Ray matrix analysis of anamorphic fractional Fourier systems

Journal of Optics A: Pure and Applied Optics

Volumn 8, Issue 5, 2006, Pages 427-435

  Moreno, Ignacio ^a   Ferreira, Carlos ^b   Sánchez López, María M ^a  

^a MIGUEL HERNÁNDEZ UNIVERSITY   (Spain)

^b UNIVERSITY OF VALENCIA   (Spain)

Author keywords

Anamorphic systems; Fractional Fourier transform; Ray matrices

Indexed keywords

FOURIER TRANSFORMS; LARGE SCALE SYSTEMS; MATRIX ALGEBRA; OPTICAL ENGINEERING; OPTICAL SYSTEMS; RAY TRACING;

ANAMORPHIC SYSTEMS; FRACTIONAL FOURIER TRANSFORM; RAY MATRICES; TUNABLE ANAMORPHIC FRACTIONAL;

FOURIER OPTICS;

EID: 33744475843     PISSN: 14644258     EISSN: 17413567     Source Type: Journal    
DOI: 10.1088/1464-4258/8/5/010     Document Type: Article

References (37)

1. Collicott S H and Hesselink L 1992 Analysis and design of an anamorphic optical processor for speckle metrology and velocimetry Appl. Opt. 31 1646
2. Marchand P J, Harvey P C and Esener S C 1995 Motionless-head parallel-readout optical-disk system: experimental results Appl. Opt. 34 7604
3. Walpole J N, Choi H K, Missaggia L J, Liau Z L, Connors MK, Turner G W, Manfra M J and Cook C C 1999 High-power high-brightness GaInAsSb-AlGaAsSb tapered laser arrays with anamorphic collimating lenses emitting at 2.05νm IEEE Photon. Technol. Lett. 11 1223
4. Beijersbergen M W, Allen L, Van der Veen H E L O and Woerdman J P 1993 Astigmatic laser mode converters and transfer of orbital angular momentum Opt. Commun. 96 123
5. Courtial J and Padgett M J 1999 Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes Opt. Commun. 159 13
6. Goodman J W 1968 Introduction to Fourier Optics (New York: McGraw-Hill)
7. Szoplik T, Kosek W and Ferreira C 1984 Nonsymmetric Fourier transforming with an anamorphic system Appl. Opt. 23 905
8. Szoplik T and Arsenault H H 1985 Rotation-variant optical data processing using the 2D nonsymmetrical Fourier transform Appl. Opt. 24 168
9. Andrés P, Ferreira C and Bonet E 1985 Fraunhofer diffraction patterns from apertures illuminated with nonparallel light in nonsymmetrical Fourier transformers Appl. Opt. 24 1549
10. Milln M S, Ferreira C, Pons A and Andrés P 1988 Application of anamorphic systems to directional pseudocolor encoding Opt. Eng. 27 129
11. Bonet E, Ferreira C, Andrés P and Pons A 1986 Nonsymmetrical Fourier correlator to increase the angular discrimination in character recognition Opt. Commun. 53 155
12. Ferreira C, Buades M J and Moya A 1989 Anamorphic correlator for character recognition. Detection of characters of different size J. Opt. 20 181
13. Ferreira C and Vzquez C 1990 Anamorphic multiple matched filter for character recognition performance with signals of equal size J. Mod. Opt. 37 1343
14. Mendlovic D and Ozaktas H M 1993 Fractional Fourier transforms and their optical implementation J. Opt. Soc. Am. 10 1875
15. Mendlovic D, Bitran Y, Dorsch R, Ferreira C, García J and Ozaktas H O 1990 Anamorphic fractional Fourier transform: optical implementation and applications Appl. Opt. 34 7451
16. García J, Mendlovic D, Zalevsky Z and Lohmann A 1996 Space-variant simultaneous detection of several objects by the use of multiple anamorphic fractional-Fourier-transform filters Appl. Opt. 35 3945
17. Unnikrishnan G, Joseph J and Singh K 2001 Fractional Fourier domain encrypted holographic memory by use of an anamorphic optical system Appl. Opt. 40 299
18. Ozaktas H M and Mendlovic D 1994 Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators Opt. Lett. 19 1678
19. Ozaktas H M and and Erden M F 1997 Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of first-order optical systems Opt. Commun. 143 75
20. Collados M V, Atencia J, Tornos J and Quintanilla M 2005 Construction and characterization of compound holographic lenses for multichannel one-dimensional Fourier transformation and optical parallel processing Opt. Commun. 249 85
21. Davis J A, Schley-Seebold H M and Cottrell D M 1992 Anamorphic optical systems using programmable spatial light modulators Appl. Opt. 31 6185
22. Pang L, Levy U, Campbell K, Groisman A and Fainman Y 2005 Set of two orthogonal adaptive cylindrical lenses in a monolith elastometer device Opt. Express 13 9003
23. Gerrard A and Burch J M 1975 Introduction to Matrix Methods in Optics (New York: Dover)
24. Collins S A 1970 Lens-system diffraction integral written in terms of matrix optics J. Opt. Soc. Am. 60 1168
25. Yura H T and Hanson S G 1987 Optical beam wave propagation through complex optical systems J. Opt. Soc. Am. 4 1931
26. Hanson S G, Jakobsen M L and Larsen H E 2005 Miniaturized optical sensors based on lens arrays Opt. Pura Apl. 38 59
27. Moreno I, Snchez-Lpez M M, Ferreira C, Davis J A and Mateos F 2005 Teaching Fourier optics through ray matrices Eur. J. Phys. 26 261
28. Arsenault H H 1980 A matrix representation for nonsymmetrical optical systems J. Opt. 11 87-91
29. Macukow B and Arsenault H H 1983 Matrix decomposition for nonsymmetrical optical systems J. Opt. Soc. Am. 73 1360
30. Bernardo L M 1996 ABCD matrix formalism of fractional Fourier optics Opt. Eng. 35 742
31. Erden M F, Ozaktas H M, Sahin A and Mendlovic D 1996 Design of dynamically adjustable anamorphic fractional Fourier transformer Opt. Commun. 136 52
32. Saleh B E A and Teich M C 1991 Fundamentals of Photonics (New York: Wiley) chapter 1 (Ray Optics)
33. Lohmann A 1993 Image rotation, Wigner rotation, and the fractional Fourier transform J. Opt. Soc. Am. 10 2181
34. Liu S, Ren H, Zhang J and Zhang X 1997 Image-scaling problem in the optical fractional Fourier transform Appl. Opt. 36 5671
35. Torre A 2002 The fractional Fourier transform and some of its applications to optics Progress in Optics vol 43 ed E Wolf (Amsterdam: Elsevier) chapter 7 p531
36. Siegman A E 1986 Lasers (Sausalito: University Science Books) chapter 15 (Ray Optics and Ray Matrices)
37. Moreno I, Davis J A and Crabtree K 2003 Fractional Fourier transform optical system with programmable diffractive lenses Appl. Opt. 42 6544