Abstract

This paper presents a field curvature correction method of designing an ultrashort throw ratio (TR) projection lens for an imaging system. The projection lens is composed of several refractive optical elements and an odd polynomial mirror surface. A curved image is formed in a direction away from the odd polynomial mirror surface by the refractive optical elements from the image formed on the digital micromirror device (DMD) panel, and the curved image formed is its virtual image. Then the odd polynomial mirror surface enlarges the curved image and a plane image is formed on the screen. Based on the relationship between the chief ray from the exit pupil of each field of view (FOV) and the corresponding predescribed position on the screen, the initial profile of the freeform mirror surface is calculated by using segments of the hyperbolic according to the laws of reflection. For further optimization, the value of the high-order odd polynomial surface is used to express the freeform mirror surface through a least-squares fitting method. As an example, an ultrashort TR projection lens that realizes projection onto a large 50 in. screen at a distance of only 510 mm is presented. The optical performance for the designed projection lens is analyzed by ray tracing method. Results show that an ultrashort TR projection lens modulation transfer function of over 60% at 0.5 cycles/mm for all optimization fields is achievable with f-number of 2.0, 126° full FOV, <1% distortion, and 0.46 TR. Moreover, in comparing the proposed projection lens’ optical specifications to that of traditional projection lenses, aspheric mirror projection lenses, and conventional short TR projection lenses, results indicate that this projection lens has the advantages of ultrashort TR, low f-number, wide full FOV, and small distortion.

© 2014 Optical Society of America

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  1. J. W. Pan, S. H. Tu, C. M. Wang, and J. Y. Chang, “High efficiency pocket-size projector with a compact projection lens and a light emitting diode-based light source system,” Appl. Opt. 47, 3406–3414 (2008).
    [Crossref]
  2. J. W. Pan and S. H. Lin, “Achromatic design in the illumination system for a mini projector with LED light source,” Opt. Express 19, 15750–15759 (2011).
    [Crossref]
  3. J. W. Pan and H. H. Wang, “High contrast ratio prism design in a mini projector,” Appl. Opt. 52, 8347–8354 (2013).
    [Crossref]
  4. J. Ogawa, “Reflection type image forming optical system and projector,” U.S. patent6,612,704 B2 (2September, 2003).
  5. K. Hirata, M. Yatsu, T. Hisada, and M. Ohki, “Projection display system including lens group and reflecting mirror,” U.S. patent8,313,199 B2 (20November, 2012).
  6. K. C. Lu, “Wide angle projection and application,” China patent102967923 A (13March, 2013).
  7. J. Hou, H. F. Li, Z. R. Zheng, and X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285, 986–991 (2012).
    [Crossref]
  8. J. Hou, H. F. Li, R. M. Wu, P. Liu, Z. R. Zheng, and X. Liu, “Method to design two aspheric surfaces for imaging system,” Appl. Opt. 52, 2294–2299 (2013).
    [Crossref]
  9. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
  10. F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
    [Crossref]
  11. R. A. Hicks and R. Bajcsy, “Catadioptric sensors that approximate wide angle perspective projections,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), Vol. 1, pp. 545–551.
  12. J. Ogawa, K. Agata, and M. Sakamoto, “Super-short focus front projector with aspheric mirror projection optical system,” SID J. 13, 111–116 (2005).
  13. Z. R. Zheng, X. T. Sun, X. Liu, and P. F. Gu, “Design of reflective projection lens with Zernike polynomials surfaces,” Displays 29, 412–417 (2008).
    [Crossref]
  14. Z. R. Zheng, “Design of off-axis reflective projection lens using spherical Fresnel surface,” Optik 122, 145–149 (2011).
    [Crossref]
  15. J. C. Miñano, P. Benítez, L. Wang, J. Infante, F. Muñoz, and A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17, 24036–24044 (2009).
    [Crossref]
  16. F. Duerr, P. Benítez, 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]
  17. F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).
    [Crossref]
  18. J. C. Miñano, P. Benítez, L. Wang, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
    [Crossref]
  19. D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
    [Crossref]
  20. D. Michaelis, P. Schreiber, C. Li, and A. Bräuer, “Construction of freeforms in illumination systems via generalized Cartesian oval representation,” Proc. SPIE 8124, 812403 (2011).
    [Crossref]
  21. Y. Chen, “Thermal forming process for precision freeform optical mirrors and micro glass optics,” Ph.D. dissertation (The Ohio State University, 2010).
  22. V. I. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis (Springer, 2002), pp. 191–222.
  23. V. I. Oliker, “Freeform optical systems with prescribed irradiance properties in near field,” Proc. SPIE 6342, 634211 (2006).
    [Crossref]
  24. J. H. Mathews and K. D. Fink, “Numerical optimization,” in Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004), pp. 376–388.
  25. Z. F. Zhuang and F. H. Yu, “A contour calculation method for rapid freeform reflector construction with ellipsoid patches,” Opt. Laser Technol. 56, 430–435 (2014).

2014 (1)

Z. F. Zhuang and F. H. Yu, “A contour calculation method for rapid freeform reflector construction with ellipsoid patches,” Opt. Laser Technol. 56, 430–435 (2014).

2013 (2)

2012 (2)

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

F. Duerr, P. Benítez, 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]

2011 (4)

Z. R. Zheng, “Design of off-axis reflective projection lens using spherical Fresnel surface,” Optik 122, 145–149 (2011).
[Crossref]

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[Crossref]

D. Michaelis, P. Schreiber, C. Li, and A. Bräuer, “Construction of freeforms in illumination systems via generalized Cartesian oval representation,” Proc. SPIE 8124, 812403 (2011).
[Crossref]

J. W. Pan and S. H. Lin, “Achromatic design in the illumination system for a mini projector with LED light source,” Opt. Express 19, 15750–15759 (2011).
[Crossref]

2009 (2)

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

2008 (3)

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).
[Crossref]

J. W. Pan, S. H. Tu, C. M. Wang, and J. Y. Chang, “High efficiency pocket-size projector with a compact projection lens and a light emitting diode-based light source system,” Appl. Opt. 47, 3406–3414 (2008).
[Crossref]

Z. R. Zheng, X. T. Sun, X. Liu, and P. F. Gu, “Design of reflective projection lens with Zernike polynomials surfaces,” Displays 29, 412–417 (2008).
[Crossref]

2006 (1)

V. I. Oliker, “Freeform optical systems with prescribed irradiance properties in near field,” Proc. SPIE 6342, 634211 (2006).
[Crossref]

2005 (1)

J. Ogawa, K. Agata, and M. Sakamoto, “Super-short focus front projector with aspheric mirror projection optical system,” SID J. 13, 111–116 (2005).

2004 (2)

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
[Crossref]

Agata, K.

J. Ogawa, K. Agata, and M. Sakamoto, “Super-short focus front projector with aspheric mirror projection optical system,” SID J. 13, 111–116 (2005).

Alvarez, J. L.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

Bajcsy, R.

R. A. Hicks and R. Bajcsy, “Catadioptric sensors that approximate wide angle perspective projections,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), Vol. 1, pp. 545–551.

Benítez, P.

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

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).
[Crossref]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
[Crossref]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

Blen, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

Bräuer, A.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[Crossref]

D. Michaelis, P. Schreiber, C. Li, and A. Bräuer, “Construction of freeforms in illumination systems via generalized Cartesian oval representation,” Proc. SPIE 8124, 812403 (2011).
[Crossref]

Chang, J. Y.

Chaves, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

Chen, Y.

Y. Chen, “Thermal forming process for precision freeform optical mirrors and micro glass optics,” Ph.D. dissertation (The Ohio State University, 2010).

Dross, O.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
[Crossref]

Duerr, F.

Falicoff, W.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

Fink, K. D.

J. H. Mathews and K. D. Fink, “Numerical optimization,” in Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004), pp. 376–388.

Gu, P. F.

Z. R. Zheng, X. T. Sun, X. Liu, and P. F. Gu, “Design of reflective projection lens with Zernike polynomials surfaces,” Displays 29, 412–417 (2008).
[Crossref]

Hernández, M.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

Hicks, R. A.

R. A. Hicks and R. Bajcsy, “Catadioptric sensors that approximate wide angle perspective projections,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), Vol. 1, pp. 545–551.

Hirata, K.

K. Hirata, M. Yatsu, T. Hisada, and M. Ohki, “Projection display system including lens group and reflecting mirror,” U.S. patent8,313,199 B2 (20November, 2012).

Hisada, T.

K. Hirata, M. Yatsu, T. Hisada, and M. Ohki, “Projection display system including lens group and reflecting mirror,” U.S. patent8,313,199 B2 (20November, 2012).

Hou, J.

J. Hou, H. F. Li, R. M. Wu, P. Liu, Z. R. Zheng, and X. Liu, “Method to design two aspheric surfaces for imaging system,” Appl. Opt. 52, 2294–2299 (2013).
[Crossref]

J. Hou, H. F. Li, Z. R. 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, L. Wang, 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, L. Wang, F. Muñoz, J. Infante, and A. Santamaría, “Overview of the SMS design method applied to imaging optics,” Proc. SPIE 7429, 74290C (2009).
[Crossref]

Li, C.

D. Michaelis, P. Schreiber, C. Li, and A. Bräuer, “Construction of freeforms in illumination systems via generalized Cartesian oval representation,” Proc. SPIE 8124, 812403 (2011).
[Crossref]

Li, H. F.

J. Hou, H. F. Li, R. M. Wu, P. Liu, Z. R. Zheng, and X. Liu, “Method to design two aspheric surfaces for imaging system,” Appl. Opt. 52, 2294–2299 (2013).
[Crossref]

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

Lin, S. H.

Liu, P.

Liu, X.

J. Hou, H. F. Li, R. M. Wu, P. Liu, Z. R. Zheng, and X. Liu, “Method to design two aspheric surfaces for imaging system,” Appl. Opt. 52, 2294–2299 (2013).
[Crossref]

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

Z. R. Zheng, X. T. Sun, X. Liu, and P. F. Gu, “Design of reflective projection lens with Zernike polynomials surfaces,” Displays 29, 412–417 (2008).
[Crossref]

Lu, K. C.

K. C. Lu, “Wide angle projection and application,” China patent102967923 A (13March, 2013).

Mathews, J. H.

J. H. Mathews and K. D. Fink, “Numerical optimization,” in Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004), pp. 376–388.

Meuret, Y.

Michaelis, D.

D. Michaelis, P. Schreiber, C. Li, and A. Bräuer, “Construction of freeforms in illumination systems via generalized Cartesian oval representation,” Proc. SPIE 8124, 812403 (2011).
[Crossref]

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[Crossref]

Miñano, J. C.

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

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).
[Crossref]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
[Crossref]

Mohedano, R.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

Muñoz, F.

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

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).
[Crossref]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
[Crossref]

Ogawa, J.

J. Ogawa, K. Agata, and M. Sakamoto, “Super-short focus front projector with aspheric mirror projection optical system,” SID J. 13, 111–116 (2005).

J. Ogawa, “Reflection type image forming optical system and projector,” U.S. patent6,612,704 B2 (2September, 2003).

Ohki, M.

K. Hirata, M. Yatsu, T. Hisada, and M. Ohki, “Projection display system including lens group and reflecting mirror,” U.S. patent8,313,199 B2 (20November, 2012).

Oliker, V. I.

V. I. Oliker, “Freeform optical systems with prescribed irradiance properties in near field,” Proc. SPIE 6342, 634211 (2006).
[Crossref]

V. I. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis (Springer, 2002), pp. 191–222.

Paikyn, B.

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
[Crossref]

Pan, J. W.

Sakamoto, M.

J. Ogawa, K. Agata, and M. Sakamoto, “Super-short focus front projector with aspheric mirror projection optical system,” SID J. 13, 111–116 (2005).

Santamaría, A.

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

Schreiber, P.

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
[Crossref]

D. Michaelis, P. Schreiber, C. Li, and A. Bräuer, “Construction of freeforms in illumination systems via generalized Cartesian oval representation,” Proc. SPIE 8124, 812403 (2011).
[Crossref]

Sun, X. T.

Z. R. Zheng, X. T. Sun, X. Liu, and P. F. Gu, “Design of reflective projection lens with Zernike polynomials surfaces,” Displays 29, 412–417 (2008).
[Crossref]

Thienpont, H.

Tu, S. H.

Wang, C. M.

Wang, H. H.

Wang, L.

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

Wu, R. M.

Yatsu, M.

K. Hirata, M. Yatsu, T. Hisada, and M. Ohki, “Projection display system including lens group and reflecting mirror,” U.S. patent8,313,199 B2 (20November, 2012).

Yu, F. H.

Z. F. Zhuang and F. H. Yu, “A contour calculation method for rapid freeform reflector construction with ellipsoid patches,” Opt. Laser Technol. 56, 430–435 (2014).

Zheng, Z. R.

J. Hou, H. F. Li, R. M. Wu, P. Liu, Z. R. Zheng, and X. Liu, “Method to design two aspheric surfaces for imaging system,” Appl. Opt. 52, 2294–2299 (2013).
[Crossref]

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

Z. R. Zheng, “Design of off-axis reflective projection lens using spherical Fresnel surface,” Optik 122, 145–149 (2011).
[Crossref]

Z. R. Zheng, X. T. Sun, X. Liu, and P. F. Gu, “Design of reflective projection lens with Zernike polynomials surfaces,” Displays 29, 412–417 (2008).
[Crossref]

Zhuang, Z. F.

Z. F. Zhuang and F. H. Yu, “A contour calculation method for rapid freeform reflector construction with ellipsoid patches,” Opt. Laser Technol. 56, 430–435 (2014).

Appl. Opt. (3)

Displays (1)

Z. R. Zheng, X. T. Sun, X. Liu, and P. F. Gu, “Design of reflective projection lens with Zernike polynomials surfaces,” Displays 29, 412–417 (2008).
[Crossref]

Opt. Commun. (1)

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

Opt. Eng. (1)

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

Z. F. Zhuang and F. H. Yu, “A contour calculation method for rapid freeform reflector construction with ellipsoid patches,” Opt. Laser Technol. 56, 430–435 (2014).

Opt. Lett. (1)

Optik (1)

Z. R. Zheng, “Design of off-axis reflective projection lens using spherical Fresnel surface,” Optik 122, 145–149 (2011).
[Crossref]

Proc. SPIE (5)

V. I. Oliker, “Freeform optical systems with prescribed irradiance properties in near field,” Proc. SPIE 6342, 634211 (2006).
[Crossref]

D. Michaelis, P. Schreiber, C. Li, and A. Bräuer, “Construction of freeforms in illumination systems via generalized Cartesian oval representation,” Proc. SPIE 8124, 812403 (2011).
[Crossref]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).
[Crossref]

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

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J. Ogawa, K. Agata, and M. Sakamoto, “Super-short focus front projector with aspheric mirror projection optical system,” SID J. 13, 111–116 (2005).

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Y. Chen, “Thermal forming process for precision freeform optical mirrors and micro glass optics,” Ph.D. dissertation (The Ohio State University, 2010).

V. I. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis (Springer, 2002), pp. 191–222.

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Figures (12)

Fig. 1.
Fig. 1.

Schematic illustration of the FCC method. (a) Field curvature caused by the convex mirror surface. A curved and enlarged image of an erect object by the convex mirror surface is obtained. (b) Approach of correcting the field curvature caused by the concave mirror surface. A plane and enlarged image of a curved object by the convex mirror surface is obtained.

Fig. 2.
Fig. 2.

Diagrammatic representation of the projection system that includes a convex mirror surface.

Fig. 3.
Fig. 3.

Optical principle of the mirror surface.

Fig. 4.
Fig. 4.

Determination of the reference surface segment by hyperbolic segments.

Fig. 5.
Fig. 5.

Determination of the second hyperbolic surface segment.

Fig. 6.
Fig. 6.

Layout of the ultrashort TR projection system.

Fig. 7.
Fig. 7.

Comparison of the shapes of the odd polynomial mirror surface before and after the optimization process.

Fig. 8.
Fig. 8.

(a) Designed odd polynomial mirror surface profile. (b) Corresponding contour map of the odd polynomial mirror surface.

Fig. 9.
Fig. 9.

Model of the odd polynomial mirror surface (overall dimensions: 98mm×49.2mm×24.6mm).

Fig. 10.
Fig. 10.

MTF diagram in the image space. Different colors represent the tangential and sagittal MTFs of different fields. The black curve represents the MTF of diffraction limited data.

Fig. 11.
Fig. 11.

Distortion grid map.

Fig. 12.
Fig. 12.

Field angle of the refractive lens and field angle of the odd polynomial mirror surface versus normalized FOV.

Tables (2)

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Table 1. Optical Specifications of the Ultrashort TR Projector System

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Table 2. Optical Specification Comparisons among Traditional Projection Lens, Aspheric-Mirror Projection Lens, Conventional Short TR Projection Lens, and Our Designed Projection Lens

Equations (12)

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R(m)=ρ×m,
m=[sin(φ)×cos(θ),sin(φ)×sin(θ),cos(φ)].
T=m2×(m×N)×N,
ρ(m)=dκ(m×v^)1,
κ=1+d2|v|2d|v|.
dk>d1,(k=1,,P1,P),
e1u=e2b,
Rmirror surface=k=1PAk,
z=c×r21+1(1+k)×c2×r2+A1×r+A2×r2++A30×r30,
fcutoff=1η×10002×a,
Dist=0.5×(Hl+Hr)HminHmin×100%.
TR=DW,

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