Use of the plate diagram in the fast evaluation of monochromators and spectrographs

Juan M. Simon; Mirta A. Gil; Angela N. Fantino

doi:10.1364/AO.27.004062

Use of the plate diagram in the fast evaluation of monochromators and spectrographs

Juan M. Simon, Mirta A. Gil, and Angela N. Fantino

Applied Optics
Vol. 27,
Issue 19,
pp. 4062-4068
(1988)
•https://doi.org/10.1364/AO.27.004062

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Juan M. Simon, Mirta A. Gil, and Angela N. Fantino, "Use of the plate diagram in the fast evaluation of monochromators and spectrographs," Appl. Opt. 27, 4062-4068 (1988)

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History
- Original Manuscript: July 22, 1987
- Published: October 1, 1988

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Abstract

In this work we show a geometrical method—the unified plate diagram—which makes it possible to estimate simply and rapidly the dependence of image sharpness aberrations (spherical, coma, and astigmatism) on the basic design parameters of plane grating spectrographic systems. We also present analytical equations with the help of which additional parameters may be adjusted, such as off-axis relations, position, and form of the focal surface.

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CONFIG.	SPHER. AB.	COMA	ASTIGMATISM
	∑Γ_i	CENTER	EDGE	CENTER	EDGE
	∑Γ_i	∑Γ_i ξ_0i	∑Γ_i l_i	(−4f/Ꝋ²) ∑Γ_i ξ_0i²	(−4f/Ꝋ) ∑Γ_i ξ_0il_i	(−4f)∑Γ_il_i²
Z₁	$- \frac{1}{16 f^{3}}$	$- \frac{α_{D}^{'} (λ)}{16 f^{2}} (1 - \frac{D}{2 f})$	—	$1 - \frac{α_{D}^{'} (λ)}{Θ} (1 - \frac{D}{2 f}) + \frac{f}{2} {[\frac{α_{D}^{'} (λ)}{Θ} (1 - \frac{D}{2 f})]}^{2}$	$1 - \frac{D}{2 f} - \frac{1}{2} \frac{α_{D}^{'} (λ)}{Ꝋ} {(1 - \frac{D}{2 f})}^{2}$	${(1 - \frac{D}{f})}^{2}$
Z₂	—	$- \frac{α_{D}^{'} (λ)}{16 f^{2}}$	—	$1 - \frac{α_{D}^{'} (λ)}{Ꝋ} (1 - \frac{D}{2 f}) + \frac{1}{2} {(\frac{α_{D}^{'} (λ)}{Ꝋ})}^{2} (1 - \frac{D}{f})$	$1 - \frac{D}{2 f} - \frac{1}{2} \frac{α_{D}^{'} (λ)}{Ꝋ} (1 - \frac{D}{f})$	$1 - \frac{D}{f}$
Z₃	—	$- \frac{α_{D}^{'} (λ)}{16 f^{2}}$	—	$1 - {(\frac{Δ {ϕ_{v}}^{D}}{2 Ꝋ f})}^{2} - \frac{α_{D}^{'} (λ)}{Ꝋ} [1 - \frac{D}{2 f} (1 + \frac{Δ {ϕ_{v}}^{D}}{2 Ꝋ f})] + \frac{1}{2} {(\frac{α_{D}^{'} (λ)}{Ꝋ})}^{2} (1 - \frac{D}{f})$	$1 - \frac{D}{2 f} (1 + \frac{Δ {ϕ_{v}}^{D}}{2 Ꝋ f}) - \frac{1}{2} \frac{α_{D}^{'} (λ)}{Ꝋ} (1 - \frac{D}{f})$	$1 - \frac{D}{f}$
U₄	—	$- \frac{α_{D}^{'} (λ)}{16 f^{2}}$	—	$\frac{α_{D}^{'} (λ)}{Ꝋ} + \frac{1}{2} {(\frac{α_{D}^{'} (λ)}{Ꝋ})}^{2} (1 - \frac{D}{f})$	$- \frac{1}{2} \frac{α_{D}^{'} (λ)}{Ꝋ} (1 - \frac{D}{f})$	$1 - \frac{D}{f}$

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