Abstract

This paper proposes a method of designing two aspheric surfaces simultaneously for an imaging system. By coupling the three rays (two marginal rays and one chief ray from the exit pupil) of each field of view to their corresponding image point, microspherical lens corresponding to each field of view can be obtained by the refraction law. Profiles of the aspheric surfaces can be obtained by employing the position and normal vector of midpoint of the microsphere corresponding to each field of view. Theoretically, through this method, we can realize any mapping relationship between the object points and their image points in 2D. Combining an original projector with the aspheric lens designed in this paper, an example that realizes projection onto a spherical surface with both low distortion and high image quality is presented.

© 2013 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]
  12. F. Duerr, P. Benitez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20, 5576–5585 (2012).
    [CrossRef]
  13. J. Hou, H. Li, Z. Zheng, and X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285, 986–991 (2012).
    [CrossRef]

2012

F. Duerr, P. Benitez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20, 5576–5585 (2012).
[CrossRef]

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

2010

2009

2007

Y. Ding, P. Gu, W. Lu, and Z. Zheng, “Using numerical solutions of differential equations to form free reflector,” J. Zhejiang Univ. 41, 1516–1518 (2007).

2006

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

1997

1961

1949

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. London Sect. B 62, 2–8 (1949).
[CrossRef]

Benitez, P.

Benítez, P.

Ding, Y.

Y. Ding, P. Gu, W. Lu, and Z. Zheng, “Using numerical solutions of differential equations to form free reflector,” J. Zhejiang Univ. 41, 1516–1518 (2007).

Duerr, F.

Grabovickic, D.

Gu, P.

Y. Ding, P. Gu, W. Lu, and Z. Zheng, “Using numerical solutions of differential equations to form free reflector,” J. Zhejiang Univ. 41, 1516–1518 (2007).

Hao, X.

Hicks, R. A.

R. A. Hicks, “Catadioptric sensors that approximate wide-angle perspective projections,” IEEE 1063-6919/00, 1–7 (2000).

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, 986–991 (2012).
[CrossRef]

Infante, J.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaríaa, “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, 24036–24044 (2009).
[CrossRef]

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, 986–991 (2012).
[CrossRef]

Lin, W.

J. C. Miñano, P. Benítez, W. Lin, F. Muñoz, J. Infante, and A. Santamaríaa, “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, 24036–24044 (2009).
[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, 986–991 (2012).
[CrossRef]

Z. Zheng, X. Hao, and X. Liu, “Freeform surface lens for LED uniform illumination,” Appl. Opt. 48, 6627–6634 (2009).
[CrossRef]

Lu, W.

Y. Ding, P. Gu, W. Lu, and Z. Zheng, “Using numerical solutions of differential equations to form free reflector,” J. Zhejiang Univ. 41, 1516–1518 (2007).

Meuret, Y.

Miñano, J. C.

Miyamoyo, K.

Muñoz, F.

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, 24036–24044 (2009).
[CrossRef]

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

Santamaría, A.

Santamaríaa, A.

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

Thienpont, H.

Tukker, T. W.

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

Wassermann, G. D.

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. London Sect. B 62, 2–8 (1949).
[CrossRef]

Wolf, E.

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. London Sect. B 62, 2–8 (1949).
[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, 986–991 (2012).
[CrossRef]

Z. Zheng, X. Hao, and X. Liu, “Freeform surface lens for LED uniform illumination,” Appl. Opt. 48, 6627–6634 (2009).
[CrossRef]

Y. Ding, P. Gu, W. Lu, and Z. Zheng, “Using numerical solutions of differential equations to form free reflector,” J. Zhejiang Univ. 41, 1516–1518 (2007).

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Zhejiang Univ.

Y. Ding, P. Gu, W. Lu, and Z. Zheng, “Using numerical solutions of differential equations to form free reflector,” J. Zhejiang Univ. 41, 1516–1518 (2007).

Opt. Commun.

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

Opt. Express

Proc. Phys. Soc. London Sect. B

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. London Sect. B 62, 2–8 (1949).
[CrossRef]

Proc. SPIE

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

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

Other

R. A. Hicks, “Catadioptric sensors that approximate wide-angle perspective projections,” IEEE 1063-6919/00, 1–7 (2000).

K. Fuerschbach, J. Rolland, and K. Thompson, “A path to freeform optics,” http://optics.nasa.gov/tech_days/tech_days_2011/Day%202%20Wed%20June%2022/29%20UoR%20Path%20to%20Freeform%20Optics.pdf .

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Figures (11)

Fig. 1.
Fig. 1.

Implementation of the algorithm.

Fig. 2.
Fig. 2.

Detail of the first field of view.

Fig. 3.
Fig. 3.

Detail of the second field of view.

Fig. 4.
Fig. 4.

Profiles of the aspheric surfaces.

Fig. 5.
Fig. 5.

Structure of the spherical projection.

Fig. 6.
Fig. 6.

Model of the aspheric lens.

Fig. 7.
Fig. 7.

Structure of the projection system.

Fig. 8.
Fig. 8.

Distortion curves of the system.

Fig. 9.
Fig. 9.

MTF curves of the system.

Fig. 10.
Fig. 10.

MTF curves using one aspheric surface.

Fig. 11.
Fig. 11.

MTF curves by enlarging pupil of the system.

Equations (4)

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noA⃗=nIA⃗+pN⃗,
p=no2nI2+nI2cos2InIcosI.
hA=0.5L×hA00.5LΔz,
δ=hAh.

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