Aberration considerations in lens tolerancing

Eric Herman; Jose Sasian

doi:10.1364/AO.53.000341

Applied Optics
Vol. 53,
Issue 3,
pp. 341-346
(2014)
•https://doi.org/10.1364/AO.53.000341

Aberration considerations in lens tolerancing

Eric Herman and Jose Sasian

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Eric Herman and Jose Sasian, "Aberration considerations in lens tolerancing," Appl. Opt. 53, 341-346 (2014)

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Abstract

Often the tolerancing of an optical system is performed by treating the optical system as a black box in which the designer sets tolerances for perturbations and then runs a Monte Carlo analysis to determine the as-built performance. When the effects of the perturbations are not considered, the tolerances might result tighter than necessary, proper compensation might be missed, and manufacturing cost can be increased. By acquiring aberration sensitivity for each type of perturbation, an optical engineer can increase tolerances by ad hoc compensation. An aberration sensitivity evaluation can be performed quickly and can be incorporated into the initial lens design phase. A lens designer can find what surfaces or elements within the optical system will be problematic before any time-consuming Monte Carlo run is performed. In this paper we use aberration theory of plane symmetric systems to remove, to some useful extent, the black-box tolerancing approach and to provide some insights into tolerancing. The tolerance sensitivities that are analyzed are with respect to surface tilt, center thickness, index value, and radius. To analyze these perturbations, exact wavefront calculations are performed for the following aberrations: uniform astigmatism, uniform coma, linear astigmatism, distortion I, distortion II, spherical aberration, linear coma, quadratic astigmatism, and cubic distortion. We provide a discussion about how the aberration tolerancing analysis is useful.

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Wavefront Coefficient	Functional Form	Aberration Name
$W_{02002}$	$(i \cdot ρ) (i \cdot ρ)$	Uniform astigmatism
$W_{11011}$	$(i \cdot H) (i \cdot ρ)$	Anamorphism
$W_{20020}$	$(i \cdot H) (i \cdot H)$	Quadratic piston
$W_{21110}$	$(H \cdot ρ) (i \cdot H)$	Quadratic distortion II (smile)
$W_{12010}$	$(ρ \cdot ρ) (i \cdot H)$	Field tilt
$W_{30010}$	$(H \cdot H) (i \cdot H)$	Cubic piston
$W_{12101}$	$(H \cdot ρ) (i \cdot ρ)$	Linear astigmatism
$W_{03001}$	$(ρ \cdot ρ) (i \cdot ρ)$	Uniform coma
$W_{21001}$	$(H \cdot H) (i \cdot ρ)$	Quadratic distortion I (keystone)
$W_{22200}$	$(H \cdot ρ) (H \cdot ρ)$	Quadratic astigmatism
$W_{13100}$	$(ρ \cdot ρ) (H \cdot ρ)$	Linear coma
$W_{31100}$	$(H \cdot H) (H \cdot ρ)$	Cubic distortion
$W_{04000}$	$(ρ \cdot ρ) (ρ \cdot ρ)$	Spherical aberration
$W_{22000}$	$(H \cdot H) (ρ \cdot ρ)$	Field curvature
$W_{40000}$	$(H \cdot H) (H \cdot H)$	Quartic piston

Tolerance Type	Tolerance Value
Surface tilt	1amin
Center thickness variation	$\pm 50 μm$
Index variation	$\pm 0.0005$
Radius variation	$\pm 0.2 %$

	A	B	C	D	E	F	G	H	I	J
Spherical aberration	1.070	1.084	1.295	1.428	1.136	1.135	1.088	1.974	2.815	1.411
Linear coma	1.438	1.565	0.614	1.478	0.792	1.322	1.305	1.651	1.716	1.309
Quadratic astigmatism	0.362	0.428	0.938	0.670	0.242	0.494	0.282	0.474	0.867	0.229
Uniform coma	0.201	0.266	0.166	0.314	0.178	0.181	0.184	0.222	0.640	0.435
Uniform astigmatism	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Linear astigmatism	0.132	0.116	0.098	0.053	0.068	0.086	0.114	0.084	0.115	0.087
Cubic distortion	0.636	0.637	1.158	1.263	0.629	0.719	0.807	1.187	1.394	0.625
Distortion I	0.747	0.756	0.786	0.824	1.104	0.795	0.939	0.971	1.324	1.316
Distortion II	0.006	0.006	0.003	0.004	0.007	0.007	0.006	0.005	0.004	0.005
Perturbed RMS WFE	0.044	0.042	0.062	0.050	0.057	0.048	0.053	0.119	0.090	0.045
Nominal RMS WFE	0.095	0.084	0.080	0.109	0.033	0.054	0.059	0.041	0.148	0.080

Wavefront Coefficient	Functional Form	Aberration Name
$W_{02002}$	$(i \cdot ρ) (i \cdot ρ)$	Uniform astigmatism
$W_{11011}$	$(i \cdot H) (i \cdot ρ)$	Anamorphism
$W_{20020}$	$(i \cdot H) (i \cdot H)$	Quadratic piston
$W_{21110}$	$(H \cdot ρ) (i \cdot H)$	Quadratic distortion II (smile)
$W_{12010}$	$(ρ \cdot ρ) (i \cdot H)$	Field tilt
$W_{30010}$	$(H \cdot H) (i \cdot H)$	Cubic piston
$W_{12101}$	$(H \cdot ρ) (i \cdot ρ)$	Linear astigmatism
$W_{03001}$	$(ρ \cdot ρ) (i \cdot ρ)$	Uniform coma
$W_{21001}$	$(H \cdot H) (i \cdot ρ)$	Quadratic distortion I (keystone)
$W_{22200}$	$(H \cdot ρ) (H \cdot ρ)$	Quadratic astigmatism
$W_{13100}$	$(ρ \cdot ρ) (H \cdot ρ)$	Linear coma
$W_{31100}$	$(H \cdot H) (H \cdot ρ)$	Cubic distortion
$W_{04000}$	$(ρ \cdot ρ) (ρ \cdot ρ)$	Spherical aberration
$W_{22000}$	$(H \cdot H) (ρ \cdot ρ)$	Field curvature
$W_{40000}$	$(H \cdot H) (H \cdot H)$	Quartic piston

Tolerance Type	Tolerance Value
Surface tilt	1amin
Center thickness variation	$\pm 50 μm$
Index variation	$\pm 0.0005$
Radius variation	$\pm 0.2 %$

Abstract

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Applied Optics