Patent Publication Number: US-2022229213-A1

Title: Diffraction element and imaging device

Description:
FIELD 
     The present disclosure relates to a diffraction element and an imaging device. 
     BACKGROUND 
     In the related art, a spectroscopic measurement method is known as a method for analyzing a composition of an object. The spectroscopic measurement method is a method for analyzing a composition (element, a molecular structure, and the like) of an object by analyzing radiation light, reflection light, or transmission light from the object. 
     A light wavelength component of the radiation light, the reflection light, or the transmission light from the object varies depending on the composition of the object. Accordingly, the composition of the object can be analyzed by analyzing the wavelength component. In general, data indicating an amount of each wavelength is referred to as a wavelength spectrum, and processing of measuring the wavelength spectrum is referred to as spectroscopic measurement processing. 
     In order to analyze the composition of each point on a surface of the object, it is necessary to acquire correspondence data between spatial information and wavelength information of the object. A snapshot method is known as a method for acquiring the correspondence data between the spatial information and the wavelength information of the object by only one processing of the correspondence data between the spatial information and the wavelength information of the object, that is, only one time of imaging processing of the spectroscopic measurement device. The spectroscopic measurement device to which the snapshot method is applied includes a combination of an optical system including a plurality of lenses, a slit (visual field stop), a spectroscopic element, and the like, and a sensor. Spatial resolution and wavelength resolution of the spectroscopic measurement device are determined by the configurations of the optical system and sensor. 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: JP 2016-90576 A 
     Non Patent Literature 
     Non Patent Literature 1: Habel, R., Kudenov, M., Wimmer, M.: Practical spectral photography. Computer Graphics Forum (Proceedings EUROGRAPHICS 2012) 31 (2), 449-458 (2012) 
     Non Patent Literature 2: Tebow, Christopher P.; Dereniak, Eustace L.; Garrood, Dennis; Dorschner, Terry A.; Volin, Curtis E.: Tunable snapshot imaging spectrometer. Proceedings of the SPIE, Volume 5159, p. 64-72 (2004) 
     Non Patent Literature 3: Dwight JG, Tkaczyk TS.: Lenslet array tunable snapshot imaging spectrometer (LATIS) for hyperspectral fluorescence microscopy. Biomed Opt Express. 2017;8: 1950-64 
     SUMMARY 
     Technical Problem 
     Here, a spectroscopic element such as a prism or a diffraction grating generally used in a spectroscopic measurement device disperses incident light in one axis direction or two axis directions according to a wavelength thereof. On the other hand, an imaging region of an image sensor for capturing the spectroscopic image is usually a rectangular region. This means that the image sensor has many imaging regions in which a spectroscopic image is not incident. 
     As described above, in a general spectroscopic element of the related art, it is difficult to efficiently use the imaging region of the image sensor used in the spectroscopic measurement device or the like. 
     According to this, the present disclosure provides a diffraction element and an imaging device in which the imaging region of the image sensor is more efficient used. 
     Solution to Problem 
     To solve the above-described problem, a diffraction element according to one aspect of the present disclosure comprises a grating pattern, wherein according to a position of light input to the diffraction element, the position being from a center of the diffraction element, an image forming position of diffracted light corresponding to the position of each wavelength is adjusted by adjusting a shape of the grating pattern at the position. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram illustrating a relationship between a type of light and a type of a wavelength. 
         FIG. 2  is a diagram illustrating an example of spectroscopic measurement of a light emitting object. 
         FIG. 3  is a diagram illustrating an example of a result of spectrum intensity analysis, the result being a result of spectroscopic analysis of output light of a certain food product. 
         FIG. 4  is a diagram illustrating a prism which is a spectroscopic element. 
         FIG. 5  is a diagram illustrating a diffraction grating which is a spectroscopic element. 
         FIG. 6  is a diagram illustrating an example of a data cube which is three-dimensional data including spatial directions (XY) and a wavelength direction (X) of a measurement object. 
         FIG. 7  is a diagram illustrating a schematic configuration example of a point measurement type (spectrometer) spectroscopic measurement device. 
         FIG. 8  is a diagram illustrating an example of data acquired by one time of imaging processing by using a point measurement type spectroscopic measurement device. 
         FIG. 9  is a diagram illustrating a schematic configuration example of a wavelength scanning type spectroscopic measurement device. 
         FIG. 10  is a diagram illustrating an example of data acquired by one time of imaging processing by using a wavelength scanning type spectroscopic measurement device. 
         FIG. 11  is a diagram illustrating a schematic configuration example of a space scanning type spectroscopic measurement device. 
         FIG. 12  is a diagram illustrating an example of data acquired by one time of imaging processing by using a space scanning type spectroscopic measurement device. 
         FIG. 13  is a diagram illustrating a schematic configuration example of a snapshot type spectroscopic measurement device. 
         FIG. 14  is a diagram illustrating an example of data acquired by one time of imaging processing by using a snapshot type spectroscopic measurement device. 
         FIG. 15  is a diagram illustrating a modified example of a snapshot type spectroscopic measurement device. 
         FIG. 16  is a diagram illustrating a restoration method of a data cube in a snapshot type. 
         FIG. 17  is a diagram illustrating a principle of spectral diffraction by a slit-type diffraction grating. 
         FIG. 18  is a diagram illustrating an example of an image of light spectrally diffracted by a grating type diffraction grating. 
         FIG. 19  is a diagram illustrating a relationship between a wavelength of incident light and a diffraction angle. 
         FIG. 20  is a diagram illustrating a problem of a snapshot type (part 1). 
         FIG. 21  is a diagram illustrating a problem of a snapshot type (part 2). 
         FIG. 22  is a diagram illustrating a first problem in a method for adjusting wavelength resolution and spatial resolution by controlling a grating interval. 
         FIG. 23  is a diagram illustrating a second problem in a method for adjusting wavelength resolution and spatial resolution by controlling a grating interval. 
         FIG. 24  is a top view illustrating an example of a basic diffraction grating and a diffraction grating according to a first embodiment. 
         FIG. 25  is a diagram illustrating an example of each of image data captured by using the diffraction grating illustrated in a left side of  FIG. 24  and image data captured by using a diffraction grating according to a first embodiment, which is illustrated in a right side of  FIG. 24 . 
         FIG. 26  is a diagram illustrating a method for designing the diffraction grating illustrated in the left side of  FIG. 24 . 
         FIG. 27  is a diagram illustrating a method for designing a diffraction grating according to a first embodiment. 
         FIG. 28  is a flowchart illustrating a design procedure of a diffraction grating according to a first embodiment. 
         FIG. 29  is a diagram illustrating a specific example of a procedure described in Step S 101  of  FIG. 28 . 
         FIG. 30  is a diagram illustrating a specific example of a procedure described in Step S 102  of  FIG. 28 . 
         FIG. 31  is a diagram illustrating a specific example of a procedure described in Step S 103  of  FIG. 28 . 
         FIG. 32  is a diagram illustrating a specific example of a procedure described in Step S 104  of  FIG. 28 . 
         FIG. 33  is a diagram illustrating a relationship between the diffraction grating illustrated in the left side of  FIG. 24  and a diffraction image. 
         FIG. 34  is a diagram illustrating a relationship between a diffraction grating according to a first embodiment and a diffraction image. 
         FIG. 35  is a diagram illustrating a data cube of light used as incident light in simulation. 
         FIG. 36  is a diagram illustrating a restoration result of a wavelength spectrum in a case where the diffraction grating illustrated in the left side of  FIG. 24  is used. 
         FIG. 37  is a diagram illustrating a restoration result of a wavelength spectrum in a case where a diffraction grating according to a first embodiment is used. 
         FIG. 38  is a plan view illustrating an example (example of CHECKER pattern) of a diffraction grating as a base in a second embodiment. 
         FIG. 39  is a plan view illustrating a diffraction grating according to a first variation example of a second embodiment, which is generated based on the diffraction grating illustrated in  FIG. 38 . 
         FIG. 40  is a plan view illustrating another example (example of COSINE pattern) of a diffraction grating as a base in a second embodiment. 
         FIG. 41  is a plan view illustrating a diffraction grating according to a second variation example of a second embodiment, which is generated based on the diffraction grating illustrated in  FIG. 40 . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present disclosure will be described in detail below with reference to the drawings. Note that, in the following embodiments, the same parts are denoted by the same reference numerals, and an overlapped description will be omitted. 
     Furthermore, the present disclosure will be described according to an order of items to be described below.
     1. Regarding Outline of Spectroscopic Measurement Device (System)   2. Regarding Problem of Snapshot Type   3. First Embodiment   3.1 Outline of Diffraction Grating   3.2 Design of Diffraction Grating   3.3 More Specific Design Procedure   3.4 Relationship between Diffraction Grating and Diffraction Image   3.5 Simulation Result   3.6 Action and Effect   4. Second Embodiment   4.1 First Variation   4.2 Second variation   

     1. Regarding Outline of Spectroscopic Measurement Device (System) 
     First, an outline of a spectroscopic measurement device (system) will be described. As light, for example, infrared light, visible light, ultraviolet light, and the like are known, but each of these light beams is a kind of electromagnetic wave, and has a wavelength (vibration period) varying depending on the type of light as illustrated in  FIG. 1 . 
     A wavelength of the visible light ranges from about 400 nm to 700 nm, and the infrared light has characteristics that a wavelength thereof is longer than that of the visible light, and the ultraviolet light has characteristics that a wavelength thereof is shorter than that of the visible light. 
     As described above, a light wavelength component of radiation light, reflection light, or transmission light from an object varies depending on the composition (element, molecular structure, and the like) of the object, and the composition of the object can be analyzed by analyzing the wavelength component. In general, data indicating an amount of each wavelength is referred to as a wavelength spectrum, and processing of measuring the wavelength spectrum is referred to as spectroscopic measurement processing. 
       FIG. 2  is a diagram illustrating a spectroscopic measurement example of a light emitting object.  FIG. 2  illustrates that light output from the Sun, an electric lamp, a neon lamp, a hydrogen lamp, a mercury lamp, and a sodium lamp is which wavelength of light in a wavelength range of the visible light (about 400 nm to 700 nm). A region in which the light is output is displayed in white, and a region in which the light is not output is displayed in black.  FIG. 2  illustrates a result obtained by performing a spectroscopic measurement on the light output from sunlight, electric lamp, and various heated substances. 
     As illustrated in  FIG. 2 , the sun, the electric lamp, the neon lamp, the hydrogen lamp, the mercury lamp, the sodium lamp, and each of these objects output the light having a unique wavelength respectively. That is, even when the object is unknown, the composition of the object can be analyzed by analyzing the wavelength component contained in the light from the object. 
     For example, in a case where a composition of a certain processed food product is unknown, it is possible to analyze a substance constituting the food product by analyzing output light (radiation light, reflection light, or transmission light) of the food product.  FIG. 3  is a diagram illustrating an example of a result of spectrum intensity analysis, the result being a result of spectroscopic analysis of output light of a certain food product. Two different spectral analysis results have been obtained from this food product. 
     By comparing a result of this spectrum intensity analysis with spectral intensity analysis result data obtained by analyzing various substances in advance, it is possible to determine what a substance A and a substance B are, and it is possible to analyze the composition of the food product. 
     As described above, when the spectroscopic measurement can be performed, various information regarding the measurement object can be acquired. However, in a general camera having a condenser lens and a sensor, light in which all wavelengths are mixed is incident on each pixel of the sensor, and thus it is difficult to analyze the intensity of each wavelength unit. 
     Therefore, an observation system of the spectroscopic measurement is provided with a spectroscopic element (spectroscopic device) for separating light of each wavelength from light coming into the camera. 
     As the most commonly known spectroscopic element, there is a prism  901  illustrated in  FIG. 4 . Light incident on the prism  901 , that is, light of various wavelengths included in the incident light is emitted from the prism  901  at an emission angle corresponding to the wavelength of the incident light, an incident angle, and a shape of the prism  901 . The observation system of the spectroscopic measurement is provided with a spectroscopic element such as the prism  901 , and has a configuration in which light in a unit of wavelength can be individually received by the sensor. 
     Note that, in the spectral diffraction by the prism having a refractive index n, an equation indicating a change in a traveling direction of the light due to the prism can be expressed by Equation (1) below. 
       δ=θ 1 −ϕ 1 +θ 2 −ϕ 2 =θ 1 +θ 2 −α  (1)
 
     Note that, each parameter of Equation (1) is as follows.
     α: apex angle of prism   θ 1 : incident angle with respect to incident plane of prism   θ 2 : emission angle with respect to emission plane of prism   ϕ 1 : refraction angle of incident plane of prism   ϕ 2 : refraction angle of emission plane of prism   δ: deflection angle (angle between incident light and emitted light)   

     Here, according to Snell&#39;s law (sinθ j =nsinΦ j ), Equation (1) can be replaced with Equation (2) below. 
       δ=θ 1 +sin −1 ( n ·sin(α−ϕ 1 ))   (2)
 
     Note that, in Equation (2), n is a refractive index of the prism, and the refractive index n depends on the wavelength. Furthermore, ϕ 1  is a refraction angle of the incident plane of the prism, and depends on the refractive index n of the prism and an incident angle θ 1  with respect to the incident plane of the prism. Accordingly, a deflection angle δ (angle between the incident light and the emitted light) depends on the incident angle θ 1  and the wavelength. 
     Furthermore, as illustrated in  FIG. 5 , spectral diffraction can be performed by a diffraction grating  902  using a property of a wave of light. An emission angle (diffraction angle) β of the light beam in accordance with the diffraction grating  902  can be expressed by Equation (3) below. 
     
       
         
           
             
               
                 
                   β 
                   = 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             m 
                             · 
                             λ 
                           
                           d 
                         
                         - 
                         
                           sin 
                           ⁢ 
                           α 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Note that, in Equation (3), d is a grating interval, α is an incident angle, β is an emission angle, and m is a diffraction order. 
     However, even when the wavelength information of the light from a certain point of the object is analyzed, only the composition of the point thereof can be analyzed. That is, in order to analyze the composition of each point on the surface of the object by one time of the observation, it is necessary to analyze all the light from each point on the surface of the object. 
     In order to analyze the composition of each point on the surface of the measurement object, it is necessary to acquire three-dimensional data including the spatial directions (XY) and the wavelength direction (λ) of the measurement object by one time of the observation.  FIG. 6  illustrates an example of three-dimensional data including the spatial directions (XY) and the wavelength direction (λ) of the measurement object, that is, a data cube. 
     As illustrated in  FIG. 6 , the data cube is three dimensional data including the spatial directions (XY) and the wavelength direction (λ) of the measurement object, the data in which a coordinate of each point on the surface of the measurement object is indicated by XY coordinate, and intensity (λ) of each wavelength light at each coordinate position (x, y) is recorded. The data cube illustrated in  FIG. 6  is configured of 8×8×8 cube data, and one cube D is data indicating light intensity of a specific wavelength (X) at a specific position (x, y). 
     Note that, the number 8×8×8 of the cube illustrated in  FIG. 6  is an example, and this number varies depending on the spatial resolution and wavelength resolution of the spectroscopic measurement device. 
     Next, an example of an existing spectroscopic measurement device that acquires the data cube illustrated in  FIG. 6 , that is, three-dimensional data including the spatial directions (XY) and the wavelength direction (λ) of the measurement object, will be described. 
     The existing spectroscopic measurement devices that acquire three-dimensional data including the spatial directions (XY) and the wavelength direction (λ) of the measurement object are classified into the following four types.
     (a) Point measurement type (Spectrometer)   (b) Wavelength scanning type   (c) Space scanning type   (d) Snapshot type   

     Hereinafter, an outline of each of these types will be described. 
     (a) Point Measurement Type (Spectrometer) 
       FIG. 7  is a diagram illustrating a schematic configuration example of the point measurement type (spectrometer) spectroscopic measurement device, and  FIG. 8  is a diagram illustrating an example of data acquired by one time of imaging processing by using the point measurement type spectroscopic measurement device. 
     As illustrated in  FIG. 7 , the point measurement type spectroscopic measurement device includes a light source  911 , a slit  912 , a prism  913 , and a linear sensor  914 , and has a configuration in which light emitted from one point of a measurement object  900  is spectrally diffracted by the prism  913  which is the spectroscopic element and the dispersed light is projected on the linear sensor  914  in which elements are arranged only in one direction. In such a configuration, different wavelength light is recorded in a different element (pixel) of the linear sensor  914 . 
     In the point measurement type, the wavelength spectrum is acquired by reading a value of each element (pixel) of the linear sensor  914 . A feature of this point measurement type is that the wavelength resolution depends on an element size (the number of pixels) of the linear sensor  914 , and a detailed wavelength information can be acquired as the number of elements (the number of pixels) increases. 
     However, in the point measurement type, light emitted from one point of the measurement object  900  is received and analyzed in one time of the imaging processing. Therefore, as illustrated in  FIG. 8 , only the wavelength information (λ) of only a certain one point of the spatial directions (XY) of the measurement object  900  can be obtained in one time of the imaging processing. Therefore, in order to obtain the wavelength information (λ) of various points of the spatial directions (XY) of the measurement object  900 , it is necessary to perform imaging and analysis several times while shifting the measurement position. 
     (b) Wavelength Scanning Type 
       FIG. 9  is a diagram illustrating a schematic configuration example of the wavelength scanning type spectroscopic measurement device, and  FIG. 10  is a diagram illustrating an example of data acquired by one time of imaging processing by using the wavelength scanning type spectroscopic measurement device. 
     As illustrated in  FIG. 9 , the wavelength scanning type spectroscopic measurement device includes a wavelength filter array  921  and an area sensor (two-dimensional image sensor)  923 , and performs imaging by switching a plurality of optical filters  922  which is disposed in front of the area sensor  923  and have different wavelength passing properties every hour. 
     According to such a procedure, as illustrated in  FIG. 10 , it is possible to acquire intensity information of one wavelength corresponding to a plurality of spatial positions in one time of imaging. Then, it is possible to acquire intensity information of a plurality of different wavelengths by switching the optical filters  922  to perform imaging. 
     However, in order to realize high wavelength resolution, it is necessary to prepare a large number of different optical filters  922  and switch the optical filters  922  to perform imaging. Therefore, there is a problem that the measurement time becomes long. Furthermore, there is also a problem that there is a wavelength band that cannot be acquired due to the characteristics of the optical filters  922 . 
     (c) Space Scanning Type 
       FIG. 11  is a diagram illustrating a schematic configuration example of the space scanning type spectroscopic measurement device, and  FIG. 12  is a diagram illustrating an example of data acquired by one time of imaging processing by using the space scanning type spectroscopic measurement device. 
     As illustrated in  FIG. 11 , the space scanning type spectroscopic measurement device includes an object lens  931 , a slit  932 , a collimating lens  933 , a spectroscopic element  934 , an image forming lens  935 , and an area sensor  936 , and records one direction of a space as an X direction of the area sensor and a wavelength direction as a Y direction of the area sensor with respect to light from the measurement object  900 , the light being spectrally diffracted by the spectroscopic element  934  (prism, diffraction grating, and the like). Moreover, as illustrated in  FIG. 12 , the spectroscopic measurement device scans the measurement object  900  in the remaining one direction. In this processing, the data cube described above with reference to  FIG. 6 , that is, the three-dimensional data cube including the spatial directions (XY) and the wavelength direction (λ) of the measurement object  900  can be acquired. 
     In this space scanning type, the high spatial resolution and the wavelength resolution can be realized, but there is a problem that a large device is required for scanning, a scan processing time is required, and a measurement time becomes long. 
     (d) Snapshot Type 
       FIG. 13  is a diagram illustrating a schematic configuration example of the snapshot type spectroscopic measurement device, and  FIG. 14  is a diagram illustrating an example of data acquired by one time of imaging processing by using the snapshot type spectroscopic measurement device. 
     As illustrated in  FIG. 13 , the snapshot type spectroscopic measurement device includes an object lens  941 , a slit  942 , a collimating lens  943 , a diffraction grating type spectroscopic element (hereinafter, simply referred to as a diffraction grating.)  944 , an image forming lens  945 , and an area sensor  946 , and has a configuration in which light from the measurement object  900  is condensed by the object lens  941 , converted into parallel light by the collimating lens  943 , and transmitted through the diffraction grating  944  to be projected on a light receiving surface of the area sensor  946 . Note that, the light receiving surface may be a surface on which photoelectric conversion units such as photodiodes in the image sensor (also referred to as a solid-state imaging device) are arranged. 
     In such a configuration, light of different wavelength components from different points on the measurement object  900  is recorded in different elements (pixels) on the light receiving surface of the area sensor  946 . 
     In this snapshot type, the data cube described with reference to  FIG. 6 , that is, the three-dimensional data cube including the spatial directions (XY) and the wavelength direction (λ) of the measurement object  900  as illustrated in  FIG. 14  can be acquired in one time of imaging. 
     However, since a light receiving area of the area sensor  946  is finite and the information of the wavelength direction is superimposed on the light receiving surface and recorded, it is necessary to perform processing of restoring the data cube by performing signal processing after the imaging. 
     Furthermore, since various coefficients used for the signal processing are linked with performance of the optical system, it is necessary to fix the optical system, that is, to fix the positional relationship between the sensor and the optical system to use the coefficients, and there is a problem that it is difficult to adjust the wavelength and the spatial resolution according to the application purpose. 
     Note that, as an application example of the snapshot type illustrated in  FIG. 13 , a configuration is proposed in which the data cube is acquired by disposing an optical filter  947  having a different transmission band spatially on the light receiving surface of the area sensor  946  as illustrated in  FIG. 15 . However, since a light receiving area is finite and it is necessary to mount the optical filter  947  on the light receiving surface of the area sensor  946 , there is a problem that the spatial resolution of the area sensor  946  decreases due to the mounting of the optical filter  947 . 
     With reference to  FIGS. 7 to 14 , the example of the existing spectroscopic measurement device that acquires three-dimensional data including the spatial directions (XY) and the wavelength direction (λ) of the measurement object, that is, four types of (a) Point measurement type (spectrometer), (b) Wavelength scanning type, (c) Space scanning type, and (d) Snapshot type have been described. 
     Among these four types, particularly in (d) Snapshot type described with reference to  FIGS. 13 and 14 , the data cube can be acquired in one time of the imaging. Therefore the snapshot type is highly useful. 
     Moreover, in order to solve the problem that the adjustment of the wavelength resolution is difficult, a configuration using a diffraction grating that can be incorporated into the existing optical system from a rear side is more suitable than a sensor configuration in which the sensor and the filter are integrated. 
     In the present disclosure, the snapshot type spectroscopic measurement device using the diffraction grating, for example, a spectroscopic measurement device using a computed tomography imaging spectrometer (CTIS) will be described below with some examples. 
     2. Regarding Problem of Snapshot Type 
     Here, a method for restoring the data cube in the snapshot type will be described with reference to  FIG. 16 .  FIG. 16  illustrates a case where the measurement object  900  is imaged by a snapshot type spectroscopic measurement device  940  including the lattice-shaped diffraction grating  944  (see  FIG. 13 ). 
     As illustrated in  FIG. 16 , in a case where the measurement object  900  is imaged by the spectroscopic measurement device  940  including the diffraction grating  944  (S 901 ), a diffraction image of ±one order or more is projected in total eight directions of up, down, right, and left directions and oblique directions around a diffraction image of zero order light positioned at a center in a captured image  951 . 
     By performing binary matrix operation processing using a modulation matrix H prepared in advance on such a captured image  951 , it is possible to restore a data cube g. Specifically, the data cube g can be restored by substituting the acquired captured image  951  into Equation (4) below. Note that, in Expression (4), x, y, and λ represent an x coordinate, a y coordinate, and a wavelength λ of a pixel in the captured image  951  (or a pixel array unit of the spectroscopic measurement device  940 ), and f(x, y, λ) represents a pixel value of a pixel (x, y, λ) in the captured image  951 . 
         g=H ƒ( x,y,λ )   (4)
 
     A solution of Equation (4) can be obtained, for example, by performing optimization using an expectation maximization (EM) algorithm using Equation (5) below (S 902 ). Accordingly, a data cube (g)  952  in which a horizontal plane is an XY coordinate system and a vertical direction is a wavelength axis can be obtained. Note that, a graph  953  illustrates a wavelength spectrum of a (x, y) pixel in a data cube  952 . 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       ^ 
                     
                     
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                         + 
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                       ) 
                     
                   
                   = 
                   
                     
                       
                         
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                           k 
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                             m 
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                             1 
                           
                           M 
                         
                         ⁢ 
                         
                           H 
                           
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     In the spectroscopic measurement device to which such a snapshot type is applied, a trade-off relationship occurs between the spatial resolution and the wavelength resolution due to a limitation on a size of the image sensor that acquires the diffraction image. For example, in a case where a dispersion angle is increased to increase spread of the dispersed light in order to increase the wavelength resolution, since spread of the diffraction image is also increased, it is not possible to perform imaging in a wide range, and the spatial resolution is decreased. On the other hand, in a case where the dispersion angle is decreased in order to increase the spatial resolution, the superimposing of the diffraction images having different wavelengths becomes large, and thus the wavelength resolution is decreased. Moreover, an increase in the wavelength range of the dispersed light incident on one pixel of the image sensor due to a decrease in size of the diffraction image also causes a decrease in the wavelength resolution. 
     This will be described more specifically.  FIG. 17  is a diagram illustrating a principle of spectral diffraction by a slit-type diffraction grating.  FIG. 18  is a diagram illustrating an example of an image of light spectrally diffracted by a grating type diffraction grating.  FIG. 19  is a diagram illustrating a relationship between a wavelength of incident light and a diffraction angle. 
     As illustrated in  FIG. 17 , light (plane wave) incident on the diffraction grating passes through two slits and reaches the screen as a spherical wave. At this time, there is a difference in an optical path length between the light passing through one slit and the light passing through the other slit. Therefore, in the image of the incident light transferred to the screen, light gradation (intensity of light) having a pattern depending on the difference in the optical path length, and an interval (grating interval P) between the wavelength λ of the incident light and the slit is generated. 
     When this is applied to the lattice-shaped diffraction grating, as illustrated in a left side of  FIG. 18 , light incident on the diffraction grating is diffracted at a different diffraction angle β obtained by Equation (3) described above depending on the wavelength λ and the grating interval P of the diffraction grating. Note that, in Equation (3), m is order. As a result, as illustrated in a right side of  FIG. 18 , the image (diffraction image) of the light passing through the diffraction grating is an image in which ± one order light, ± two order light, . . . are arranged around the zero order light as the center. 
     This means that in a case where the grating interval P is fixed, a relationship between the wavelength λ and the diffraction angle β is a linear relationship as illustrated in  FIG. 19 . Note that, in  FIG. 19 , straight lines P 1 , P 2 , and P 3  correspond to grating intervals P 1 , P 2 , and P 3 , and the grating intervals P 1 , P 2 , and P 3  have a relationship of P 1 &lt;P 2 &lt;P 3 . 
     From such a relationship, when the grating interval P is decreased, the diffraction angle β increases. Accordingly, as illustrated in  FIG. 20 , since the spread of a diffraction image  961  in a captured image  960  increases, the wavelength resolution can be increased. On the other hand, when the grating interval P is increased, the diffraction angle β is decreased. Accordingly, as illustrated in  FIG. 21 , since the spread of a diffraction image  962  in the captured image  960  decreases, the imaging can be performed in a wider range, and the spatial resolution can be increased. 
     However, in a method for adjusting the wavelength resolution and the spatial resolution by simply controlling the grating interval, the following problems occur. 
       FIG. 22  is a diagram illustrating a first problem. As illustrated in  FIG. 22 , when the grating interval P is decreased, the diffraction angle β increases at all the observed wavelengths. Therefore, although the range of the diffraction image  971  is widened, depending on setting of the sensor size or the like of the area sensor, an event easily occurs in which a diffraction image  971  protrudes from an observable range  970  of the area sensor and accurate measurement cannot be performed. This means that the wavelength range and the wavelength resolution to be measured are in a trade-off relationship with each other. 
     Furthermore,  FIG. 23  is a diagram illustrating a second problem. As illustrated in  FIG. 23 , when the grating interval P is increased, the spread of the entire diffraction image is decreased, so that the spatial resolution can be increased. On the other hand, since the superimposing portion of the diffraction images  981  to  985  of each wavelength is increased, the wavelength resolution is decreased. This means that the spatial resolution and the wavelength resolution are in a trade-off relationship with each other. Note that, in  FIG. 23 , the diffraction images  981  to  985  are slightly shifted in a lateral direction for understanding, but may be aligned in a longitudinal direction in practice. 
     As described above, in the snapshot type spectroscopic measurement device using the diffraction grating of the related art, since the spatial resolution and the wavelength resolution are in a trade-off relationship, it is difficult to achieve the high wavelength resolution while maintaining the spatial resolution. 
     In the following embodiment, by proposing a new diffraction element, it is possible to effectively utilize an element of a sensor, which has not been used for measurement as the diffraction element so far, and thus decrease the trade-off relationship between an observable wavelength range and the spatial resolution. 
     3. First Embodiment 
     Next, a diffraction element and an imaging device according to a first embodiment will be described in detail with reference to the drawings. Note that, the first embodiment is based on the snapshot type spectroscopic measurement device using the diffraction grating described above with reference to  FIGS. 13, 14, and 16 . However, the present disclosure is not limited to this, and the embodiment can be applied to various optical devices using the diffraction grating as the spectroscopic element. 
     3.1 Outline of Diffraction Grating 
       FIG. 24  is a top view illustrating an example of a basic diffraction grating and the diffraction grating according to the first embodiment.  FIG. 25  is a diagram illustrating an example of each of image data captured by using the diffraction grating illustrated in the left side of  FIG. 24  and image data captured by using the diffraction grating according to the first embodiment, which is illustrated in the right side of  FIG. 24 . Note that, in the present description, a diffraction grating in which grating patterns are arranged in a uniaxial direction (vertical direction in the drawing) will be described as an example of the diffraction grating  944  of the related art. The grating pattern may be a pattern of a convex portion and a concave portion or an opening pattern in the diffraction grating. 
     In the first embodiment, for example, as illustrated in  FIG. 24 , in the related art, the diffraction grating  944  that has been used as the diffraction grating type spectroscopic element (see  FIG. 13 ) in the snapshot type spectroscopic measurement device is replaced with a diffraction grating  100  including a grating pattern generated by converting the grating pattern of the diffraction grating  944  into a polar coordinate system. 
     In the diffraction grating  944  of the related art as illustrated in the left side of  FIG. 24 , as illustrated in a left side of  FIG. 25 , diffraction images  9 R(+1),  9 B(+1),  9 R(−1), and  9 B(−1) of ± one order light are rectangular images similarly to a diffraction image  9 RB 0  of zero order light. Therefore, diffraction images having different wavelengths in each order are superimposed on each other, and the wavelength resolution is decreased. 
     On the other hand, when the grating pattern of the diffraction grating  100  is a grating pattern of a polar coordinate system as in the embodiment, at least one of the grating interval and the arrangement direction (also referred to as a grating angle) of the grating pattern can be changed according to a position on the surface on which the grating pattern is provided. 
     The grating pattern may be, for example, an uneven pattern in which a plurality of the convex portions and a plurality of the concave portions are arranged, or an opening pattern in which a plurality of openings are arranged. Furthermore, the grating interval may be an interval between the adjacent convex portions or the adjacent concave portions, or a width or a diameter of an opening. Moreover, the arrangement direction may be an arrangement direction of the convex portions and the concave portions or an arrangement direction of the openings. 
     With such a configuration, in the diffraction grating  944  of the related art, as illustrated in the left side of  FIG. 25 , the diffraction images  9 RB 0 ,  9 R(+1),  9 B(+1),  9 R(−1), and  9 B(−1) that appears so as to be arranged in a direction according to the arrangement direction (vertical direction in the drawing) of the grating pattern can be converted into elongated diffraction images  1 RB 0 ,  1 R(+1),  1 B(+1),  1 R(−1), and  1 B(−1) that spirally swirl around the center of the image corresponding to the center of the diffraction grating  100  as illustrated in a right side of  FIG. 25 . 
     Note that, in the description of  FIG. 25 , light including a red component (R) and a blue component (B) is used as incident light. Furthermore, in  FIG. 25 , the diffraction images  9 RB 0  and  1 RB 0  indicate diffraction images of zero order light of R and B, the diffraction images  9 R(+1) and  1 R(+1) indicate diffraction images of + one order light of R, the diffraction images  9 B(+1) and  1 B(+1) indicate diffraction images of + one order light of B, the diffraction images  9 R(−1) and  1 R(−1) indicate diffraction images of − one order light of R, and the diffraction images  9 B(−1) and  1 B(−1) indicate diffraction images of − one order light of B. 
     As described above, by forming the diffraction images  1 R(+1),  1 B(+1),  1 R (−1), and  1 B(−1) of orders of ± one order light or more into swirling diffraction images, the diffraction images  1 R(+1),  1 B(+1),  1 R(−1), and  1 B(−1) can be incident in a region on the light receiving surface of the area sensor  946 , for example, in a region that is not used in the diffraction grating  944  of the related art as illustrated in the left side of  FIG. 24 . 
     Accordingly, since it is possible to reduce or eliminate the superimposition of the diffraction images having different wavelengths, it is possible to increase the wavelength resolution. 
     Furthermore, even when the grating interval is decreased, the diffraction image spreads in a rotational direction instead of a uniaxial direction, and protrusion of the diffraction image from the light receiving surface is decreased, so that the grating interval can be decreased so as to further increase the spatial resolution. 
     As described above, in the embodiment, by using the grating pattern of the diffraction grating  100  as the grating pattern of the polar coordinate system, it is possible to simultaneously improve both the wavelength resolution and the spatial resolution by more efficiently using the imaging region of the image sensor. 
     3.2 Design of Diffraction Grating 
     Next, a method for designing the diffraction grating  100  according to the embodiment will be described below. Note that, in the following description, a specific example of the design of the diffraction grating  100  illustrated in the right side of  FIG. 24  from the diffraction grating  944  illustrated in the left side of  FIG. 24  will be described, but the present disclosure is not limited to this, and it is possible to design a diffraction work of the polar coordinate system according to the embodiment based on various diffraction gratings. 
       FIG. 26  is a diagram illustrating a method for designing the diffraction grating illustrated in the left side of  FIG. 24 .  FIG. 27  is a diagram illustrating a method for designing the diffraction grating according to the first embodiment. Note that, in the following description, a height of the convex portion from a bottom surface of the concave portion is z. 
     In the design of the diffraction grating  944  in which the concave portion and the convex portion are alternately arranged in a Y direction as illustrated in the left side of  FIG. 24 , as illustrated in  FIG. 26 , for example, an orthogonal coordinate system (also referred to as an XY coordinate system or a Cartesian coordinate system) with an upper left of the diffraction grating  944  as an origin O is adopted, and the diffraction grating  944  is designed by performing calculation expressed in Equation (6) below with respect to one or a plurality of directions in this coordinate system. 
     
       
         
           
             
               
                 
                   
                     z 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           t 
                         
                         
                           
                             
                               
                                 y 
                                 ⁢ 
                                 mod 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               p 
                             
                             = 
                             0 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Note that, in Equation (6), p is a grating interval, and t is a height of a convex portion (also referred to as a lattice). 
     On the other hand, in the first embodiment, as illustrated in  FIG. 27 , the polar coordinate system is used in which a center of the diffraction grating  100  is set to the origin O, a distance from the origin O is set to r, and a rotation angle from a horizontal direction is set to ϕ. Then, the diffraction grating  100  is designed by performing calculation expressed in Equation (7) below in the polar coordinate system. 
     
       
         
           
             
               
                 
                   
                     z 
                     ⁡ 
                     
                       ( 
                       
                         r 
                         , 
                         
                           ϕ 
                           ′ 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           t 
                         
                         
                           
                             
                               ϕ 
                               ′ 
                             
                             = 
                             
                               ϕ 
                               + 
                               
                                 μ 
                                 · 
                                 r 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Note that, in Equation (7), μ is a parameter for controlling the rotation angle of the grating pattern. 
     With such a design, the diffraction grating  944  of the Cartesian coordinate system illustrated in the left side of  FIG. 24  can be converted into the diffraction grating  100  of the polar coordinate system illustrated in the right side of  FIG. 24 . Accordingly, image data  9  (corresponding to the left side of  FIG. 25 ) of the diffraction image as illustrated in a right side of  FIG. 26  can be converted into image data  1  (corresponding to the right side of  FIG. 25 ) of the diffraction image as illustrated in a right side of  FIG. 27 . 
     3.3 More Specific Design Procedure 
     A more specific design procedure of the diffraction grating according to the embodiment will be described below.  FIG. 28  is a flowchart illustrating a design procedure of the diffraction grating according to the first embodiment.  FIGS. 29 to 32  are diagrams illustrating a specific example of each procedure illustrated in  FIG. 28 . 
     As illustrated in  FIG. 28 , in the design of the diffraction grating  100 , first, a diffraction grating  101  (for example, corresponding to the diffraction grating  944 ) is designed in the Cartesian coordinate system (Step S 101 ). More specifically, as illustrated in  FIG. 29 , the diffraction grating  101  is designed by using the Cartesian coordinate system by a method similar to the designing method described with reference to  FIG. 26 . However, in the description, the center of the diffraction grating is the origin O. Furthermore, in the description, a height I (x, y) (corresponding to a height z (x, y)) of the grating pattern at a position of each Cartesian coordinate (x, y) is expressed in Equation (8) below. Note that, in Equation (8), a and b are constants. 
     
       
         
           
             
               
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           1 
                         
                         
                           
                             
                               mod 
                               ⁡ 
                               
                                 ( 
                                 
                                   y 
                                   , 
                                   a 
                                 
                                 ) 
                               
                             
                             ≥ 
                             b 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Next, the Cartesian coordinate system is converted into the polar coordinate system by applying the polar coordinate system to the diffraction grating  101  designed in  FIG. 29  (Step S 102 ). Specifically, as illustrated in  FIG. 30 , the polar coordinate system is applied to the diffraction grating  101  designed in  FIG. 29 , and a height I (r, ϕ) (=I (x, y)) of the grating pattern at each polar coordinate (r, ϕ) is obtained. Note that, the polar coordinate corresponding to a Cartesian coordinate (x, y) can be obtained by Equation (9) below. 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           r 
                           = 
                           
                             
                               
                                 x 
                                 2 
                               
                               + 
                               
                                 y 
                                 2 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           ϕ 
                           = 
                           
                             
                               tan 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               
                                 y 
                                 x 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Next, the diffraction grating  101  according to the first embodiment is designed by rotating the diffraction grating  101  in the polar coordinate system (Step S 103 ). Specifically, as illustrated in  FIG. 31 , the diffraction grating  100  according to the first embodiment is designed by rotating the diffraction grating  101  designed in  FIG. 29  by a predetermined angle μ·r in the polar coordinate system. Note that, μ may be a constant. A polar coordinate after the rotation is expressed in Equation (10) below. 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           r 
                           = 
                           r 
                         
                       
                     
                     
                       
                         
                           
                             ϕ 
                             ′ 
                           
                           = 
                           
                             ϕ 
                             + 
                             
                               μ 
                               · 
                               r 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Furthermore, the height of the grating pattern at each polar coordinate after the rotation is expressed in Equation (11) below. 
         I ( r′, ϕ′ )= I ( r,  ϕ)   (11)
 
     Finally, the polar coordinate system is converted into the Cartesian coordinate system by applying the Cartesian coordinate system to the diffraction grating  100  after the rotation (Step S 104 ). Specifically, as illustrated in  FIG. 32 , the Cartesian coordinate system is applied to the diffraction grating  100  after the rotation, and a height I (x′, y′) (=I (r′, ϕ′) of the grating pattern at each Cartesian coordinate (x′, y′) is obtained. Note that, the Cartesian coordinate (x′, y′) corresponding to a polar coordinate (r′, ϕ′) can be obtained by Equation (12) below. 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             x 
                             ′ 
                           
                           = 
                           
                             
                               
                                 r 
                                 ′ 
                               
                               · 
                               cos 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ϕ 
                               ′ 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             y 
                             ′ 
                           
                           = 
                           
                             
                               
                                 r 
                                 ′ 
                               
                               · 
                               sin 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ϕ 
                               ′ 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     3.4 Relationship Between Diffraction Grating and Diffraction Image 
     Next, a relationship between the diffraction grating and the diffraction image will be described.  FIG. 33  is a diagram illustrating a relationship between the diffraction grating illustrated in the left side of  FIG. 24  and the diffraction image.  FIG. 34  is a diagram illustrating a relationship between the diffraction grating according to the first embodiment and the diffraction image. Note that,  FIGS. 33 and 34  illustrate a case where a beam cross section is square and monochromatic light is used as incident light L 1 . 
     As illustrated in  FIG. 33 , in the diffraction grating  944  illustrated in the left side of  FIG. 24 , the grating interval p and the arrangement direction (gap length direction) of the grating pattern are constant with respect to an incident position of the incident light L 1  with respect to the diffraction grating  944 . Therefore, diffraction images  9   a  to  9   c  projected on a screen SCR at a certain distance from the diffraction grating  944  are rectangular regions reflecting the beam cross section of the incident light L 1  as it is. 
     On the other hand, as illustrated in  FIG. 34 , in the diffraction grating  100  according to the first embodiment, the grating intervals p 1  to p 4  and the arrangement direction (gap length direction) of the grating pattern change depending on the incident position of the incident light L 1  with respect to the diffraction grating  944 . Therefore, diffraction images  1   a  to  1   c  projected on the screen SCR at a certain distance from the diffraction grating  100  are regions of which shapes are distorted depending on the grating interval p of the diffraction grating  100  and the arrangement direction of the grating pattern. 
     3.5 Simulation Result 
     Next, the restoration result of the wavelength spectrum obtained by performing simulation on the snapshot type spectroscopic measurement device using the diffraction grating according to the embodiment will be described. 
       FIG. 35  is a diagram illustrating a data cube (hereinafter, referred to as an input data cube) of light used as the incident light in the simulation.  FIG. 36  is a diagram illustrating the restoration result of the wavelength spectrum in a case where the diffraction grating illustrated in the left side of  FIG. 24  is used.  FIG. 37  is a diagram illustrating the restoration result of the wavelength spectrum in a case where the diffraction grating according to the first embodiment is used. 
     As illustrated in  FIG. 35 , in the simulation, light of a single wavelength having a spatial spread in the XY direction is used as the incident light for simplicity. Furthermore, in  FIGS. 36 and 37 , a spectrum S 0  indicates a spectrum of the incident light, that is, a true value of the input data cube. 
     As illustrated in  FIG. 36 , in a case where the diffraction grating  944  illustrated in the left side of  FIG. 24  is used, the restored wavelength spectrum greatly deviates from the spectrum S 0  of the true value. Note that, in the simulation, root mean squared error (RMSE) was 2.9 and mean absolute error (MAE) was 1.9 in the result illustrated in  FIG. 36 . 
     On the other hand, as illustrated in  FIG. 37 , in a case where the diffraction grating  100  according to the first embodiment is used, the restored wavelength spectrum substantially coincides with the spectrum S 0  of the true value. Note that, in the simulation, root mean squared error (RMSE) was 0.55 and mean absolute error (MAE) was 0.4 in the result illustrated in  FIG. 37 . 
     As described above, by using the diffraction grating according to the first embodiment, the restoration performance of the wavelength spectrum can be significantly improved. This indicates that the wavelength resolution can be significantly improved by using the diffraction grating according to the first embodiment. 
     3.6 Action and Effect 
     As described above, according to the embodiment, since the diffraction image can be an elongated diffraction image spirally swirling, the superimposition of the diffraction images having different wavelengths can be decreased or eliminated, and the wavelength resolution can be increased. Furthermore, even when the grating interval is decreased, the diffraction image spreads in a rotational direction instead of a uniaxial direction, and protrusion of the diffraction image from the light receiving surface is decreased, so that the grating interval can be decreased so as to further increase the spatial resolution. Accordingly, it is possible to simultaneously improve both the wavelength resolution and the spatial resolution by using the imaging region of the image sensor more efficiently. 
     4. Second Embodiment 
     In the first embodiment described above, a case has been described in which the diffraction grating serving as a base for generating the diffraction grating  100  is the diffraction grating  944  in which the grating patterns are arranged in a uniaxial direction as illustrated in the left side of  FIG. 24 . However, as described above, the diffraction grating as the base is not limited to the diffraction grating  944 . Accordingly, in the second embodiment, variations of the diffraction grating  100  described in the first embodiment will be described with some examples. 
     4.1 First Variation 
       FIG. 38  is a plan view illustrating an example (example of CHECKER pattern) of a diffraction grating as a base.  FIG. 39  is a plan view illustrating a diffraction grating according to a first variation example of the second embodiment, which is generated based on the diffraction grating illustrated in  FIG. 38 . 
     As illustrated in  FIG. 38 , the diffraction grating generated in the procedure described using Step S 101  of  FIG. 28  in the first embodiment may be a diffraction grating  201  of a so-called CHECKER pattern in which the convex portions are arranged in a grating shape. In this case, in the description using  FIG. 29 , the height I (x, y) of the grating pattern at a position of each Cartesian coordinate (x, y) is expressed in Equation (13) below. Note that, in Equation (13), a and b are constants. 
     
       
         
           
             
               
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           1 
                         
                         
                           
                             
                               mod 
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   
                                     a 
                                     x 
                                   
                                 
                                 ) 
                               
                             
                             ≥ 
                             
                               
                                 b 
                                 x 
                               
                               ⋂ 
                               
                                 mod 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     y 
                                     , 
                                     
                                       a 
                                       y 
                                     
                                   
                                   ) 
                                 
                               
                             
                             ≥ 
                             
                               b 
                               y 
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     In a case where the procedures of Steps S 102  to S 104  in  FIG. 28  are executed for the diffraction grating  201  of the CHECKER pattern generated in this manner, it is possible to design a diffraction grating  202  in which the convex portions are rotated in an XY plane direction around the entire center as illustrated in  FIG. 39 . 
     4.2 Second Variation 
       FIG. 40  is a plan view illustrating another example (example of COSINE pattern) of the diffraction grating as a base.  FIG. 41  is a plan view illustrating a diffraction grating according to the second variation example of the second embodiment, which is generated based on the diffraction grating illustrated in  FIG. 40 . 
     As illustrated in  FIG. 40 , the diffraction grating generated in the procedure described using Step S 101  of  FIG. 28  in the first embodiment may be a diffraction grating  211  of a so-called COSINE pattern in which the convex portions, of which distal ends are rounded, are arranged in a grating shape. In this case, in the description using  FIG. 29 , the height I (x, y) of the grating pattern at a position of each Cartesian coordinate (x, y) is expressed in Equation (14) below. Note that, in Equation (14), a and b are constants. 
     
       
         
           
             
               
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     e 
                     
                       i 
                       · 
                       
                         [ 
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   2 
                                   · 
                                   π 
                                 
                                 ⁢ 
                                 
                                   x 
                                   
                                     p 
                                     x 
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             c 
                             ⁢ 
                             o 
                             ⁢ 
                             
                               s 
                               ⁡ 
                               
                                 ( 
                                 
                                   2 
                                   · 
                                   π 
                                   · 
                                   
                                     y 
                                     
                                       p 
                                       y 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     In a case where the procedures of Steps S 102  to S 104  in  FIG. 28  are executed for the diffraction grating  211  of the COSINE pattern generated in this manner, it is possible to design a diffraction grating  212  in which the convex portions, of which the distal ends are rounded, is rotated in the XY plane direction around the entire center as illustrated in  FIG. 41 . 
     As described above, the diffraction grating serving as the base can be variously deformed, and by deforming the diffraction grating serving as the base, it is possible to create various diffraction gratings according to a purpose. 
     Since other configurations, operations, and effects may be similar to those of the above-described embodiment, a detailed description thereof will be omitted here. 
     Although the embodiments of the present disclosure have been described above, the technical scope of the present disclosure is not limited to the above-described embodiments as it is, and various modifications can be made without departing from the gist of the present disclosure. Furthermore, constituent elements of different embodiments and modified examples may be appropriately combined. 
     Furthermore, the effect of each of the embodiments described in the present specification is merely an example and is not limited, and other effects may be obtained. 
     Moreover, each of the above-described embodiments may be used alone, or may be used in combination with other embodiments. 
     Note that, the present technique can also have the following configurations. 
     (1) 
     A diffraction element comprising a grating pattern, wherein according to a position of light input to the diffraction element, the position being from a center of the diffraction element, an image forming position of diffracted light corresponding to the position of each wavelength is adjusted by adjusting a shape of the grating pattern at the position. 
     (2) 
     The diffraction element according to (1), wherein the grating pattern includes a grating interval and a grating angle. 
     (3) 
     The diffraction element according to (2), wherein the grating pattern is an uneven pattern in which a plurality of convex portions and a plurality of concave portions are arranged, or an opening pattern in which a plurality of openings are arranged. 
     (4) 
     The diffraction element according to (3), wherein the grating interval is an interval between the convex portions adjacent to each other or the concave portions adjacent to each other, or a width or a diameter of the openings. 
     (5) 
     The diffraction element according to (3) or (4), wherein the grating angle is an arrangement direction of the convex portions and the concave portions or an arrangement direction of the openings. 
     (6) 
     The diffraction element according to any one of (1) to (5), wherein the grating pattern includes a spiral shape. 
     (7) 
     The diffraction element according to any one of (1) to (6), wherein the grating pattern is a grating pattern designed by rotating a grating pattern designed in a Cartesian coordinate system in a polar coordinate system. 
     (8) 
     The diffraction element according to (7), wherein the grating pattern is a grating pattern generated by rotating, in the polar coordinate system, a grating pattern in which convex portions and concave portions, or openings are arranged in one direction. 
     (9) 
     The diffraction element according to (7), wherein the grating pattern is a grating pattern generated by rotating, in the polar coordinate system, a grating pattern in which convex portions are arranged in a grating shape. 
     (10) 
     The diffraction element according to (9), wherein distal ends of the convex portions are rounded. 
     (11) 
     An imaging device comprising: 
     a diffraction element including a grating pattern; and 
     a solid-state imaging device in which the diffraction element is disposed on a light receiving surface side; 
     wherein according to a position of light input to the diffraction element, the position being from a center of the diffraction element, the diffraction element adjusts an image forming position of diffracted light corresponding to the position of each wavelength by adjusting a shape of the grating pattern at the position. 
     REFERENCE SIGNS LIST 
       100 ,  101 ,  201 ,  202 ,  211 ,  212 ,  902  DIFFRACTION GRATING 
       900  MEASUREMENT OBJECT 
       901 ,  913  PRISM 
       911  LIGHT SOURCE 
       912 ,  932 ,  942  SLIT 
       914  LINEAR SENSOR 
       921  WAVELENGTH FILTER ARRAY 
       922 ,  947  OPTICAL FILTER 
       923 ,  936 ,  946  AREA SENSOR 
       931 ,  941  OBJECT LENS 
       933 ,  943  COLLIMATING LENS 
       934  SPECTROSCOPIC ELEMENT 
       944  DIFFRACTION GRATING TYPE SPECTROSCOPIC ELEMENT (DIFFRACTION GRATING) 
       935 ,  945  IMAGE FORMING LENS