OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 5 — May. 1, 2014
  • pp: 996–1006

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data

Jem Teresa, Mamatha Venugopal, Debasish Roy, Ram Mohan Vasu, and Rajan Kanhirodan  »View Author Affiliations

JOSA A, Vol. 31, Issue 5, pp. 996-1006 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1216 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We develop iterative diffraction tomography algorithms, which are similar to the distorted Born algorithms, for inverting scattered intensity data. Within the Born approximation, the unknown scattered field is expressed as a multiplicative perturbation to the incident field. With this, the forward equation becomes stable, which helps us compute nearly oscillation-free solutions that have immediate bearing on the accuracy of the Jacobian computed for use in a deterministic Gauss–Newton (GN) reconstruction. However, since the data are inherently noisy and the sensitivity of measurement to refractive index away from the detectors is poor, we report a derivative-free evolutionary stochastic scheme, providing strictly additive updates in order to bridge the measurement-prediction misfit, to arrive at the refractive index distribution from intensity transport data. The superiority of the stochastic algorithm over the GN scheme for similar settings is demonstrated by the reconstruction of the refractive index profile from simulated and experimentally acquired intensity data.

© 2014 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(110.6960) Imaging systems : Tomography
(290.3200) Scattering : Inverse scattering

ToC Category:
Imaging Systems

Original Manuscript: December 20, 2013
Revised Manuscript: March 12, 2014
Manuscript Accepted: March 12, 2014
Published: April 9, 2014

Virtual Issues
Vol. 9, Iss. 7 Virtual Journal for Biomedical Optics

Jem Teresa, Mamatha Venugopal, Debasish Roy, Ram Mohan Vasu, and Rajan Kanhirodan, "Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data," J. Opt. Soc. Am. A 31, 996-1006 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. C. Kak and M. Slaney, “Tomographic imaging with diffracting sources,” in Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 203–273.
  2. I. H. Lira and C. M. Vest, “Refraction correction in holographic interferometry and tomography of transparent objects,” Appl. Opt. 26, 3919–3928 (1987). [CrossRef]
  3. A. H. Andersen, “Tomography transform and inverse in geometrical optics,” J. Opt. Soc. Am. A 4, 1385–1395 (1987). [CrossRef]
  4. A. C. Kak, “Tomographic imaging with diffracting and non-diffracting sources,” in Array Signal Processing, S. Haykin, ed. (Prentice-Hall, 1985).
  5. A. J. Devaney and G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imag. 6, 181–193 (1984).
  6. M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microw. Theory Technol. 32, 860–874 (1984). [CrossRef]
  7. P. Guo and A. J. Devaney, “Comparison of reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 22, 2338–2347 (2005). [CrossRef]
  8. G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46, 1748–1761 (2000). [CrossRef]
  9. W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imag. 9, 218–225 (1990). [CrossRef]
  10. A. H. Hielscher, A. D. Klose, and K. M. Hansen, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999). [CrossRef]
  11. K. Belkebir and A. G. Tijhuis, “Modified gradient method and modified Born method for solving a two-dimensional inverse scattering problem,” Inverse Probl. 17, 1671–1688 (2001). [CrossRef]
  12. R. F. Harrington, Field Computation by Moment Method (Macmillan, 1968).
  13. F. Natterer and F. Wübbeling, “A propagation-backpropagation method for ultrasound tomography,” Inverse Probl. 11, 1225–1232 (1995). [CrossRef]
  14. N. Pimprikar, J. Teresa, D. Roy, R. M. Vasu, and K. Rajan, “An approximately H1-optimal Petrov-Galerkin mesh-free method: application to computation of scattered light for optical tomography,” CMES—Computer Modeling in Engineering and Sciences 92, 33–61 (2013).
  15. P. Guo and A. J. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. 29, 857–859 (2004). [CrossRef]
  16. N. Jayashree, G. K. Datta, and R. M. Vasu, “Optical tomographic microscope for quantitative imaging of phase objects,” Appl. Opt. 39, 277–283 (2000). [CrossRef]
  17. M. H. Maleki and A. J. Devaney, “Phase retrieval and intensity-only reconstruction algorithm for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993). [CrossRef]
  18. G. Gbur and E. Wolf, “Hybrid diffraction tomography without phase information,” J. Opt. Soc. Am. A 19, 2194–2202 (2002). [CrossRef]
  19. M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image reconstruction in spherical-wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 2651–2661 (2005). [CrossRef]
  20. H. M. Varma, R. M. Vasu, and A. K. Nandakumaran, “Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative of intensity,” J. Opt. Soc. Am. A 24, 3089–3099 (2007). [CrossRef]
  21. A. M. Stuart, “Inverse problems: a Bayesian perspective,” Acta Numerica 19, 451–559 (2010). [CrossRef]
  22. M. Venugopal, D. Roy, and R. M. Vasu, “A new evolutionary Bayesian approach incorporating additive path correction for nonlinear inverse problems,” arxiv.org/pdf/1305.2702.
  23. D. L. Marks, “A family of approximations scanning the Born and Rytov scattering series,” Opt. Express 14, 8837–8848 (2006). [CrossRef]
  24. F. C. Klebaner, Introduction to Stochastic Calculus with Applications, 2nd ed. (Imperial College, 2005).
  25. T. Raveendran, S. Sarkar, D. Roy, and R. M. Vasu, “A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems,” Inverse Probl. 29, 065002 (2013). [CrossRef]
  26. S. Sarkar, S. R. Chowdhury, M. Venugopal, R. M. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014). [CrossRef]
  27. D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008). [CrossRef]
  28. B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009). [CrossRef]
  29. D. Roy, “A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics,” Int. J. Numer. Methods Eng. 61, 764–790 (2004). [CrossRef]
  30. L. S. Ramachandra and D. Roy, “A new method for nonlinear two-point boundary value problems in solid mechanics,” J. Appl. Mech. 68, 776–786 (2001). [CrossRef]
  31. D. Roy and L. S. Ramachandra, “A semi-analytical locally transversal linearization method for non-linear dynamical systems,” Int. J. Numer. Methods Eng. 51, 203–224 (2001). [CrossRef]

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