Diffraction grating and spectrometer

Abstract

The purpose of the technology disclosed in the present specification is to inhibit occurrence of comatic aberration.　This diffraction grating has a body, a reflection surface, and a plurality of grating grooves. The reflection surface is formed on the surface of the body. The reflection surface is provided in a recess surface shape. The grating grooves are formed on the reflection surface. The grating grooves are arranged along the reflection surface such that intervals are narrowed from a first edge of the reflection surface toward a second edge opposite to the first edge. The grating grooves extend along the reflection surface in a direction orthogonal to the arrangement direction of the grating grooves. The grating grooves have triangular cross-sectional shapes in cross sections perpendicular to the extending direction of the grating grooves. The closer the grating grooves are to the first edge, the smaller the widths of the grating grooves in the arrangement direction are. The closer the adjacent grating grooves are to the first edge, the greater the differences in width between the adjacent grating grooves are.

Description

Diffraction Gratings and Spectrometers

[0001] The technology disclosed in this specification relates to a diffraction grating and a spectrometer.

[0002] Patent Document 1 discloses a spectrometer and a concave diffraction grating used therein. The reflective surface of the concave diffraction grating is formed in a sawtooth pattern. That is, multiple grating grooves with triangular cross sections are closely spaced along a spherical concave surface, forming a sawtooth arrangement. The grating grooves have a width in the direction of arrangement. The grating grooves are arranged in ascending order of width, and the difference in width between adjacent grating grooves is the same. Even with such a regular arrangement of the grating grooves, coma aberration occurs in light diffracted by the concave diffraction grating.

[0003] JP 2020-34693 A

[0004] Therefore, the technology disclosed in this specification aims to suppress the occurrence of coma aberration.

[0005] In order to solve the above problems, this specification discloses a diffraction grating. The diffraction grating has a body, a reflecting surface, and a plurality of grating grooves. The reflecting surface is formed on the surface of the body. The reflecting surface is concave. The grating grooves are formed on the reflecting surface. The grating grooves are arranged closely spaced along the reflecting surface from a first edge of the reflecting surface toward a second edge opposite the first edge. The grating grooves extend along the reflecting surface in a direction perpendicular to their arrangement direction. The grating grooves have a triangular cross-sectional shape in a cross section perpendicular to their extension direction. The closer a grating groove is to the first edge, the smaller the width of the grating groove in the arrangement direction. The closer adjacent grating grooves are to the first edge, the greater the difference in width between adjacent grating grooves.

[0006] The technology disclosed in this specification contributes to suppressing the occurrence of coma aberration.

[0007] FIG. 1 is a diagram showing the overall configuration of a spectrometer. FIG. 2 is an enlarged view of a reflecting surface of a diffraction grating. FIG. 3 is a schematic diagram for explaining the shape of a diffraction grating. FIG. 4 is a schematic diagram for explaining the shape of a diffraction grating. FIG. 5 is a chart showing the relationship between the number of levels, the step shape, the maximum first-order diffraction efficiency, and the optimal height of the grating grooves. FIG. 6 is a diagram showing a function obtained by dividing the phase function by the normalized wavelength. FIG. 7 is a diagram showing the relationship between the position in the Y direction and the width of the grating grooves. FIG. 8 is a diagram showing the relationship between the position in the Y direction and the width of the grating grooves. FIG. 9 is a diagram showing the relationship between the position in the Y direction and the difference in width between adjacent grating grooves. FIG. 10 is a diagram showing the relationship between the position in the Y direction and the difference in width between adjacent grating grooves. FIG. 11 is a diagram showing the half width for each wavelength. FIG. 12 is a diagram showing the half width for each wavelength.

[0008] One or more embodiments will be described below with reference to the drawings. Features and technical advantages of the embodiments will be understood from the following detailed description and drawings. However, the scope of the present invention is not limited to the embodiments disclosed below. Because the drawings are provided for illustrative purposes only, the scope of the present invention is not limited to the examples in the drawings.

[0009] <<1. Spectroscopic Measurement Instrument>> Fig. 1 is a diagram showing the overall configuration of a spectroscopic measurement instrument 1. The spectroscopic measurement instrument 1 measures the spectral characteristics of a light source. As shown in Fig. 1, the spectroscopic measurement instrument 1 includes a diffuser plate 10, a mirror 20, a condenser lens 30, a light-blocking member 40, a diffraction grating 50, and a light-receiving sensor 90.

[0010] <<2. Diffusion Plate>> The diffusion plate 10 is disposed opposite the light source. When light from the light source is incident on the diffusion plate 10, the light is diffused and transmitted by the diffusion plate 10. The light to be measured that has been diffused and transmitted through the diffusion plate 10 is incident on the mirror 20.

[0011] <<3. Mirror>> The mirror 20 is disposed on the opposite side of the diffuser plate 10 from the light source. The mirror 20 is inclined from a plane parallel to the diffuser plate 10 toward the condenser lens 30. The mirror 20 reflects the light to be measured received from the diffuser plate 10 to the condenser lens 30.

[0012] <<4. Condenser Lens>> The condenser lens 30 is disposed on the side where the mirror 20 reflects the light to be measured. The condenser lens 30 condenses the light to be measured received from the mirror 20 onto the slit 41 of the light-shielding member 40. The optical axis of the condenser lens 30 is parallel to the plane of the paper in FIG. 1 . Hereinafter, the direction parallel to the optical axis of the condenser lens 30 is referred to as the z direction.

[0013] <<5. Slit>> The light-blocking member 40 is disposed on the opposite side of the condensing lens 30 from the mirror 20. The light-blocking member 40 has a slit 41 penetrating the light-blocking member 40. The slit 41 is formed in a long, narrow rectangular shape extending in a direction perpendicular to the optical axis of the condensing lens 30. The direction in which the slit 41 extends is perpendicular to the plane of FIG. 1 . The plane defined by the long and short sides of the slit 41 is perpendicular to the optical axis of the condensing lens 30. Hereinafter, the direction parallel to the long side of the slit 41 is referred to as the x-direction, and the direction parallel to the short side of the slit 41 is referred to as the y-direction. The x-direction, y-direction, and z-direction are perpendicular to one another. The optical axis of the condensing lens 30 passes through the slit 41 and intersects with the center of the diffraction grating 50, which will be described later. A coordinate system defined by mutually perpendicular x-, y-, and z-axes is referred to as an absolute coordinate system. The origin of the absolute coordinate system is set at the center of the slit 41, and the optical axis of the condenser lens 30 coincides with the z-axis.

[0014] <<6. Diffraction Grating>> The diffraction grating 50 is disposed on the opposite side of the light-blocking member 40 from the condensing lens 30. The diffraction grating 50 is tilted around a rotation axis from a position facing the light-blocking member 40 and the condensing lens 30. The rotation axis is orthogonal to the optical axis of the condensing lens 30 and parallel to the x direction.

[0015] The diffraction grating 50 is a reflective blazed concave diffraction grating. The diffraction grating 50 disperses the light to be measured that has passed through the slit 41 by diffraction and reflects the light to be measured toward the light-receiving sensor 90, arranging images of the light to be measured in the slit 41 for each wavelength and forming the images on the light-receiving sensor 90. Hereinafter, the band of light formed on the light-receiving sensor 90 by arranging the images of the light to be measured for each wavelength in the longitudinal direction of the light-receiving sensor 90 is referred to as a spectrum.

[0016] <<7. Light-Receiving Sensor>> The light-receiving sensor 90 is positioned offset from the optical axis from the slit 41 of the light-shielding member 40 to a reflecting surface 53 (described later) of the diffraction grating 50 in the direction in which the diffraction grating 50 is tilted. Therefore, the light-receiving sensor 90 is positioned on the side where the diffraction grating 50 reflects the measured light. The light-receiving sensor 90 detects the intensity of the spectrum formed on the light-receiving sensor 90 by the diffraction grating 50 for each wavelength. The light-receiving sensor 90 has multiple photoelectric conversion elements that convert the light intensity into an electrical signal. These photoelectric conversion elements are arranged in a straight line in the longitudinal direction of the light-receiving sensor 90, so the light-receiving sensor 90 is a line sensor. The light-receiving sensor 90 is tilted around an axis parallel to the x direction from an orientation in which the longitudinal direction of the light-receiving sensor 90 is parallel to the y direction.

[0017] <<8. Reflecting Surface of Diffraction Grating>> (1) Free-form Surface The diffraction grating 50 has a plate-shaped main body 51. The main body 51 has a concave, aspherical reflecting surface 53 on a surface 52 that faces obliquely toward the condenser lens 30 and the light-blocking member 40. The reflecting surface 53 is formed in the shape of a free-form surface. When the shape of the reflecting surface 53 is defined by a relative coordinate system set for the diffraction grating 50, the X-coordinate, Y-coordinate, and Z-coordinate of each point on the reflecting surface 53 are expressed by the following polynomial (1). The relative coordinate system set for the diffraction grating 50 is defined by an X-axis, a Y-axis, and a Z-axis that are orthogonal to each other.

[0018]

[0019] In formula (1), C is the curvature of the reference surface, which is the reciprocal of the radius of curvature of the reference surface. The reference surface when determining the shape of the reflecting surface 53 is the XY plane, and since the radius of curvature of the XY plane is infinite, C=0. The coefficient C in formula (1) ａｂ The values ​​are, for example, as shown in Table I or Table II below.

[0020]

[0021] When the degree of X is odd, the coefficient C ａｂ Since the value of is zero, the reflecting surface 53 is plane-symmetric with respect to the YZ plane.

[0022] The center 54 of the reflecting surface 53 is set to the origin of the relative coordinate system. The diffraction grating 50 is positioned so that the optical axis of the condensing lens 30 passes through the center 54 of the reflecting surface 53. In other words, the diffraction grating 50 is positioned so that the optical axis of the condensing lens 30 passes through the origin of the relative coordinate system. The diffraction grating 50 is tilted around the aforementioned rotation axis in the absolute coordinate system from an attitude in which the X axis of the relative coordinate system for defining the shape of the reflecting surface 53 is parallel to the x axis of the absolute coordinate system and the Y axis of the relative coordinate system is parallel to the y axis of the absolute coordinate system. As described above, the rotation axis is parallel to the x direction and passes through the center 54 of the reflecting surface 53. Therefore, the direction in which the reflecting surface 53 reflects the light to be measured is tilted from the optical axis of the condensing lens 30 toward the light-receiving sensor 90. The reflecting surface 53 has edges 55 and 56 in the Y direction. The edge 55 is the edge proximal to the light-receiving sensor 90, and the edge 56 is the edge distal to the light-receiving sensor 90. That is, edge 55 is the edge on which diffraction grating 50 is tilted, and edge 56 is the edge on the opposite side from which diffraction grating 50 is tilted.

[0023] In a region of the reflecting surface 53 closer to the edge 55 than the center 54, the curvature of the reflecting surface 53 increases as the distance from the center 54 increases. The region of the reflecting surface 53 closer to the edge 55 than the center 54 refers to a region closer to the light-receiving sensor 90 than the center 54. In addition, the region of the reflecting surface 53 closer to the edge 55 than the center 54 refers to a region where the diffraction grating 50 is inclined relative to the center 54.

[0024] In a region of the reflecting surface 53 closer to the edge 56 than the center 54, the curvature of the reflecting surface 53 decreases as the distance from the center 54 increases. The region of the reflecting surface 53 closer to the edge 56 than the center 54 refers to a region farther from the light-receiving sensor 90 than the center 54. Furthermore, the region of the reflecting surface 53 closer to the edge 56 than the center 54 refers to a region on the opposite side of the center 54 to the inclination of the diffraction grating 50.

[0025] (2) Sawtooth Shape and Reflective Film As shown in FIG. 2, an arrangement of a plurality of grating grooves 60 is formed on the reflecting surface 53 having the above-described free-form surface shape 57, and the arrangement of these grating grooves 60 forms a sawtooth shape. A reflective coating 70 is formed on the surface of these grating grooves 60. The reflective coating 70 is made of a dielectric multilayer film grown by a film formation method such as vapor deposition or sputtering, a metal film, or a combination thereof. The reflective coating 70 can reflect wavelengths in the range of 360-1100 nm, and reflects not only visible light but also infrared light with a high reflectance.

[0026] The plurality of grating grooves 60 extend in the X direction along the reflecting surface 53 and are arranged at close intervals in the Y direction along the reflecting surface 53. The arrangement direction of these grating grooves 60 is the Y direction. These grating grooves 60 have a triangular cross-sectional shape in a cross section parallel to the YZ plane and the yz plane. In other words, these grating grooves 60 have a triangular cross-sectional shape in a cross section perpendicular to the X direction and the x direction. The arrangement of these grating grooves 60 forms a sawtooth shape. The edges of the arrangement area of ​​the grating grooves 60 in the Y direction correspond to edges 55 and 56.

[0027] Each grating groove 60 has a height H [nm] from the free-form surface to an apex angle 61 of the grating groove 60. The grating groove 60 has a width W [nm] between base corners 62 of the grating groove 60. The base corner 62 of the grating groove 60 forms a boundary between the grating groove 60 and the adjacent grating groove 60.

[0028] 3, the plurality of grating grooves 60 are formed in a shape superimposed on the free-form surface 81 as described above. In other words, the plurality of grating grooves 60 can be said to have a shape formed by attaching a plurality of grating grooves 83 on a plane 82 to the free-form surface 81. Here, a tangent plane 85 parallel to the X direction and the Y direction is in contact with the free-form surface 81 at the center 54, and the plane 82 is parallel to the tangent plane 85. The plurality of grating grooves 83 extend in the X direction along the plane 82, and are arranged at close intervals in the Y direction along the plane 82.

[0029] The apex angles 61 of the grating grooves 60 form mountain lines, and the base angles 62 of the grating grooves 60 form valley lines. If these mountain lines and valley lines are lines 86 on the free-form surface 81 in Figure 4, when these lines 86 are parallel projected onto a tangent plane 85, a straight line 87 appears on the tangent plane 85. The straight line 87 is parallel to the X direction and perpendicular to the Y direction.

[0030] (3) Height of the grating grooves All of the grating grooves 60 have the same height. When the design wavelength is λ [nm], the height H of the grating grooves 60 is half the design wavelength λ, as shown in the following formula (2). The design wavelength λ refers to the wavelength at which high diffraction efficiency is desired to be obtained by the diffraction grating 50. For example, the design wavelength λ is 500 nm.

[0031]

[0032] Since the heights H of the grating grooves 60 are equal, the diffraction efficiency of the diffraction grating 50 is maximized at the design wavelength λ. This can be explained by scalar theory. FIG. 5 shows the relationship between the number of levels, the step shape, the maximum first-order diffraction efficiency, and the optimal height of the grating grooves when the shape of the triangular grating grooves of a typical diffraction grating is approximated by a step shape. The maximum first-order diffraction efficiency and the optimal height of the grating grooves in FIG. 5 are calculated by scalar theory. According to scalar theory, when the width of the grating grooves is sufficiently larger than the design wavelength λ, if the optimal height h of the grating grooves satisfies equation (3), the first-order diffraction efficiency η will be maximized as shown in equation (4). In equations (3) and (4), p is the number of levels, and n is the refractive index of the substrate. When the shape of the triangular grating grooves is approximated by a step shape, the number of levels p is the number of grating grooves of the step shape minus 1.

[0033]

[0034] When this scalar theory is applied to the diffraction grating 50, the number of levels p is infinite and the refractive index n is 1. Therefore, equation (3) becomes equation (2), and the maximum first-order diffraction efficiency η obtained from equation (4) is 100%.

[0035] (4) Width of Grating Groove The closer the grating groove 60 is to the edge 55, the smaller the width W of the grating groove 60 is. The farther the grating groove 60 is from the edge 55, the larger the width W of the grating groove 60 is. In other words, the closer the grating groove 60 is to the light-receiving sensor 90, the smaller the width W of the grating groove 60 is. The farther the grating groove 60 is from the light-receiving sensor 90, the larger the width W of the grating groove 60 is. In other words, the closer the grating groove 60 is to the inclination of the diffraction grating 50, the smaller the width W of the grating groove 60 is. The closer the grating groove 60 is to the opposite side of the inclination of the diffraction grating 50, the larger the width W of the grating groove 60 is.

[0036] The difference in width W between adjacent grating grooves 60, that is, the difference obtained by subtracting the width W of the grating groove 60 closer to the edge 55 from the W of the adjacent grating groove 60 farther from the edge 55, is not constant. Specifically, the closer the adjacent grating grooves 60 are to the edge 55, the greater the difference in width W between the adjacent grating grooves 60. The farther the adjacent grating grooves 60 are from the edge 55, the smaller the difference in width W between the adjacent grating grooves 60. In other words, the closer the adjacent grating grooves 60 are to the light-receiving sensor 90, the greater the difference in width W between the adjacent grating grooves 60. The farther the adjacent grating grooves 60 are from the light-receiving sensor 90, the smaller the difference in width W between the adjacent grating grooves 60. In other words, the closer the adjacent grating grooves 60 are to the inclination of the diffraction grating 50, the greater the width W of the adjacent grating grooves 60. The width W of adjacent grating grooves 60 decreases as they move away from the inclination of the diffraction grating 50. The absolute value of the rate of change of the difference in width W of adjacent grating grooves 60 at the center of the reflecting surface 53 may be smaller than the absolute value of the rate of change of the difference in width W of adjacent grating grooves 60 at the portions closer to the edges 55 and 56.

[0037] The shape of the grating grooves 60 of the diffraction grating 50 is designed by the phase function method. In such design, a phase function, which is a polynomial, is used. The shape of the grating grooves 60 of the diffraction grating 50 is designed using not only the first and second orders of the phase function, but also higher orders such as third order and higher. The reason why the difference in width W between adjacent grating grooves 60 is not constant is because higher orders such as third order and higher order of the phase function are also used.

[0038] The phase function f(X, Y) defines the phase difference of a ray in the X coordinate and the Y coordinate. The phase function f(X, Y) is expressed by the following equation (5).

[0039]

[0040] Here, since i=0, equation (5) becomes equation (6).

[0041]

[0042] Equation (6) is the normalized wavelength λ ｎ Dividing by [nm] gives equation (7).

[0043]

[0044] Normalized wavelength λ ｎ may be equal to the design wavelength λ. ｎ may be different from the design wavelength λ. ｊ The values ​​of coefficient D are, for example, as shown in Table III or Table IV below. ｊ The values ​​of are as shown in Table III below, and the normalized wavelength λ ｎ When is 500 nm, the formula (7) is expressed by a graph as shown in Fig. 6. In Fig. 6, the horizontal axis represents Y and the vertical axis represents F(Y).

[0045]

[0046] When the function F(Y) takes an integer value, the value of Y is the width W of the grating groove 60. ｊ The values ​​of are as shown in Table III below, and the normalized wavelength λ ｎ When the coefficient D is 500 nm, the width W of the grating groove 60 is expressed by a graph as shown in FIG. ｊ The values ​​of are as shown in Table IV below, and the normalized wavelength λ ｎWhen the angle .theta. is 500 nm, the width W of the grating groove 60 is expressed by a graph such as that shown in FIG. 7 and FIG. 8. In FIG. 7 and FIG. 8, the horizontal axis is the Y coordinate, and the vertical axis is the width W of the grating groove 60. As is clear from FIG. 7 and FIG. 8, the closer the grating groove 60 is to the edge 55, the smaller the width W of the grating groove 60. The farther the grating groove 60 is from the edge 55, the larger the width W of the grating groove 60. This is due to the use of a phase function of higher order than the third order.

[0047] Coefficient D ｊ The values ​​of are as shown in Table III, and the normalized wavelength λ ｎ When the coefficient D is 500 nm, the difference in width W between adjacent grating grooves 60 is expressed by a graph such as that shown in FIG. ｊ The values ​​of are as shown in Table IV, and the normalized wavelength λ ｎ When the distance θ is 500 nm, the difference in width W between adjacent grating grooves 60 is represented by a graph such as that shown in FIG. 9 and FIG. 10 . In FIGS. 9 and 10 , the vertical axis is negative. This is because the vertical axis represents the difference obtained by subtracting the width W of the grating groove 60 farther from the edge 55 from the width W of the adjacent grating groove 60 closer to the edge 55. The difference obtained by subtracting the width W of the adjacent grating groove 60 farther from the edge 55 from the W of the adjacent grating groove 60 farther from the edge 55 is positive. Therefore, as is clear from FIGS. 9 and 10 , the closer the adjacent grating grooves 60 are to the edge 55, the greater the difference in width W between the grating grooves 60. The farther the adjacent grating grooves 60 are from the edge 55, the smaller the difference in width W between the grating grooves 60. This is due to the use of a phase function of higher orders (third or higher), which contributes to the reduction of high-order coma in the Y direction. As shown in Figure 9, the absolute value of the rate of change of the difference in width W of adjacent grating grooves 60 in the central part of the reflecting surface 53 is smaller than the absolute value of the rate of change of the difference in width W of adjacent grating grooves 60 in the parts closer to the edges 55 and 56.

[0048] <<9. Simulation>> (1) The inventors simulated the spectral characteristics of the diffraction grating 50. Specifically, the inventors simulated the half-width of the diffraction grating 50 for each wavelength. The simulation conditions were as follows:

[0049] ・ Shape of free-form surface Coefficient C in formula (1) ａｂ The values ​​are as shown in Table I.

[0050] Height of grating grooves: The design wavelength λ in formula (2) is 500 nm. The height H of the grating grooves 60 is 250 nm.

[0051] Width of the grating grooves Normalized wavelength λ in Equation (7) ｎ is 500 nm. ｊ The values ​​of are as shown in Table III below. The width W of the grating groove 60 is expressed by a graph such as Fig. 7. The difference in width W between adjacent grating grooves 60 is expressed by a graph such as Fig. 9.

[0052] Positions and attitudes of the light-shielding member, diffraction grating, and light-receiving sensor The positions of the center of the slit 41, the center of the diffraction grating 50, and the center of the light-receiving sensor 90 in the absolute coordinate system are as shown in Table V below. The size of the slit 41, the size of the photoelectric conversion elements, and the number of photoelectric conversion elements are as shown in Table VI. The tilt angle of the diffraction grating 50 from the position facing the light-shielding member 40 and the condenser lens 30 is as shown below. The tilt angle of the light-receiving sensor 90 from the position in which the longitudinal direction of the light-receiving sensor 90 is parallel to the y direction is as shown in Table V below.

[0053] Meanwhile, the inventors simulated the spectral characteristics of a diffraction grating in a comparative example. The simulation conditions for the diffraction grating in the comparative example differed from those for the diffraction grating 50 only in terms of the width of the grating grooves. The diffraction grating in the comparative example was designed so that the shape of the grating grooves did not use third or higher orders of the phase function, but only first and second orders, and therefore the difference in width between adjacent grating grooves was the same.

[0054] FIG. 11 shows the simulation results. As is clear from FIG. 11, the half-width of the diffraction grating 50 is smaller than that of the comparative example in the wavelength range of visible light and infrared light. Therefore, in the diffraction grating 50, the reduction of high-order coma aberration in the Y direction reduces the aberration (spread) of the diffraction image in the wavelength direction. As a result, the optical wavelength resolution can be increased, and the half-width can be reduced. Conversely, when high-order coma aberration cannot be reduced over a wide wavelength range (as in the comparative example), the spread of the diffraction image in the wavelength direction becomes large at the ends of the wavelength range, resulting in a large half-width.

[0055] (2) The inventors simulated the spectral characteristics of the diffraction grating 50 and the comparative example under conditions different from those in (1) above. The simulation conditions were as follows:

[0056] ・ Shape of free-form surface Coefficient C in formula (1) ａｂ The values ​​are as shown in Table II.

[0057] Height of grating grooves: The design wavelength λ in formula (2) is 500 nm. The height H of the grating grooves 60 is 250 nm.

[0058] Width of the grating grooves Normalized wavelength λ in Equation (7) ｎ is 500 nm. ｊ The values ​​of are as shown in Table IV below. The width W of the grating groove 60 is expressed by a graph such as Fig. 8. The difference in width W between adjacent grating grooves 60 is expressed by a graph such as Fig. 10.

[0059] Positions and attitudes of the light-shielding member, diffraction grating, and light-receiving sensor The positions of the center of the slit 41, the center of the diffraction grating 50, and the center of the light-receiving sensor 90 in the absolute coordinate system are as shown in Table VII below. The size of the slit 41, the size of the photoelectric conversion elements, and the number of photoelectric conversion elements are as shown in Table VIII. The tilt angle of the diffraction grating 50 from the position facing the light-shielding member 40 and the condenser lens 30 is as shown below. The tilt angle of the light-receiving sensor 90 from the position in which the longitudinal direction of the light-receiving sensor 90 is parallel to the y direction is as shown in Table VII below.

[0060] 12 shows the simulation results. As is clear from FIG. 12, the half-width of the diffraction grating 50 is smaller than that of the comparative example diffraction grating in the wavelength ranges of visible light and infrared light. Therefore, the diffraction grating 50 suppresses high-order coma aberration due to diffraction, and the optical characteristics of the diffraction grating 50 are superior to those of the comparative example diffraction grating.

[0061] <<10. Summary>> (1) As described above, the diffraction grating 50 has a main body 51, a reflecting surface 53, and a plurality of grating grooves 60. The reflecting surface 53 is formed on the surface of the main body 51. The reflecting surface 53 is concave. A plurality of grating grooves 60 are formed on the reflecting surface 53. The plurality of grating grooves 60 are closely spaced along the reflecting surface 53 from a first edge 55 of the reflecting surface 53 toward a second edge 56 on the opposite side. The plurality of grating grooves 60 extend along the reflecting surface 53 in the X direction, which is orthogonal to the Y direction in which they are arranged. The plurality of grating grooves 60 have a triangular cross-sectional shape in a YZ plane perpendicular to the X direction. The closer a grating groove 60 is to the first edge 55, the smaller the width of the grating groove 60. The farther a grating groove 60 is from the first edge 55, the larger the width of the grating groove 60. The closer adjacent grating grooves 60 are to the first edge 55, the greater the difference in width W between adjacent grating grooves 60. The farther adjacent grating grooves 60 are from the first edge 55, the smaller the difference in width W between the adjacent grating grooves 60. This contributes to improving the spectral characteristics of the diffraction grating 50. In other words, high-order coma aberration caused by diffraction of the diffraction grating 50 is suppressed.

[0062] (2) The height H of the plurality of grating grooves 60 is the same. This contributes to the diffraction grating 50 having high diffraction efficiency at the design wavelength λ. In particular, the diffraction efficiency of the diffraction grating 50 is maximum at the design wavelength λ.

[0063] (3) The reflecting surface 53 of the diffraction grating 50 is formed as a free-form surface. In a region of the reflecting surface 53 closer to the first edge 55 than the center 54, the curvature of the reflecting surface 53 increases as the distance from the center 54 increases. In a region of the reflecting surface 53 closer to the second edge 56 than the center 54, the curvature of the reflecting surface 53 decreases as the distance from the center 54 increases. These factors contribute to suppressing coma aberration of the reflecting surface 53.

[0064] (4) When the apex angle 61 and base angle of the grating groove 60 are parallel projected onto the tangent plane 85, a straight line 87 appears on the tangent plane 85. This makes it easy to form the grating groove 60. For example, the grating groove 60 can be easily formed by machining or the like.

[0065] (5) Because the reflecting surface 53 of the diffraction grating 50 has a light-condensing effect, no separate lens is required between the diffraction grating 50 and the light-receiving sensor 90. Such a diffraction grating 50 contributes to the miniaturization of the spectrometer 1 employing the diffraction grating 50.

[0066] (6) One or more embodiments have been described and illustrated in detail above. The above-disclosed embodiments have been made for purposes of illustration and example only, and are not intended to limit the scope of the present invention, which should be interpreted by the terms of the claims.

[0067] REFERENCE SIGNS LIST 1 spectrometer 40 light-shielding member 41 slit 50 diffraction grating 51 main body 55 first edge 56 second edge 60 grating groove 90 light-receiving sensor

Claims

1. A diffraction grating comprising a main body, a reflecting surface formed on the surface of the main body and provided in a concave shape, and a plurality of grating grooves formed on the reflecting surface, wherein the grating grooves are arranged along the reflecting surface with intervals decreasing from a first edge of the reflecting surface toward a second edge opposite to the first edge, the grating grooves extend along the reflecting surface in a direction orthogonal to their arrangement direction, the grating grooves have a triangular cross-sectional shape in a cross-section perpendicular to their extending direction, the width of the grating grooves in the arrangement direction becomes smaller as the grating grooves are closer to the first edge, and the difference in width between adjacent grating grooves becomes larger as the adjacent grating grooves are closer to the first edge.

2. The diffraction grating according to claim 1, wherein the grating grooves have equal heights.

3. The diffraction grating according to claim 1 or 2, wherein the reflecting surface is provided in a free-form surface shape.

4. The diffraction grating according to claim 3, wherein in a region of the reflecting surface on the first edge side of the center of the reflecting surface, the curvature of the reflecting surface increases as the distance from the center increases, and in a region of the reflecting surface on the second edge side of the center, the curvature of the reflecting surface decreases as the distance from the center increases.

5. The diffraction grating according to claim 1 or 2, further comprising a reflective film covering the grating grooves and reflecting visible light and infrared light.

6. A spectroscopic measuring instrument comprising a light-shielding member having a slit, a diffraction grating, and a light-receiving sensor, wherein the diffraction grating is the diffraction grating according to claim 1 or 2, the diffraction grating is inclined toward the first edge from a posture in which the reflecting surface faces the light-shielding member, and the light-receiving sensor is arranged offset in the inclined direction of the diffraction grating from the optical axis from the slit to the reflecting surface.

Images