Annular Radon transform and axicon transform

Optical Engineering

Volumn 45, Issue 7, 2006, Pages

  Kotlyar, V V ^a,b   Kovalev, A A ^a,b  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

^b SAMARA NATIONAL RESEARCH UNIVERSITY   (Russian Federation)

Author keywords

Fourier optics; Image processing; Optical signal processing

Indexed keywords

FOURIER OPTICS; IMAGE RECONSTRUCTION; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; OPTICAL SYSTEMS;

ANNULAR RADON TRANSFORM; AXICON TRANSFORM; OPTICAL SIGNAL PROCESSING;

IMAGING SYSTEMS;

EID: 33749397813     PISSN: 00913286     EISSN: 15602303     Source Type: Journal    
DOI: 10.1117/1.2226990     Document Type: Article

References (24)

1. J. Radon, "Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten, Ber. Verh. Saechs. Akad. Wiss. Leipzig, Math. Phys. Kl. 69, 262-277 (1917).
2. S. R. Deans, The Radon Transform and Some of Its Applications, Wiley-Interscience, New York (1982).
3. A. G. Rann and A. I. Katsevich, The Radon Transform and Local Tomography, CRC Press, Boca Raton, FL (1996).
4. P. Ambs, S. H. Lee, Q. Tain, and Y. Fainmann, "Optical implementation of the Hough transform by a matrix of holograms," Appl. Opt. 25(22), 4035-4045 (1986).
5. P. Woodford and D. Casasent "High-accuracy and fast new format optical Hough-transform," Opt. Mem. Neural Networks 1, 1-16 (1997).
6. V. A. Soifer, V. V. Kotlyar, and R. V. Skidanov, "Optical implementation of the Hough-Radon transform," Computer Opt. (IPSI RAS, Samara) 17, 143-144 (1997).
7. F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations, Interscience, New York (1955).
8. J. A. Fawcett, "Inversion of N-dimensional spherical averages," SIAM J. Appl. Math. 45, 336-341 (1985).
9. L. A. Anderson, "On the determination of a function from spherical averages," SIAM J. Math. Anal. 19, 214-232 (1988).
10. A. E. Yagle, "Inversion of spherical means using inversion and Radon transforms," Inverse Probl. 8, 949-964 (1992).
11. A. M. Cormack, "The Radon transform on a family of curves in the plane (I)," Proc. Am. Math. Soc. 83, 325-330 (1981).
12. A. M. Cormack, "The Radon transform on a family of curves in the plane (II)," Proc. Am. Math. Soc. 86, 293-298 (1982).
13. L. Zalcman, "Offbeat integral geometry," Am. Math. Monthly 17, 161-175 (1980).
14. E. I. Quinto, "Radon transforms on curves in the plane," Appl. Math. (Germany) 30, 231-244 (1994).
15. J. U. McLeod, "The axicon: a new type optical element," J. Opt. Soc. Am. 44(8), 592-597 (1954).
16. 2-TEA laser beam in a high-pressure gas," Opt. Commun. 28(2), 193-196 (1979).
17. I. A. Michaltsova, V. I. Nalivaiko, and L. S. Soldatenkov, "Kinoform axicon," Optik (Jena) 67(3), 267 (1984).
18. P. Belenger and M. Rioux, "Ring pattern of a lens-axicon doublet illuminated by a Gaussian beam," Appl. Opt. 17(7), 1080-1086 (1978).
19. A. Fedotovsky and H. Lehovec, "Optical filter design for annular imaging," Appl. Opt. 13(12), 2919-2923 (1974).
20. A. Ya. Astakhov, G. M. Komov, V. I. Sidorov, I. I. Skryl, and L. M. Soroko, "Design of a Fourier microscope for nuclear emulsion," Report 13-83-119, Joint Institute of Nuclear Research, Dubna (1983).
21. L. M. Soroko, Mesooptics, Foundations and Application, World Scientific, Singapore (1996).
22. V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, "Calculation of phase formers of non-diffracting images and a set of concentric rings," Optik (Jena) 102(2), 45-50 (1996).
23. V. V. Kotlyar and A. A. Kovalev, "The equation for a imaging system a with an axicon" (in Russian), Avtometriya (Novosibirsk) 40(3), 90-99 (2004).
24. Y. S. Chow and H. Teiher, Probability Theory, Springer-Verlag, New York (1978).