OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 22 — Aug. 1, 2014
  • pp: E69–E76

Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface

Zhenfeng Zhuang, Yanting Chen, Feihong Yu, and Xiaowei Sun  »View Author Affiliations

Applied Optics, Vol. 53, Issue 22, pp. E69-E76 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (800 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(220.4830) Optical design and fabrication : Systems design
(080.4225) Geometric optics : Nonspherical lens design

Original Manuscript: February 24, 2014
Revised Manuscript: July 19, 2014
Manuscript Accepted: July 21, 2014
Published: August 1, 2014

Zhenfeng Zhuang, Yanting Chen, Feihong Yu, and Xiaowei Sun, "Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface," Appl. Opt. 53, E69-E76 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited