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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 8 — Apr. 21, 2014
  • pp: 9193–9205

Design method of freeform off-axis reflective imaging systems with a direct construction process

Tong Yang, Jun Zhu, Wei Hou, and Guofan Jin  »View Author Affiliations

Optics Express, Vol. 22, Issue 8, pp. 9193-9205 (2014)

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In this paper, a novel method is proposed to design the freeform off-axis reflective imaging systems. A special algorithm is demonstrated to calculate the data points on the unknown freeform surface using the rays from multiple fields and different pupil coordinates. These points are used to construct the multiple three-dimensional freeform surfaces in an imaging system which works for a certain object size and a certain width of light beam. An unobscured design with freeform surfaces can be obtained directly with this method, and it can be taken as a good starting point for further optimization. The benefit of this design method is demonstrated by designing a freeform off-axis three-mirror imaging system with high performance and system specifications. The final system operates at F/1.49 with a 64mm entrance pupil diameter and an 8° × 9° field-of-view (FOV). The performance of the system is diffraction limited at LWIR (long-wavelength-infrared).

© 2014 Optical Society of America

OCIS Codes
(220.2740) Optical design and fabrication : Geometric optical design
(080.4225) Geometric optics : Nonspherical lens design
(080.4228) Geometric optics : Nonspherical mirror surfaces

ToC Category:
Geometric Optics

Original Manuscript: February 12, 2014
Revised Manuscript: March 31, 2014
Manuscript Accepted: April 1, 2014
Published: April 8, 2014

Tong Yang, Jun Zhu, Wei Hou, and Guofan Jin, "Design method of freeform off-axis reflective imaging systems with a direct construction process," Opt. Express 22, 9193-9205 (2014)

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  1. J. M. Rodgers, “Unobscured mirror designs,” Proc. SPIE 4832, 33–60 (2002). [CrossRef]
  2. J. M. Rodgers, “Aberrations of unobscured reflective optical systems,” Ph.D. Thesis, University of Arizona (1983).
  3. W. B. Wetherell and D. A. Womble, “All-reflective three element objective,” U.S. Patent 4,240,707 (23 December, 1980).
  4. R. N. Wilson, Reflecting Telescope Optics (Springer, 2000).
  5. K. P. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry,” J. Opt. Soc. Am. A 22(7), 1389–1401 (2005). [CrossRef] [PubMed]
  6. J. W. Figoski, W. H. Taylor and D. T. Moore, eds., “Aberration characteristics of nonsymmetric systems,” in 1985 International Optical Design Conference, W. H. Taylor and D. T. Moore, eds. (SPIE, 1985), pp. 104–111.
  7. K. Fuerschbach, J. P. Rolland, K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011). [CrossRef] [PubMed]
  8. R. A. Hicks, “Controlling a ray bundle with a free-form reflector,” Opt. Lett. 33(15), 1672–1674 (2008). [CrossRef] [PubMed]
  9. G. D. Wassermann, E. Wolf, “On the Theory of Aplanatic Aspheric Systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949). [CrossRef]
  10. D. Knapp, “Conformal optical design,” Ph.D. Thesis, University of Arizona (2002).
  11. D. Cheng, Y. Wang, H. Hua, “Free form optical system design with differential equations,” Proc. SPIE 7849, 78490Q (2010). [CrossRef]
  12. J. Rubinstein, G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8(4), 281–283 (2001). [CrossRef]
  13. O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics (Wiley-VCH, 2006).
  14. J. Hou, H. Li, Z. Zheng, X. Liu, “Distortion correction for imaging on non-planar surface using freeform lens,” Opt. Commun. 285(6), 986–991 (2012). [CrossRef]
  15. J. C. Miñano, P. Benítez, W. Lin, J. Infante, F. Muñoz, A. Santamaría, “An application of the SMS method for imaging designs,” Opt. Express 17(26), 24036–24044 (2009). [CrossRef] [PubMed]
  16. F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20(5), 5576–5585 (2012). [CrossRef] [PubMed]
  17. J. Zhu, T. Yang, G. Jin, “Design method of surface contour for a freeform lens with wide linear field-of-view,” Opt. Express 21(22), 26080–26092 (2013). [CrossRef] [PubMed]
  18. L. Wang, K. Qian, Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007). [CrossRef] [PubMed]
  19. Code V Reference Manual, Synopsys Inc. (2012).

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