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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 9 — Sep. 1, 2014
  • pp: 2011–2020

Realization of first-order optical systems using thin convex lenses of fixed focal length

P. A. Ameen Yasir and J. Solomon Ivan  »View Author Affiliations


JOSA A, Vol. 31, Issue 9, pp. 2011-2020 (2014)
http://dx.doi.org/10.1364/JOSAA.31.002011


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Abstract

A general axially symmetric first-order optical system is realized using free propagation and thin convex lenses of fixed focal length. It is shown that not more than five convex lenses of fixed focal length are required to realize the most general first-order optical system, with the required number of lenses depending on the situation. The free propagation distances are evaluated explicitly in each situation. The optimality of the decomposition obtained in each situation is brought out. Decompositions for some familiar subgroups of SL2(R) are also worked out. Convex or concave lenses of arbitrary focal length are realized using three or two convex lenses of fixed focal length, respectively. It is further shown that three convex lenses of arbitrary focal length are sufficient to realize the most general first-order optical system.

© 2014 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.3620) Geometric optics : Lens system design
(080.2468) Geometric optics : First-order optics

ToC Category:
Geometric Optics

History
Original Manuscript: April 8, 2014
Revised Manuscript: June 28, 2014
Manuscript Accepted: July 14, 2014
Published: August 20, 2014

Citation
P. A. Ameen Yasir and J. Solomon Ivan, "Realization of first-order optical systems using thin convex lenses of fixed focal length," J. Opt. Soc. Am. A 31, 2011-2020 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-9-2011


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References

  1. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef]
  2. R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984). [CrossRef]
  3. H. H. Arsenault, “Generalization of the principal plane concept in matrix optics,” Am. J. Phys. 48, 397–399 (1980). [CrossRef]
  4. E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985). [CrossRef]
  5. M. Nazarathy and J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982). [CrossRef]
  6. M. Nazarathy and J. Shamir, “Fourier optics described by operator algebra,” J. Opt. Soc. Am. 70, 150–159 (1980). [CrossRef]
  7. R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,” J. Opt. Soc. Am. A 17, 342–355 (2000). [CrossRef]
  8. L. W. Casperson, “Synthesis of Gaussian beam optical systems,” Appl. Opt. 20, 2243–2249 (1981). [CrossRef]
  9. H. H. Arsenault and B. Macukow, “Factorization of the transfer matrix for symmetrical optical systems,” J. Opt. Soc. Am. 73, 1350–1359 (1983). [CrossRef]
  10. S. Cornbleet, “Geometrical optics reviewed: a new light on an old subject,” Proc. IEEE 71, 471–502 (1983). [CrossRef]
  11. N. Mukunda, “Role of symmetry and group structure in optics,” Current Sci. 59, 1135–1151 (1990).
  12. O. N. Stavroudis, “The lens group,” in The Optics of Rays, Wavefronts, and Caustics, H. S. W. Massey and K. A. Brueckner, eds. (Academic, 1972), pp. 281–297.
  13. M. J. Bastiaans and T. Alieva, “Synthesis of an arbitrary ABCD system with fixed lens positions,” Opt. Lett 31, 2414–2416 (2006). [CrossRef]
  14. M. J. Bastiaans and T. Alieva, “Classification of lossless first-order optical systems and the linear canonical transformation,” J. Opt. Soc. Am. A 24, 1053–1062 (2007). [CrossRef]
  15. T. Alieva and M. J. Bastiaans, “Properties of the linear canonical integral transformation,” J. Opt. Soc. Am. A 24, 3658–3665 (2007). [CrossRef]
  16. X. Liu and K. H. Brenner, “Minimal optical decomposition of ray transfer matrices,” Appl. Opt. 47, E88–E98 (2008). [CrossRef]
  17. D. J. Ming and F. H. Yi, “New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems,” Chin. Phys. B 22, 060302 (2013). [CrossRef]
  18. Arvind, B. Dutta, N. Mukunda, and R. Simon, “The real symplectic groups in quantum mechanics and optics,” Pramana 45, 471–497 (1995). [CrossRef]
  19. R. A. Horn and C. R. Johnson, “Canonical forms for similarity and triangular factorizations,” in Matrix Analysis (Cambridge University, 2013), pp. 163–224.
  20. R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns generalized to Sp(2,R),” Phys. Rev. Lett. 62, 1331–1334 (1989). [CrossRef]
  21. R. Simon, N. Mukunda, and E. C. G. Sudarshan, “The theory of screws: a new geometric representation for the group SU(1,1),” J. Math. Phys. 30, 1000–1006 (1989). [CrossRef]
  22. K. B. Wolf, “Construction and properties of canonical transforms,” in Integral Transforms in Science and Engineering, A. Miele, ed. (Springer, 1979), pp. 381–416.
  23. K. B. Wolf, “Canonical transforms. I. Complex linear transforms,” J. Math. Phys. 15, 1295–1301 (1974). [CrossRef]
  24. N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999). [CrossRef]
  25. R. Simon and K. B. Wolf, “Fractional Fourier transforms in two dimensions,” J. Opt. Soc. Am. A 17, 2368–2381 (2000). [CrossRef]
  26. J. Shamir and N. Cohen, “Root and power transformations in optics,” J. Opt. Soc. Am. A 12, 2415–2423 (1995). [CrossRef]
  27. K. B. Wolf, “Canonical transformations,” in Geometric Optics on Phase Space (Springer, 2004), pp. 25–46.
  28. A. Yariv and P. Yeh, “Rays and optical beams,” in Photonics, A. S. Sedra, ed. (Oxford, 2007), pp. 66–109.

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