Analytic aspheric coefficients to reduce the spherical aberration of lens elements used in collimated light

Gabriel Castillo-Santiago; Maximino Avendaño-Alejo; Rufino Díaz-Uribe; Luis Castañeda

doi:10.1364/AO.53.004939

Applied Optics
Vol. 53,
Issue 22,
pp. 4939-4946
(2014)
•https://doi.org/10.1364/AO.53.004939

Analytic aspheric coefficients to reduce the spherical aberration of lens elements used in collimated light

Gabriel Castillo-Santiago, Maximino Avendaño-Alejo, Rufino Díaz-Uribe, and Luis Castañeda

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Gabriel Castillo-Santiago, Maximino Avendaño-Alejo, Rufino Díaz-Uribe, and Luis Castañeda, "Analytic aspheric coefficients to reduce the spherical aberration of lens elements used in collimated light," Appl. Opt. 53, 4939-4946 (2014)

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Related Topics
Table of Contents Category
- Optical Design and Fabrication
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Geometric optical design (080.2740)
- Aberration expansions (080.1005)
- First-order optics (080.2468)
- Total internal reflection (260.6970)

About this Article
History
- Original Manuscript: May 7, 2014
- Manuscript Accepted: June 4, 2014
- Published: July 23, 2014

Abstract

We provide closed-form formulas for aspheric terms for either plano–convex or convex–plano aspheric lenses as functions of the paraxial parameters involved in the process of refraction. These formulas are obtained through an expansion in Taylor’s series from the exact caustic equation produced by aspheric lenses considering a plane wavefront propagating parallel to the optical axis and impinging on the refracting surface. A comparison of the aspheric coefficients obtained through our analytic formulas and commercial optical design software is presented, showing good agreement. This is useful in reducing spherical aberration.

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Equations (15)

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$A_{4} \times 10^{6}$	$A_{6} \times 10^{10}$	$A_{8} \times 10^{14}$	$A_{10} \times 10^{17}$	$A_{12} \times 10^{20}$	$A_{14} \times 10^{24}$	$A_{16} \times 10^{27}$
1.1796631	$- 2.9493795$	9.0581199	$- 3.1147917$	1.1475742	$- 4.4293081$	1.7678675

$A_{4} \times 10^{6}$	$A_{6} \times 10^{10}$	$A_{8} \times 10^{14}$	$A_{10} \times 10^{17}$	$A_{12} \times 10^{21}$	$A_{14} \times 10^{25}$	$A_{16} \times 10^{43}$
1.1795179	$- 2.9409532$	8.7763940	$- 2.6033925$	5.9914064	$- 7.5642811$	4.1062874

$A_{4} \times 10^{7}$	$A_{6} \times 10^{11}$	$A_{8} \times 10^{15}$	$A_{10} \times 10^{20}$	$A_{12} \times 10^{24}$	$A_{14} \times 10^{28}$	$A_{16} \times 10^{31}$
4.4278927	2.8715019	1.9201195	9.2124803	$- 1.6052264$	$- 5.863837$	$- 3.0821914$

$A_{4} \times 10^{7}$	$A_{6} \times 10^{11}$	$A_{8} \times 10^{15}$	$A_{10} \times 10^{20}$	$A_{12} \times 10^{24}$	$A_{14} \times 10^{27}$	$A_{16} \times 10^{31}$
4.4278977	2.8715802	1.9185578	9.2409282	$- 1.1134865$	$- 1.0370183$	$- 1.613004$

$A_{4} \times 10^{6}$	$A_{6} \times 10^{10}$	$A_{8} \times 10^{14}$	$A_{10} \times 10^{17}$	$A_{12} \times 10^{20}$	$A_{14} \times 10^{24}$	$A_{16} \times 10^{27}$
1.1796631	$- 2.9493795$	9.0581199	$- 3.1147917$	1.1475742	$- 4.4293081$	1.7678675

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