Efficient approach to designing a Schmidt-Cassegrain objective for a remote sensing satellite

Tamer M. Tawfik

doi:10.1364/AO.48.006832

Applied Optics
Vol. 48,
Issue 35,
pp. 6832-6840
(2009)
•https://doi.org/10.1364/AO.48.006832

Efficient approach to designing a Schmidt–Cassegrain objective for a remote sensing satellite

Tamer M. Tawfik

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Tamer M. Tawfik, "Efficient approach to designing a Schmidt-Cassegrain objective for a remote sensing satellite," Appl. Opt. 48, 6832-6840 (2009)

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Abstract

This paper presents an efficient approach to designing a Schmidt–Cassegrain objective for a remote sensing satellite. The objective is required to have multispectral operational bands, with three spectral channels distributed along the range (0.5 to $0.9 μm$ ), as well as a panchromatic channel; $4 °$ field of view; distortion smaller than 0.3%; and a modulation transfer function, at $50 lines / mm$ spatial frequency, better than 0.5 and 0.35 at the center and edge of the field of view. The proposed design approach is based on Slyusarev’s theory of aberrations and optical design. An image quality index is formulated as a function of optical system component powers and axial distances. For each combination of parameters, there exists a possible solution that can be realized into a thin lens system by solving Seidel sum equations. The final design is then reached by a simple and quick optimization step. The best three designs are compared in terms of initial values of optical system parameters and final design specifications. The best system image quality is thoroughly analyzed. All three presented designs meet and exceed the required design specifications.

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		Solutions
	Parameters	A	B	C	Requirements
Initial Settings
	d	0.22	0.199	0.22
	$d_{1}$	0.11	0.106	0.12
	$d_{2}$	0.11	0.11	0.11
	$δ^{'}$	0.129	0.14	0.131
	$φ_{1}$	0.1	0.11	0.1
	$φ_{21}$	$- 5.9$	$- 6.1$	$- 6$
	$φ_{22}$	4.35	4	4.34
	k	0.34	0.357	0.36
Results
Back focal length		860	858	860	860
Max. distortion(%)		0.1	0.09	0.11	0.3
Overall length (mm)		367	366	366	370
FOV (deg.)		2	2	2	2
MTF
Panchromatic channel	Axial	0.62	0.59	0.62	0.5
Panchromatic channel	Off-axis	0.52	0.52	0.52	0.38
Channel I	Axial	0.67	0.63	0.69	0.5
Channel I	Off-axis	0.63	0.59	0.63	0.45
Channel II	Axial	0.64	0.62	0.64	0.5
Channel II	Off-axis	0.57	0.52	0.56	0.4
Channel III	Axial	0.55	0.52	0.55	0.4
Channel III	Off-axis	0.46	0.45	0.45	0.37
Strehl Ratio
Panchromatic channel	Axial	0.98	0.94	0.98
Panchromatic channel	Off-axis	0.78	0.8	0.81
Channel I	Axial	0.92	0.87	0.98
Channel I	Off-axis	0.94	0.89	0.96
Channel II	Axial	0.98	0.95	0.99
Channel II	Off-axis	0.97	0.92	0.96
Channel III	Axial	1	0.97	1
Channel III	Off-axis	0.98	0.95	0.96

	Variation %
	Solution A	Solution B	Solution C
$R_{Primary Mirror}$	10	7.7	8.5
$R_{Secondary Mirror}$	18.5	13.9	11.43
d	3.7	0.25	2.2
$d_{1}$	8.4	9	5.4
$d_{2}$	14	12.3	6.5
$δ^{'}$	14	6.7	23

	$S_{I}$	$S_{I I}$	$S_{I I I}$	$S_{I V}$	$S_{V}$	$S_{I chromatic}$	$S_{I I chromatic}$
Initial solution	$- 0.02817$	0.03954	0.03982	$- 0.02407$	1.11983	0.00328	$- 0.00085$
Final system	$- 0.00663$	0.04463	0.05414	$- 0.02903$	1.98471	0	0.00045

		Solutions
	Parameters	A	B	C	Requirements
Initial Settings
	d	0.22	0.199	0.22
	$d_{1}$	0.11	0.106	0.12
	$d_{2}$	0.11	0.11	0.11
	$δ^{'}$	0.129	0.14	0.131
	$φ_{1}$	0.1	0.11	0.1
	$φ_{21}$	$- 5.9$	$- 6.1$	$- 6$
	$φ_{22}$	4.35	4	4.34
	k	0.34	0.357	0.36
Results
Back focal length		860	858	860	860
Max. distortion(%)		0.1	0.09	0.11	0.3
Overall length (mm)		367	366	366	370
FOV (deg.)		2	2	2	2
MTF
Panchromatic channel	Axial	0.62	0.59	0.62	0.5
Panchromatic channel	Off-axis	0.52	0.52	0.52	0.38
Channel I	Axial	0.67	0.63	0.69	0.5
Channel I	Off-axis	0.63	0.59	0.63	0.45
Channel II	Axial	0.64	0.62	0.64	0.5
Channel II	Off-axis	0.57	0.52	0.56	0.4
Channel III	Axial	0.55	0.52	0.55	0.4
Channel III	Off-axis	0.46	0.45	0.45	0.37
Strehl Ratio
Panchromatic channel	Axial	0.98	0.94	0.98
Panchromatic channel	Off-axis	0.78	0.8	0.81
Channel I	Axial	0.92	0.87	0.98
Channel I	Off-axis	0.94	0.89	0.96
Channel II	Axial	0.98	0.95	0.99
Channel II	Off-axis	0.97	0.92	0.96
Channel III	Axial	1	0.97	1
Channel III	Off-axis	0.98	0.95	0.96

	Variation %
	Solution A	Solution B	Solution C
$R_{Primary Mirror}$	10	7.7	8.5
$R_{Secondary Mirror}$	18.5	13.9	11.43
d	3.7	0.25	2.2
$d_{1}$	8.4	9	5.4
$d_{2}$	14	12.3	6.5
$δ^{'}$	14	6.7	23

Abstract

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Figures (13)

Tables (3)

Equations (41)

Applied Optics