Design of a linear field-of-view oblique imaging system with a low
distortion

Chen Xu; Chen Gong; Yongtian Wang; Weitao Song

doi:10.1364/AO.456083

Applied Optics
Vol. 61,
Issue 17,
pp. 5189-5197
(2022)
•https://doi.org/10.1364/AO.456083

Design of a linear field-of-view oblique imaging system with a low distortion

Chen Xu, Chen Gong, Yongtian Wang, and Weitao Song

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Chen Xu, Chen Gong, Yongtian Wang, and Weitao Song, "Design of a linear field-of-view oblique imaging system with a low distortion," Appl. Opt. 61, 5189-5197 (2022)

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Abstract

For conventional ultra-wide-angle or oblique cameras, it is difficult to fully correct the $f - {\tan}\theta$ distortion without the scarification of the edge image performance. In this paper, we propose a linear field-of-view (FOV) oblique imaging system by varying the entrance pupil size over the FOV with freeform mirrors, and thus the diffraction limit around the edge field can be improved. An off-axis reflective system with conic surfaces has been selected as the initial system, and a point-by-point surface design method is then applied on the primary mirror to increase the entrance pupil size for edge fields in the FOV direction. All surfaces for the system converted to freeform during the optimization process, and the FOV of the final design can achieve ${+}{{35}}^\circ$ to ${+}{{65}}^\circ$, with a distortion less than 1.1%. It is possible to achieve a wide-linear FOV over 130° with a low distortion by the integration of two oblique systems and a central imaging channel.

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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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Surface	Type	Surface Para.	( $Y, Z$ ) Coord. (mm)	Tilt (°)
M1	Off-axis hyperboloid	$l_{1} = 150, l_{2} = 450, ω_{1} = 30^{\circ}$	(229.813, 192.836)	−100
M2	Plane	–	( $- 99.079$ . 312.543)	85
M3	Off-axis ellipsoid	$l_{3} = 300, l_{4} = 575, ω_{3} = 8^{\circ}$	(160.728, 462.543)	68
Image	Plane	–	( $- 86.254$ , 400.964)	76

Surface	( $Y, Z$ ) Coord. (mm)	Tilt (°)
M1	(176.374, 182.199)	−100.418
M2	(−156.377, 291.050)	85.344
M3	(154.238, 450.232)	72.323
Image	(−64.9767, 433.972)	91.477

Surface Parameters	M1	M2	M3
Radius	2104.876	9606.748	−7476.040
$k$	0	−19.2907	5.0892
$y$	$- 2.54710 \times 1 0^{- 4}$	0	$- 3.04199 \times 1 0^{- 2}$
$x^{2}$	$- 1.93826 \times 1 0^{- 3}$	$- 3.45181 \times 1 0^{- 6}$	$- 1.37040 \times 1 0^{- 3}$
$y^{2}$	$- 9.09005 \times 1 0^{- 4}$	$- 1.23739 \times 1 0^{- 4}$	$- 1.31756 \times 1 0^{- 3}$
$x^{2} y$	$- 6.99435 \times 1 0^{- 6}$	0	$4.80269 \times 1 0^{- 7}$
$y^{3}$	$3.39497 \times 1 0^{- 6}$	$1.43795 \times 1 0^{- 6}$	$6.58988 \times 1 0^{- 7}$
$x^{4}$	$5.12620 \times 1 0^{- 7}$	$1.02860 \times 1 0^{- 9}$	$- 1.01260 \times 1 0^{- 9}$
$x^{2} y^{2}$	$- 2.30696 \times 1 0^{- 8}$	$- 1.20229 \times 1 0^{- 8}$	$- 5.76250 \times 1 0^{- 9}$
$y^{4}$	$- 1.40492 \times 1 0^{- 8}$	$- 6.41951 \times 1 0^{- 9}$	$- 2.68956 \times 1 0^{- 9}$
$x^{4} y$	$9.44383 \times 1 0^{- 9}$	$- 2.29843 \times 1 0^{- 10}$	$3.24911 \times 1 0^{- 12}$
$x^{2} y^{3}$	$1.51468 \times 1 0^{- 10}$	$- 1.37215 \times 1 0^{- 10}$	$4.16001 \times 1 0^{- 12}$
$y^{5}$	$4.95480 \times 1 0^{- 11}$	$4.76706 \times 1 0^{- 11}$	$3.61123 \times 1 0^{- 12}$
$x^{6}$	0	0	$- 6.24675 \times 1 0^{- 15}$
$x^{4} y^{2}$	0	0	$- 7.20294 \times 1 0^{- 14}$
$x^{2} y^{4}$	0	0	$- 4.91628 \times 1 0^{- 14}$
$y^{6}$	0	0	$- 6.58997 \times 1 0^{- 15}$

Surface	Type	Surface Para.	( $Y, Z$ ) Coord. (mm)	Tilt (°)
M1	Off-axis hyperboloid	$l_{1} = 150, l_{2} = 450, ω_{1} = 30^{\circ}$	(229.813, 192.836)	−100
M2	Plane	–	( $- 99.079$ . 312.543)	85
M3	Off-axis ellipsoid	$l_{3} = 300, l_{4} = 575, ω_{3} = 8^{\circ}$	(160.728, 462.543)	68
Image	Plane	–	( $- 86.254$ , 400.964)	76

Surface	( $Y, Z$ ) Coord. (mm)	Tilt (°)
M1	(176.374, 182.199)	−100.418
M2	(−156.377, 291.050)	85.344
M3	(154.238, 450.232)	72.323
Image	(−64.9767, 433.972)	91.477

Abstract

Data availability

Cited By

Figures (9)

Tables (3)

Equations (7)

Applied Optics