Differential method for freeform optics applied to two-mirror off-axis telescope design

Jean-Baptiste Volatier; Guillaume Druart

doi:10.1364/OL.44.001174

Optics Letters
Vol. 44,
Issue 5,
pp. 1174-1177
(2019)
•https://doi.org/10.1364/OL.44.001174

Differential method for freeform optics applied to two-mirror off-axis telescope design

Jean-Baptiste Volatier and Guillaume Druart

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Jean-Baptiste Volatier and Guillaume Druart, "Differential method for freeform optics applied to two-mirror off-axis telescope design," Opt. Lett. 44, 1174-1177 (2019)

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Abstract

In this Letter, we present a method to design the freeform surfaces of an off-axis unobscured two-mirror telescope by integration of a system of differential equations. The system is derived from the differentiation of Fermat’s path principle and is integrated as an ordinary differential equation problem. The method is used to design the freeform surfaces of a telescope whose performance is verified in off-the-shelf optical design software (Zemax).

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Variable	Parabasal	Off-Axis
$P_{0, \dots, 3}$	set ^a	integrated ^b
$\partial Z_{1, 2}$	derived ^c	derived
$\partial P_{3}$	set or solved ^d	constant ^e
$\partial^{2} Z_{1, 2}$	solved ^f	integrated
$\partial^{3} Z_{1, 2}$	solved	solved
$\partial^{1, 2} w_{0, 1}$	derived	derived
$\partial w_{1}$	solved	integrated
$\partial^{2} w_{1}$	solved	solved
$\partial w_{3}$	set	integrated
$\partial^{2} w_{3}$	set	set or solved

Variable	Parabasal	Off-Axis
$P_{0, \dots, 3}$	set ^a	integrated ^b
$\partial Z_{1, 2}$	derived ^c	derived
$\partial P_{3}$	set or solved ^d	constant ^e
$\partial^{2} Z_{1, 2}$	solved ^f	integrated
$\partial^{3} Z_{1, 2}$	solved	solved
$\partial^{1, 2} w_{0, 1}$	derived	derived
$\partial w_{1}$	solved	integrated
$\partial^{2} w_{1}$	solved	solved
$\partial w_{3}$	set	integrated
$\partial^{2} w_{3}$	set	set or solved

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Equations (9)

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