Abstract

In this paper, mixed-surface-type optical system is defined as the optical system comprised of various types of surfaces, including spherical, aspheric, and freeform surfaces. A general point-by-point design method for mixed-surface-type systems is proposed. In detail, methods for spherical system design and optical power assignment are proposed during the point-by-point design process. Additionally, three surface evolutions are proposed: from spherical to aspheric surfaces and freeform surfaces, and from aspheric surfaces to freeform surfaces. A mixed-surface-type off-axis three-mirror system is designed as an example and as a starting point for further optimization. The sphere receives most of the system optical power while the freeform surface has little power, which can reduce system fabrication difficulty.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  22. T. Yang, J. Zhu, W. Hou, and G. Jin, “Design method of freeform off-axis reflective imaging systems with a direct construction process,” Opt. Express 22(8), 9193–9205 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  26. Z. Guan and J. F. Lu, “The fundamental of numerical analysis,” High. Educ. (1998) (in Chinese).

2016 (2)

2015 (6)

T. Yang, J. Zhu, X. Wu, and G. Jin, “Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method,” Opt. Express 23(8), 10233–10246 (2015).
[Crossref] [PubMed]

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

C. Huang and X. Liu, “Design of off-axis four-mirror optical system without obscuration based on free-form surface,” Proc. SPIE 97952, 97952D (2015).

G. Xie, J. Chang, J. Zhou, K. Zhang, and X. Wang, “Research on all movable reflective zoom system with three mirrors,” Proc. SPIE 9618, 96180O (2015).
[Crossref]

Y. Bian, H. Li, Y. Wang, Z. Zheng, and X. Liu, “Method to design two aspheric surfaces for a wide field of view imaging system with low distortion,” Appl. Opt. 54(27), 8241–8247 (2015).
[Crossref] [PubMed]

2014 (4)

2011 (2)

2009 (3)

2007 (1)

2006 (1)

T. W. Tukker, “Beam-shaping lenses in illumination optics,” Proc. SPIE 6338, 63380A (2006).
[Crossref]

2002 (1)

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

1979 (1)

L. G. Cook, “three-mirror anastigmatic used off-axis in aperture and field,” Proc. SPIE 183, 207–211 (1979).
[Crossref]

1978 (1)

1977 (1)

1949 (1)

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

Bauer, A.

Benítez, P.

J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
[Crossref] [PubMed]

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

Bian, Y.

Broemel, A.

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

Cakmakci, O.

Chang, J.

G. Xie, J. Chang, J. Zhou, K. Zhang, and X. Wang, “Research on all movable reflective zoom system with three mirrors,” Proc. SPIE 9618, 96180O (2015).
[Crossref]

Cheng, D.

Cook, L. G.

L. G. Cook, “three-mirror anastigmatic used off-axis in aperture and field,” Proc. SPIE 183, 207–211 (1979).
[Crossref]

Dong, J.

Fuerschbach, K.

Gong, T.

Gross, H.

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

Guan, Z.

Z. Guan and J. F. Lu, “The fundamental of numerical analysis,” High. Educ. (1998) (in Chinese).

Hou, W.

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

T. Yang, J. Zhu, W. Hou, and G. Jin, “Design method of freeform off-axis reflective imaging systems with a direct construction process,” Opt. Express 22(8), 9193–9205 (2014).
[Crossref] [PubMed]

Hua, H.

Huang, C.

C. Huang and X. Liu, “Design of off-axis four-mirror optical system without obscuration based on free-form surface,” Proc. SPIE 97952, 97952D (2015).

Infante, J.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
[Crossref] [PubMed]

Ji, Z.

Jin, G.

Kirschstein, S.

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

Korsch, D.

Li, H.

Lin, W.

J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
[Crossref] [PubMed]

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

Liu, X.

Lu, J. F.

Z. Guan and J. F. Lu, “The fundamental of numerical analysis,” High. Educ. (1998) (in Chinese).

Ma, H.

Meng, Q.

Miñano, J. C.

J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
[Crossref] [PubMed]

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

Muñoz, F.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
[Crossref] [PubMed]

Pan, J. H.

J. H. Pan, “The Design, Manufacture and Test of the Aspheric Optical Surface,” Science (1994) (in Chinese).

Petruck, P.

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

Robb, P. N.

Rodgers, J. M.

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

Rolland, J.

Rolland, J. P.

Santamaría, A.

J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009).
[Crossref] [PubMed]

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

Talha, M. M.

Thompson, K. P.

Tuennermann, A.

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

Tukker, T. W.

T. W. Tukker, “Beam-shaping lenses in illumination optics,” Proc. SPIE 6338, 63380A (2006).
[Crossref]

Wang, D.

Wang, H.

Wang, K.

Wang, W.

Wang, X.

G. Xie, J. Chang, J. Zhou, K. Zhang, and X. Wang, “Research on all movable reflective zoom system with three mirrors,” Proc. SPIE 9618, 96180O (2015).
[Crossref]

Wang, Y.

Wassermann, G. D.

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

Wolf, E.

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

Wu, R.

Wu, X.

Xie, G.

G. Xie, J. Chang, J. Zhou, K. Zhang, and X. Wang, “Research on all movable reflective zoom system with three mirrors,” Proc. SPIE 9618, 96180O (2015).
[Crossref]

Yang, T.

Zhang, K.

G. Xie, J. Chang, J. Zhou, K. Zhang, and X. Wang, “Research on all movable reflective zoom system with three mirrors,” Proc. SPIE 9618, 96180O (2015).
[Crossref]

Zhang, X.

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

Zheng, Z.

Zhong, Y.

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

Zhou, J.

G. Xie, J. Chang, J. Zhou, K. Zhang, and X. Wang, “Research on all movable reflective zoom system with three mirrors,” Proc. SPIE 9618, 96180O (2015).
[Crossref]

Zhu, J.

Appl. Opt. (7)

J. Opt. (1)

J. Zhu, W. Hou, X. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Express (6)

Opt. Lett. (1)

Proc. Phys. Soc. B (1)

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

Proc. SPIE (7)

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

T. W. Tukker, “Beam-shaping lenses in illumination optics,” Proc. SPIE 6338, 63380A (2006).
[Crossref]

L. G. Cook, “three-mirror anastigmatic used off-axis in aperture and field,” Proc. SPIE 183, 207–211 (1979).
[Crossref]

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

G. Xie, J. Chang, J. Zhou, K. Zhang, and X. Wang, “Research on all movable reflective zoom system with three mirrors,” Proc. SPIE 9618, 96180O (2015).
[Crossref]

C. Huang and X. Liu, “Design of off-axis four-mirror optical system without obscuration based on free-form surface,” Proc. SPIE 97952, 97952D (2015).

Y. Zhong, H. Gross, A. Broemel, S. Kirschstein, P. Petruck, and A. Tuennermann, “Investigation of TMA systems with different freeform surfaces,” Proc. SPIE 9626, 96260X (2015).
[Crossref]

Other (2)

J. H. Pan, “The Design, Manufacture and Test of the Aspheric Optical Surface,” Science (1994) (in Chinese).

Z. Guan and J. F. Lu, “The fundamental of numerical analysis,” High. Educ. (1998) (in Chinese).

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Figures (11)

Fig. 1
Fig. 1 Design process for mixed-surface-type optical systems.
Fig. 2
Fig. 2 (a) Calculation of feature data points Pi (2≤ im); (b) calculation of Pj+1, where Rj + 1 is the feature ray of Pj+1. (c) The feature data point Pi represents the intersection of the corresponding feature ray Ri with the unknown surface. The intersections of Ri with two surfaces neighboring the unknown surface are designated the start point Si and the end point Ei of Ri. Ii is the image point.
Fig. 3
Fig. 3 System structure: (a) initial planar system; (b) calculated spherical tertiary mirror; (c) spherical system after calculation (without optical power assigned during the calculation).
Fig. 4
Fig. 4 Optical power assignment process (a) Sphere C is calculated first. (b) rC' = εC × rC is used to change the power of the tertiary mirror. (c) Sphere B is calculated to compensate for the changed optical power of C'. (d) rB' = εB × rB is used to change the power of the secondary mirror. (e) Sphere A' is calculated to compensate for the changed optical power of B'.
Fig. 5
Fig. 5 Use local search algorithm around the sampled data points to find the optimal aspheric vertex among the grid nodes.
Fig. 6
Fig. 6 Example optical structure.
Fig. 7
Fig. 7 RMS spot diameters of different surfaces (a) Sphere calculated from plane. (b) Aspheric surface calculated from plane. (c) Aspheric surface evolved from sphere. (d) Freeform surface calculated from plane. (e) Freeform surface evolved from sphere. (f) Freeform surface evolved from aspheric surface.
Fig. 8
Fig. 8 (a) Initial off-axis three-mirror plane system; (b) spherical system without optical power assignment; (c) spherical system after optical power assignment.
Fig. 9
Fig. 9 System with three spheres: (a) system structure and (b) RMS spot diameter; mixed system with spherical and aspheric surfaces: (c) system structure and (d) RMS spot diameter; mixed system with spherical, aspheric and freeform surfaces: (e) system structure and (f) RMS spot diameter.
Fig. 10
Fig. 10 Optical system structure: (a) initial structure; (b) structure after optimization.
Fig. 11
Fig. 11 (a) MTF and (b) RMS wavefront error of the example design after optimization.

Tables (1)

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Table 1 Optical System Specifications

Equations (14)

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r i '× N i = r i × N i ,
( xA ) 2 + ( yB ) 2 + ( zC ) 2 = r 2 .
[ x 1 y 1 z 1 1 x K y K z K 1 ][ 2A 2B 2C A 2 + B 2 + C 2 r 2 ]=[ x 1 2 + y 1 2 + z 1 2 x K 2 + y K 2 + z K 2 ].
[ x i 2 x i y i x i z i x i x i y i y i 2 y i z i y i x i z i y i z i z i 2 z i x i y i z i n ][ 2A 2B 2C D ]=[ x i ( x i 2 + y i 2 + z i 2 ) y i ( x i 2 + y i 2 + z i 2 ) z i ( x i 2 + y i 2 + z i 2 ) ( x i 2 + y i 2 + z i 2 ) ].
[ ( x i ( x i x ¯ ) ) ( x i ( y i y ¯ ) ) ( x i ( z i z ¯ ) ) ( x i ( y i y ¯ ) ) ( y i ( y i y ¯ ) ) ( y i ( z i z ¯ ) ) ( x i ( z i z ¯ ) ) ( y i ( z i z ¯ ) ) ( z i ( z i z ¯ ) ) ][ 2A 2B 2C ]=[ ( ( x i 2 + y i 2 + z i 2 )( x i x ¯ ) ) ( ( x i 2 + y i 2 + z i 2 )( y i y ¯ ) ) ( ( x i 2 + y i 2 + z i 2 )( z i z ¯ ) ) ].
( 1+ 1 u 2 ) ( xA ) 2 + ( yB ) 2 = r 2 .
( xA ) 2 +( 1+ 1 v 2 ) ( yB ) 2 = r 2 .
[ U i ( U i U ¯ ) U i ( y i y ¯ ) 0 U i ( y i y ¯ ) y i ( y i y ¯ ) 0 0 0 0 ][ 2A 2B 2C ]=[ ( U i x i + y i 2 )( U i U ¯ ) ( U i x i + y i 2 )( y i y ¯ ) 0 ].
[ x i ( x i x ¯ ) V i ( x i x ¯ ) 0 V i ( x i x ¯ ) V i ( V i V ¯ ) 0 0 0 0 ][ 2A 2B 2C ]=[ ( x i 2 + V i y i )( x i x ¯ ) ( x i 2 + V i y i )( V i V ¯ ) 0 ].
Eq. ( 5 )+ω×Eq. ( 8 )+ω×Eq. ( 9 ).
Eq. ( 2 )+ω×Eq. ( 6 )+ω×Eq. ( 7 ).
| Φ C |>>| Φ B |>| Φ A |.
Z= c r 2 1+ 1( 1+k ) c 2 r 2 + a 1 r 4 + a 2 r 6 r 2 = x 2 + y 2 .
Z= c r 2 1+ 1( 1+k ) c 2 r 2 + b 1 y+ b 2 x 2 + b 3 y 2 + b 4 x 2 y+ b 5 y 3 + b 6 x 4 + b 7 x 2 y 2 + b 8 y 4 + b 9 x 6 + b 10 x 4 y 2 + b 11 x 2 y 4 + b 12 y 6 .

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