Astigmatism-free Czerny–Turner spectrometer with a low f-number by a bicylinder lens

Qian Zhou; Zhiyong Zou

doi:10.1364/AO.470322

Applied Optics
Vol. 61,
Issue 27,
pp. 7985-7990
(2022)
•https://doi.org/10.1364/AO.470322

Astigmatism-free Czerny–Turner spectrometer with a low f-number by a bicylinder lens

Qian Zhou and Zhiyong Zou

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Qian Zhou and Zhiyong Zou, "Astigmatism-free Czerny–Turner spectrometer with a low f-number by a bicylinder lens," Appl. Opt. 61, 7985-7990 (2022)

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Abstract

A modified optical design for a broadband astigmatism-corrected Czerny–Turner spectrometer with high resolution and large throughput is presented. The theory of astigmatism correction is analyzed with the use of a bicylinder lens with different radii of curvature in tangential and sagittal planes. The optical performances of a modified spectrometer and two traditional spectrometers are compared in detail. The results show that the modified Czerny–Turner spectrometer can obtain superior astigmatism-free performance, an $f$-number of 2.5, and spectral resolution of 1.5 nm in 350–750 nm. Its volume decreases by approximately 77% compared with a traditional spectrometer with the same $f$-number.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter	Value
$F$ -number	2.5
Wave band	350–750 nm
Spectral resolution	$< 1.5 n m$
Slit	25 µm
Bicylinder lens	$R_{F} = 5.1 m m$ , $R_{2} = - 8.3 m m$
Collimating mirror	$R_{M 1} = 105 m m$ , $α = {6.5}^{\circ}$
Focusing mirror	$R_{M 2} = 143 m m$ , $β = {12.5}^{\circ}$
Grating	600 l/mm, $i = 24^{\circ}$ , $θ = {4.4}^{\circ}$
Lateral off-axis air distance of slit	7 mm

Parameters	Initial	Optimized
$l_{SB}$ (mm)	5.53	5.13
$l_{M_{1} M_{2}}$ (mm)	47.12	47.63
$θ_{D}$ (°)	0	7.3
$l_{M_{3} D}$ (mm)	60.92	61.34

Surface Tolerance	Value
Radius	$\pm 0.02 m m$
Decenter in $x$	$\pm 0.02 m m$
Decenter in $y$	$\pm 0.02 m m$
Tilt in $x$	$\pm {0.04}^{\circ}$
Tilt in $y$	$\pm {0.04}^{\circ}$
S $+$ A irregularity	0.2 fringes
Element Tolerance	Value
Decenter in $x$	$\pm 0.02 m m$
Decenter in $y$	$\pm 0.02 m m$
Tilt in $x$	$\pm {0.04}^{\circ}$
Tilt in $y$	$\pm {0.04}^{\circ}$
Index Tolerances	Value
Index	0.001
Abbe	1%

Tolerance	Decrease in MTF
TABB (tolerance of Abbe or $V_{d}$ number) of bicylinder lens	0.038
TETX (tolerance of tilt in elements about $x$ axis) of bicylinder lens	0.029
TTHI (tolerance of thickness) between bicylinder lens and collimating mirror	0.043
TRAD (tolerance of radius) of front surface of bicylinder lens	0.045
TRAD (tolerance of radius) of back surface of bicylinder lens	0.047

Parameter	Value
$F$ -number	2.5
Wave band	350–750 nm
Spectral resolution	$< 1.5 n m$
Slit	25 µm
Bicylinder lens	$R_{F} = 5.1 m m$ , $R_{2} = - 8.3 m m$
Collimating mirror	$R_{M 1} = 105 m m$ , $α = {6.5}^{\circ}$
Focusing mirror	$R_{M 2} = 143 m m$ , $β = {12.5}^{\circ}$
Grating	600 l/mm, $i = 24^{\circ}$ , $θ = {4.4}^{\circ}$
Lateral off-axis air distance of slit	7 mm

Abstract

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Tables (4)

Equations (9)

Applied Optics