Imaging spectrometer with single component of freeform concave grating

Benqi Zhang; Yilin Tan; Guofan Jin; Jun Zhu

doi:10.1364/OL.431975

Optics Letters
Vol. 46,
Issue 14,
pp. 3412-3415
(2021)
•https://doi.org/10.1364/OL.431975

Imaging spectrometer with single component of freeform concave grating

Benqi Zhang, Yilin Tan, Guofan Jin, and Jun Zhu

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Benqi Zhang, Yilin Tan, Guofan Jin, and Jun Zhu, "Imaging spectrometer with single component of freeform concave grating," Opt. Lett. 46, 3412-3415 (2021)

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Abstract

In this Letter, an imaging spectrometer in which a freeform concave grating is the only optical component in the system is introduced. The degrees of freedom of optical freeform surfaces and a variable line-spacing (VLS) grating are used to realize imaging spectrometers. A point-by-point system design method is proposed that can generate a good initial solution rapidly. By exploring the limitations of the system specifications, it is demonstrated that the spectral dispersion, spectral resolving power, and system length can be improved significantly by using the freeform VLS concave grating. It is also found that freeform surfaces with higher degrees of freedom than a toroid can further improve system performance when using a VLS grating.

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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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System No.	Grating Line-Spacing	Spectral Band (nm)	Spectral Dispersion (nm/mm)	Slit Length (mm)	Numerical Aperture	System Length (mm)	Spectral Resolving Power
1	Constant	400–1000	340	1.0	0.10	100	482
2			340	Up to 2.1	0.10	100	—
3		$\binom{}{600 - 1000}$	340	1.0	Up to 0.13	100	627
4			340	1.0	0.10	Down to 61	—
5	$\binom{}{Constant}$		Limited by 240	1.0	0.10	100	683
6			340	Up to 1.6	0.10	100	—
7		$\binom{}{400 - 800}$	340	1.0	Up to 0.11	100	530
8			340	1.0	0.10	Down to 73	—
9			Limited by 260	1.0	0.10	100	631
10			340	Up to 1.8	0.10	100	—
11		$\binom{}{400 - 1000}$	340	1.0	Up to 0.14	100	675
12			340	1.0	0.10	Down to 52	—
13			Limited by 140	1.0	0.10	100	1171
14			340	Up to 2.3	0.10	100	—
15	$\binom{}{Variable}$	$\binom{}{600 - 1000}$	340	1.0	Up to 0.16	100	771
16			340	1.0	0.10	Down to 37	—
17			Limited by 100	1.0	0.10	100	1639
18			340	Up to 1.8	0.10	100	—
19		$\binom{}{400 - 800}$	340	1.0	Up to 0.14	100	675
20			340	1.0	0.10	Down to 52	—
21			Limited by 120	1.0	0.10	100	1366

Spectral Band (nm)	Spectral Dispersion	Slit Length	Numerical Aperture	System Length	Spectral Resolving Power
400–1000	143%	80%	40%	92%	143%
600–1000	140%	10%	23%	65%	140%
400–800	117%	12%	27%	40%	117%

Grating Line-Spacing	Initial Spectral Band (nm)	Spectral Dispersion	Slit Length	Numerical Aperture	System Length	Spectral Resolving Power
CLS	$\binom{}{600 - 1000}$	$- 42 %$	$- 110 %$	$- 30 %$	$- 64 %$	$- 42 %$
VLS	$\binom{}{600 - 1000}$	$- 40 %$	$- 28 %$	$- 14 %$	$- 41 %$	$- 40 %$
CLS	$\binom{}{400 - 800}$	$- 31 %$	$- 60 %$	$- 10 %$	$- 37 %$	$- 31 %$
VLS	$\binom{}{400 - 800}$	$- 17 %$	$- 0 %$	$- 0 %$	$- 0 %$	$- 17 %$

System No.	Grating Line-Spacing	Spectral Band (nm)	Spectral Dispersion (nm/mm)	Slit Length (mm)	Numerical Aperture	System Length (mm)	Spectral Resolving Power
1	Constant	400–1000	340	1.0	0.10	100	482
2			340	Up to 2.1	0.10	100	—
3		$\binom{}{600 - 1000}$	340	1.0	Up to 0.13	100	627
4			340	1.0	0.10	Down to 61	—
5	$\binom{}{Constant}$		Limited by 240	1.0	0.10	100	683
6			340	Up to 1.6	0.10	100	—
7		$\binom{}{400 - 800}$	340	1.0	Up to 0.11	100	530
8			340	1.0	0.10	Down to 73	—
9			Limited by 260	1.0	0.10	100	631
10			340	Up to 1.8	0.10	100	—
11		$\binom{}{400 - 1000}$	340	1.0	Up to 0.14	100	675
12			340	1.0	0.10	Down to 52	—
13			Limited by 140	1.0	0.10	100	1171
14			340	Up to 2.3	0.10	100	—
15	$\binom{}{Variable}$	$\binom{}{600 - 1000}$	340	1.0	Up to 0.16	100	771
16			340	1.0	0.10	Down to 37	—
17			Limited by 100	1.0	0.10	100	1639
18			340	Up to 1.8	0.10	100	—
19		$\binom{}{400 - 800}$	340	1.0	Up to 0.14	100	675
20			340	1.0	0.10	Down to 52	—
21			Limited by 120	1.0	0.10	100	1366

Spectral Band (nm)	Spectral Dispersion	Slit Length	Numerical Aperture	System Length	Spectral Resolving Power
400–1000	143%	80%	40%	92%	143%
600–1000	140%	10%	23%	65%	140%
400–800	117%	12%	27%	40%	117%

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Optics Letters