Design of freeform mirrors in Czerny-Turner spectrometers to suppress astigmatism

Li Xu; Kexin Chen; Qingsheng He; Guofan Jin

doi:10.1364/AO.48.002871

Applied Optics
Vol. 48,
Issue 15,
pp. 2871-2879
(2009)
•https://doi.org/10.1364/AO.48.002871

Design of freeform mirrors in Czerny–Turner spectrometers to suppress astigmatism

Li Xu, Kexin Chen, Qingsheng He, and Guofan Jin

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Li Xu, Kexin Chen, Qingsheng He, and Guofan Jin, "Design of freeform mirrors in Czerny-Turner spectrometers to suppress astigmatism," Appl. Opt. 48, 2871-2879 (2009)

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Abstract

Astigmatism is left uncorrected in traditional Czerny–Turner spectrometers with spherical mirrors, which leads to low throughput of modern instruments applying line-array detectors. By gradually varying the sagittal curvature, freeform mirrors are introduced to suppress astigmatism for a wide wavelength range simultaneously. So as not to reduce spectrum resolution, further calculations of the light path are performed for extra coma compensation. A design example is presented with optimized parameters. The ray-tracing result has revealed a reduction in sagittal spot size from several hundred micrometers to around $10 μm$ in the wavelength range from $200 nm$ to $800 nm$ .

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Parameter	Value	Parameter	Value
Wavelength range ( $λ_{min} - λ_{max}$ )	$200 nm - 800 nm$	Design Wavelength (λ)	$500 nm$
$M_{1}$		$M_{2}$
$R_{1}$	$100.00 mm$	$R_{2}$	$150.00 mm$
α	$10.00 °$	$β_{- 500}$	$23.47 °$
Grating
$α_{g}$	$5.00 °$	Groove	$600 / mm$
$β_{g - 500}$	$22.78 °$	Grating size	$10 mm \times 10 mm$
Distance between Elements
$S - O_{1}$	$49.24 mm$	$O_{1} - O_{g}$	$55.00 mm$
$O_{g} - O_{2}$	$49.09 mm$	$O_{2} - O_{p}$	$68.70 mm$

Wavelength (nm)	RMS Spot X $S ize (μm)$	RMS Spot Y $S ize (μm)$
800	27.1	10.6
650	14.7	13.2
500	8.4	12.4
350	16.5	8.7
200	27.5	11.9

$Wavelength / nm$	(a) Spherical		(b) Toroidal		(c) $q = 0$
$Wavelength / nm$	$X / μm$	$Y / μm$	$X / μm$	$Y / μm$	$X / μm$	$Y / μm$
800	32.5	325.0	30.1	331.4	74.0	53.9
650	18.1	438.4	16.8	164.6	65.3	57.4
500	7.1	559.1	5.0	7.8	59.5	60.2
350	14.4	687.4	14.0	142.3	57.4	62.7
200	27.6	823.9	28.6	283.6	59.3	66.4

Parameter	Value	Parameter	Value
Wavelength range ( $λ_{min} - λ_{max}$ )	$200 nm - 800 nm$	Design Wavelength (λ)	$500 nm$
$M_{1}$		$M_{2}$
$R_{1}$	$100.00 mm$	$R_{2}$	$150.00 mm$
α	$10.00 °$	$β_{- 500}$	$23.47 °$
Grating
$α_{g}$	$5.00 °$	Groove	$600 / mm$
$β_{g - 500}$	$22.78 °$	Grating size	$10 mm \times 10 mm$
Distance between Elements
$S - O_{1}$	$49.24 mm$	$O_{1} - O_{g}$	$55.00 mm$
$O_{g} - O_{2}$	$49.09 mm$	$O_{2} - O_{p}$	$68.70 mm$

Wavelength (nm)	RMS Spot X $S ize (μm)$	RMS Spot Y $S ize (μm)$
800	27.1	10.6
650	14.7	13.2
500	8.4	12.4
350	16.5	8.7
200	27.5	11.9

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Applied Optics