Design of Compact and Broadband Imaging Spectrometer Based on Free-Form Surface

Jizhou Han; Shijia Zhao; Anwei Feng; Xingyun Zhang; Yiqun Ji

doi:10.3788/AOS230474

Acta Optica Sinica, Volume. 43, Issue 14, 1422002(2023)

Design of Compact and Broadband Imaging Spectrometer Based on Free-Form Surface

Jizhou Han^1,2,3, Shijia Zhao^1,2,3, Anwei Feng^1,2,3, Xingyun Zhang^1,2,3, and Yiqun Ji^1,2,3、*

Author Affiliations

¹School of Optoelectronic Science and Engineering, Soochow University, Suzhou 215006, Jiangsu, China

²Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Suzhou 215006, Jiangsu, China

³Collaborarive Innovation Center of Suzhou Nano Science and Technology & Engineering Research Center of Digital Imaging and Display, Ministry of Education, Suzhou 215006, Jiangsu, China

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Figures & Tables(13)

Fig. 1. Schematic diagram of optical path of Offner imaging spectrometer

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Fig. 2. Schematic diagram of pupil shift . (a) Schematic diagram of pupil shift in off-axis field; (b) schematic diagram of pupil shift for dispersion

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Fig. 3. Diagram of expression function of astigmatism coefficient introduced by Zernike terms. (a) Functional diagram of coefficient expressions introduced into Z₆ by Z₉ term; (b) functional diagram of coefficient expressions introduced into Z₆ by Z₁₇ term; (c) functional diagram of coefficient expressions introduced into Z₅ by Z₉ term; (d) functional diagram of coefficient expressions introduced into Z₅ by Z₁₇ term

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Fig. 4. Structure diagram of dual-band Offner imaging spectrometer

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Fig. 5. Zernike astigmatism of system when designing with individual different Zernike terms for M₃ mirror

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Fig. 6. Image point RMS radii for full wavelength bands of imaging spectrometer. (a) M₃ is designed as a free-form surface; (b) M₃ is designed as a spherical surface; (c) M₃ is designed as a spherical surface and system size is enlarged by approximately three times

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Fig. 7. MTF at different wavelengths of imaging spectrometer. (a) 400 nm; (b) 1450 nm; (c) 2500 nm

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Fig. 8. Smiles and keystones in two bands of imaging spectrometer. (a) Smiles for VNIR; (b) keystones for VNIR; (c) smiles for SWIR; (d) keystones for SWIR

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Table 1. Fringe Zernike polynomial

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Table 1. Fringe Zernike polynomial

Term	Zernike polynomial	Term	Zernike polynomial	Term	Zernike polynomial
Z₁	1	Z₇	$(3 ρ^{3} - 2 ρ) c o s ϕ$	Z₁₃	$(4 ρ^{4} - 3 ρ^{2}) s i n (2 ϕ)$
Z₂	$ρ c o s ϕ$	Z₈	$(3 ρ^{3} - 2 ρ) s i n ϕ$	Z₁₄	$(10 ρ^{5} - 12 ρ^{3} + 3 ρ) c o s ϕ$
Z₃	$ρ s i n ϕ$	Z₉	$6 ρ^{4} - 6 ρ^{2} + 1$	Z₁₅	$(10 ρ^{5} - 12 ρ^{3} + 3 ρ) s i n ϕ$
Z₄	$2 ρ^{2} - 1$	Z₁₀	$ρ^{3} c o s (3 ϕ)$	Z₁₆	$20 ρ^{6} - 30 ρ^{4} + 12 ρ^{2} - 1$
Z₅	$ρ^{2} c o s (2 ϕ)$	Z₁₁	$ρ^{3} s i n (3 ϕ)$	Z₁₇	$ρ^{4} c o s (4 ϕ)$
Z₆	$ρ^{2} s i n (2 ϕ)$	Z₁₂	$(4 ρ^{4} - 3 ρ^{2}) c o s (2 ϕ)$	Z₁₈	$ρ^{4} s i n (4 ϕ)$

Table 2. Astigmatism generated by different Zernike terms

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Table 2. Astigmatism generated by different Zernike terms

Zernike term added on surface	Generated Zernike astigmatism
Zernike term added on surface	Z₅	Z₆
M₅Z₅	$M_{5} Z_{5}$	—
M₈Z₈	$- 3 Δ h_{λ y} M_{8} Z_{5}$	$3 Δ h_{H x} M_{8} Z_{6}$
M₉Z₉	$(12 Δ h_{_{H x}}^{2} - 12 Δ h_{_{λ y}}^{2}) M_{9} Z_{5}$	$24 Δ h_{H x} Δ h_{λ y} M_{9} Z_{6}$
M₁₁Z₁₁	$3 Δ h_{λ y} M_{11} Z_{5}$	$3 Δ h_{H x} M_{11} Z_{6}$
M₁₂Z₁₂	$(12 Δ h_{_{H x}}^{2} + 12 Δ h_{_{λ y}}^{2}) M_{12} Z_{5}$	—
M₁₇Z₁₇	$(6 Δ h_{_{H x}}^{2} - 6 Δ h_{_{λ y}}^{2}) M_{17} Z_{5}$	$- 12 Δ h_{H x} Δ h_{λ y} M_{17} Z_{6}$

Table 3. Specifications of Offner imaging spectrometer
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Table 3. Specifications of Offner imaging spectrometer
Parameter Value Unit
Wavelength for VNIR 400-1000 nm
Wavelength for SWIR 1000-2500 nm
Numerical aperture 0.143
Length of slit 14 mm
Spectral channel ≥589
Spectral resolution 2.8/4 nm
Volume 42×82×100 mm³

Table 4. Basic parameters of system
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Table 4. Basic parameters of system
Element Curvature radius /mm Distance /mm Tilt angle /（°）
Entrance slit — 98.67 0
M₁ $-$ 101.62 $-$ 51.83 $-$ 8.59
M₂（diffraction grating） $-$ 51.41 42.93 0
M₃ $-$ 95.37 $-$ 72.94 13.14
Filter — $-$ 18.81 45
Image plane — — 0

Table 5. Coefficient of Zernike terms in M₃
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Table 5. Coefficient of Zernike terms in M₃
Term Z₈ Z₁₁ Z₁₂
Coefficient 5.3287×10^-4 $-$ 2.8874×10^-4 4.5452×10^-5

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Jizhou Han, Shijia Zhao, Anwei Feng, Xingyun Zhang, Yiqun Ji. Design of Compact and Broadband Imaging Spectrometer Based on Free-Form Surface[J]. Acta Optica Sinica, 2023, 43(14): 1422002

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