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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21919–21928

A new family of optical systems employing φ-polynomial surfaces

Kyle Fuerschbach, Jannick P. Rolland, and Kevin P. Thompson  »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 21919-21928 (2011)

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Unobscured optical systems have been in production since the 1960s. In each case, the unobscured system is an intrinsically rotationally symmetric optical system with an offset aperture stop, a biased input field, or both. This paper presents a new family of truly nonsymmetric optical systems that exploit a new fabrication degree of freedom enabled by the introduction of slow-servos to diamond machining; surfaces whose departure from a sphere varies both radially and azimuthally in the aperture. The benefit of this surface representation is demonstrated by designing a compact, long wave infrared (LWIR) reflective imager using nodal aberration theory. The resulting optical system operates at F/1.9 with a thirty millimeter pupil and a ten degree diagonal full field of view representing an order of magnitude increase in both speed and field area coverage when compared to the same design form with only conic mirror surfaces.

© 2011 OSA

OCIS Codes
(220.1920) Optical design and fabrication : Diamond machining
(220.2740) Optical design and fabrication : Geometric optical design
(080.4035) Geometric optics : Mirror system design
(080.4228) Geometric optics : Nonspherical mirror surfaces

ToC Category:
Optical Design and Fabrication

Original Manuscript: August 3, 2011
Revised Manuscript: September 27, 2011
Manuscript Accepted: September 28, 2011
Published: October 21, 2011

Kyle Fuerschbach, Jannick P. Rolland, and Kevin P. Thompson, "A new family of optical systems employing φ-polynomial surfaces," Opt. Express 19, 21919-21928 (2011)

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  1. O. Cakmakci, B. Moore, H. Foroosh, and J. P. Rolland, “Optimal local shape description for rotationally non-symmetric optical surface design and analysis,” Opt. Express 16(3), 1583–1589 (2008). [CrossRef] [PubMed]
  2. R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).
  3. 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]
  4. T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18(16), 17433–17447 (2010). [CrossRef] [PubMed]
  5. Synopsys Inc, “Zernike polynomials,” in CODE V Reference Manual, (2011), Volume IV, Appendix C.
  6. L. Lundström and P. Unsbo, “Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils,” J. Opt. Soc. Am. A 24(3), 569–577 (2007). [CrossRef] [PubMed]
  7. Air Force Avionics Laboratory, “Three mirror objective,” in Aerial Camera Lenses, Report 027000 from RECON Central, the Reconnaissance Division/Reconnaissance Applications Branch, (1967), pp. 2–109.
  8. K. P. Thompson, T. Schmid, O. Cakmakci, and J. P. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” J. Opt. Soc. Am. A 26(6), 1503–1517 (2009). [CrossRef] [PubMed]
  9. J. M. Rodgers, “Catoptric optical system including concave and convex reflectors,” Optical Research Associates, US Patent 5,309,276 (1994).
  10. T. Nakano and Y. Tamagawa, “Configuration of an off-axis three-mirror system focused on compactness and brightness,” Appl. Opt. 44(5), 776–783 (2005). [CrossRef] [PubMed]
  11. J. W. Figoski, “Aberration characteristics of nonsymmetric systems,” in 1985 International Optical Design Conference, W.H. Taylor, and D.T. Moore, eds. (SPIE, 1985), pp. 104–111.
  12. K. P. Thompson, T. Schmid, and J. P. Rolland, “The misalignment induced aberrations of TMA telescopes,” Opt. Express 16(25), 20345–20353 (2008). [CrossRef] [PubMed]

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