Abstract

In this paper, a novel method is proposed to design the freeform off-axis reflective imaging systems. A special algorithm is demonstrated to calculate the data points on the unknown freeform surface using the rays from multiple fields and different pupil coordinates. These points are used to construct the multiple three-dimensional freeform surfaces in an imaging system which works for a certain object size and a certain width of light beam. An unobscured design with freeform surfaces can be obtained directly with this method, and it can be taken as a good starting point for further optimization. The benefit of this design method is demonstrated by designing a freeform off-axis three-mirror imaging system with high performance and system specifications. The final system operates at F/1.49 with a 64mm entrance pupil diameter and an 8° × 9° field-of-view (FOV). The performance of the system is diffraction limited at LWIR (long-wavelength-infrared).

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013

2012

2011

2010

D. Cheng, Y. Wang, H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[CrossRef]

2009

2008

2007

2005

2002

J. M. Rodgers, “Unobscured mirror designs,” Proc. SPIE 4832, 33–60 (2002).
[CrossRef]

2001

J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8(4), 281–283 (2001).
[CrossRef]

1949

G. D. Wassermann, E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Benítez, P.

Cheng, D.

D. Cheng, Y. Wang, H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[CrossRef]

Duerr, F.

Fuerschbach, K.

Hicks, R. A.

Hou, J.

J. Hou, H. Li, Z. Zheng, X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285(6), 986–991 (2012).
[CrossRef]

Hua, H.

D. Cheng, Y. Wang, H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[CrossRef]

Infante, J.

Jin, G.

Li, H.

J. Hou, H. Li, Z. Zheng, X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285(6), 986–991 (2012).
[CrossRef]

Lin, W.

Liu, X.

J. Hou, H. Li, Z. Zheng, X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285(6), 986–991 (2012).
[CrossRef]

Luo, Y.

Meuret, Y.

Miñano, J. C.

Muñoz, F.

Qian, K.

Rodgers, J. M.

J. M. Rodgers, “Unobscured mirror designs,” Proc. SPIE 4832, 33–60 (2002).
[CrossRef]

Rolland, J. P.

Rubinstein, J.

J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8(4), 281–283 (2001).
[CrossRef]

Santamaría, A.

Thienpont, H.

Thompson, K. P.

Wang, L.

Wang, Y.

D. Cheng, Y. Wang, H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[CrossRef]

Wassermann, G. D.

G. D. Wassermann, E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Wolansky, G.

J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8(4), 281–283 (2001).
[CrossRef]

Wolf, E.

G. D. Wassermann, E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Yang, T.

Zheng, Z.

J. Hou, H. Li, Z. Zheng, X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285(6), 986–991 (2012).
[CrossRef]

Zhu, J.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

J. Hou, H. Li, Z. Zheng, X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285(6), 986–991 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8(4), 281–283 (2001).
[CrossRef]

Proc. Phys. Soc. B

G. D. Wassermann, E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Proc. SPIE

J. M. Rodgers, “Unobscured mirror designs,” Proc. SPIE 4832, 33–60 (2002).
[CrossRef]

D. Cheng, Y. Wang, H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010).
[CrossRef]

Other

J. M. Rodgers, “Aberrations of unobscured reflective optical systems,” Ph.D. Thesis, University of Arizona (1983).

W. B. Wetherell and D. A. Womble, “All-reflective three element objective,” U.S. Patent 4,240,707 (23 December, 1980).

R. N. Wilson, Reflecting Telescope Optics (Springer, 2000).

J. W. Figoski, W. H. Taylor and D. T. Moore, eds., “Aberration characteristics of nonsymmetric systems,” in 1985 International Optical Design Conference, W. H. Taylor and D. T. Moore, eds. (SPIE, 1985), pp. 104–111.

Code V Reference Manual, Synopsys Inc. (2012).

D. Knapp, “Conformal optical design,” Ph.D. Thesis, University of Arizona (2002).

O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics (Wiley-VCH, 2006).

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Figures (12)

Fig. 1
Fig. 1

Two basic ways of defining the feature rays of each field for circular aperture. (a) The polar ray grids. (b) The rectangular ray grids. Each point denotes a different pupil coordinate.

Fig. 2
Fig. 2

The two neighboring surfaces Ω' and Ω of the unknown surface Ω. The red ray stands for the feature ray Ri corresponding to the data point Pi. The intersection of the ray with surface Ω' and Ω are defined as the start point Si and the end point Ei of the feature ray respectively. (a) The case when there are other surfaces between Ω and the image plane (also shown in (c)). (b) The case when Ω” is the image plane. (c) The case when Ω is the first surface of the system.

Fig. 3
Fig. 3

For two points on an optical surface: P and another point Q in the small neighborhood of P, Q is approximately on the tangential plane of P.

Fig. 4
Fig. 4

The method to calculate the data point Pi+1. (a) The way to find the next feature ray Ri+1. (b) When didi', Qi+1 is taken as the next data point Pi+1. (c) When di>di', Q'i+1 is taken as the next data point Pi+1. In order to make this figure more clearly, the tangential planes of the data point are not plotted in (b) and (c). The purple dotted lines represent the distances between the data points and the intersections of the tangential planes with the feature rays. The yellow points represent the data points which have been calculated before Pi.

Fig. 5
Fig. 5

The flow diagram of the calculation process.

Fig. 6
Fig. 6

An example of the calculation for 13 unknown feature data points corresponding to 13 feature rays. Each blue point denotes an unused feature ray. The yellow points represent the feature rays which have been used already. The red point denotes the next feature ray to be used.

Fig. 7
Fig. 7

The layout of the initial system with three planes.

Fig. 8
Fig. 8

The layouts of the systems with one, two and three freeform surfaces, which are respectively shown in (a), (b) and (c).

Fig. 9
Fig. 9

The effect of the proposed method. (a) The comparison of the average RMS spot diameter between the systems with one, two and three freeform surfaces. (b) The distortion grid of the system with three freeform surfaces.

Fig. 10
Fig. 10

Optical layout of the final system after optimization.

Fig. 11
Fig. 11

MTF plots of the system at LWIR. (a) Center fields. (b) Marginal fields.

Fig. 12
Fig. 12

(a) The RMS wavefront error of the system. (b) The distortion grid.

Tables (1)

Tables Icon

Table 1 Specifications of the freeform off-axis three-mirror system.

Equations (5)

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r i '× N i = r i × N i ,
T(K)= i=1 K1 i(Ki )= 1 6 K 3 1 6 K=O( K 3 ).
N i = r i ' r i | r i ' r i | .
T(K)= i=1 K1 Ki+i 1= (K1) 2 =O( K 2 ),
z(x,y)= c( x 2 + y 2 ) 1+ 1(1+k) c 2 ( x 2 + y 2 ) + A 2 y+ A 3 x 2 + A 5 y 2 + A 7 x 2 y + A 9 y 3 + A 10 x 4 + A 12 x 2 y 2 + A 14 y 4 + A 16 x 4 y+ A 18 x 2 y 3 + A 20 y 5 .

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