Ukrainian Journal of Physical Optics 

Number  1, Volume  2, March  2001

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Binary phase elements: optical and statistical properties 
Shovgenyk M.V., Krokhmalskii T.Ye., Kozlovskii M.P.

Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine 1 Svientsitskii Str. 79011, Lviv, Ukraine.

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The optical properties of binary phase elements (BPE) are described by using the method of coordinate-frequency distribution of signals. The analytical expressions for the autocorrelation function and the Wiener spectrum of the BPE spatial frequencies are obtained. On their basis the generalized optical parameter for a quantitative estimation of the level of optical noise and the fluctuation of the intensity of the Wiener spectrum interference is calculated. A statistical description of the phase elements is suggested, on the basis of wich the parameter of non-orthogonality is introduced. It characterizes the binary phase distribution for the classes of orthogonal, quasi-orthogonal and random phase elements. A diagram representation (optical parameter vs non-orthogonality parameter) for the description of the classes of orthogonal, quasi-orthogonal and random phase elements is introduced.

Key words: image processing, phase masks, signal/noise ratio

doi 10.3116/16091833/2/1/1/2001
References
1. Burckhardt C. B., Appl. Opt., 9 (1970) 695.
2. Javidi B., Horner J. L., Opt. Eng. 33 (1994) 1752.
3. Fitio V., Muravsky L., Stefansky A., Proc. SPIE, 2747 (1995) 224.
4. Kallman R. R., Goldstein D. H., Opt. Eng, 33 (1994) 1806.
5. Weaver C. S, Goodman J. W, Appl. Opt., 5 (1966) 1248.
6. Takeda Y., Osliida Y., Miyamura Y., Appl. Opt., 11 (1972) 818.
7. Nakayama Y., Kato M., JOS A, 69 (1979) 1367.
8. Walker S. J, Jahns J, J. Opt. Soc. Am. A, 7 (1990) 1509.
9. Gao G,KostukR, Appl. Opt, 36 (1997) 4853.
10. Hall M, Combinatorial Theory, Braisdel Publishing Company (1967).
11. Harmuth H.F, Transmission of Information by Orthogonal Function. Springer-Verlag (1969).
12. Pratt W. K. Digital Image Processing, v.l, A Wiley-Intersciences Publication, John Wiley and Sons (1978).
13. Shovgenyuk M. V, Krokhmalskii T. Ye, Kozlovskii M. P, Ukr. Phys. J, 43 (1998) 1613 (in Ukrainian).
14. Gaskill J. D, Linear Systems. Fourier Transforms, and Optics, John Wiley & Sons (1978).
15. Bellman R., Introduction to Matrix Analysis, McGraw-Hill (1960).
16. Shovgenyuk M.V, ICMP NASU, Preprint ICMP-92-25U, Lviv (1992) (in Ukrainian).
17. Shovgenyuk M.V, ICMP NASU, Preprint ICMP-92-21U, Lviv (1992) (in Ukrainian).
18. Shovgenyuk M. V, ICMP NASU, Preprint ICMP-93-22U, Lviv (1994) (in Ukrainian).
19. Shovgenyuk M. V, Hlushak P. A, Proc. SPIE, 2747 (1995) 468.
20. Paley R. E. A. C, J. Math. and Physics, 12 (1933) 311.
21. Drouin N.. Building Hadamard Matrices in Step 4 to Order 200, U.S. Department of Commerce, NISTIR 5121 (1993).
22. Sylvester J. J, Phil. Mag, 34 (1867) 461.
23. Kovalenko I. M, Hnedenko H. M, Probability Theory, Vyshcha shkola, Kyiv (1990) (in Russian).
24. Feller W., An Introduction to Probability Theory and its Applications, vol. 1, John Wiley & Sons, Chapman & Hall (1957).
25. Horn R. A, Johnson Ch. R, Matrix Analysis, Cambridge University Press (1986).
26. Stanley H, Introduction to Phase Transitions and Critical Phenomena, Clarendor Press (1971).
27. Ma S.-K, Modern Theory of Critical Phenomena, Benjamin (1976).
28. Shovgenyuk M. V, Krokhmalskii T. Ye, Kozlovskii M. P, ICMP NASU, Preprint ICMP-99-18U, Lviv (1999) (in Ukrainian).
29. Papoulis A, J.Opt.Soc. Amer, 64 (1974) 779.
30. Ojeda-Castaneda J, Sicre E. E, Opt. Acta, 31 (1984) 255.
31. Shovgenyuk M. V, Krokhmalskii T. Ye, Kozlovskii M. P, Proc. SPIE, 3749 (1999) 689.
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