JPS5928248B2 - Holographic plane diffraction grating creation device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an apparatus for producing a holographic plane diffraction grating suitable for Monk-Gilson mounting, and improvements to the mounting apparatus.

Conventional Monk-Gilson mounting has caused quite large aberrations, and in order to improve this, a method has been proposed in which the grating is rotated around a point other than the center of the flat diffraction grating. However, with this method, the spectroscopic device becomes complicated, and considerable comatic aberration still remains at wavelengths other than a certain specific wavelength. An object of the present invention is to provide an apparatus for producing a holographic plane diffraction grating with extremely few aberrations, which is suitable for Monk-Gilson mounting.

Another object is to provide a Monk-Gilson mounting device with extremely low aberrations.

In FIG. 1 showing the Monk-Gilson mounting, light from an entrance slit 1 is reflected and focused by a concave mirror 2.
The light enters the plane diffraction grating 3, is diffracted there, and forms an image on the exit slit 4.

The grating 3 is rotated around the center G of the grating 3 to perform wavelength scanning. Now, the centers of the entrance and exit slits 1 and 4 are A and B, respectively, the center of the grid 3 is G, and the center of the concave mirror 2 is O.
If we calculate the optical path function F for a ray passing through point P on the concave mirror and point Q on the grating 3, we get F=AP+PQ+QB+n-
m・λ (1).

Here, AP, PQ, and QB are the distances between A and P, between P and Q, and between Q(5B), m is the order of diffraction, λ is the wavelength,
And n is the number of grating lines from the center G to Q, which is determined by the recording constant of the holographic diffraction grating. In FIG. 2, which shows a recording system or production device for a holographic diffraction grating, Z-axes are arranged at right angles to each other on the surface of a photosensitive material 3' such as a photoresist, which is the material of the diffraction grating, with the center G serving as the coordinate origin. , the Y axis, and the X axis perpendicular to both axes. Light from two point light sources C and D existing on the XY plane records interference fringes on the photosensitive material 3' to create a grating. n as the grid material 3′TI. where λr is the laser wavelength used for recording.

If n is deleted from equations (1) and (2), 1r- Thus, the optical path function F can be expressed by a constant of the spectroscopic system and a constant of the recording system.

Now, let this F be the coordinate of point Q of the diffraction grating (or its material) (ω
, t) (R is the radius of curvature of the concave mirror), where the coefficient FiJ of ω or t can be further written as.

Here, MiJ is a coefficient based on AP+PQ+QB in equation (1), that is, a coefficient caused by the spectroscopic system, and Hij is a coefficient caused by the recording system.

The condition that there is no aberration of the diffraction grating in the spectroscopic system is Ferma UEUr.
From the principle of unity, 1=O −=0 aω ”At.

Therefore, the coefficients FlO, F2O, F of ω or t in equation (3)
The recording constant and the device constant of the spectroscopic system may be determined so that O2... becomes zero or as small as possible.

Next, for this purpose, FlO, F2O, FO2, F3O,
Find Fl2 specifically. In FIG. 1, AO=R,
OG=RO, GB=r', the radius of curvature of the concave mirror is R. ZA
OG=2θ, ZOGB=2α01 The angle of incidence on the diffraction grating is α and the diffraction angle is β.

However, it is assumed that α−β=2αぃα, αo×0, and β>0. According to the diffraction equation, σ is the lattice constant.

In addition, in Fig. 2, CG=Rc, DG=Rd, and ρd
=-.

Rd Using these variables, Fij can be expressed as follows.

however 1r0OtsuRO a=-1 {-μsθ+COsθ-1} --Gu'Un It is.

FlO is calculated by considering equation (5) Therefore, it can always be zero.

Next, F2O}FO2)F3OjFl2 are both (4)
As can be seen from the formula, when mλ=0, M2O, MO2, and M3 are respectively
It becomes equal to O, Ml2.

That is, when mλ=0, F2O, FO2, F3O, and Fl2 are determined only by the constants of the spectroscopic system. Therefore, in a spectroscopic system, it is desirable that the coefficients of the ω2 and ω3 terms such as F2O and F3O are as small as possible, so first mλ=0 and F2O=
Let F3O=0. That is, λ=0 is F2O,F in equation (6)
Substituting into 3O and setting F2O=F3O=0, r=RcO
sθ, r'=r-RO (8). Next is α.

and find the recording constants (ρC, ρD, γ, δ). Therefore, as a condition for reducing aberrations, at a certain wavelength λ = λo,
Select so that Fij=0. That is, λ=λ0 and F2O=
0, F02=0, Ftsuo=0, F12=0,
(9) α by a total of five simultaneous equations, equations (7) and (9).

, ρC, ρD, γ, and δ can be obtained. Below is an example of solving the above simultaneous equations. The values in Example 1 and above are the best, but considering the aberrations that can be tolerated in practice, each of the above values is practically within the range of light if it is within the following range.

As described above, according to the present invention, it is possible to create a holographic plane diffraction grating with extremely small aberrations, which is suitable for Monk-Gilson mounting.

Furthermore, α obtained above. Aberrations can be further reduced by using the diffraction grating produced by the grating production apparatus of the present invention in a Monk-Gilson mounting apparatus that satisfies the relationships of , and (8).

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a perspective view of a Monk-Gilson mounting device, and FIG. 2 is a perspective view of a holographic plane diffraction grating production device. [Explanation of symbols of main parts], 3'...Photosensitive material (
Grid material), C, D... point light source.

Claims (1)

[Scope of Claims] 1. In an apparatus for creating a holographic flat diffraction grating for Monk-Gilson mounting, which includes a first light source, a second light source, and a photosensitive material for a flat diffraction grating, a reference point between the first light source and the photosensitive material is provided. The distance is r_c, the separation between the second light source and the reference point is r_d, the angle between the straight line connecting the first light source and the reference point and the normal to the reference point is γ, and the angle between the first light source and the reference point is γ. δ is the angle formed by the straight line connecting the second light source and the reference point and the normal line, R is the radius of curvature of the concave mirror of the mounting device, and is the sum of the incident angle and the diffraction angle of the diffraction grating of the mounting device. When α_0 is α_0 and the wavelength used by the mounting device is λ, when the optical path function F is expanded in terms of coordinates (ω, l) on the grating, ω, ω^2,
Coefficients F_1_0, F_2 of l^2, ω^3 and ωl^2
F_1_0=0 for _0, F_3_0 and F_1_2
and when λ=λ_0 (λ_0 is an arbitrary wavelength), F_2_0=F_0_2=F_3_0=F_1
Assuming _2=0, R/rc, R/rd, γ, δ and α_
0, and the photosensitive material and the first and second light sources are arranged so as to substantially satisfy the values of R/rc, R/rd, γ and δ. 2 Each of the above values α_0, R, rc, rd, γ, and δ are −
14°≦α_0≦−13°, 2.00≦R/rc≦2.
02, 1.78≦R/rd≦1.79, −6°≦γ≦−
5°, 10.7°≦δ≦11.8°, the holographic plane diffraction grating producing device according to claim 1, wherein the holographic plane diffraction grating production device satisfies the following. 3 The above values α_0, R, rc, rd, γ, and δ are −
19.5°≦α_0≦-18.5°, 1.88≦R/r
c≦1.90, 1.50≦R/rd≦1.52, -8°
The holographic plane diffraction grating production device according to claim 1, wherein the holographic plane diffraction grating production device satisfies ≦γ≦−6.8°, 8.8°≦δ≦10°.