No Access Submitted: 05 February 2002 Accepted: 21 March 2002 Published Online: 21 June 2002
Review of Scientific Instruments 73, 2634 (2002);
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  • Vladimir Dribinski
  • Alexei Ossadtchi
  • Vladimir A. Mandelshtam
  • Hanna Reisler
In this article we present a new method for reconstructing three-dimensional (3D) images with cylindrical symmetry from their two-dimensional projections. The method is based on expanding the projection in a basis set of functions that are analytical projections of known well-behaved functions. The original 3D image can then be reconstructed as a linear combination of these well-behaved functions, which have a Gaussian-like shape, with the same expansion coefficients as the projection. In the process of finding the expansion coefficients, regularization is used to achieve a more reliable reconstruction of noisy projections. The method is efficient and computationally cheap and is particularly well suited for transforming projections obtained in photoion and photoelectron imaging experiments. It can be used for any image with cylindrical symmetry, requires minimal user’s input, and provides a reliable reconstruction in certain cases when the commonly used Fourier–Hankel Abel transform method fails.
  1. 1. A. G. Suitsand R. E. Continetti, ACS Symp. Ser. 770 (2001) and papers therein. Google Scholar
  2. 2. A. T. J. B. Eppinkand D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997). Google ScholarScitation, ISI
  3. 3. Y. Tanaka, M. Kawasaki, Y. Matsumi, H. Fujiwara, T. Ishiwata, L. J. Rogers, R. N. Dixon, and M. N. R. Ashfold, J. Chem. Phys. 109, 1315 (1998). Google ScholarScitation, ISI
  4. 4. B.-Y. Chang, R. C. Hoetzlein, J. A. Mueller, J. D. Geiser, and P. L. Houston, Rev. Sci. Instrum. 69, 1665 (1998). Google ScholarScitation, ISI
  5. 5. F. B. Hildebrand, Methods of Applied Mathematics (Prentice-Hall, Englewood Cliffs, NJ, 1952). Google Scholar
  6. 6. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1978). Google Scholar
  7. 7. K. Bockasten, J. Opt. Soc. Am. 51, 943 (1961). Google ScholarCrossref
  8. 8. M. P. Freemanand S. Katz, J. Opt. Soc. Am. 53, 1172 (1963). Google ScholarCrossref
  9. 9. C. J. Cremersand R. C. Birkebak, Appl. Opt. 5, 1057 (1966). Google ScholarCrossref
  10. 10. L. M. Smith, D. R. Keefer, and S. I. Sudharsanan, J. Quant. Spectrosc. Radiat. Transf. 39, 367 (1988). Google ScholarCrossref
  11. 11. Y. Sato, Y. Matsumi, M. Kawasaki, K. Tsukiyama, and R. Bersohn, J. Phys. Chem. 99, 16307 (1995). Google ScholarCrossref, ISI
  12. 12. C. Bordas, F. Paulig, H. Helm, and D. L. Huestis, Rev. Sci. Instrum. 67, 2257 (1996). Google ScholarScitation, ISI
  13. 13. J. Winterhalter, D. Maier, J. Honerkamp, V. Schyja, and H. Helm, J. Chem. Phys. 110, 11187 (1999). Google ScholarScitation
  14. 14. M. J. J. Vrakking, Rev. Sci. Instrum. 72, 4084 (2001). Google ScholarScitation, ISI
  15. 15. R. N. Stricklandand D. W. Chandler, Appl. Opt. 30, 1811 (1991). Google ScholarCrossref
  16. 16. A. N. Tikhonov, Sov. Math. Dokl. 4, 1035 (1963). Google Scholar
  17. 17. R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York, 1988). Google Scholar
  18. 18. V. Dribinski, A. B. Potter, A. V. Demyanenko, and H. Reisler, J. Chem. Phys. 115, 7474 (2001). Google ScholarScitation
  19. 19. D. H. Parkerand A. T. J. B. Eppink, J. Chem. Phys. 107, 2357 (1997); Google ScholarScitation, ISI
    (private communication). , Google Scholar
  20. 20. A. Neumaier, SIAM Rev. 40, 636 (1998). Google ScholarCrossref
  21. 21. A Windows-compatible version of the code is available by contacting H. Reisler at [email protected], Google Scholar
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