Rigorously aplanatic Descartes ovoids

Alberto Silva-Lora; Rafael Torres

doi:10.1364/JOSAA.422809

Journal of the Optical Society of America A
Vol. 38,
Issue 8,
pp. 1160-1169
(2021)
•https://doi.org/10.1364/JOSAA.422809

Rigorously aplanatic Descartes ovoids

Alberto Silva-Lora and Rafael Torres

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Alberto Silva-Lora and Rafael Torres, "Rigorously aplanatic Descartes ovoids," J. Opt. Soc. Am. A 38, 1160-1169 (2021)

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Abstract

It is known that, besides being stigmatic, spherical refracting surfaces are aplanatic at their Young points since they satisfy the Abbe sine condition rigorously. The Abbe sine condition is commonly applied to different optical systems using numerical methods or optimization processes, obtaining a design of approximately aplanatic systems. Here, we found several families of Cartesian surfaces, whose sets of each of these families constitute exactly aplanatic systems free of spherical aberration and coma. So, studying the different types of systems, it is found that rigorous aplanatism occurs for objects and images on curved surfaces.

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Data Availability

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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$k$	$ζ_{k}$	$n_{k}$	$n_{k + 1}$	$d_{k}$	$d_{k + 1}$	$G_{k}$	$O_{k}$	$T_{k}$	$S_{k}$
0	0	1	1.48656	$- 30$	$- \infty$	−2.20986	0.06850	0	0
1	15	1.48656	1	$- \infty$	45	−2.20986	−0.06850	0	0

$k$	$ζ_{k}$	$n_{k}$	$n_{k + 1}$	$d_{k}$	$d_{k + 1}$	$G_{k}$	$O_{k}$	$T_{k}$	$S_{k}$
0	0	−40.00	−74.01	1.00	1.85	$\infty$	0	$- 3.25 e - 6$	$5.72 e - 4$
1	10	−74.01	−35.40	1.85	1.00	$\infty$	0	$- 2.22 e - 6$	$4.44 e - 4$

$k$	$ζ_{k}$	$n_{k}$	$n_{k + 1}$	$d_{k}$	$d_{k + 1}$	$G_{k}$	$O_{k}$	$T_{k}$	$S_{k}$
0	0	−40.00	−18.87	1.00	1.45	0	−0.11	$4.99 e - 5$	0
1	10	−18.87	−51.20	1.45	1.00	0	−0.07	$1.39 e - 5$	0

$k$	$ζ_{k}$	$n_{k}$	$n_{k + 1}$	$d_{k}$	$d_{k + 1}$	$G_{k}$	$O_{k}$	$T_{k}$	$S_{k}$
0	0	1	1.48656	$- 30$	$- \infty$	−2.20986	0.06850	0	0
1	15	1.48656	1	$- \infty$	45	−2.20986	−0.06850	0	0

$k$	$ζ_{k}$	$n_{k}$	$n_{k + 1}$	$d_{k}$	$d_{k + 1}$	$G_{k}$	$O_{k}$	$T_{k}$	$S_{k}$
0	0	−40.00	−74.01	1.00	1.85	$\infty$	0	$- 3.25 e - 6$	$5.72 e - 4$
1	10	−74.01	−35.40	1.85	1.00	$\infty$	0	$- 2.22 e - 6$	$4.44 e - 4$

Abstract

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Equations (56)

Journal of the Optical Society of America A