Wigner formulation of optical processing with light of arbitrary coherence

Applied Optics

Volumn 40, Issue 2, 2001, Pages 249-256

  Pe’er, Avi ^a   Wang, Dayong ^a,b   Lohmann, Adolf W ^a,c   Friesemer, Asher A ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b Polytechnic University   (Hong Kong)

^c UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COHERENT LIGHT; FOURIER TRANSFORMS; IMAGING TECHNIQUES; LIGHT PROPAGATION; LIGHTING; OPTICAL FILTERS;

OPTICAL PROCESSORS;

OPTICAL SYSTEMS;

EID: 0038164947     PISSN: 1559128X     EISSN: 21553165     Source Type: Journal    
DOI: 10.1364/AO.40.000249     Document Type: Article

References (21)

1. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).
2. T. Alieva and M. J. Bastiaans, “Self-affinity in phase space,” J. Opt. Soc. Am. A 17, 756-761 (2000).
3. D. Peris and V. C. Georgopoulos, “Wigner distribution representation and analysis of audio signals: an illustrated tutorial review,” J. Audio Eng. Soc. 47, 1043-1053 (1999).
4. K. Banaszek and K. Wodkiewicz, “Non-locality of the Einstein-Podolsky-Rosen state in the Wigner representation,” Phys. Rev. A 58, 4345-4347 (1998).
5. T. A. C. M. Classen and W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis: Part I. Continuous time signals”; “Part II. Discrete time signals”; “Part III. “Relations with other time-frequency signal transformations,” Philips J. Res. 35, 217-250, 276-300, 372-389 (1980).
6. M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227-1238 (1986).
7. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710-1716 (1979).
8. M. J. Bastiaans, “New class of uncertainty relations for partially coherent light,” J. Opt. Soc. Am. A 1, 711-715 (1984).
9. G. A. Deschamps, “Ray techniques in electromagnetism,” Proc. IEEE 60, 1022-1035 (1972).
10. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).
11. A. W. Lohmann, D. Wang, A. Pe’er, and A. A. Friesem, “Design of an achromatic Fourier system by means of Wigner algebra,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, and T. Asakura, eds., Proc. SPIE 3749, 6-7 (1999).
12. R. H. Katyl, “Compensating optical systems. III. Achromatic Fourier transformation,” Appl. Opt. 11, 1255-1260 (1972).
13. S. Leon and E. N. Leith, “Optical processing and holography with polychromatic point source illumination,” Appl. Opt. 24, 3638-3642 (1985).
14. P. Andres, J. Lancis, and W. D. Furlan, “White-light Fourier transformer with low chromatic aberration,” Appl. Opt. 31, 4682-4687 (1992).
15. E. Tajahuerce, J. Lancis, V. Climent, and P. Andres, “Hybrid (refractive-diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband pointsource illumination,” Opt. Commun. 151, 86-92 (1998).
16. G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017-2025 (1981).
17. P. Andres, V. Climent, J. Lancis, G. Minguez-Vega, E. Tajahuerce, and A. W. Lohmann, “All-incoherent dispersion-compensated optical correlator,” Opt. Lett. 24, 1331-1333 (1999).
18. A. Pe’er, D. Wang, A. W. Lohmann, and A. A. Friesem, “Optical correlation with totally incoherent light,” Opt. Lett. 24, 1469-1471 (1999).
19. D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform,” Appl. Opt. 33, 6188-6193 (1994).
20. H. M. Ozaktas and D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743-751 (1995).
21. Y. Bitran, Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Fractional correlation operation: performance analysis,” Appl. Opt. 35, 297-303 (1996).