JP2000039359A - Conical diffraction oblique incidence spectrometer and diffraction grating for the spectrometer - Google Patents

Abstract

(57) [Summary] (with correction) PROBLEM TO BE SOLVED: To provide a diffraction grating designed to minimize aberration of a conical diffraction grazing incidence spectrometer. SOLUTION: A yz coordinate is determined on a grating surface of a diffraction grating in which grooves are formed at unequal intervals, and a point (w, l) on an n-th groove from a coordinate origin is expressed by the following series expansion equation. , And all expansion coefficients n _jk (k ≠
0) is defined as 0, and the focal length r ′ of the diffraction grating is:
The following equation corresponding to two different values θ ₁ and θ ₂ of the rotation angle θ of the diffraction grating corresponding to the scanning wavelength λ _i = λ ₀ / cos θ _i (i = 1, 2) So that r ′ and the expansion coefficient n of the series expansion equation
Determine the value of ₂₀ .

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a conical diffraction grazing incidence spectrometer and a design of a non-equidistant groove grating suitable for the spectroscope.

[0002]

2. Description of the Related Art In a conventional spectroscope comprising a single diffraction grating, an entrance slit, an exit slit, etc., a plane formed by the centers of the entrance slit, exit slit and the diffraction grating is diffracted. In a spectroscope having a so-called off-plane arrangement which is not perpendicular to the grating groove direction of the grating, as long as a diffraction grating having equally spaced parallel grooves is used, a large aberration occurs. Therefore, an improvement using a holographic diffraction grating having unequally spaced and non-parallel grooves has been proposed (M. Koike, "Monochromator with concave grating", U.
S patent No. 4,455,088). However, in this method, exposure is extremely difficult in an extreme off-plane arrangement.

In a conventional spectroscope that rotates a diffraction grating around an axis in the same direction as a grating groove and performs wavelength scanning, as the rotation angle increases, the area ratio of the shadow of the grating groove to be illuminated increases. As the wavelength becomes longer, the diffraction efficiency decreases significantly. To compensate for this drawback, a scheme has been devised in which the wavelength scanning is performed by rotating the diffraction grating around an axis perpendicular to the diffraction grating plane (for example, MC Hettrick, "Grating monochro
mators and spectrometers based on surface normal r
otation, Monochromator with concave grating ", US p
atent No. 5,274,435). By this method, the reduction in diffraction efficiency has been greatly improved, but large aberrations still remain.

The present invention has been made to solve such a problem, and an object of the present invention is to provide a diffraction grating designed to minimize the aberration of a conical diffractive grazing incidence spectroscope, and to provide such a diffraction grating. It is an object of the present invention to provide a conical diffraction grazing incidence spectrometer having a diffraction grating.

[0005]

SUMMARY OF THE INVENTION In order to solve the above-mentioned problems, the present invention is directed to a convergent light generating means for converting divergent light from a light source into convergent light, and from the light source to a focal point of the convergent light. A diffraction grating disposed on an optical path, and the diffraction grating is used for a conical diffraction grazing incidence spectrometer that performs wavelength scanning by rotating the diffraction grating around an axis determined in parallel to the normal of the grating surface. In the diffraction grating, the groove pattern of the diffraction grating is set such that the value of the expansion coefficient of the optical path function representing the focal point of the spectral optical system including the diffraction grating is substantially zero at at least one wavelength within the wavelength range in which wavelength scanning is performed. The present invention provides a diffraction grating characterized in that the expansion coefficient of a groove function, which is a series expansion equation, is determined.

[0006]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The inventors of the present invention have developed a conical diffraction grazing incidence spectrometer that performs wavelength scanning by rotating a diffraction grating about an axis defined parallel to the normal of the grating surface. Device, so that the value of the expansion coefficient of the optical path function representing the focus of the spectral optical system including the diffraction grating is substantially zero at at least one wavelength within the wavelength range in which wavelength scanning is performed.
It has been found that the diffraction efficiency of the spectroscope can be improved by determining the expansion coefficient of the groove function, which is a series expansion expression indicating the groove pattern of the diffraction grating.

More specifically, the expansion coefficient of the groove function may be determined by, for example, the following analytical method. That is, the analytical method is such that the y-axis and the z-axis which are orthogonal to each other in the grating plane of the diffraction grating are set so that the z-axis is parallel to the grating groove of the diffraction grating, and the y-axis is =
0, and the angle formed by the meridional plane, which is a plane including the optical path of the incident light on the diffraction grating and the optical path of the diffracted light exiting from the diffraction grating, and the y-axis is θ, and θ =
When 0, the wavelength of the diffracted light generated by the diffraction grating is λ ₀ , the two different θ values are θ ₁ and θ _2, and θ =
When θ ₁ and θ = θ ₂ , the wavelengths of the diffracted light generated by the diffraction grating are λ ₁ and λ ₂ , respectively, and the incident angle of the incident light on the diffraction grating is α, and The angle of diffraction of the diffracted light is β, the distance from the center of the diffraction grating to the focal point of the incident light in the meridian plane is r, and the meridional plane of the diffracted light having the wavelength λ ₀ from the center of the diffraction grating. , The distance to the focal point in r is r ′, the lattice constant at the center of the diffraction grating is d, the diffraction order is m, and the point (w, l) in the yz coordinate system is the center of the diffraction grating, that is, the coordinate. A groove function indicating a condition for existing on the n-th groove from the origin (0,0) is expressed by the following series expansion formula.

(Equation 7) When represented by, the expansion coefficient n ₂₀ and the distance r ′ are
The following simultaneous equations

(Equation 8) However,

(Equation 9) Is satisfied, and at least the expansion coefficients n ₀₂ , n ₁₂ and n ₂₂ are effectively set to 0.

[0008] The above analytical method will be more specifically described below with reference to the accompanying drawings.

FIG. 1 is a perspective view showing the mounting (arrangement) of optical elements in a conical diffraction grazing incidence spectroscope. In this spectroscope, light from the entrance slit 1 is reflected by the concave mirror 2
The light is converted into convergent light, is incident on a plane diffraction grating (hereinafter simply referred to as a diffraction grating) 3, is diffracted there, and forms an image on an exit slit 4. The incident angle of the incident light on the diffraction grating 3 is indicated by α, and the diffraction angle of the diffracted light from the diffraction grating 3 is indicated by β. The xyz coordinate system shown in the figure is a rectangular coordinate system having an origin at the center of the lattice plane of the diffraction grating 3, the x axis of which is orthogonal to the lattice plane, the y axis is orthogonal to the lattice groove, and the z axis is Parallel to the grating grooves. The lattice constant at the center of the diffraction grating 3 is d, and the diffraction order is m.

In this spectroscope, wavelength scanning is performed by rotating the diffraction grating 3 around the x-axis. The rotation angle of the diffraction grating 3 is an angle (or a meridional plane) formed by a plane (hereinafter, a meridional plane) determined by the principal ray of light incident on the diffraction grating 3 and the principal ray of diffraction from the diffraction grating 3 (or
As shown in FIG. 1, it is represented by an angle (θ) formed by the normal of the meridian plane and the z-axis. For the above conical diffraction oblique incidence spectrometer, the above-described equations are made for two different values of the rotation angle θ of the diffraction grating 3. In the following description, as an example, assume that 0 and θ ₂ are selected as two different values of θ. Further, according to the above, the wavelength of the diffracted light when θ = 0 (this wavelength corresponds to the minimum wavelength of the diffracted light generated by the diffraction grating 3) is λ ₀ , and when θ = θ ₂ The wavelength of the diffracted light is λ ₂ .

FIG. 2 is a side view showing the conical diffraction oblique incidence spectrometer when the rotation angle θ of the diffraction grating 3 is set to zero. In this figure, the symbol F indicates the focal point of the convergent light generated by the concave mirror 2 in the meridional plane, the symbol D indicates the distance from the center of the concave mirror 2 to the center of the diffraction grating 3, and the symbol r indicates the diffraction grating 3 Denotes the distance from the center of the diffraction grating 3 to the focal point F, and the symbol r ′ denotes the distance from the center of the diffraction grating 3 to the focal point F ′ in the meridional plane of the diffracted light having the wavelength λ ₀ .

Under the above conditions, the following equations (8) and (9)

(Equation 10) Holds, the following equation (1) including λ ₂ , λ ₀ and θ ₂ is obtained.
0)

[Equation 11] Holds. This corresponds to the above equation (3).

A groove function indicating a pattern for forming a groove on a lattice plane is generally represented by a series expansion equation shown in the above equation (1). That is, Expression (1) represents a set of all points (w, l) existing on the n-th groove counted from the groove passing through the origin (0, 0). As shown in FIG. 3, in order to make the n-th groove parallel to the z-axis, the expansion coefficient (that is, k ≠ 0) related to the term including 1 included in the above equation 1 All n _jk ) are defined as 0. Here, all the expansion coefficients relating to the term including l may be set to 0, but actually, even if the expansion coefficients n ₀₂ , n ₁₂ , and n ₂₂ relating to the low-order terms of l are set to 0, the lattice groove is It is parallel to the z-axis with sufficient accuracy for practical use. Through the above processing, the equation (1) can be treated as an equation including substantially only n, d, w, and n _j0 (where j is an integer) as a variable.

The above groove function constitutes a part of an optical path function representing a distance from a point (w, l) on a groove of the diffraction grating 3 to a focal point F 'of diffracted light. Therefore, in order to make the focal length of the diffracted light as constant as possible irrespective of the wavelength, the focal length r ′ is set so that the expansion coefficient of the optical path function representing the focal point becomes zero, and the expansion coefficient n in the groove function is set. Determine ₂₀ . That is, in the case of the present embodiment, in the above equation (2), θ
The following two equations (11) obtained as = 0 and θ = θ ₂
And (12)

(Equation 12) N ₂₀ and r ′ may be determined so as to satisfy the following. here,
The variable groups α ₀ , β ₀ , r _0, and r ₀ ′ corresponding to θ = 0 are represented by α ₀ = α, β ₀ = β by setting θ _i = 0 in the above equations (4) to (7). , R ₀ = r, r ₀ ′ = r ′. On the other hand, corresponds to the _{θ = θ 2 α 2, β} 2, r 2
And r ₂ ′ are calculated by the following four equations (13) to (16) obtained as θ _i = θ _{2 in} the above equations (4) to (7).

(Equation 13) Defined by As a specific example, d = 1200 lines / m
m, λ ₀ = 0.5 nm, λ ₂ = 1.0 nm, θ ₂ = 60 °, m = -1, α =
87.777 °, β = -89.000 °, r = -9805mm,
r ′ = 2007 mm and n ₂₀ = −2.773758 × 10 ⁻⁶ mm ⁻² .

In the above example, one of the two values having different θ is set to 0. However, even when _two different values θ ₁ and θ ₂ other than 0 are used, the same calculation as described above is performed to obtain the equation. (1) it is of course possible to obtain the focal length r 'expansion coefficients n ₂₀ and the diffraction grating.

Next, a spherical mirror is used as a concave mirror for illuminating the diffraction grating, and the incident divergent light and the emergent convergent light in the meridional plane of the spherical mirror are almost symmetrical (1) and asymmetrical (2).
The following two design examples will be described. Note that under the above conditions, m
There is no solution when only changing to +1.

(Design Example 1) When the distance ra from the entrance slit to the spherical mirror is 10005 mm, the incident angle is 88 °, and the distance D from the spherical mirror to the diffraction grating is 200 mm, the radius of curvature R of the spherical mirror is
= 286687mm. In this case, since the focal point in the meridian plane is at 10005 mm from the spherical mirror, the coma of the spherical mirror is small. Therefore, ignoring the coma of the spherical mirror, any wavelength λ ₃ (=
λ ₀ / cos θ ₃ ), the following equation representing the coma of the diffraction grating

[Equation 14] Just like decreases, the coma aberration in a wavelength region centering wavelength lambda ₃ can be greatly reduced. here

(Equation 15) It is. And concrete calculation example, the value of n ₃₀ to minimize the coma aberration of the diffraction grating is also 7.34761 × 10 ^-8 mm ^-3, when the wavelength of the diffracted light is 0.5 nm, the wavelength of the diffracted light Is 1.0
In the case of nm, it becomes -3.222903 × 10 ^-7 mm ^-3 . Since the focal point of the incident light is -9800 mm and the focal point of the diffracted light is 2000 mm as viewed from the diffraction grating, a reduced image of the light source of about 1 / 4.9 times can be formed on the exit slit.

(Design Example 2) When the distance ra from the entrance slit to the spherical mirror is 2800 mm, the incident angle φ is 88 °, and the distance D from the spherical mirror to the diffraction grating is 200 mm, the radius of curvature R of the spherical mirror is 125374 mm. In this case, since the focal point in the meridional plane is at 10005 mm from the spherical mirror, the magnification is about 3.6 times as seen from the spherical mirror, and the coma of the spherical mirror cannot be neglected. Therefore, equation (17) cannot be generally applied. The wavelength is obtained from the condition for removing coma aberration in a two-mirror system including the coma aberration of a spherical mirror. Ie

(Equation 16) here

[Equation 17] It is. The value of n ₃₀ to optimize lambda = 0.5 nm than (13)
7.34761 × 10 ^-8 mm ^-3 . The optimum value at 1.0 nm is 4.13679 × 10 ⁻⁷ mm ⁻³ by numerical calculation of the ray tracing method.
Also, the focus of the incident light from the diffraction grating is -9805 mm
Since the focal point of the diffracted light beam is 2007 mm, a reduced image of the light source of about 0.73 times is formed on the exit slit.

The slope Ψ of the exit slit changes with wavelength scanning, and is expressed by the following equation.

(Equation 18) Here, r _Y is a distance from the light source in a spherically defective plane viewed from the diffraction grating.

The results obtained so far are summarized as follows.

[Table 1] Becomes

Next, a spot diagram and a spectral line profile obtained by a ray tracing method for evaluating the spectroscope and the diffraction grating according to the present invention will be described.

FIG. 4 shows that n ₃₀ = −4.001377 × 10 ⁻⁷ mm ⁻³ so that the parameter of the above condition (1) and coma are corrected at 1.0 nm.
In this case, the size of the entrance slit is 20 μm × 1 mm, the divergence angle of light rays from the entrance slit is 2 × ² mrad ² , and the size of the diffraction grating is a circle having a diameter of 100 mm. The three spectral lines have a wavelength difference corresponding to a resolution of 1000, and the actual resolution is indicated as R in the figure. The value of T is a geometric optical throughput considering vignetting caused by the effective area of the diffraction grating. From this figure 1.
It can be seen that the aberration is comprehensively corrected at 0 nm. When the size of the entrance slit is infinitely small among the above conditions, the resolution is 1161 (0.5 nm), 2510 (0.75 nm), 2
963 (1.0 nm) and 2447 (1.5 nm).

FIG. 5 shows the parameters of the above condition (2) and
N so that coma is corrected at 0.5 nm ₃₀= 7.34761 × 10^-8
mm^-3And the size of the entrance slit is 20μm × 1m
m, the divergence angle of the ray from it is 2 × 2mrad^Two, Large diffraction grating
This shows a case where the size is a circle having a diameter of 100 mm.
The three spectral lines have a wavelength difference equivalent to a resolution of 1000
The actual resolution is indicated as R in the figure.
Also, the value of T indicates the vignetting caused by the effective area of the diffraction grating.
This is the geometric optical throughput considered. From this figure
The coma aberration correction wavelength is 0.5 nm, but the total
It can be seen that the aberration is corrected in the wavelength region. In addition, above
If the size of the entrance slit is infinitely small,
Resolution is 23321 (0.5 nm), 3894 (0.75 nm), 2671
(1.0 nm) and 1986 (1.5 nm).

Although the embodiment of the diffraction grating according to the present invention has been specifically described above, the embodiment of the present invention is not limited to the above. For example, in the spectroscope of FIG. 1, the entire optical path from the entrance slit 1 to the exit slit 4 is included in the same plane (meridian plane), but this is not essential. For example, as shown in FIG. 6, arranging the entrance slit 1 so that the light incident on the concave mirror 2 goes out of the meridian plane does not hinder the practice of the present invention. Furthermore,
1 or 6, the light from the entrance slit 1 is converted into convergent light by the concave mirror 2, the convergent light is received by the diffraction grating 3, and the diffracted light exiting therefrom is sent to the exit slit 4. The optical element is arranged, for example, as shown in FIG.
The spectroscope in which the optical elements are arranged such that the light from the entrance slit 1 is first received by the diffraction grating 3, the diffracted light emitted therefrom is converted into convergent light by the concave mirror 2 and sent to the exit slit 4,
The present invention is applicable.

[0025]

As described above, in the diffraction grating according to the present invention, the groove spacing that minimizes the aberration is determined by an analytical method, and the grating grooves are provided at the groove spacing. If a grazing incidence spectrometer is configured, spectral analysis with much higher accuracy than conventional products can be performed.

[Brief description of the drawings]

FIG. 1 is a perspective view showing an arrangement of optical elements in a conical diffraction grazing incidence spectrometer according to one embodiment of the present invention.

FIG. 2 is a side view showing the spectroscope of FIG.

FIG. 3 is a diagram showing an example of a groove pattern on a lattice plane.

FIG. 4 is a spot diagram and a spectral line profile obtained by a ray tracing method using specific examples of a spectroscope and a diffraction grating according to the present invention.

FIG. 5 is a spot diagram and a spectral line profile obtained by a ray tracing method using specific examples of a spectroscope and a diffraction grating according to the present invention.

FIG. 6 is a perspective view showing another conical diffraction grazing incidence spectroscope to which the present invention can be applied.

FIG. 7 is a side view showing still another conical diffraction grazing incidence spectrometer to which the present invention can be applied.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Inlet slit 2 ... Concave mirror 3 ... Planar diffraction grating 4 ... Exit slit

 ──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Kazuo Sano 1-Nishinokyo-kuwabara-cho, Nakagyo-ku, Kyoto-shi Inside the Sanjo Plant, Shimadzu Corporation (72) Inventor Yoshihisa Harada 1-Nishi-no-Kyowa-cho, Nakagyo-ku, Kyoto-Shimadzu Corporation F term in Sanjo factory (reference) 2G020 CA03 CC04 CC07 CC42 CC51 CD31 CD36 2H049 AA06 AA51 AA58 AA69

Claims (4)

[Claims] 1. A converging light generating means for converting divergent light from a light source into convergent light, and a diffraction grating arranged on an optical path from the light source to a focal point of the converging light, wherein the diffraction grating comprises In a diffraction grating used in a conical diffraction grazing incidence spectroscope that performs wavelength scanning by rotating about an axis determined parallel to the surface normal, an optical path function representing a focal point of a spectroscopic optical system including the diffraction grating The expansion coefficient of the groove function, which is a series expansion expression indicating the groove pattern of the diffraction grating, is determined such that the value of the expansion coefficient becomes substantially zero at at least one wavelength within the wavelength range in which wavelength scanning is performed. A diffraction grating. 2. The diffraction grating according to claim 1, wherein a y-axis and a z-axis orthogonal to each other in a grating plane of the diffraction grating.
So that the z-axis is parallel to the grating groove of the diffraction grating.
The y-axis is defined to be orthogonal to the lattice groove at z = 0.
The optical path of light incident on the diffraction grating and the light exiting from the diffraction grating.
The meridional plane, which is a plane including the optical path of the diffracted light, and the y-axis
The angle formed is θ, and when θ = 0, the angle
Let the wavelength of the diffracted light₀And two different values of θ
To θ₁And θ_TwoAnd θ = θ₁And θ = θ_TwoAt the time of the diffraction
Let the wavelength of the diffracted light generated by the grating be λ₁as well as
λ_TwoAnd the incident angle of the incident light on the diffraction grating is α.
And the diffraction angle of the diffracted light from the diffraction grating is β,
In the meridional plane of the incident light from the center of the diffraction grating
Let r be the distance to the focal point and the wave from the center of the diffraction grating.
Long λ ₀To the focal point of the diffracted light in the meridional plane
Is r ′, and the lattice constant at the center of the diffraction grating is d and
And the diffraction order is m, and the point in the yz coordinate system is
(W, l) is the center of the diffraction grating, that is, the coordinate origin (0,
0) the groove relation indicating the condition for existence on the n-th groove
The number is expressed by the following series expansion formula.When expressed as, the expansion coefficient n₂₀And the distance r ′ is
The following simultaneous equationsHowever,A diffraction grating characterized by satisfying the following. 3. The diffraction grating according to claim 2, wherein 0
Any θ in the angle range from ° to 90 °
Each of the following equations corresponding to the value of Α _θ , β _θ , r _θ , r _θ ′ are determined by the following equation, and T _A and T _B are determined by the following equations. , The expansion coefficient n ₃₀ included in the series
Or the following two equations including n ₄₀ Wherein at least one of the diffraction gratings is satisfied. 4. A conical diffraction grazing incidence spectrometer configured using the diffraction grating according to claim 1.