Easy-aligned off-axis three-mirror system with wide field of view using freeform surface based on integration of primary and tertiary mirror

Qingyu Meng; Wei Wang; Hongcai Ma; Jihong Dong

doi:10.1364/AO.53.003028

Applied Optics
Vol. 53,
Issue 14,
pp. 3028-3034
(2014)
•https://doi.org/10.1364/AO.53.003028

Easy-aligned off-axis three-mirror system with wide field of view using freeform surface based on integration of primary and tertiary mirror

Qingyu Meng, Wei Wang, Hongcai Ma, and Jihong Dong

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Qingyu Meng, Wei Wang, Hongcai Ma, and Jihong Dong, "Easy-aligned off-axis three-mirror system with wide field of view using freeform surface based on integration of primary and tertiary mirror," Appl. Opt. 53, 3028-3034 (2014)

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Abstract

An off-axis three-mirror system (OTS) was designed based on the primary mirror and tertiary mirror (TM) integrated on a single substrate in order to solve the OTS drawbacks, such as the alignment difficulty and the large opto-mechanical weight. Furthermore, an optical freeform surface that can increase the optimizing degrees of freedom (DOF) was applied on the TM in order to achieve a wide field of view (FOV). An example with a focal length of 1200 mm, F-number of 12, and FOV of $10 ° \times 4 °$ was given, and the maximum wave front error (WFE) RMS was $0.0126 λ$ , indicating a good imaging quality. The design result shows that the number of alignment DOF was reduced from 12 to 6, and the weight of the mirror support assembly can also be lighter. An XY polynomial, established as an even function of x, was employed as the TM surface, so we obtained an axial symmetrical imaging quality about the $x$ axis, and the axial symmetry aberration performance also brings considerable convenience to alignment and testing for the OTS.

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					Aspheric Surface High-Order Term
	Surface Type	Radius (mm)	Distance (mm)	Conic	6th	8th	10th	Mirror Size (mm)
PM	Even Asphere	$- 1489.4$	$- 406.8$	$- 1.7402$	$- 6.0274 e - 17$	$6.7990 e - 22$	$- 5.2044 e - 27$	$260 \times 200$
SM	Conic	$- 624$	$- 406.8$	$- 1.8983$				$Φ 50$
TM	XY Polynomial	$- 1489.4$	$- 600$	$- 1.7402$				$213 \times 145$

No.	Item	Coefficient $A_{i j}$	No.	Item	Coefficient $A_{i j}$	No.	Item	Coefficient $A_{i j}$	No.	Item	Coefficient $A_{i j}$
1	$X^{1} Y^{0}$	0	10	$X^{4} Y^{0}$	$- 5.0680 e - 011$	19	$X^{1} Y^{4}$	0	28	$X^{7} Y^{0}$	0
2	$X^{0} Y^{1}$	$3.7014 e - 009$	11	$X^{3} Y^{1}$	0	20	$X^{0} Y^{5}$	$- 2.0290 e - 013$	29	$X^{6} Y^{1}$	$- 9.1690 e - 019$
3	$X^{2} Y^{0}$	$- 1.3710 e - 004$	12	$X^{2} Y^{2}$	$- 2.9650 e - 010$	21	$X^{6} Y^{0}$	$6.2147 e - 016$	30	$X^{5} Y^{2}$	0
4	$X^{1} Y^{1}$	0	13	$X^{1} Y^{3}$	0	22	$X^{5} Y^{1}$	0	31	$X^{4} Y^{3}$	$3.9609 e - 018$
5	$X^{0} Y^{2}$	$- 1.3790 e - 004$	14	$X^{0} Y^{4}$	$- 1.6180 e - 010$	23	$X^{4} Y^{2}$	$1.6520 e - 015$	32	$X^{3} Y^{4}$	0
6	$X^{3} Y^{0}$	0	15	$X^{5} Y^{0}$	0	24	$X^{3} Y^{3}$	0	33	$X^{2} Y^{5}$	$- 2.3490 e - 017$
7	$X^{2} Y^{1}$	$- 9.1300 e - 009$	16	$X^{4} Y^{1}$	$1.1878 e - 013$	25	$X^{2} Y^{4}$	$- 1.0610 e - 014$	34	$X^{1} Y^{6}$	0
8	$X^{1} Y^{2}$	0	17	$X^{3} Y^{2}$	0	26	$X^{1} Y^{5}$	0	35	$X^{0} Y^{7}$	$5.4357 e - 018$
9	$X^{0} Y^{3}$	$- 1.5630 e - 008$	18	$X^{2} Y^{3}$	$- 2.0540 e - 012$	27	$X^{0} Y^{6}$	$1.5116 e - 015$	36	$X^{8} Y^{0}$	$- 3.0140 e - 020$

FOV	( $0 °, - 4 °$ )	( $0 °, - 6 °$ )	( $0 °, - 8 °$ )	( $2.5 °, - 4 °$ )	( $2.5 °, - 6 °$ )
WFE (RMS)	$0.0115 λ$	$0.0084 λ$	$0.0114 λ$	$0.0088 λ$	$0.0127 λ$
FOV	( $2.5 °, - 8 °$ )	( $5 °, - 4 °$ )	( $5 °, - 6 °$ )	( $5 °, - 8 °$ )
WFE (RMS)	$0.0122 λ$	$0.0109 λ$	$0.0136 λ$	$0.0144 λ$

FOV	( $0 °, - 4 °$ )	( $0 °, - 6 °$ )	( $0 °, - 8 °$ )	( $2.5 °, - 4 °$ )	( $2.5 °, - 6 °$ )
Rad. Dist. (%)	$- 0.19$	$- 0.21$	$- 0.07$	$- 0.2$	$- 0.35$
Tan. Dist. (%)	0	0	0	0.1	$- 0.01$
FOV	( $2.5 °, - 8 °$ )	( $5 °, - 4 °$ )	( $5 °, - 6 °$ )	( $5 °, - 8 °$ )
Rad. Dist. (%)	$- 0.37$	$- 0.02$	$- 0.44$	$- 0.92$
Tan. Dist. (%)	$- 0.25$	0.34	0.34	0.06

	Manufacturing Tolerance			Alignment Tolerance
	Shape error $RMS (λ)$	Radius (mm)	Conic	Decenter (mm)	Tilt (″)
PM	1/80	$\pm 0.75$	$\pm 0.0005$	reference for alignment
SM	1/80	$\pm 0.3$	$\pm 0.0005$	$\pm 0.05$	$\pm 20$
TM	1/80	$\pm 0.75$	$\pm 0.0005$	reference for alignment

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Applied Optics