Initial design with confocal conic mirrors for freeform optical imaging systems

Linyue Fang; Hongzuo Chen; Ting Chen; Rengmao Wu; Rengmao Wu

doi:10.1364/AO.522603

Applied Optics
Vol. 63,
Issue 19,
pp. F11-F17
(2024)
•https://doi.org/10.1364/AO.522603

Initial design with confocal conic mirrors for freeform optical imaging systems

Linyue Fang, Hongzuo Chen, Ting Chen, and Rengmao Wu

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Linyue Fang, Hongzuo Chen, Ting Chen, and Rengmao Wu, "Initial design with confocal conic mirrors for freeform optical imaging systems," Appl. Opt. 63, F11-F17 (2024)

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Abstract

Freeform surfaces that can offer high degrees of freedom for aberration correction have been widely used in various imaging applications. Initial design is particularly critical in the optical design of freeform imaging systems due to the significantly expanded solution space. Here, we present a method to find an initial point for the optical design of four-mirror freeform imaging systems. The method is computationally simple, easily accessible, and theoretically supported. The effectiveness of the method is demonstrated by designing a four-mirror confocal system without field-constant aberration and linear astigmatism. We also generalize the proposed method to four-mirror confocal systems with “double-pass surface.” The proposed method can yield a promising starting point for the design of freeform off-axis imaging systems.

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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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Parameter	Specifications
Effective focal length	75 mm
Pupil diameter	10 mm
Field of view	$5 m m (H) \times 5 m m (V)$
Numerical Aperture	0.036
Magnification	−0.5

Parameter	$M_{1}$	$M_{2}$	$M_{3}$	$M_{4}$
$R / m m$	559.8076	242.9354	134.4099	197.8316
$K$	−23.3923	−0.0833	−0.1854	−0.0635
$l / m m$	150	230	180	250
$l^{'} / m m$	100	300	150	172.5
$m$	−0.6667	1.3043	0.8333	0.6900
$i /^{\circ}$	−15	15	−25	10.1263
$u /^{\circ}$	−11.9325	−101.2393	53.9683	−34.1091

Parameter	$M_{1}$	$M_{2}$	$M_{3}$	$M_{4}$
$R / m m$	264.9014	201.0019	97.9574	201.0019
$K$	−7.9579	−0.1067	−0.2865	−0.1067
$l / m m$	150	200	144.3119	236.8421
$l^{'} / m m$	73.8564	250	130.2635	213.1579
$m$	−0.4924	1.2500	0.9027	0.9000
$i /^{\circ}$	−17.4226	18	−32.2414	18.8302
$u /^{\circ}$	−11.3298	−90.8789	53.1211	−62.3961

Parameter	Specifications
Effective focal length	75 mm
Pupil diameter	10 mm
Field of view	$5 m m (H) \times 5 m m (V)$
Numerical Aperture	0.036
Magnification	−0.5

Parameter	$M_{1}$	$M_{2}$	$M_{3}$	$M_{4}$
$R / m m$	559.8076	242.9354	134.4099	197.8316
$K$	−23.3923	−0.0833	−0.1854	−0.0635
$l / m m$	150	230	180	250
$l^{'} / m m$	100	300	150	172.5
$m$	−0.6667	1.3043	0.8333	0.6900
$i /^{\circ}$	−15	15	−25	10.1263
$u /^{\circ}$	−11.9325	−101.2393	53.9683	−34.1091

Abstract

Data availability

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Figures (8)

Tables (3)

Equations (13)

Applied Optics