Algebraic ray trace analysis of spatial heterodyne spectrometers

John M. Harlander; John M. Harlander

doi:10.1364/AO.486840

Applied Optics
Vol. 62,
Issue 16,
pp. 4288-4300
(2023)
•https://doi.org/10.1364/AO.486840

Algebraic ray trace analysis of spatial heterodyne spectrometers

John M. Harlander

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John M. Harlander, "Algebraic ray trace analysis of spatial heterodyne spectrometers," Appl. Opt. 62, 4288-4300 (2023)

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- Instrumentation and Measurements
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About this Article
History
- Original Manuscript: February 3, 2023
- Revised Manuscript: April 23, 2023
- Manuscript Accepted: April 26, 2023
- Published: May 24, 2023

Abstract

Algebraic ray traces of various configurations of spatial heterodyne spectrometers are developed to derive general, approximate, formulas for resolving the power, fringe localization plane, and admissible off-axis angle for each configuration. Michelson, all-reflective, and field-widened configurations are considered separately. The derived formulas for each configuration are tested against exact numerical ray traces using optical design software and in general found to be in good agreement.

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Parameters	$σ_{0}$ ( ${c m}^{- 1}$ )	$1 / a$ (l/mm)	$θ_{2} = - θ_{1}$ (deg)	$x_{m a x}$ (mm)
Input	18,181.8	1000	15.96	10
Output	$R = σ / δ σ$	$z_{L o c}$ (mm)	$β_{m a x}$ (rad)	$ϕ_{m a x}$ (rad)
Analytic	41,600	0	0.00693	0.00693
ZEMAX	41,600	0	0.00693	0.00693

Parameter	$σ_{0}$ ( ${c m}^{- 1}$ )	$1 / a$ (l/mm)	$1 / a^{'}$ (l/mm)	$θ$ (deg)	$θ^{'}$ (deg)	$x_{m a x}$ (mm)	$d$ (mm)
Conf 4 A,4B	20,000	1000	1000	30	30	10	80
Conf 4C	20,000	500	1000	−14.48	30	10	133.81
Output		$R = σ / δ σ$	$z_{L o c}$ (mm)	$β_{m a x}$ (rad)		$ϕ_{m a x}$ (rad)
Conf 4 A,4B	Analytic	80,000	−53.33	0.00433		0.00500
	ZEMAX	80,000	−53.33	0.00433		0.00500
Conf 4C	Analytic	21,100	$+ 144.34$	0.00921		0.00951
	ZEMAX	21,100	$+ 144.34$	0.00921		0.00951

Parameter	$σ_{0}$ ( ${c m}^{- 1}$ )	$1 / a$ (l/mm)	$θ_{2} = - θ_{1}$ (deg)	Prism	$n$	$α$ (deg)	$η$ (deg)	$x_{m a x}$ (mm)
Input	18,181.8	1000	15.96	N-Bk7	1.51852	18.331	13.998	10
Output	$R = σ / δ σ$		$z_{L o c}$ (mm)		$β_{m a x}$ (rad)		$ϕ_{m a x}$ (rad)
Analytic	42940		−66.3		0.061		−0.061
ZEMAX	42980		−66.1		0.061		−0.062

Parameter	$σ_{0}$ ( ${c m}^{- 1}$ )	$1 / a$ (l/mm)	$θ_{2} = - θ_{1}$ (deg)	Prism	$n$	$α$ (deg)	$η$ (deg)	$x_{m a x}$ (mm)
Input	18,181.8	1000	15.96	N-Bk7	1.51852	18.256	10.635	10
Output	$R = σ / δ σ$		$z_{L o c}$ (mm)		$β_{m a x}$ (rad)		$ϕ_{m a x}$ (rad)
Analytic	42940		−66.4		0.074		−0.074
ZEMAX	42270		−66.6		0.064		−0.096

Parameter	$σ_{0}$ ( ${c m}^{- 1}$ )	$1 / a$ (l/mm)	$θ_{2} = - θ_{1}$ (deg)	Prism	$n$	$α$ (deg)	$η$ (deg)	$x_{m a x}$ (mm)
Input	18,181.8	1000	15.96	ZnS	2.38616	8.054	3.559	10
Output	$R = σ / δ σ$		$z_{L o c}$ (mm)		$β_{m a x}$ (rad)		$ϕ_{m a x}$ (rad)
Analytic	47790		−64.2		0.182		0.182
ZEMAX	46570		−64.8		0.134		0.135

Abstract

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Equations (54)

Applied Optics