Abstract

The relative aperture size and the field-of-view (FOV) are two significant parameters for optical imaging systems. However, it is difficult to improve relative aperture size and FOV simultaneously. In this paper, a freeform design method is proposed that is particularly effective for high performance systems. In this step-by-step method, the FOV is enlarged from a small initial value in equal-length steps until it reaches the full FOV; in each step, part of the area of one system surface is constructed. A freeform off-axis three-mirror imaging system with large relative aperture size and a wide FOV is designed as an example. The system operates at F/2.5 with 150 mm effective focal length and a 60° × 1° FOV. The average root-mean-square wavefront error of the system is 0.089λ (working wavelength λ = 530.5 nm).

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2017 (4)

2016 (4)

2015 (4)

W. Hou, J. Zhu, T. Yang, and G. Jin, “Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems,” J. Opt. 17(5), 055603 (2015).
[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]

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, 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]

2014 (4)

2013 (1)

2012 (2)

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

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (2)

2008 (1)

2005 (1)

2002 (1)

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

1985 (1)

J. W. Figoski, “Aberration characteristics of nonsymmetric systems,” Proc. SPIE 554, 104–111 (1985).
[Crossref]

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.

Chambion, B.

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.

Duerr, F.

Feng, Z.

Ferrari, M.

Figoski, J. W.

J. W. Figoski, “Aberration characteristics of nonsymmetric systems,” Proc. SPIE 554, 104–111 (1985).
[Crossref]

Fuerschbach, K.

Gaschet, C.

Gong, M.

Gong, T.

Gross, H.

Han, Y.

He, X.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Henry, D.

Hicks, R. A.

Hou, J.

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

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]

W. Hou, J. Zhu, T. Yang, and G. Jin, “Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems,” J. Opt. 17(5), 055603 (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, L.

Hugot, E.

Infante, J.

Jahn, W.

Ji, Z.

Jin, G.

X. Wu, G. Jin, and J. Zhu, “Freeform illumination design model for multiple light sources simultaneously,” Appl. Opt. 56(9), 2405–2411 (2017).
[Crossref] [PubMed]

T. Yang, G. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6(10), e17081 (2017).
[Crossref]

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 60801 (2016).
[Crossref]

T. Gong, G. Jin, and J. Zhu, “Full-field point-by-point direct design method of off-axis aspheric imaging systems,” Opt. Express 24(26), 29417–29426 (2016).
[Crossref] [PubMed]

T. Yang, J. Zhu, and G. Jin, “Design of a freeform, dual fields-of-view, dual focal lengths, off-axis three-mirror imaging system with a point-by-point construction-iteration process,” Chin. Opt. Lett. 14(10), 100801 (2016).
[Crossref]

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]

W. Hou, J. Zhu, T. Yang, and G. Jin, “Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems,” J. Opt. 17(5), 055603 (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]

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]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31(11), 2401–2408 (2014).
[Crossref] [PubMed]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).
[Crossref] [PubMed]

Li, H.

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

Lin, W.

Liu, Q.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Liu, X.

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

Luo, Y.

Meng, Q.

Miñano, J. C.

Muñoz, F.

Muslimov, E.

Nie, Y.

Rodgers, J. M.

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

Rolland, J. P.

Santamaría, A.

Sasian, J.

Shi, G.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Talha, M. M.

Thompson, K.

Thompson, K. P.

Vives, S.

Wang, D.

Wang, H.

Wang, K.

Wang, L.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Wang, T.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

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, 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.

Yu, S.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Zhang, B.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Zhang, F.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

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]

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Zheng, L.

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

Zheng, Z.

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

Zhong, Y.

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.

T. Yang, G. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6(10), e17081 (2017).
[Crossref]

X. Wu, G. Jin, and J. Zhu, “Freeform illumination design model for multiple light sources simultaneously,” Appl. Opt. 56(9), 2405–2411 (2017).
[Crossref] [PubMed]

T. Gong, G. Jin, and J. Zhu, “Full-field point-by-point direct design method of off-axis aspheric imaging systems,” Opt. Express 24(26), 29417–29426 (2016).
[Crossref] [PubMed]

T. Yang, J. Zhu, and G. Jin, “Design of a freeform, dual fields-of-view, dual focal lengths, off-axis three-mirror imaging system with a point-by-point construction-iteration process,” Chin. Opt. Lett. 14(10), 100801 (2016).
[Crossref]

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 60801 (2016).
[Crossref]

W. Hou, J. Zhu, T. Yang, and G. Jin, “Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems,” J. Opt. 17(5), 055603 (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]

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]

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]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31(11), 2401–2408 (2014).
[Crossref] [PubMed]

Appl. Opt. (4)

Chin. Opt. Lett. (2)

T. Yang, J. Zhu, and G. Jin, “Design of a freeform, dual fields-of-view, dual focal lengths, off-axis three-mirror imaging system with a point-by-point construction-iteration process,” Chin. Opt. Lett. 14(10), 100801 (2016).
[Crossref]

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 60801 (2016).
[Crossref]

J. Opt. (2)

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]

W. Hou, J. Zhu, T. Yang, and G. Jin, “Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems,” J. Opt. 17(5), 055603 (2015).
[Crossref]

J. Opt. Soc. Am. A (2)

Light Sci. Appl. (1)

T. Yang, G. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6(10), e17081 (2017).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (10)

A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” Opt. Express 22(22), 26585–26606 (2014).
[Crossref] [PubMed]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).
[Crossref] [PubMed]

Z. Feng, Y. Luo, and Y. Han, “Design of LED freeform optical system for road lighting with high luminance/illuminance ratio,” Opt. Express 18(21), 22020–22031 (2010).
[Crossref] [PubMed]

E. Muslimov, E. Hugot, W. Jahn, S. Vives, M. Ferrari, B. Chambion, D. Henry, and C. Gaschet, “Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture,” Opt. Express 25(13), 14598–14610 (2017).
[Crossref] [PubMed]

T. Gong, G. Jin, and J. Zhu, “Full-field point-by-point direct design method of off-axis aspheric imaging systems,” Opt. Express 24(26), 29417–29426 (2016).
[Crossref] [PubMed]

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]

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]

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]

Opt. Lett. (2)

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 (4)

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]

X. Zhang, L. Zheng, X. He, L. Wang, F. Zhang, S. Yu, G. Shi, B. Zhang, Q. Liu, and T. Wang, “Design and fabrication of imaging optical systems with freeform surfaces,” Proc. SPIE 8486, 848607 (2012).
[Crossref]

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

J. W. Figoski, “Aberration characteristics of nonsymmetric systems,” Proc. SPIE 554, 104–111 (1985).
[Crossref]

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Figures (16)

Fig. 1
Fig. 1 Object-image relationships of ray Rm(n) on surface Ωk.
Fig. 2
Fig. 2 Object-image relationships of ray Rm(n) on the surface Ωk..
Fig. 3
Fig. 3 System construction process. (a) The rays of field φ1 converge nicely to the ideal point after being reflected by surface Ω1. (b) X1,2 is used as an extension of X1,1. (c) The two fields can converge nicely to their ideal points after X2,1 and X2,2 are obtained.
Fig. 4
Fig. 4 Flow diagram of the design method.
Fig. 5
Fig. 5 Field enlargement directions.
Fig. 6
Fig. 6 Surface schematic diagrams showing (a) construction of surface Ωk and (b) the system after all surfaces have been constructed.
Fig. 7
Fig. 7 The calculation process. The yellow dotted frame indicates calculation of an item in the current step. The red dotted frame indicates the items that are initial values given by the initial planar system. The green dotted frame indicates items that had been calculated. The blue dotted frame indicates items that are extension areas from the previous item.
Fig. 8
Fig. 8 Surface expansion process. (a) Before surface expansion. (b) Expanded surface after one expansion field is added during the reconstruction process.
Fig. 9
Fig. 9 Constructed fields are enlarged and surfaces are expanded alternately. (a) Surface Ω1 is expanded after reconstruction. (b) The full FOV is achieved after surface Ωk is expanded. (c) Other surfaces are reconstructed using the full FOV.
Fig. 10
Fig. 10 The process of surface expansion. The yellow dotted frame represents item being calculated in the current step. The green dotted frame represents items that had been calculated. The blue dotted frame represents items from the mathematical extension area of the previous item.
Fig. 11
Fig. 11 Establishment of initial system. (a) Layout of the initial system. (b) 61 fields along the X-direction and three fields along the Y-direction are sampled.
Fig. 12
Fig. 12 System layout. (a)The operates in the −0.5° to 0.5° fields in the X-direction. (b) The system operates over the −15° to 15°° field in the X-direction. (c) Surface expansion is finished, and the system operates over the −30° to 30° field in the X-direction.
Fig. 13
Fig. 13 The spot diagram of system after triple-scaled.
Fig. 14
Fig. 14 The final design layout. (a) Cross-sectional view from the YOZ plane. (b) Cross-sectional view from the XOZ plane.
Fig. 15
Fig. 15 (a) Modulation-transfer-function (MTF) plot for the final system. (b) Field map of the RMS wavefront error.
Fig. 16
Fig. 16 Distortion grid for the final system.

Tables (1)

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Table 1 Optical system specifications.

Equations (6)

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r k,m (n) '× N k,m (n) = r k,m (n) × N k,m (n) ,
X k,m (n) =( C k,m (n) , N k,m (n) ),
X k,m =[ X k,m (1) X k,m (2) X k,m (N) ],
X k =[ X k,1 X k,2 X k,M ].
X=[ X 1 X 2 X K ]=[ X 1,1 X 1,2 X 1,M X 2,1 X 2,2 X 2,M X K,1 X K,2 X K,M ].
z= 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

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