OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 42, Iss. 16 — Jun. 1, 2003
  • pp: 3284–3289

Exact ray-trace beam for an off-axis paraboloid surface

Pedro Arguijo and Marija Strojnik Scholl  »View Author Affiliations

Applied Optics, Vol. 42, Issue 16, pp. 3284-3289 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (96 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameters that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.

© 2003 Optical Society of America

OCIS Codes
(220.1010) Optical design and fabrication : Aberrations (global)
(220.1140) Optical design and fabrication : Alignment
(220.1250) Optical design and fabrication : Aspherics
(220.4830) Optical design and fabrication : Systems design

Original Manuscript: November 18, 2002
Revised Manuscript: February 12, 2003
Published: June 1, 2003

Pedro Arguijo and Marija Strojnik Scholl, "Exact ray-trace beam for an off-axis paraboloid surface," Appl. Opt. 42, 3284-3289 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. M. Sasian, “Review of methods for the design of unsymmetrical optical systems,” in Applications of Optical Engineering: Proceedings of OE/Midwest ’90, R. P. Guzik, H. E. Eppinger, R. E. Gillespie, J. E. Pearson, M. K. Dubiel, eds., Proc. SPIE1396, 453–466 (1991). [CrossRef]
  2. J. Nelson, “University of California ten meter telescope project,” in International Conference on Advanced Technology Optical Telescopes, G. Burbidge, L. Barr, eds., Proc. SPIE332, 109–116 (1982). [CrossRef]
  3. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998). [CrossRef]
  4. R. Díaz-Uribe, “Medium-precision null-screen testing of off-axis parabolic mirrors for segmented primary telescope optics: the Large Millimeter Telescope,” Appl. Opt. 39, 2790–2804 (2000). [CrossRef]
  5. P. Arguijo, M. S. Scholl, G. Paez, “Diffraction patterns formed by an off-axis paraboloid surface,” Appl. Opt. 40, 2909–2916 (2001). [CrossRef]
  6. J. B. Scarborough, “The caustic curve of an off-axis parabola,” Appl. Opt. 3, 1445–1146 (1964). [CrossRef]
  7. E. W. Young, G. C. Dente, “The effects of rigid body motion in interferometric test of large-aperture, off-axis, aspheric optics,” in Southwest Conference on Optics, S. C. Stotlar, ed., Proc. SPIE540, 59–68 (1985). [CrossRef]
  8. E. W. Young, S. M. Lawson, “Misalignment tolerances for an imaging system with a segmented primary mirror,” Opt. Eng. 28, 990–995 (1989). [CrossRef]
  9. M. S. Scholl, “Signal generated by an extra-solar-system planet detected by a rotating rotationally shearing interferometer,” J. Opt. Soc. Am. A 13, 1584–1592 (1996). [CrossRef]
  10. J. Lubliner, J. E. Nelson, “Stressed mirror polishing. 1: A technique for producing nonaxisymmetric mirrors,” Appl. Opt. 19, 2332–2340 (1980). [CrossRef] [PubMed]
  11. O. Cardona-Nunez, A. Cornejo-Rodriguez, R. Diaz-Uribe, A. Cordero-Davila, J. Pedraza-Contreras, “Conic that best fits an off-axis conic section,” Appl. Opt. 25, 3585–3588 (1986). [CrossRef] [PubMed]
  12. M. Dragovan, “Cutting surfaces of revolution for millimeter wave optics,” Appl. Opt. 27, 4076–4078 (1988). [CrossRef] [PubMed]
  13. D. Malacara, “Some parameters and characteristics of an off-axis paraboloid,” Opt. Eng. 30, 1277–1280 (1991). [CrossRef]
  14. J. M. Sasian, “Double-curvature surfaces in mirror system design,” Opt. Eng. 36, 183–188 (1997). [CrossRef]
  15. M. Scholl, J. W. Scholl, “Optical systems with off-axis mirrors,” in Recent Trends in Optical Systems Design and Computer Lens Design Workshop, R. E. Fischer, C. Londono, eds., Proc. SPIE766, 174–178 (1987). [CrossRef]
  16. M. S. Scholl, “Design parameters for a two-mirror telescope for stray-light sensitive infrared applications,” Infrared Phys. Technol. 37, 251–257 (1996). [CrossRef]
  17. M. S. Scholl, G. Paez, “Using the y, y-bar diagram to control stray light noise in IR systems,” Infrared Phys. Technol. 38, 25–30 (1997). [CrossRef]
  18. M. S. Scholl, “Recursive ray trace equations through the foci of the tilted off-axis confocal prolate spheroids,” J. Mod. Opt. 43, 1583–1588 (1996). [CrossRef]
  19. B. D. Stone, G. Forbes, “Characterization of first-order optical properties for asymmetric systems,” J. Opt. Soc. Am. A 9, 478–489 (1992). [CrossRef]
  20. B. D. Stone, G. Forbes, “Foundations of second-order layout for asymmetric systems,” J. Opt. Soc. Am. A 9, 2067–2082 (1992). [CrossRef]

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited