Page 325 - Phase Space Optics Fundamentals and Applications

306 Chapter Nine

to exhausting the use of phase-space optics for exploring the self-
imaging phenomenon. A number of related phenomena still await a
thorough phase-space interpretation. It would be even more exciting,
however, if the phase-space interpretation helped us to discover new
self-imaging phenomena and applications not obvious from a Fourier
optics perspective.

References
1. M. Bastiaans, “Application of the Wigner distribution function in optics,” in
W. Mecklenbr¨auker and F. Hlawatsch (eds.), The Wigner Distribution—Theory
and Applications in Signal Processing, Elsevier, Amsterdam, 1997, pp. 375–426.
2. A. Torre, Linear Ray and Wave Optics in Phase Space, Elsevier, Amsterdam, 2005.
3. M. Testorf, J. Ojeda-Casta˜neda, and A. W. Lohmann (eds.), Selected Papers on
Phase-Space Optics, volume MS 181 of SPIE Milestone Series. SPIE, Bellingham,
Wash., 2006.
4. R. Castaneda, “Phase space representation of spatially partially coherent imag-
ing,” Appl. Opt. 47: E53–E62 (2008).
5. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley, New York, 1991.
6. H. F. Talbot, “Facts relating to optical science. No IV,” Philosophical Mag., J. Sci.,
9: 401–407 (1836).
7. Lord Rayleigh, “On copying diffraction gratings, and on some phenomena
connected therewith,” Philosophical Mag., 11: 196–205 (1881).
8. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am.
57: 772–778 (1967).
9. K. Patorski, “The self-imaging phenomenon and its applications,” in E. Wolf
(ed.), Progress in Optics, vol. XXVII, Elsevier Science, Amsterdam, 1989, pp.
1–108.
10. J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images. I. Plane peri-
odic objects in monochromatic light,” J. Opt. Soc. Am. 55: 373–381 (1965).
11. J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with
applicationto structuredeterminationof phaseobjects,” Opt.Comm. 18: 677–682
(1971).
12. J. Westerholm, J. Turunen, and J. Huttunen, “Fresnel diffraction in fractional
Talbot planes: A new formulation,” J. Opt. Soc. Am. A 11: 1283–1290 (1994).
13. H. Hamam, “Simplified linear formulation of Fresnel diffraction,” Opt. Comm.
144: 89–98 (1997).
14. V. Arriz´on and J. Ojeda-Casta˜neda, “Fresnel diffraction of substructured grat-
ings: Matrix description,” Opt. Lett. 20: 118–120 (1995).
15. V. Arriz´on, J. G. Ibarra, and J. Ojeda-Casta˜neda, “Matrix formulation of the
Fresnel transform of complex transmittance gratings,” J. Opt. Soc. Am. A 13:
2414–2422 (1996).
16. S. B. Tucker, J. Ojeda-Casta˜neda, and W. T. Cathey, “Matrix description of near
field diffraction and the fractional Fourier transform,” J. Opt. Soc. Am. A 16:
316–322 (1999).
17. A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik 79:
41–45 (1988).
18. A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the
Talbot effect,” Appl. Opt. 29: 4337–4340 (1990).
19. J. R. Leger and G. J. Swanson, “Efficient array illuminator using binary-optics
phase plates at fractional Talbot planes,” Opt. Lett. 15: 288–290 (1990).
20. V. Arriz´on and J. Ojeda-Casta˜neda, “Multilevel phase gratings for array illumi-
nators,” Appl. Opt. 33: 5925–5931 (1994).