Ukrainian Journal of Physical Optics 

Number  3, Volume 4,  2003

Home page

Other articles 
in this issue

Generalized fractional Fourier transform in optical systems
Kozlovskii Yu.M.

Institute for Condensed Matter Physics of the NAS of Ukraine,1 Svientsitskii Str., 79011 Lviv, Ukraine

download full version

We investigate the properties of intensity distribution of the two optical signals, which are shifted and modulated by a plane wave and correspond to the generalized fractional Fourier transform (FFT). The results of analytic and numerical calculations show the possibilities for designing new systems for the processing of information. As an example, the correlator based on the generalized FFT is considered. The domains of the generalized FFT in the practicable optical systems are obtained and analyzed. A principal possibility for the formation and recording of the interference pattern is demonstrated for the case when the images of the FFT, starting from the general form of the cascade matrix, are optically superimposed.

Key words: fractional Fourier transform, fractional correlation, cross shifting, image forming rectangular slit, ambiguity function
PACS: 42.30.K, 42.30.V, 42.79, 42.15.E, 42.25.F

doi 10.3116/16091833/4/3/124/2003

1. Namias V, 1980. J. Instr. Maths Applics. 25: 241-265.
2. Ozaktas HM, Mendlovic D, 1993. Opt. Commun. 101: 163-169.
3. Shovgenyuk MV, Kozlovskii YuM, 2001. Preprint ICMP-01-05U Lviv 42.
4. Shovgenyuk MV, Kozlovskii YuM, 2000. Dep. NAS Ukraine 6: 92-97.
5. Lohmann AW, 1993. J. Opt. Soc. Am. 10: 2181-2186
6. Mendlovic D, Ozaktas H, Lohmann A, 1995. J. Opt. Soc. Am. 34: 303-309
7. Granieri S, Arizaga R, Sicre E, 1997. Appl. Opt. 36: 6636-6645.
8. Lohmann AW, Mendlovic D, 1997. Appl. Opt. 36: 7402-7407.
9. Kuo CJ, Luo Y, 1998. Appl. Opt. 37: 8270-8276.
10. Jin S, Lee S, 2002. Opt. Commun. 207: 161-168.
11. Weaver C, Goodman J, 1966. Appl. Opt. 5: 1234-1249.
12. Shovgenyuk MV, Kozlovskii YuM, Muravsky L, Fitio V, 2002. Ukr. J. Phys. Opt. 3: 106-115
13. Shovgenyuk MV, Kozlovskii YuM, 2001. Phys. Collection of Shevchenko Sci. Soc. (Lviv), 4: 289-306.
14. Shovgenyuk MV, Kozlovskii YuM, 2000. Proc. 2nd Int. Smakula’s Symp., Ternopil.

Home | Instructions to Authors | Editorial Board | Meetings & Exhibitions