Borders of spot diagrams are always caustic surfaces and/or marginal rays

Alberto Cordero-Dávila; Diego Gabriel Reyes-Olguín; Jorge González-García

doi:10.1364/AO.435850

Applied Optics
Vol. 61,
Issue 6,
pp. C20-C26
(2022)
•https://doi.org/10.1364/AO.435850

Borders of spot diagrams are always caustic surfaces and/or marginal rays

Alberto Cordero-Dávila, Diego Gabriel Reyes-Olguín, and Jorge González-García

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Alberto Cordero-Dávila, Diego Gabriel Reyes-Olguín, and Jorge González-García, "Borders of spot diagrams are always caustic surfaces and/or marginal rays," Appl. Opt. 61, C20-C26 (2022)

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About this Article
History
- Original Manuscript: July 2, 2021
- Revised Manuscript: September 14, 2021
- Manuscript Accepted: September 21, 2021
- Published: October 11, 2021
Virtual Issues
Applied Optics Radiography, Applied Optics and Data Science (2022)

Abstract

In this paper, it is proven that for any optical system with a circular exit pupil and wavefronts affected by any aberrations, the borders of all leaving rays are caustic surfaces and/or marginal rays. Several examples are shown for wavefronts affected by linear combinations of Zernike aberrations.

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Number	Meaning	Orthonormal Zernike Polynomial
1	Piston	1
2	Tilt about $y$	$2 x$
3	Tilt about $x$	$2 y$
4	Defocus	$\sqrt{3} (2 x^{2} + 2 y^{2} - 1)$
5	Primary astigmatism 45°	$2 \sqrt{6} x y$
6	Primary astigmatism 0°	$\sqrt{6} (x^{2} - y^{2})$
7	Primary coma about $y$	$\sqrt{8} y (3 x^{2} + 3 y^{2} - 2)$
8	Primary coma about $x$	$\sqrt{8} x (3 x^{2} + 3 y^{2} - 2)$
9	Trefoil about $y$	$\sqrt{8} y (3 x^{2} - y^{2})$
10	Trefoil about $x$	$\sqrt{8} x (x^{2} - 3 y^{2})$
11	Primary spherical	$\sqrt{5} (6 {(x^{2} + y^{2})}^{2} - 6 (x^{2} + y^{2}) + 1)$
12	Secondary astigmatism at 0°	$\sqrt{10} (4 x^{4} - 4 y^{4} - 3 x^{2} + 3 y^{2})$
13	Secondary astigmatism at 45°	$2 \sqrt{10} (4 x^{3} y - 4 x y^{3} - 3 x y)$
14	Vertical quatrefoil	$\sqrt{10} [{(x^{2} + y^{2})}^{2} - 8 x^{2} y^{2}]$
15	Oblique quatrefoil	$4 \sqrt{10} x y (x^{2} - y^{2})$

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Applied Optics