Focalization process of spherical concave diffraction gratings

• US 3,973,850 A
• Filed: 08/16/1974
• Issued: 08/10/1976
• Est. Priority Date: 04/21/1972
• Status: Expired due to Term

• Current Assignee: Agence Nationale de Valorisation de la Recherche (Bpifrance SA /Old/)
• Original Assignee: Agence Nationale de Valorisation de la Recherche (Bpifrance SA /Old/)
• Inventors: Pouey, Michel
• Primary Examiner(s): Stern, Ronald J.
• Application Number:
  US05/497,940
• Time in Patent Office: 725 Days
• Field of Search: 350/162 R, 350/3.5, 350/168, 356/79, 356/100, 356/101
• US Class Current: 356/334
• CPC Class Codes: G01J 3/1838 Holographic gratings
• CPC Class Codes: G01J 3/189 using at least one grating in an off-plane configuration
• CPC Class Codes: Y10S 359/90 Methods

Abstract

Spectrometric gratings formed by holographic techniques are disclosed. The gratings are employed in monochromator mounts of the type in which fixed entrance and exit slits are combined with simple rotation of the grating to scan the spectral range of interest, the angles of incidence and diffraction and the positions of the slits being so related that the mounts are characterized by improved optical performance due to phase balancing and improved focussing properties according both to geometrical and diffraction theories. The parameters involved in the holographic formation of the gratings, specifically the angularities and positions of the point sources forming the holographic image of the grating lines, are specifically related to the characteristics of the mount as to improve further their optical characteristics, particularly with respect to mounts either employing "normal" (i.e., relatively small) angles of incidence with large grating apertures or employing grazing incidence (i.e., for use in the far ultraviolet region).

Claims

1. The method of making a monochromator using a concave, reflective holographic grating, which comprises the steps of:

a. determining the physical parameters of the monochromator by using a concave classical reflective diffraction grating having straight, parallel lines which are equidistantly spaced to provide a line density 1/n, a height H₀ and a width W₀, the monochromator having fixed entrance and exit slits with the grating being mounted for rotation only with respect to said slits whereby to scan a spectral range of interest, said physical parameters being the positions of said entrance and exit slits with respect to the intersection of their optical axes at the center of the reflective surface of said grating, and said physical parameters being selected to provide a defect of focus which balances second order aberration terms excepting astigmatism whereby the partial derivative δ

F₁ /δ

w is equal to zero, F₁ being the optical path associated with said classical grating and w and h being Cartesian coordinates with respect to said center of the grating extending respectively perpendicular and parallel to said grating lines;

b. holographically forming a grating by locating two point sources of monochromatic light of wavelength λ

_o in the w plane passing through the center of a holographic blank having the concavity of said classical grating, such that said point sources are located by four position parameters which are the respective distances rc and rd of said point sources from said center of the holographic blank and the angles γ and

η

which lines from such point sources to said center respectively make with a line passing through such center and normal to said holographic blank, said four position parameters being established by four simultaneous equations the first of which is sinη

-sinγ

= nγ

₀ and the remaining three of which are determined on the basis of ##EQU34## and ##EQU35## and by cancelation of the two principal coma terms associated with the coma contribution of said point sources, F₁ as before being the optical path associated with said classical grating and F₂ being the optical path relative to said entrance and exit slits associated with said holographically formed grating; and

substituting the holographically formed grating for said classical grating.

2. The method as defined in claim 1 wherein said classical grating and said holographic blank are spherical, having a radius of curvature R;

the condition ##EQU36## establishing the relation;

##EQU37## where;

m is the order of diffraction

λ

is the wavelength of use

ρ

_c = R/r_c

ρ

_d = R/r_d

e = r/R where r is the distance along the optical axis from the entrance slit to the center of the grating

e'"'"' = r'"'"'/R where r'"'"' is the distance along the optical axis from the exit slit to the center of the grating

ρ

= 1/e

X_e = D₀₄ + D₄ where D₀₄ and D₄ are the aberration coefficients of w⁴ and h⁴ respectively due to said point sources, and

V_e = D₂₂ + 2D₄ where D₂₂ and D₄ are the aberration coefficients of w² h² and h⁴ respectively due to said point sources;

the condition ##EQU38## establishes the relation;

##EQU39## where;

α

is the angle between the optical axis from the entrance slit to the grating and the line normal to the center of the grating, and β

is the angle between the optical axis from the exit slit to the grating and said line.

3. The method as defined in claim 2 wherein said relations are combined in the form:

##EQU40## where f(λ

) = qnλ

_o, q being a constant such that;

##EQU41##

4. The method as defined in claim 2 wherein said relations are combined in the form ##EQU42## where f(λ

) = q'"'"'nλ

_o, q'"'"' having the value;

##EQU43## where λ

_i and λ

_f are two wavelengths for which astigmatism is corrected.

5. The method as defined in claim 4 wherein the two principal coma terms are corrected according to:

##EQU44## where C₀₃ and C₂₁ respectively are the aberration coefficients of H³ and W² H associated with the classical grating and D₀₃ and D₂₁ respectively are the aberration coefficients of H³ and W² H associated with said point sources, and λ

* is a wavelength within the spectrum of interest.

6. The method as defined in claim 3 wherein the two principal coma terms are corrected according to:

##EQU45## where C₀₃ and C₂₁ respectively are the aberration coefficients of H³ and W² H associated with the classical grating and D₀₃ and D₂₁ respectively are the aberration coefficients of H³ and W² H associated with said point sources, and λ

* is a wavelength within the spectrum of interest.

7. The method according to claim 2 wherein cancellation of the two principal coma terms is effected as follows:

##EQU46## where C₀₃ and C₂₁ respectively are the aberration coefficients of H³ and W² H associated with the classical grating and D₀₃ and D₂₁ respectively are the aberration coefficients of H³ and W² H associated with said point sources, and λ

* is a wavelength within the spectrum of interest.

8. A monochromator constructed according to the method of claim 1.

9. A monochromator constructed according to the method of claim 2.

10. A monochromator constructed according to the method of claim 3.

11. A monochromator constructed according to the method of claim 4.

12. A monochromator constructed according to the method of claim 5.

13. A monochromator constructed according to the method of claim 6.

14. A monochromator constructed according to the method of claim 7.