Wavefront aberration determination in non-axially symmetrical optical systems

Psang Dain Lin

doi:10.1364/JOSAA.510253

Journal of the Optical Society of America A
Vol. 41,
Issue 4,
pp. 674-685
(2024)
•https://doi.org/10.1364/JOSAA.510253

Wavefront aberration determination in non-axially symmetrical optical systems

Psang Dain Lin

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Psang Dain Lin, "Wavefront aberration determination in non-axially symmetrical optical systems," J. Opt. Soc. Am. A 41, 674-685 (2024)

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Abstract

Non-axially symmetrical optical systems can provide better solutions to several optical design problems. However, determining their wavefront aberrations is challenging due to the great diversity of their configurations. Accordingly, in the present study, the optical path length (OPL) between two boundaries in a non-axially symmetrical system is expanded by a Taylor series expansion with respect to the base ray. This expansion converts the OPL from a deep composite function to a polynomial form. The various order wavefront aberrations are then obtained from the coefficients of the polynomials in terms of the system independent variables. The proposed method is equally valid for axially symmetrical systems provided that the object is placed on the meridional plane. Overall, the method provides a systematic approach for analyzing the wavefront aberrations in a wide range of optical systems.

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Data availability

The author confirms that the data supporting the findings of this study are either available within the paper or can be obtained from the author upon reasonable request.

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Equations (93)

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	Radius $R_{i}$	Separation $s_{i}$	Refractive Index $ξ_{i}$
$i = 1$	33.7	3	1.638543
$i = 2$	0	8.3	1
$i = 3$	−37.8	1	1.603420
$i = 4$	37.8	3	1
$i = 5$	0	5.3	1
$i = 6$	0	3	1. 638543
$i = 7$	−30.9	12	1
$i = 8$	0	15	1
$i = 9$	$R_{9}$	$s_{9}$	1
$i = 10$	0		1

	Results from	Proposed
	Zemax	Method	% Error
spherical aberration W040	−3.102870	−3.102867	0.00%
coma W131	−0.612456	−0.612456	0.00%
astigmatism W222	0.644711	0.644711	0.00%
field curvature W220S	−0.1262	−0.126226	0.00%
distortion W311	0.041378	0.041378	0.00%

$g_{0010} = 0.000058 υ_{0}$	$g_{0001} = 0.000010 υ_{0}$	$g_{1010} = - 5.688554 υ_{0}$	$g_{1001} = 0.000000 υ_{0}$	$g_{0110} = 0.000000 υ_{0}$
$g_{0101} = - 0.000006 υ_{0}$	$g_{0020} = - 1.289051 υ_{0}$	$g_{0011} = 0.000000 υ_{0}$	$g_{0002} = 0.000003 υ_{0}$	$g_{2010} = - 0.001437 υ_{0}$
$g_{2001} = 0.000000 υ_{0}$	$g_{1110} = 0.000000 υ_{0}$	$g_{1101} = 0.000084 υ_{0}$	$g_{1020} = - 0.000738 υ_{0}$	$g_{1011} = 0.000000 υ_{0}$
$g_{1002} = 0.000142 υ_{0}$	$g_{0210} = 0.001629 υ_{0}$	$g_{0201} = 0.000000 υ_{0}$	$g_{0120} = 0.000000 υ_{0}$	$g_{0111} = - 0.007544 υ_{0}$
$g_{0102} = 0.000000 υ_{0}$	$g_{0030} = - 0.024011 υ_{0}$	$g_{0021} = 0.000000 υ_{0}$	$g_{0012} = - 0.012807 υ_{0}$	$g_{0003} = 0.000000 υ_{0}$
$g_{3010} = - 0.009871 υ_{0}$	$g_{3001} = 0.000000 υ_{0}$	$g_{2110} = 0.000000 υ_{0}$	$g_{2101} = - 0.007191 υ_{0}$	$g_{2020} = 0.004746 υ_{0}$
$g_{2011} = 0.000000 υ_{0}$	$g_{2002} = 0.001101 υ_{0}$	$g_{1210} = - 0.004942 υ_{0}$	$g_{1201} = 0.000000 υ_{0}$	$g_{1120} = 0.000000 υ_{0}$
$g_{1111} = 0.004936 υ_{0}$	$g_{1102} = 0.000000 υ_{0}$	$g_{1030} = - 0.000126 υ_{0}$	$g_{1021} = 0.000000 υ_{0}$	$g_{1012} = 0.000031 υ_{0}$
$g_{1003} = 0.000000 υ_{0}$	$g_{0310} = 0.000000 υ_{0}$	$g_{0301} = 0.000006 υ_{0}$	$g_{0220} = - 0.000007 υ_{0}$	$g_{0211} = 0.000000 υ_{0}$
$g_{0202} = 0.000019 υ_{0}$	$g_{0130} = 0.000000 υ_{0}$	$g_{0121} = - 0.000235 υ_{0}$	$g_{0112} = 0.000000 υ_{0}$	$g_{0103} = - 0.000087 υ_{0}$
$g_{0040} = - 0.000728 υ_{0}$	$g_{0031} = 0.000000 υ_{0}$	$g_{0022} = - 0.001132 υ_{0}$	$g_{0013} = 0.000000 υ_{0}$	$g_{0004} = - 0.000505 υ_{0}$

	Radius $R_{i}$	Separation $s_{i}$	Refractive Index $ξ_{i}$
$i = 1$	33.7	3	1.638543
$i = 2$	0	8.3	1
$i = 3$	−37.8	1	1.603420
$i = 4$	37.8	3	1
$i = 5$	0	5.3	1
$i = 6$	0	3	1. 638543
$i = 7$	−30.9	12	1
$i = 8$	0	15	1
$i = 9$	$R_{9}$	$s_{9}$	1
$i = 10$	0		1

	Results from	Proposed
	Zemax	Method	% Error
spherical aberration W040	−3.102870	−3.102867	0.00%
coma W131	−0.612456	−0.612456	0.00%
astigmatism W222	0.644711	0.644711	0.00%
field curvature W220S	−0.1262	−0.126226	0.00%
distortion W311	0.041378	0.041378	0.00%

Abstract

Data availability

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Figures (4)

Tables (3)

Equations (93)

Journal of the Optical Society of America A