OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 14 — May. 10, 1998
  • pp: 2996–3006

Validity of Diffraction Tomography Based on the First Born and the First Rytov Approximations

Bingquan Chen and Jakob J. Stamnes  »View Author Affiliations


Applied Optics, Vol. 37, Issue 14, pp. 2996-3006 (1998)
http://dx.doi.org/10.1364/AO.37.002996


View Full Text Article

Acrobat PDF (274 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Using computer simulations we examine the ranges of validity of the first Born and first Rytov approximations employed in diffraction tomography. To that end we apply the filtered backpropagation(FBP) algorithm in conjunction with the first Born approximation and the hybrid FBP algorithm in conjunction with the first Rytov approximation. We find that the range of validity of the first Born approximation is approximately 3 times smaller than that of the first Rytov approximation and that the range of validity of each approximation can be expressed in terms of the product of the refractive-index difference between the object and the background and the size of the object. Also, we establish precise criteria for the validity of diffraction tomography within each of these two approximations. For the first Rytov approximation the validity of the hybrid FBP algorithm is found to be limited by phase-unwrapping problems.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(110.6960) Imaging systems : Tomography
(350.5030) Other areas of optics : Phase

Citation
Bingquan Chen and Jakob J. Stamnes, "Validity of Diffraction Tomography Based on the First Born and the First Rytov Approximations," Appl. Opt. 37, 2996-3006 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-14-2996


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imag. 4, 336–350 (1982).
  2. N. Sponheim, I. Johansen, and A. J. Devaney, “Initial testing of a clinical ultrasound mammograph,” in Acoustical Imaging, H. Lee and G. Wade, eds. (Plenum, New York, 1991), Vol. 18, pp. 401–411.
  3. N. Sponheim, L.-J. Gelius, I. Johansen, and J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. UFFC 38, 370–379 (1991).
  4. M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
  5. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1987), Chap. 6.
  6. T. C. Wedberg and J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
  7. M. I. Sancer and A. D. Varvatsis, “A comparison of the Born and Rytov methods,” Proc. IEEE 58, 140–141 (1970).
  8. J. B. Keller, “Accuracy and validity of the Born and Rytov approximations,” J. Opt. Soc. Am. 59, 1003–1004 (1969).
  9. W. J. Hadden, Jr. and D. Mintzer, “Test of the Born and Rytov approximations using the Epstein problem,” J. Acoust. Soc. Am. 63(5), 1279–1286 (1978).
  10. M. L. Oristaglio, “Accuracy of the Born and Rytov approximations for reflection and refraction at a plane interface,” J. Opt. Soc. Am. A 2, 1987–1993 (1985).
  11. A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6, 374–376 (1981).
  12. M. A. Fiddy, “Inversion of optical scattered field data,” J. Phys. D: Appl. Phys. 19, 301–317 (1986).
  13. T. C. Wedberg, J. J. Stamnes, and W. Singer, “Comparison of the filtered backpropagation and the filtered backprojection algorithms for quantitative tomography,” Appl. Opt. 34, 6575–6581 (1995).
  14. H. T. Yura, C. C. Sung, S. F. Clifford, and R. J. Hill, “Second-order Rytov approximation,” J. Opt. Soc. Am. 73, 500–502 (1983).
  15. W. P. Brown, Jr., “Validity of the Rytov approximation in optical propagation calculations,” J. Opt. Soc. Am. 56, 1045–1052 (1966).
  16. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 7.
  17. K. Iwata and R. Nagata, “Calculation of refractive index distribution from interferograms using the Born and Rytov’s approximation,” Jap. J. Appl. Phys. 14, 1921–1927 (1975).
  18. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955), Chap. 7.
  19. J. J. Stamnes, B. Spjelkavik, and H. M. Pedersen, “Evaluation of diffraction integrals using local phase and amplitude approximations,” Opt. Acta 30, 207–222 (1983).
  20. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 7.
  21. B. Chen and J. J. Stamnes, “Scattering by simple and nonsimple shapes by the combined method of ray tracing and diffraction: application to circular cylinders,” Appl. Opt. 37, 1999–2010 (1998).
  22. D. W. Robinson, “Phase unwrapping methods,” in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 194–229.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited