Fourier spectrum of radially periodic images

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 14, Issue 4, 1997, Pages 816-826

  Amidror, Isaac ^a  

^a EPFL   (Switzerland)

Author keywords

Circular Fourier series; Fourier analysis; Fourier spectrum; Half order derivatives; Impulse rings; Radially periodic images

Indexed keywords

EID: 0000818955     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.14.000816     Document Type: Article

References (29)

1. E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice-Hall, Englewood Cliffs, N.J., 1988), pp. 101–103, 172–173.
2. R. N. Bracewell, Two Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995), p. 358.
3. M. Cartwright, Fourier Methods for Mathematicians, Scientists and Engineers (Ellis Horwood, Chichester, W. Sussex, UK, 1990), pp. 186–191.
4. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 158–160.
5. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), p. 244.
6. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), p. 330
7. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces (Princeton U. Press, Princeton, N.J., 1971), p. 171.
8. I. M. Gelfand and G. E. Shilov, Generalized Functions (Academic, San Diego, Calif., 1964), Vol. 1, p. 185.
9. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), p. 122.
10. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives (Gordon & Breach, Yverdon, Switzerland, 1993).
11. K. B. Oldham and J. Spanier, The Fractional Calculus (Academic, New York, 1974).
12. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y. 1986), pp. 80–82.
13. I. M. Gelfand and G. E. Shilov, Generalized Functions (Academic, San Diego, Calif., 1964), Vol. 1, p. 117.
14. I. M. Gelfand and G. E. Shilov, Generalized Functions (Academic, San Diego, Calif., 1964), Vol. 1, p. 237.
15. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), p. 249.
16. R. N. Bracewell and A. R. Thompson, “The main beam and ringlobes of an east-west rotation-synthesis array,” Astrophys. J. 182, 77–94 (1973).
17. R. N. Bracewell, Two Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995), pp. 371–375.
18. R. N. Bracewell, Two Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995), p. 374.
19. I. M. Gelfand and G. E. Shilov, Generalized Functions (Academic, San Diego, Calif., 1964), Vol. 1, p. 359.
20. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), p. 253.
21. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, pp. 842–847.
22. R. S. Strichartz, A Guide to Distribution Theory and Fourier Transforms (CRC, Boca Raton, Fla., 1994), pp. 62–67.
23. J. Lighthill, Waves in Fluids (Cambridge, London, 1978), pp. 20–21.
24. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 99–110.
25. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), pp. 72–73.
26. R. N. Bracewell, Two Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995), p. 121.
27. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), p. 100.
28. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), p. 149.
29. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986), p. 82.