modulated with a preset complex amplitude distribution at positions facing each other, The complex amplitude values ​​of the complex amplitude distribution of the first optical element are complex amplitude modulated using the following formula (1) when the wavelength of incident light is λ, to form a modulation region of the first optical element, and the complex amplitude values ​​of the complex amplitude distribution of the second optical element are complex amplitude modulated using the following formula (2) to form the modulation region, JPEG0007813565000001.jpg20165 Set according to the formula (1) and the formula (2), In the formula (1) and the formula (2), (x, y) and (u, v) are spatial coordinates and corresponding spatial frequency coordinates, respectively. In the formula (1), (r, θ) is the coordinate format of the spatial coordinates, where FT[...] is the Fourier transform operator, FT-1[…] is the inverse Fourier transform operator, The above A 1 (x,y), A 2 (x, y) are aperture functions that determine the light transmission area, α(r) is a phase that varies depending on the radial direction, β(θ) is a phase that changes in accordance with the circumferential direction, The optical element is configured to change the relative angle between the first optical element and the second optical element with the center of one of the first optical element and the second optical element as the center of a rotation axis. [Effects of the Invention]

[0010] The optical device and variable optical apparatus according to the present invention can design and fabricate optical devices with variable optical characteristics with a high degree of freedom, without any restrictions on the distance between two optical elements. Furthermore, even if the distance between the two optical elements is large, it is possible to generate rotationally symmetric light waves, such as lens phase, axicon phase, helical phase, uniform phase, or a phase obtained by adding these, with high precision. In other words, the optical device and variable optical apparatus according to the present invention can dynamically change the optical characteristics of incident light by arbitrarily varying the amplitude and phase of the incident light within a certain range of values, rather than by a single, fixed value. Furthermore, because the present invention modulates the complex amplitude distribution of the light wave, the apodization function can be achieved without introducing additional optical components or relying on special coating processes. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a perspective view schematically illustrating an optical device according to a first embodiment. [Figure 2] 1A, 1B, 1C, and 1D are schematic diagrams showing the complex amplitude modulation patterns of the first and second optical elements of the optical device according to the first embodiment, separated into amplitude patterns and phase patterns. [Figure 3] FIG. 3 is a schematic diagram showing a complex amplitude modulation pattern of a first optical element of the optical device according to the first embodiment. [Figure 4] 1A, 1B, 1C, and 1D are schematic diagrams respectively showing a lens phase, an axicon phase, a helical phase, and a uniform phase that can be dynamically controlled by the optical device according to the first embodiment. [Figure 5]5A and 5B are schematic diagrams showing an example of setting complex amplitude values ​​for each modulation region in the complex amplitude distributions of the first optical element and the second optical element according to the first embodiment. [Figure 6] 1A and 1B are perspective views schematically showing a configuration in which the optical device of the first embodiment is used in a variable optical device as an example. [Figure 7] 1A and 1B are schematic diagrams respectively showing a circular pupil and an apodization mask applied to the first optical element or the second optical element according to the first embodiment. [Figure 8] 10 is a schematic diagram showing an example in which complex amplitude values ​​in the complex amplitude distributions of the first optical element and the second optical element according to the second embodiment are set for each modulation region. FIG. [Figure 9] 10(a), (b), and (c) are schematic diagrams showing the configuration of the optical device according to the third embodiment as a metasurface. [Figure 10] (a) and (b) are schematic diagrams showing the configuration of an optical device when a metasurface is used as an optical element. [Figure 11] FIG. 2 is a perspective view schematically illustrating the configuration of an optical device used in the first example. [Figure 12] FIG. 2 is a schematic diagram showing a complex amplitude modulation pattern of a first optical element used in the first embodiment. [Figure 13] FIG. 10 is a schematic diagram showing a complex amplitude modulation pattern of a second optical element used in the first embodiment. [Figure 14] 10(a) and 10(b) are schematic diagrams showing modulation patterns of the first and second diffractive optical elements in a comparative example used in the first embodiment. [Figure 15] 10 is data showing the results of simulating images of focused spots in the first embodiment and the comparative example. [Figure 16] 10 is data showing the results of simulating images of focused spots in the second embodiment and the comparative example. [Figure 17]10 shows data representing the results of simulating images of focused spots in the present embodiment and the comparative example in the third embodiment. [Figure 18] (a) is a schematic diagram showing the amplitude pattern and phase pattern of a circular pupil realized in the verification shown in the first to third embodiments, (b) is a schematic diagram showing the complex amplitude modulation pattern of (a) and a partially enlarged state, (c) is a schematic diagram showing the amplitude pattern and phase pattern of apodization separately, and (d) is a schematic diagram showing the complex amplitude modulation pattern of apodization of (c) and a partially enlarged state. [Figure 19] (a) is a graph showing the state of apodization, (b) is data showing the results of a simulation of a state without apodization, and (c) is data showing the results of a simulation of a state with apodization. [Figure 20] FIG. 10 is a perspective view schematically illustrating the configuration of an optical device used in a fourth embodiment. [Figure 21] 10A is a schematic diagram showing the complex amplitude modulation pattern of the first optical element of the present embodiment used in the fourth embodiment, FIG. 10B is a schematic diagram showing the complex amplitude modulation pattern of the second optical element of the present embodiment used in the fourth embodiment, FIG. 10C is a schematic diagram showing the modulation pattern forming the first diffractive optical element of the conventional example of the fourth embodiment, and FIG. 10D is a schematic diagram showing the modulation pattern forming the second diffractive optical element of the conventional example of the fourth embodiment. [Figure 22] 10 is data showing the results of a simulation of the fourth embodiment. [Figure 23] 10A is a schematic diagram showing the complex amplitude modulation pattern of the first optical element of the present embodiment used in the fifth embodiment, FIG. 10B is a schematic diagram showing the complex amplitude modulation pattern of the second optical element of the present embodiment used in the fifth embodiment, FIG. 10C is a schematic diagram showing the modulation pattern forming the first diffractive optical element of the conventional example of the fifth embodiment, and FIG. 10D is a schematic diagram showing the modulation pattern forming the second diffractive optical element of the conventional example of the fifth embodiment. [Figure 24] 10 is data showing the results of a simulation of the fifth embodiment. [Figure 25] FIG. 13 is a perspective view schematically illustrating the configuration of an optical device used in a sixth embodiment. [Figure 26] 10(a) and 10(b) are schematic diagrams showing the generation patterns of the first and second optical elements of the sixth embodiment, and 10(c) and 10(d) are schematic diagrams showing the generation patterns of the first and second diffractive optical elements of a comparative example of the sixth embodiment. [Figure 27] 13 is data showing the results of a simulation of the sixth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0012] Embodiments of the present invention will be described below with reference to the drawings. However, each embodiment described below is intended to embody the technical concept of the present invention, and unless otherwise specified, the present invention is not limited to the following. Furthermore, identical means may be designated by the same reference numerals, and their description may be omitted. In each drawing, up, down, left, right, front, and back indicate relative directions, not absolute directions. Furthermore, arrows in FIGS. 1, 10(a), 10(b), 11, 20, and 25 indicate that the optical elements arranged in front and behind can rotate around the center of the element. However, these arrows indicate that either one or both of the two optical elements can rotate relative to each other, as long as the two optical elements form a predetermined angle. Furthermore, the same reference numerals may indicate different configurations, or different reference numerals may indicate the same configuration.

[0013] First Embodiment As shown in FIG. 1 , the optical device 1 includes a first optical element 10 and a second optical element 20 arranged at a distance z from each other. The first optical element 10 and the second optical element 20 are aligned and parallel to each other so that the optical element center of the first optical element 10 coincides with the optical element center of the second optical element 20. The first optical element 10 and the second optical element 20 are each formed by complex amplitude modulation to have a predetermined complex amplitude modulation distribution. The optical device 1 can dynamically change the optical characteristics of the phase of a rotationally symmetric light wave by changing the relative angle of one of the first optical element 10 and the second optical element 20 around the optical element center. Dynamically changing the optical characteristics means arbitrarily changing the amplitude and phase of incident light within a certain range of values, rather than to a fixed single value.

[0014] The distance z between the first optical element 10 and the second optical element 20 can be set, for example, within a range of 0.01 mm to 30 mm. This distance z is set in advance depending on the intended use of the first optical element 10 and the second optical element 20. As shown in FIG. 3, the first optical element 10 has a complex amplitude modulation pattern 10A formed on a translucent member such as glass, which is concentric from the center. This complex amplitude modulation pattern 10A is a combination of the amplitude modulation pattern 10A1 shown in FIG. 2(a) and the phase modulation pattern 10A2 shown in FIG. 2(b). As shown in FIG. 2(a), the amplitude modulation pattern 10A1 is set so that the modulation region of the first optical element 10 has an amplitude ranging from "0" to "1." Similarly, as shown in FIG. 2(b), the phase modulation pattern 10A2 is set so that the modulation region of the first optical element 10 has a phase modulation pattern that varies from "0" to "2π." Here, the amplitude pattern 10A1 and the phase modulation pattern 10A2 each set amplitude or phase values ​​in concentric band-shaped regions from the center to the outer edge, and also set amplitude or phase values ​​in the circumferential direction.

[0015] In Figures 2(a), (b) and 3, the amplitude modulation patterns, phase modulation patterns and complex amplitude modulation patterns are depicted in grayscale and colored for visual clarity, but in reality they are not colored in any particular way. Furthermore, in the first optical element 10, the amplitude modulation pattern 10A1 and the phase modulation pattern 10A2 are displayed separately for ease of understanding, but when forming a pattern on the optical element, the entire pattern is formed as a complex amplitude modulation pattern 10A that combines the amplitude modulation pattern 10A1 and the phase modulation pattern 10A2.

[0016] The first optical element 10 is configured to apply a diffraction integral calculation to the complex amplitude distribution in the modulation region of the first optical element 10 and to apply an operation of backpropagating a distance of -z against a distance z, so that a phase distribution having the same shape as the modulation region of the second optical element 20 and a phase distribution that is the sum of a phase distribution that varies in the radial direction and a phase distribution that varies in the circumferential direction can be generated.The complex amplitude distribution obtained by applying a diffraction integral calculation to the complex amplitude distribution in the modulation region of the first optical element 10 and an operation of backpropagating a distance of -z against a distance z is imparted to the modulation region of the first optical element. Furthermore, in the case of the first optical element 10, when the complex amplitude modulation pattern 10A is formed over the entire optical element, a predetermined complex amplitude distribution may be obtained by setting two-dimensional spatial coordinates over the entire surface of the optical element and setting complex amplitude values ​​for each modulation area partitioned by the spatial coordinates. As a modulation region for performing complex amplitude modulation, for example, a region U1(x, y) is set over the entire area of ​​the optical element, which is the entire two-dimensional spatial coordinate system, as shown in Fig. 5. Then, over all the set modulation regions, a complex amplitude modulation distribution is calculated collectively using the following equation (1), which becomes a complex amplitude modulation pattern 10A as shown in Fig. 3.

[0017]

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[0018] In equation (1), (x, y) and (u, v) are the spatial coordinates and the corresponding spatial frequency coordinates, respectively. Also, in equation (1), (r, θ) is the coordinate format of the spatial coordinates, FT[…] is the Fourier transform operator, and FT -1 [...] is the inverse Fourier transform operator. Also, in equation (1), A1(x, y) is the aperture function that determines the light transmission area and transmission distribution. Furthermore, in equation (1), α(r) is the phase that changes according to the radial direction, and β(θ) is the phase that changes according to the circumferential direction. Also, z is the distance between the first optical element and the second optical element.

[0019] As shown in equation (1), for U1(x, y), complex amplitude values ​​are calculated and set all at once across the entire two-dimensional spatial coordinate system, from U1(0,0), U1(0,1), ..., U1(0,n), U1(1,0), U1(1,1), ..., U1(1,n), ..., U1(n,0), U1(n,1), ..., U1(n,n). Note that in Fig. 3, the modulation area set as a square is schematically shown enlarged in size relative to the complex amplitude modulation pattern 10A so that it can be visually recognized. For example, a light-transmitting member such as a rectangular glass substrate formed in a sheet or plate shape is used as the first optical element 10. By irradiating a laser onto the glass substrate as the optical element, it is possible to form a complex amplitude modulation pattern 10A that has a specific complex amplitude modulation distribution by changing the cutting depth for each modulation region based on the complex amplitude value calculated by equation (1).

[0020] Similarly to the first optical element 10, the second optical element 20 is configured to have, as shown in FIG. 2(c), an amplitude modulation pattern 20A1 in which the amplitude at the center of the modulation region is close to "1" and changes similarly in the radial direction so as to approach "0" toward the periphery. At the same time, the second optical element 20 is configured to have a phase modulation pattern 20A2 in which the phase value of concentric band-shaped regions changes circumferentially from the center to the outer edge in the range of "0" to "2π", as shown in FIG. 2(d). That is, the second optical element 20 is formed to have a complex amplitude modulation pattern 20A that is the amplitude modulation pattern 20A1 and the phase modulation pattern 20A2 shown in FIGS. 2(c) and 2(d). The second optical element 20 is also illustrated with grayscales and colors added to enable visual recognition of the amplitude modulation pattern 20A1 and the phase modulation pattern 20A2.

[0021] As an example, the second optical element 20 can form a complex amplitude modulation pattern 20A by laser processing an optical element that is a translucent glass substrate formed into a rectangular sheet or plate shape for each modulation area so that a predetermined complex amplitude modulation distribution is obtained. As with the first optical element 10, when the complex amplitude modulation pattern 20A is formed over the entire optical element, the second optical element 20 can have a predetermined complex amplitude distribution by setting two-dimensional spatial coordinates over the entire surface of the optical element and setting complex amplitude values ​​for each modulation area defined by the spatial coordinates. As the minimum area of ​​the complex amplitude domain, for example, as shown in Figure 5, X (x, y) is set, and the entire surface of the optical element is set collectively over the entire two-dimensional spatial coordinate system using the following equation (2) to form complex amplitude modulation pattern 20A.

[0022]

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[0023] In equation (2), A2(x, y) is the aperture function that determines the light transmission area and transmission distribution, α(r) is the phase that changes in the radial direction, and β(θ) is the phase that changes in the circumferential direction. As shown in equation (2), for U2(x, y), the complex amplitude values ​​are calculated and set all at once across the entire two-dimensional space coordinate system, from U2(0,0), U2(0,1), ..., U2(0,n), U2(1,0), U2(1,1), ..., U2(1,n), ..., U2(n,0), U2(n,1), ..., U2(n,n).

[0024] For example, a light-transmitting member such as a rectangular glass substrate formed in a sheet or plate shape is used as the second optical element 20. By irradiating a laser onto the glass substrate as the optical element, it is possible to form a complex amplitude modulation pattern 20A that has a specific complex amplitude modulation distribution by changing the cutting depth for each modulation region based on the complex amplitude value calculated by equation (2). The optical device 1 can be formed by setting the complex amplitude values ​​of the first optical element 10 and the second optical element 20 in the complex amplitude region using equations (1) and (2). In the optical device 1, the optical characteristics of the phase of a light wave having rotational symmetry can be dynamically changed by changing the relative angle of at least one of the first optical element 10 and the second optical element 20 with the element center as the center of rotation. For example, as shown in FIGS. 4(a) to (d), it is possible to dynamically control the optical characteristics of a lens phase, an axicon phase, a spiral phase, a uniform phase, or a phase that is a combination of two or more of these.

[0025] Although the first optical element 10 and the second optical element 20 have been described as being glass substrates on which the complex amplitude modulation patterns 10A and 20A are formed, they may be made of, for example, the following materials. The first optical element 10 and the second optical element 20 may be made of silver halide photosensitive material. The resolution of silver halide photosensitive material is 2000 lines / mm or more. The developed material may be used as an amplitude hologram, or it may be bleached and used as a phase hologram.

[0026] Also, a sheet material in which LiNbO3 is attached to quartz glass can be used as an optical element. By using LiNbO3, the refractive index of the irradiated area changes when a strong laser beam is applied, allowing a thick phase hologram to be recorded. However, LiNbO3 as it is has low sensitivity (several hundred J / cm 2 ), but adding impurities such as Fe, Rh, and U increases the sensitivity (1-5 J / cm 2 ) can be made. The lasers used for processing are often Ar lasers of 514.5nm and 488nm, but HeNe lasers (632.8nm) can also be used. The change in refractive index occurs due to the extraordinary ray refractive index. -3 ~10 -4 Although the diffraction efficiency is only about 60%, it reaches a diffraction efficiency of 60% or more. No special development process is required, and after use, the pattern formed can be erased with uniform light from a strong mercury lamp or short-wavelength laser, and it does not deteriorate even with repeated recording and erasure. After recording, it can be stored stably at room temperature for about a year. When LiNbO3 is used, the resolution is 2500 lines / mm or more.

[0027] Thermoplastics can also be used as the optical elements for the first optical element 10 and the second optical element 20. This thermoplastic is a type of electrophotographic recording method, and an optical element can be created by providing a transparent electrode on a glass substrate, coating a photoconductor (PVK) film of about 1 to 3 μm on top of that, and then coating a thermoplastic (Staybelite: product name) of 0.3 to 1 μm on top of that. When an electrode N is placed near the thermoplastic and corona charging is performed at 5 to 10 kV, photosensitivity occurs, and the thermoplastic becomes almost panchromatic (sensitive to almost all visible light from ultraviolet to red) and has a fairly high sensitivity (10 -3 mJ / cm 2 When exposed to light, charges move within the PVK, resulting in variations in the electric field strength inside the thermoplastic. By passing an appropriate current through the transparent electrodes to generate Joule heat and softening the thermoplastic, electrostatic attraction creates irregularities, creating a thin phase hologram.

[0028] This requires additional charging to increase the electrostatic attraction. This can be done sequentially, where recharging is performed after exposure, or simultaneously, where charging continues during exposure. Resolution varies depending on the thickness of the thermoplastic layer. Typical values, where spatial frequency (μ: lines / mm) is plotted on the horizontal axis and diffraction efficiency (η: %) on the vertical axis, are: 4-5% diffraction efficiency at 200 lines / mm, peak at over 20% at approximately 700-800 lines / mm, and resolution is comparable to that of 200 lines / mm at 1400 lines / mm. This thermoplastic can be reused by heating the hologram after use to a temperature slightly higher than that used for development, neutralizing the charge and smoothing out the irregularities, thereby erasing the hologram.

[0029] Furthermore, the first optical element 10 and the second optical element 20 can also be made of dichromated gelatin. Gelatin can be applied to a glass plate and then immersed in an ammonium dichromate solution to create a hologram. As the gelatin hardens when exposed to light, it can be created in two ways: a non-hardening type, in which the remaining parts are dissolved to create a relief hologram, and a hardening type, in which a hardening treatment is applied and then rapid dehydration is performed to record a change in refractive index. Normally, dichromated gelatin is only sensitive to light shorter than green, but its sensitivity is low (5 to 30 mJ / cm). 2 ,488nm). Gelatin has a maximum thickness of about 50μm, has little scattering, and is an excellent material for phase-type Lippmann holograms. Since the recorded hologram disappears when exposed to moisture, it is sandwiched between two glass plates and sealed with resin or the like to eliminate the effects of humidity. Diffraction efficiency has been reported to reach 90%.

[0030] As shown in Figures 6(a) and (b), the optical device 1 is used as a variable optical device 100 in a configuration in which a first optical element 10 and a second optical element 20 are arranged at a distance z in the optical path of an optical system. For example, the first optical element 10 and the second optical element 20 are supported by frames 11 and 21 and are arranged in the optical path with the centers of the optical elements aligned. A transmission drive unit 31 of a rotation drive mechanism 30 is brought into contact with the frame 11 of the first optical element 10. The rotation drive mechanism 30 includes a drive unit 32 such as a servo motor or a stepping motor, and the transmission drive unit 31 installed via a speed reducer that engages with the drive shaft of the drive unit 32. The rotation drive mechanism 30 drives the drive unit 32 using an external electrical signal to rotate the drive shaft, thereby rotating the transmission drive unit 31 by a predetermined angle or a predetermined number of times via the speed reducer, thereby changing the relative angle between the first optical element 10 and the second optical element 20 and dynamically changing the optical characteristics of the phase of light waves having rotational symmetry.

[0031] Here, the variable optical device 100 is shown as an example in which the first optical element 10 is rotated 45 degrees in the direction indicated by the arrow from the state shown in FIG. 6(a) to the state shown in FIG. 6(b). In the variable optical device 100, a rectangular plate is placed in front and a star-shaped plate is placed behind it as an image subject, and the image is captured on the image sensor 40 or the like via the first optical element 10 and the second optical element 20. Note that the variable optical device 100 shown here does not include other optical and mechanical components, such as lenses, that are required for capturing images. As shown in FIG. 6(a), before the angle of the first optical element 10 is changed, the star-shaped plate, which is the subject of the captured image, is in focus, while the rectangular plate is captured out of focus. 6(b), in the variable optical device 100, when the first optical element 10 is rotated 45 degrees relative to the second optical element 20 via the rotation drive mechanism 30, the rectangular plate is brought into focus and the star-shaped plate is made out of focus. In other words, the variable optical device 100 can achieve a focus position shift (focal length shift) without changing the distance z between the first optical element 10 and the second optical element 20. Therefore, the variable optical device 100 is effective for use in cameras, telescopes, microscopes, video cameras, etc.

[0032] Note that a circular pupil function or apodization may be applied to one of the first optical element 10 and the second optical element 20. For example, as shown in FIG. 7(a), applying a simple circular pupil to the second optical element 20 can adjust the depth of field of the lens and block unwanted light waves. Also, as shown in FIG. 7(b), apodization can be applied to the second optical element 20 by using a complex amplitude modulation pattern 20A that indicates a function whose amplitude decreases from the center to the periphery. Apodization can produce smooth blurring during imaging. Note that while FIG. 7(b) shows an example of apodization, any distribution may be applied and may be designed arbitrarily as long as apodization can be achieved.

[0033] Apodization can be achieved by adjusting the value of α(r), which is the phase that changes depending on the radial direction in equations (1) and (2). For example, if you want to generate a light wave with a lens phase, axicon phase, helical phase, or uniform phase distribution, you can use α(r) as 2 ), α(cr), α(c), α(c) can be set according to the type of phase. Note that c in α(c) is a constant that determines the optical characteristics of each phase. In the formula, c is positioned as a constant function of α(r). In other words, α(r)=c+d×r+e×r 2 +f×r 3 +…m×r n In this case, the coefficient of r is 0.

[0034] Furthermore, by adjusting α(r), it corresponds to the focal length in the case of the lens phase, the apex angle in the case of the axicon phase, the topological charge (or orbital angular momentum) in the case of the helical phase, and the initial phase in the case of the uniform phase. Furthermore, in equations (1) and (2), the phase can be adjusted by adjusting β(θ), which is the phase that changes depending on the circumferential direction. For example, in the case of lens phase, axicon phase, and uniform phase, it is θ^n (|n|>0, arbitrary constant), and a high-quality phase can be generated when n = 1. In the case of helical phase, it is θ^2, and a high-quality phase can be generated at this time.

[0035] <Variation 1> Furthermore, when generating a lens phase, an axicon phase, or a uniform phase, if you want to reduce unnecessary scattered wave components, it is preferable to use the following equations (3) and (4) instead of equations (1) and (2).

[0036]

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[0037]

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[0038] In formulas (3) and (4), round[...] is an operation that rounds off the decimal point to an integer.

[0039] <Variation 2> Furthermore, when a helical phase is included in the generated symmetric light wave and it is desired to reduce unnecessary scattered wave components, it is preferable to use the following equations (5) and (6) instead of equations (1) and (2).

[0040]

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[0041]

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[0042] Second Embodiment In addition, when the complex amplitude modulation type optical element shown in the above-described formulas (1) to (6) is realized as a double-phase hologram according to the reference literature (Reference literature V. Arrizon, “Improved double-phase computer-generated holograms implemented with phase-modulation devices,” Optics Letters Vol. 27, Issue 8, pp. 595-597

[2002] ), as shown in Figure 8, X The complex amplitude values ​​of (x, y): (X=1, 2) are converted into two types of phase values ​​φ based on the following equations (7) and (8). A , φ B Alternatively, the signal may be encoded as a 2×2 sub-modulation area.

[0043]

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[0044]

number

[0045] In equations (7) and (8), angle[...] is a calculation to extract the argument of the complex amplitude value. As shown in Figure 8, the upper left and lower right of the 2x2 sub-area surrounded by the thick line are denoted by φ A The bottom left and top right are φ B Here, one diagonally opposing region is set as the sum of the phase value to be generated and the value of the inverse cosine function of the amplitude value to be generated, and the other diagonally opposing region is set as the difference between the phase value to be generated and the value of the inverse cosine function of the amplitude value to be generated, thereby setting the complex amplitude value to be generated. Note that these values ​​are expressed as φ A and φ B It is also possible to reverse the above, for example, by placing the sub-regions at the top left and bottom right. A complex amplitude modulation distribution can be formed by setting such sub-regions over the entire two-dimensional spatial coordinate system that is the entire surface of the optical element. The size of the sub-regions may be any size, n×n, as shown in FIG. 5, and in this case, the size of the sub-regions may be set to a checkerboard pattern with φA and φ B Just assign the value of

[0046] <Third embodiment> Instead of using a dual-phase hologram to realize the optical device 1 including the first optical element 10 and the second optical element 20, a complex amplitude modulation type optical element may be realized by a metasurface. As shown in Figures 9(a), (b), and (c), a metasurface is an array of elements M1 to M3 in which meta-atoms, which are protrusion structures smaller than the product of the real part n of the refractive index of the material and λ, are formed on an optically transparent substrate material such as SiO2 in an in-plane area smaller than the wavelength λ of light, with multiple such elements arranged at intervals comparable to or smaller than the wavelength λ.

[0047] These minute elements M1 to M3 enable complex amplitude modulation by utilizing the resonance phenomenon or waveguide effect caused by the minute protrusion structure. Figures 9(a) to 9(c) show examples in which multiple square-shaped in-plane regions are defined on the entire surface of each of the optical elements 10M1 to 10M3. However, honeycomb-shaped in-plane regions may also be defined instead of squares. Materials for the protrusion structures include plasmonic metals such as Au, Ag, and Al, and dielectrics such as SiO2, Si, SiN, GaN, and TiO2. For example, Figure 9(a) shows an example of element M1 using a rectangular meta-atom. The amplitude can be controlled by changing the aspect ratio within the plane of the rectangular parallelepiped, and the phase can be controlled by changing the rotation angle of the rectangular parallelepiped. Figure 9(b) shows an example of element M2 using a cross-shaped meta-atom. The amplitude and phase can be controlled by changing the rotation angle of the meta-atom and the angle between the vertical and horizontal lines of the cross. Figure 9(c) shows an example of element M3, which uses two meta-atoms as a pair. By changing the aspect ratio and rotation angle of each element, the amplitude and phase can be controlled. The shape of the meta-atom is not limited to the rectangular parallelepiped protrusion structure shown in Figure 9(a). The planar shape of the special structure can be circular, elliptical, hexagonal, octagonal, or annular. These shapes can also be combined.

[0048] Unlike dual-phase holograms, deterministic design based on analytical theory is currently impossible for metasurfaces. Instead, a shape that achieves the desired complex amplitude modulation function must be identified and designed by numerically solving Maxwell's equations or wave equations using the finite element method or the finite-difference time-domain method. Therefore, to achieve the desired amplitude and phase modulation function, the dimensions and shape of the protrusion structure vary depending on the material, and there are countless options. The key point is that the concepts of meta-atoms and metasurfaces generate the complex amplitude distributions shown in Equations (1) to (6).

[0049] Depending on the design of the metasurface and meta-atoms, the polarization state of the incident light that can be modulated may be limited. For example, the metasurface shown in Figure 9(a) requires that the polarization state of the incident light be circularly polarized. Therefore, as shown in Figure 10(a), when using a metasurface as the first optical element for complex amplitude modulation, a polarizer 5 and a quarter-wave plate 6 must be placed in front of the optical device to circularly polarize the incident light. Furthermore, the metasurface shown in Figure 9(a) may contain unwanted polarization components in the output light. In such cases, the unwanted polarization components can be removed by combining wave plates 7a and 8a and polarizers 7b and 8b before and after the optical device 1, as shown in Figure 10(b). Alternatively, although not shown, a single polarizer may be simply placed before and after the optical device 1 to reduce the unwanted polarization components.

[0050] Furthermore, if the metasurface only works for linearly polarized incident light and the polarization state of the incident light is not linearly polarized, a polarizer must be placed in front of the first optical element. Rotating the first optical element in this state will change the relative angle of linear polarization of the incident light, making it impossible to obtain the desired modulation function. In this case, a half-wave plate is placed between the polarizer and the first optical element, and the half-wave plate is rotated according to the rotation angle of the first optical element. Note that when rotating the second optical element, it is not necessary to rotate the polarizer or wave plate placed in front of the first optical element.

[0051] <Fourth embodiment> The first optical element 10 and the second optical element 20 used in the optical device 1 may be realized as complex amplitude modulation optical elements using holographic optical elements. The holographic optical element can be fabricated by interfering light U1(x, y) or U2(x, y), which forms the complex amplitude distribution to be generated, with a plane wave reference light in a photosensitive material such as a photopolymer or photorefractive crystal to create optical elements corresponding to the first optical element 10 and the second optical element 20. In this case, the thicker the photosensitive material, the more selectivity of the incident angle or wavelength is exhibited, thereby enabling the addition of a light filtering function. Furthermore, by converting the reference light into a spherical wave and causing it to interfere, depth selectivity can be added according to the curvature of the incident light or the depth position of the light emission point and reflection point.

[0052] [Example] Next, the verification results obtained by actually simulating the optical device 1 in Examples 1 to 6 are shown below. Note that in Figures 11, 20, and 25, which show the configurations of the optical devices in Examples 1 to 6, the configuration of this Example, which is the proposed method, and the configuration of the Comparative Example, which is the conventional method, have the same arrangement conditions for the first and second optical elements, and therefore the configurations are shown on the same drawing. The simulation conditions are described below. Any software capable of performing calculations such as Fourier transforms and arithmetic operations can be used. Examples include "Python" (registered trademark) and "Matlab." Here, "Matlab" was used. The calculations used were based on the angular spectrum method, a typical method for calculating light propagation. The angular spectrum method is a common method in the field of light and is known to be able to accurately handle actual physical phenomena.

[0053] Software: Matlab Sampling interval: 2.5 μm Number of pixels: 1024 x 1024 pixels Light source wavelength (λ): 633 nm α=11·r2 β=θ z=0, 5, 10, 15, 20, 25, 30mm

[0054] <First Example> As shown in FIG. 11, two optical elements for complex amplitude modulation were designated as a first optical element 10 and a second optical element 20, and were arranged at a distance z between them as a setting condition for the simulation, to form an optical device 1A that generates light with a variable lens phase. In the first example, the wavelength λ of the light source was set to 633 nm, and the dual-phase hologram shown in FIG. 8 and equations (7) and (8) already described as a method for modulating the complex amplitude distribution was used, with the first optical element 10 being the first optical element A10 and the second optical element 20 being the second optical element A20. Furthermore, the amplitude distribution of the second optical element 20 was set to a circular pupil with a diameter of 2 mm. In the first example, the complex amplitude modulation patterns 10A and 20A of the first optical element A10 and the second optical element A20 in this example are shown in FIGS. 12 and 13.

[0055] 14(a) and 14(b) show the modulation patterns of optical elements B10 and B20, which are two diffractive optical elements in a comparative example that is a conventional method for comparison. The first optical element B10 in the comparative example is set to perform only phase modulation based on the formula round[α(r)θ]θ. The second optical element B20 in the comparative example is set to perform only phase modulation based on the formula -round[α(r)θ]θ. In the above formula in the comparative example, α is 11·r 2 It is set as.

[0056] In Example 1, taking into consideration that the present example and the comparative example can theoretically obtain a focused spot on a surface 431 mm away from the second optical elements A20 and B20, the state of the image at the focused spot position SC 431 mm from the second optical element was evaluated. Note that both the first optical element B10 and the second optical element B20 of the comparative example have amplitude distribution regions of circular pupils with a diameter of 2 mm. In addition, in the first embodiment, when the second optical element of the two optical elements arranged in parallel is rotated relative to the first optical element so that it is shifted by 60 degrees around the center of the element as the center of rotation, the distance z is changed from 0 to 30 mm in 5 mm intervals to simulate the image of the focused spot emitted from the second optical element at the focused spot position SC. The results are shown in Figure 15.

[0057] As shown in Figure 15, in the comparative example using the conventional method, as the distance z increases, the image deviates from the theory of the moiré lens, and the quality of the focused spot shown in white in the center deteriorates. This is because, in the conventional method, after light passes through the first optical element B10, the light propagates over the distance z, causing the light wave to be diffracted, and by the time it enters the second optical element B20, its amplitude and phase are disturbed. Due to this disturbance, in the conventional method, it was necessary to position the second optical element B20 at a distance of 10 μm or less from the first optical element B10. On the other hand, in the present embodiment, which is the proposed method, the effect of diffraction is calculated in advance by the first optical element A10 and the complex amplitude modulation distribution is modulated. Therefore, it can be seen that no disturbances in amplitude or phase due to diffraction occur, and a high-quality focused spot can be obtained regardless of the size of the distance z.

[0058] <Second Example> Next, as a second example, we simulated and compared the focused spots of the proposed method and the conventional method when the diameters of the second optical elements A20 and B20 were each 5 mm. Other conditions were the same as those in the first example. The simulated evaluation results for the second example are shown in Figure 16. In the comparative example using the conventional method, as with the 2 mm diameter, the focused spot deforms significantly as the distance z increases. Furthermore, as the diameter of the region forming the complex amplitude modulation distribution increases, i.e., the NA of the lens phase increases, the effect of diffraction becomes more pronounced, resulting in a greater distortion of the focused spot compared to the 2 mm diameter case. On the other hand, in this example of the proposed method, even when the diameter of the region forming the complex amplitude modulation distribution increases, the focused spot remains clearly visible as a white spot in the center, demonstrating that a high-quality focused spot is consistently obtained regardless of the change in distance z.

[0059] <Third Example> Next, a third example was constructed using the optical system shown in Figure 11. The diameter of the second optical element A20 in this example and the diameter of the second optical element B20 in the comparative example were both set to 2 mm, and the distance z between the two optical elements was fixed at 20 mm. The relative rotation angle between the two optical elements was then increased from 60 degrees to 70 degrees in 2-degree increments, and the results of simulating the state of the focused spot when the focal length of the lens phase was changed are shown in Figure 17. In the comparative example, which is a conventional method, there is a gap of distance z between the two optical elements, so when the focal length is changed, the focused spot displayed in white appears uneven, indicating low quality of the focused spot. On the other hand, in the present embodiment, which is the proposed method, in addition to having the function of varying the focal length of the lens phase, it is clear that even if the two optical elements are separated, the state of the focused spot is such that the white color in the center is clearly displayed, and a high-quality focused spot can be obtained without any problems.

[0060] In the above verification of the first to third examples, as shown in Figures 18(a) and 18(b), the second optical element A20 of the proposed method achieved a simple circular pupil amplitude distribution. In the first to third examples of the proposed method, the complex amplitude, including amplitude and phase, can be freely controlled. This demonstrates that apodization can be applied, as shown in Figure 18(c), to generate light with a non-uniform amplitude distribution. Figure 18(d) also shows the complex amplitude modulation pattern of a dual-phase hologram used to generate light with the complex amplitude distribution shown in Figure 18(c). Figure 19(a) shows the results of verifying the effect of applying apodization in an example of the proposed method. It can be seen that applying apodization increases the width of the main lobe, but suppresses the occurrence of side lobes. Figure 19(b) shows the state of the focused spot without apodization, and Figure 19(c) shows the state of the focused spot with apodization. In the comparative example, which is a conventional method, the amplitude and phase of light cannot be modulated because a diffractive optical element is used, and apodization cannot be applied. As shown in Figures 18(b) and 18(d), in the partially enlarged schematic diagrams, a small checkered square corresponds to one of the modulation regions shown in Figure 8.

[0061] <Fourth Example> Next, as a fourth example, axicon phase light was generated using the optical system shown in Figure 20. To evaluate the function of the axicon phase in the optical system of the fourth example, the output light was Fourier transformed using a lens LN with a focal length of 200 mm to obtain the light intensity distribution at the Fourier plane. The first optical elements A110 and B110 and the second optical elements A120 and B120 were fixed at a distance z = 20 mm. Figures 21(a) and 21(b) show complex amplitude patterns representing the complex amplitude distributions of the optical elements A110 and A120 of this example, which represent the proposed method, and Figures 21(c) and 21(d) show patterns for a diffractive optical element of a comparative example, which represents a conventional method. Figure 22 shows the results of a simulation performed on the optical system of the fourth example, in which the first optical element A110 was rotated relative to the second optical elements A120 and B120 in 10-degree increments from 0 to 50 degrees.

[0062] In each of the optical systems of this example and the comparative example, ideally, a ring-shaped light pattern is obtained as the focused light pattern by Fourier transforming the axicon phase light. Here, the Fourier transform is performed using lens LN. Furthermore, in the optical system of this example, a focused light spot is obtained when the relative angle between the first optical element A110 and the second optical element A120 is 0 degrees. As shown in Figure 22, in the comparative example of the conventional method, the ring-shaped light pattern is discontinuous in the circumferential direction. On the other hand, in this example of the proposed method, a high-quality ring-shaped light pattern is obtained when the relative angle is changed. Using the configuration of this example, a ring-shaped light pattern can be generated with high precision and its diameter can be changed. Therefore, the technology of this example is useful, for example, when laser processing a ring shape.

[0063] <Fifth Example> Next, as a fifth example, a simulation was performed to generate helical phase light using the optical system shown in FIG. 20 . In this optical system, the distance z between the first optical elements A210 and B210 and the second optical elements A220 and B220 was fixed at 10 mm, and the simulation was performed while varying the relative angle between the first optical elements A210 and B210 and the second optical elements A220 and B220 to 0 degrees, 1.1 degrees, 2.2 degrees, and 3.3 degrees. The first optical element A210 and the second optical element A220 of this example, which represents the proposed method, are shown in FIGS. 23( a) and (b), while the first diffractive optical element B210 and the second diffractive optical element B220 of the comparative example, which represents the conventional method, are shown in FIGS. 23( c) and (d). The results of the generated simulation are also shown in FIG. 24. As shown in FIG. 24, in the case of helical phase, ideally, a donut-shaped light pattern with a singular point with zero intensity at the center should be formed. In the comparative example using the conventional method, the light pattern is completely deformed.

[0064] On the other hand, in this example, the proposed method successfully generated a doughnut-shaped optical pattern, demonstrating high-quality helical phase generation. Furthermore, increasing the relative rotation angle increased the diameter of the doughnut-shaped optical pattern. This indicates that the number of turns in the helical phase, i.e., the topological charge, increased, demonstrating that the parameters of the helical phase could be varied. Relative angles of 1.1, 2.2, and 3.3 degrees correspond to topological charges of 1, 2, and 3, respectively. This method can generate helical phases with high precision and change the topological charge, enabling it to be used as a topological charge conversion technology in the field of optical communications, where topological charge is used as a signal carrier. Furthermore, in the field of imaging, it can be applied to stimulated emission depletion microscopy and incoherent digital holography.

[0065] <Sixth Example> Finally, as a sixth example, as shown in FIG. 25, we present the results of a simulation in which uniform-phase light was generated using an optical system consisting of first optical elements A310 and B310 and second optical elements A320 and B320. A uniform phase can be used when applying a phase-shifting method in interferometry or digital holography. Therefore, in the optical system of the sixth example, the phase distribution of light immediately after passing through the second optical element was evaluated. In the sixth example, the first optical elements A310 and B310 and the second optical elements A320 and B320 were rotated relative to each other by angles of 0, 90, 180, and 270 degrees, and the phase distribution of light immediately after passing through the second optical elements A320 and B320 was evaluated by simulation. Figures 26(a) and (b) show the generation patterns for the first optical element A310 and the second optical element A320 of this example, which is the proposed method.

[0066] 26(c) and 26(d) show the generation patterns for the first diffractive optical element B310 and the two-plane diffractive optical element B320 of the comparative example, which is a conventional method. FIG. 27 shows the results of a phase evaluation simulation for the sixth embodiment, which is a proposed method, and the comparative example, which is a conventional method. Both the proposed method and the conventional method achieved the desired phase shifts of 0, π / 2, π, and 3π / 2 by rotating the element by 90 degrees. However, as shown in FIG. 27, the comparative example, which is a conventional method, exhibited unwanted phase shifts in the central region. Even in this embodiment, which is a proposed method, slight phase shifts occurred near the center. However, it can be seen that the proposed method produced a more uniform phase than the comparative example, which is a conventional method. The sixth embodiment demonstrates that a phase shifting method can be achieved simply by rotating optical elements. In conventional interferometry technology and phase shifting methods, the phase of light is mainly shifted using piezoelectric elements or liquid crystal elements, but piezoelectric elements have the issue of hysteresis, and liquid crystal elements have the issue of phase shift due to fluctuations in liquid crystal molecules. Therefore, the technology shown in the sixth embodiment is not affected by hysteresis, and does not use organic molecules, so it is possible to achieve highly accurate and stable phase shifting.

[0067] As described above, as shown in the examples of the proposed method, by using an optical device including a first optical element and a second optical element that is positioned parallel to the first optical element at a distance z from the first optical element and with its center aligned with that of the first optical element, it is possible to remove the constraint between the two optical elements that was a problem with conventional methods, and it is possible to generate desired light even at any separation distance, making it possible to use the proposed method in a variety of optical systems. In the present invention, complex amplitude modulation refers to modulating amplitude and phase. A complex amplitude modulation pattern refers to a pattern formed on an optical element for modulating amplitude and phase. A complex amplitude distribution refers to a distribution formed by combined values ​​of amplitude and phase. A modulation region refers to a region of an optical element that modulates one or both of the amplitude and phase. A complex amplitude value refers to the combined value of the amplitude and phase values ​​in the modulation region. An amplitude hologram refers to a hologram in which diffraction during reconstruction occurs due to changes in the amplitude of light. A phase hologram refers to a hologram in which interference fringes are recorded as changes in thickness or refractive index, and diffraction occurs due to changes in the phase of light. [Explanation of symbols]

[0068] 1 Optical Devices 10 First optical element 10A Complex Amplitude Modulation Pattern 10A1 Amplitude Modulation Pattern 10A2 Phase modulation pattern 20 Second optical element 20A Complex Amplitude Modulation Pattern 20A1 Amplitude Modulation Pattern 20A2 phase modulation pattern 30 Rotation drive mechanism 31 Transmission drive unit 32 Drive unit A10, A110, A210, A310 First optical element (first optical element) A20, A120, A220, A320 Second optical element (second optical element) B10, B110, B210, B310 First optical element (diffractive optical element) B20, B120, B220, B320 Second optical element (diffractive optical element)

Claims

1. An optical device comprising: a first optical element; and a second optical element disposed parallel to the first optical element with a distance z away from the first optical element and with the optical element center aligned with the first optical element, the first optical element and the second optical element have modulation regions that are complex amplitude modulated with a preset complex amplitude distribution, at positions facing each other; When the wavelength of incident light is λ, the complex amplitude values ​​of the complex amplitude distribution of the first optical element are complex amplitude modulated using the following formula (1) to form a modulation region of the first optical element, and the complex amplitude values ​​of the complex amplitude distribution of the second optical element are complex amplitude modulated using the following formula (2) to form the modulation region, Set according to the formula (1) and the formula (2), In the formula (1) and the formula (2), The (x, y) and (u, v) are spatial coordinates and corresponding spatial frequency coordinates, respectively. In the formula (1), (r, θ) is the coordinate format of the spatial coordinate system, where FT[...] is the Fourier transform operator, FT-1[...] is the inverse Fourier transform operator, The above A １ (x, y), A ２ (x, y) are aperture functions that determine the light transmission area, α(r) is a phase that varies depending on the radial direction, β(θ) is a phase that changes in accordance with the circumferential direction, An optical device that changes the relative angle between the first optical element and the second optical element around a center of one of the first optical element and the second optical element as a rotation axis center.

2. Instead of the formula (1), the following formula (3) is used, and further, instead of the formula (2), the following formula (4) is used: setting complex amplitude values ​​of the complex amplitude distributions of the first optical element and the second optical element according to the formulas (3) and (4); 2. The optical device according to claim 1, wherein roundud[...] is a function that rounds off a value after the decimal point to an integer.

3. The following formula (5) is used instead of the formula (1), and the following formula (6) is used instead of the formula (2): The optical device according to claim 1 , wherein complex amplitude values ​​of the complex amplitude distributions of the first optical element and the second optical element are set.

4. The regions of the first optical element and the second optical element are calculated by calculating the complex amplitude values ​​of U1(x, y) and U2(x, y) based on the following equations: Two types of phase values ​​φ Ａ , φ Ｂ and encoding the signal as a 2×2 sub-modulation region consisting of:

4. The optical device according to claim 1, wherein one diagonally opposing sub-modulation region of the 2×2 sub-modulation regions is set to the sum of a phase value to be generated and the value of the inverse cosine function of the amplitude value to be generated, and the other diagonally opposing sub-modulation region is set to the difference between the phase value to be generated and the value of the inverse cosine function of the amplitude value to be generated, thereby setting a complex amplitude value to be generated, wherein in the formula, angle [...] is a calculation for extracting the argument of the complex amplitude value.

5. 5. The optical device of claim 1, wherein one of the first optical element and the second optical element has an apodized amplitude distribution for amplitude modulation in the complex amplitude modulation, in which the transmittance is continuously changed from the periphery to the center of the modulation region.

6. 6. The optical device according to claim 5, wherein one complex amplitude value of the modulation region is encoded as at least 2 × 2 sub-modulation regions, and one diagonally opposing region of the 2 × 2 sub-modulation regions is set to the sum of the phase value to be generated and the value of the inverse cosine function of the amplitude value to be generated, and the other diagonally opposing region is set to the difference between the phase value to be generated and the value of the inverse cosine function of the amplitude value to be generated, thereby setting the complex amplitude value to be generated.

7. 7. The optical device according to claim 1, wherein the first optical element and the second optical element are holographic optical elements that record interference fringes between the light wave of the complex amplitude distribution and a reference light in a photosensitive material.

8. The optical device described in any one of claims 1 to 6, wherein the first optical element and the second optical element are metasurfaces that modulate the complex amplitude distribution by resonance caused by meta-atoms with protrusion structures finer than the wavelength, or by a waveguide effect.

9. The optical device described in claim 8, wherein a polarizer or a wave plate, or a polarizing element and a wave plate, are arranged in front of the first optical element or behind the second optical element when the meta-atom has a dependency on the incident polarization or when the output polarization contains unnecessary polarization components.

10. A variable optical apparatus using an optical device according to any one of claims 1 to 9, a frame body that supports each of the first optical element and the second optical element; and a rotation drive mechanism that is disposed in contact with at least one of the frame bodies, A variable optical device that changes the relative angle of at least one of the first optical element and the second optical element, with the optical element center of the first optical element and the second optical element as the rotation axis center, via a transmission drive unit of the rotation drive mechanism that abuts against the frame body.

Images