OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 8 — Aug. 1, 1980
  • pp: 976–985

Generalized ray tracing, caustic surfaces, generalized bending, and the construction of a novel merit function for optical design

Rong-Seng Chang and Orestes N. Stavroudis  »View Author Affiliations


JOSA, Vol. 70, Issue 8, pp. 976-985 (1980)
http://dx.doi.org/10.1364/JOSA.70.000976


View Full Text Article

Acrobat PDF (859 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Generalized ray tracing is an algorithm for calculating the geometrical parameters of a wave front in the neighborhood of a traced ray. These calculations are applied, surface by surface, for each traced ray, to an optical system being designed. These calculations determine the two points of contact of each traced ray with the two sheets of a caustic surface. The caustic surfaces are, in fact, aberrated three-dimensional images of object points and therefore contain all information on the geometrical aberrations of the subject lens. Generalized bending is a procedure in which the curvature of a pair of adjacent spherical refracting surfaces, their separation, and the distance to the next succeeding or next preceding surface may be changed so that any paraxial ray is left invariant except at the two affected surfaces. In this study we show that the displacement of a caustic point caused by a generalized bending is in essentially a straight line, that the direction of the displacement is determined by which refracting surfaces are selected, and that the magnitude of the displacement is proportional to the logarithm of the bending parameter. This suggests that caustic surfaces can be used as a merit function in the optical design process, that the merit functions can be calculated by means of generalized ray tracing, and that generalized bending provides an effective means of optimizing the design when included in a feedback loop.

© 1980 Optical Society of America

Citation
Rong-Seng Chang and Orestes N. Stavroudis, "Generalized ray tracing, caustic surfaces, generalized bending, and the construction of a novel merit function for optical design," J. Opt. Soc. Am. 70, 976-985 (1980)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-70-8-976


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. H. Coddington, A System of Optics (Simkin and Marshal, London, 1829, 1830), Parts I and II.
  2. A. Gullstrand, "Die Reelle Optische Abbildung," Sven. Vetensk. Handl. 41, 1–119 (1906).
  3. See, for example, J. J. Stoker, Differential Geometry (Wiley-Interscience, New York, 1969).
  4. C. S. Hastings, New Methods in Geometrical Optics (MacMillan, New York, 1927).
  5. O. Altrichter and G. Schäfer, "Herleitung der Gullstrandschen Grundgleischungen für Schiefe Strahlenbuschel aus den Hauptkrummungen der Wellenflasche," Optik 13, 241–253 (1956).
  6. J. A. Kneisley, III, "Local Curvatures of Wave Fronts in an Optical System," J. Opt. Soc. Am. 54, 229–235 (1964).
  7. S. C. Parker, "Properties and Applications of Generalized Ray Tracing," Thesis, University of Arizona, 1971; Optical Sciences Center Technical Report 71, University of Arizona, Tucson, Arizona, November 1971 (unpublished).
  8. O. N. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York and London, 1972), pp. 313.
  9. O. N. Stavroudis, "A simpler derivation of the formulas for generalized ray tracing," J. Opt. Soc. Am. 66, 1330–1333 (1976).
  10. Dirk J. Struik, Lectures on Classical Differential Geometry, 2nd ed. (Addison-Wesley, Reading, Mass., 1961).
  11. Michel Cagnet, Maurice Francis, and Jean Claude Thrierr, Atlas of Optical Phenomena (Pretice-Hall, Englewood Cliffs, N.J., 1962), plate 1.
  12. O. N. Stavroudis and R. C. Fronczek, "Generalized Ray Tracing and the Caustic Surface," Opt. Laser Technol. 10, 185–19l (1978).
  13. David L. Shealy and Donald G. Burkhard, "Analytical Illuminance Calculation in a Multi-Interface Optical System," Opt. Acta 22, 485–501 (1975).
  14. David L. Shealy, "Analytical illuminance and caustic surface calculations in geometrical optics," Appl. Opt. 15; 2588–2596 (1976).
  15. David L. Shealy, "Caustic surface and the Coddington equations," J. Opt. Soc. Am. 66, 76–77 (1976).
  16. L. E. Sutton, "A method for localized variation of the paths of two paraxial rays," Appl. Opt. 2, 1275–1280 (1963).
  17. John Edward Campbell, Continuous Groups (Chelsea, New York, 1966), Chaps. 1 and 2.
  18. J. H. Darnauer, "Properties of Generalized Bending," Thesis, University of Arizona, 1970; Optical Sciences Center Technical Report No. 64, University of Arizona, Tucson, Arizona, 28 February 1971 (unpublished).
  19. R. S. Chang and O. N. Stavroudis, "Third-order approximation of the displacement of a caustic point due to a generalized bending," J. Opt. Soc. Am. 70, 535–538 (1980).

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  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited