Optimization method for ultra-wide-angle and panoramic optical systems

Li-Jun Lu; Xiao-Yan Hu; Cui-Yuan Sheng

doi:10.1364/AO.51.003776

Optimization method for ultra-wide-angle and panoramic optical systems

Li-Jun Lu, Xiao-Yan Hu, and Cui-Yuan Sheng

Applied Optics
Vol. 51,
Issue 17,
pp. 3776-3786
(2012)
•https://doi.org/10.1364/AO.51.003776

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Li-Jun Lu, Xiao-Yan Hu, and Cui-Yuan Sheng, "Optimization method for ultra-wide-angle and panoramic optical systems," Appl. Opt. 51, 3776-3786 (2012)

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Related Topics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Aberrations (global) (080.1010)
- Geometric optical design (080.2740)
- Computation methods (080.1753)
- Algorithms (150.1135)
- Systems design (220.4830)

About this Article
History
- Original Manuscript: October 13, 2011
- Revised Manuscript: December 12, 2011
- Manuscript Accepted: December 17, 2011
- Published: June 6, 2012

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Abstract

To an ultra-wide-angle and panoramic optical system, the aberrations of point object at any field angle are separated into two types: the aperture-ray aberrations of off-axis point object and the chief-ray aberrations. A simple form of the triangular formulae of tracing an oblique-incidence ray is derived to calculate the chief-ray parameters and their aberrations; moreover, the aperture-ray aberrations of an off-axis point object are analyzed with the plane-symmetric aberration theory. Based on the two types of aberrations, we present a merit function for ultra-wide-angle and panoramic optical systems; the optimization program with the differential-evolution algorithm is then developed. To validate the optimization method we finally optimize a fish-eye lens and a catadioptric omnidirectional imaging system.

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Surface # $i$	Radius ( $R_{i}$ )		Spacing ( $d_{i}$ )		Index	Glass
Surface # $i$	Ref. Design	Our Result	Ref. Design	Our Result	Index	Glass
0					1.0	Air
1	54.45	52.4	1.60	1.61	1.6986	N-LAK14
2	18.256	18.7	13.86	13.9	1.0	Air
3	74.25	74.1	1.40	1.30	1.6986	N-LAK14
4	14.0	13.1	18.81	19.8	1.0	Air
5	16.483	16.43	3.374	2.5	1.6727	N-SF5
6	81.18	80.2	9.0	10.0	1.0	Air
7	Stop aperture		2.35	2.30	1.0	Air
8	48.51	47.31	3.572	3.6	1.48656	N-FK51
9	$- 8.306$	$- 8.5$	1.782	1.80	1.80518	SFL6
10	$- 16.39$	$- 16.4$	37.22	37.93	1.0	Air

# $i$		1	2	3	4	5
Field angle $ω_{0 (i)}$		10°	25°	40°	55°	80°
$Q_{x (i)} (mm)$	Ref. design	9.4	10.7	13.4	18.1	36.6
$Q_{x (i)} (mm)$	Our result	7.2	7.1	7.8	11.5	33.6
$Q_{y (i)} (mm)$	Ref. design	9.3	9.9	11.0	12.8	18.7
$Q_{y (i)} (mm)$	Our result	7.2	7.2	7.2	7.6	11.7
$Q_{c (i)} (mm)$	Ref. design	0.41	1.2	2.6	6.2	23.6
$Q_{c (i)} (mm)$	Our result	5.2	12.1	15.7	11.9	31.7
$Q_{i}^{2} {(mm)}^{2}$ a	Ref. design	0.175	0.214	0.307	0.530	2.246
$Q_{i}^{2} {(mm)}^{2}$ a	Our result	0.131	0.248	0.359	0.331	2.271
$\sum_{i} Q_{i}^{2} {(mm)}^{2}$	Ref. design	3.47
$\sum_{i} Q_{i}^{2} {(mm)}^{2}$	Our result	3.34

	Radius ( $R_{i}$ )		Spacing ( $d_{i}$ )
Surface $# i$	Ref. Design	Our Result	Ref. Design	Our Result	Index	Glass
0					1.0	Air
1	7.238	7.30	3.203	3.10	1.5168	BK7
2	13.71	13.67	0.894	0.8333	1.0	Air
3	$- 17.21$	$- 17.30$	2.0	1.967	1.5168	BK7
4	3.887	3.90	3.207	3.30	1.0	Air
5	Stop aperture		0.198	0.1	1.0	Air
6	$- 27.52$	$- 27.46$	2.0	2.10	1.5168	BK7
7	6.612	6.357	4.64	4.70	1.4978	BK3
8	$- 6.648$	$- 6.566$	0.1	0.08	1.0	Air
9	22.81	22.67	3.205	3.30	1.5168	BK7
10	$- 20.27$	$- 20.27$	20.752	20.044	1.0	Air

	$S_{1}$	$a_{1}$	$a_{2}$
Our result	52.28	99.53	0.30
Ref. design	52.47	99.62	0.349

$# i$		1	2	3	4	5
Field angle $ω_{0 (i)}$		$25^{°}$	$37^{°}$	$48^{°}$	$65^{°}$	$80^{°}$
$Q_{x (i)} (mm)$	Ref. design	5.13	6.40	10.16	18.51	27.13
$Q_{x (i)} (mm)$	Our result	4.18	6.98	9.48	18.6	26.3
$Q_{y (i)} (mm)$	Ref. design	5.77	5.45	6.0	8.88	12.82
$Q_{y (i)} (mm)$	Our result	3.60	4.44	6.0	9.5	13.53
$Q_{s (i)}$	Ref. design	0.86	0.84	0.82	0.77	0.72
$Q_{s (i)}$	Our result	0.82	0.80	0.78	0.73	0.68
$Q_{c (i)} (mm)$	Ref. design	19.8	29.4	38.2	51.6	63
$Q_{c (i)} (mm)$	Our result	19.1	28.3	36.7	49.5	60.3
$Q_{i}^{2} {(mm)}^{2}$ a	Ref. design	0.452	0.936	1.60	3.084	4.870
$Q_{i}^{2} {(mm)}^{2}$ a	Our result	0.396	0.870	1.473	2.887	4.511
$\sum_{i} Q_{i}^{2} (mm)^{2}$	Ref. design	10.942
$\sum_{i} Q_{i}^{2} (mm)^{2}$	Our result	10.137

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