Lie algebraic treatment of dioptric power and optical aberrations

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 15, Issue 9, 1998, Pages 2497-2503

  Lakshminarayanan, V ^a   Sridhar, R ^b   Jagannathan, R ^b  

^a UNIVERSITY OF MISSOURI ST LOUIS   (United States)

^b INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; HUMAN; OPTICS; PATHOPHYSIOLOGY; REFRACTION ERROR; VISUAL SYSTEM FUNCTION;

HUMANS; MODELS, BIOLOGICAL; OCULAR PHYSIOLOGY; OPTICS; REFRACTIVE ERRORS;

EID: 0032160581     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.15.002497     Document Type: Article

References (32)

1. W. F. Harris, “Dioptric power: its nature and its represen-tation in three and four dimensional space” Optom. Vision Sci. 74, 349–366 (1997). This issue of the journal (June 1997) is a feature issue on visual optics and contains many related articles.
2. V. Lakshminarayanan and S. Varadharajan, “Expressions for aberration coefficients using nonlinear transforms” Op-tom. Vision Sci. 74, 676–686 (1997).
3. V. Lakshminarayanan and S. Varadharajan, “Calculation of aberration coefficients: a matrix method” in Basic and Clinical Applications of Vision Science, V. Lakshminara-yanan, ed. (Kluwer, Dordrecht, The Netherlands, 1997), pp. 111–115.
4. M. Kondo and Y. Takeuchi, “Matrix method for nonlinear transformation and its application to an optical system” J. Opt. Soc. Am. A 13, 71–89 (1996).
5. A. J. Dragt, “Lie algebraic theory of geometrical optics and optical aberrations” J. Opt. Soc. Am. 72, 372–379 (1982).
6. A. J. Dragt, “Elementary and advanced Lie algebraic meth-ods with applications to accelerator design, electron micro-scopes and light optics” Nucl. Instrum. Methods Phys. Res. A 258, 339–354 (1987).
7. A. J. Dragt, E. Forest, and K. B. Wolf, “Foundations of a Lie algebraic theory of geometrical optics” in Lie Methods in Optics, Vol. 250 of Lecture Notes in Physics, J. Sanchez Mondragon and K. B. Wolf, eds. (Springer-Verlag, Heidel-berg, 1986), pp. 105–157. This book contains an extensive overview of Lie group theory and applications in optics. See also the book edited by K. B. Wolf (Ref. 26) for related ar-ticles.
8. See, for example, W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964)
9. A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover, New York, 1994).
10. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Dover, New York, 1993).
11. See also A. K. Ghatak and K. Thyagarajan, Contemporary Optics (Plenum, New York, 1978).
12. A. J. Dragt, “Nonlinear orbit dynamics” in Physics of High Energy Particle Accelerators, R. A. Carrigan, ed., AIP Con-ference Proceedings 87 (American Institute of Physics, Woodbury, N.Y., 1982), pp. 147–313.
13. E. Forest, “Lie algebraic methods for charged particle beams and light optics” Ph.D. dissertation (University of Maryland, College Park, Md., 1984).
14. O. Stavroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972).
15. For a general treatment of symplectic methods, see V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U. Press, Cambridge, UK, 1984).
16. G. Nemes, “Measuring and handling general astigmatic beams” in Laser Beam Characterization, P. M. Medjias, H. Weber, R. Martinez-Herrero, A. Gonzales-Urena, eds. (So-ciedad Espanola de Optica, Madrid, 1993), pp. 325–356.
17. E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realiza-tion of first order optical systems using thin lenses” Opt. Acta 32, 855–872 (1985).
18. J. A. Arnaud, “Nonorthogonal optical waveguides and reso-nators” Bell Syst. Tech. J. 49, 2311–2348 (1970).
19. M. J. Bastianns, “ABCD law for partially coherent Gauss-ian light, propagating through first order optical systems” Opt. Quantum Electron. 24, 1011–1019 (1992).
20. W. F. Harris, “Ray vector fields, prismatic effect and thick astigmatic optical systems” Optom. Vision Sci. 73, 418–423 (1996).
21. A. J. Dragt and J. M. Finn, “Lie series and invariant func-tions for analytic symplectic maps” J. Math Phys. (N.Y.) 17, 2215–2227 (1976).
22. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Mass., 1980).
23. A. J. Dragt and E. Forest, “Computation of non-linear be-havior of Hamiltonian systems using Lie algebraic methods” J. Math. Phys. (N.Y.) 24, 2734–2744 (1983).
24. G. Rangarajan and M. Sachidanand, “Spherical aberration and its correction using Lie algebraic techniques” Pramana J. Phys. 49, 635–643 (1997).
25. M. Born and E. Wolf, Principles of Optics, 6th ed. (Perga-mon, New York, 1980).
26. D. A. Atchison and G. Smith, “Continuous gradient index and shell models of the human lens” Vision Res. 35, 2529–2538 (1995).
27. A computer code, MARYLIE 3.0, a program for charged par-ticle beam transport based on Lie algebraic methods, has been developed by A. J. Dragt and his colleagues. For in-formation contact A. Dragt, Dynamical Systems and Accel-erator Theory Group, Department of Physics, University of Maryland, College Park, Maryland 20742-4111.
28. P. W. Hawkes, “Lie methods in optics: an assessment” in Lie Methods in Optics II, K. B. Wolf, ed., Vol. 352 of Springer Lecture Notes in Physics (Springer-Verlag, Heidelberg, 1989), pp. 1–17.
29. C. Campbell, “The refractive group” Optom. Vision Sci. 74, 381–387 (1997).
30. See, for example, W. C. Hoffman, “The Lie algebra of visual perception” J. Math. Psychol. 3, 65–98 (1966).
31. See also P. Dodwell, Visual Pattern Recognition (Holt, Rinehart & Win-ston, New York, 1970). The Lie group approach has been used in the invariance coding problem by M. Ferraro and T. Caelli, “Relationship between integral transform invari-ances and Lie group theory” J. Opt. Soc. Am. A 5, 738–742 (1988).
32. V. Lakshminarayanan and T. S. Santhanam, “Representa-tion of rigid stimulus transformations by cortical activity patterns” in Geometric Representations of Perceptual Phe-nomena, R. D. Luce, M. D’Zmura, D. Hoffman, G. Iverson, and A. K. Romney, eds. (Erlbaum, Mahwah, N.J., 1995), pp. 61–69.