OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 10 — Oct. 1, 2007
  • pp: 3089–3099

Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative of intensity

Hari M. Varma, R. Mohan Vasu, and A. K. Nandakumaran  »View Author Affiliations


JOSA A, Vol. 24, Issue 10, pp. 3089-3099 (2007)
http://dx.doi.org/10.1364/JOSAA.24.003089


View Full Text Article

Enhanced HTML    Acrobat PDF (438 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present an optical tomographic reconstruction method to recover the complex refractive index distribution from boundary measurements based on intensity, which are the logarithm of intensity and normal derivative of intensity. The method, which is iterative, repeatedly implements the forward propagation equation for light amplitude, the Helmholtz equation, and computes appropriate sensitivity matrices for these measurements. The sensitivity matrices are computed by solving the forward propagation equation for light and its adjoint. The results of numerical experiments show that the data types ln ( I ) and I n reconstructed, respectively, the imaginary and the real part of the object refractive index distribution. Moreover, the imaginary part of the refractive index reconstructed from I n and the real part from ln ( I ) failed to show the object’s inhomogeneity. The value of the propagation constant, k, used in our simulations was 50, and this value resulted in smoothing of the reconstructed inhomogeneities. Thus we have shown that it is possible to reconstruct the complex refractive index distribution directly from the measured intensity without having to first find the light amplitude, as is done in most of the currently available reconstruction algorithms of diffraction tomography.

© 2007 Optical Society of America

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

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 16, 2007
Manuscript Accepted: June 5, 2007
Published: September 7, 2007

Citation
Hari M. Varma, R. Mohan 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-10-3089


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Soumekh and J. H. Choi, "Reconstruction in diffraction imaging," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 36, 93-100 (1989). [CrossRef] [PubMed]
  2. 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). [CrossRef]
  3. S. Gutman and M. Klibanov, "Regularized quasi-Newton method for inverse scattering problems," Math. Comput. Modell. 18, 5-31 (1993). [CrossRef]
  4. R. E. Kleinmann and P. M. Van den Berg, "Modified gradient method for 2-d problem in tomography," J. Comput. Appl. Math. 42, 17-35 (1992). [CrossRef]
  5. A. C. Kak and M. Slaney, "Tomographic imaging with diffracting sources," in Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 211-217.
  6. F. Natterer and F. Wübbeling, "A propagation-backpropagation method for ultrasound tomography," Inverse Probl. 11, 1225-1232 (1995). [CrossRef]
  7. S. S. Cha and H. Sun, "Tomography for reconstructing continuous fields from ill-posed multidirectional interferometric data," Appl. Opt. 29, 251-258 (1990). [CrossRef] [PubMed]
  8. T. E. Gureyev, A. Roberts, and K. A. Nugent, "Phase retrieval with the transport of intensity equation: matrix solution with use of zernite polynomial," J. Opt. Soc. Am. A 12, 1932-1941 (1995). [CrossRef]
  9. K. Ichikawa, A. W. Lohmann, and M. Takeda, "Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments," Appl. Opt. 27, 3433-3436 (1988). [CrossRef] [PubMed]
  10. T. C. Wedberg and J. J. Stamnes, "Comparison of phase retrieval methods in optical diffraction tomography," Pure Appl. Opt. 4, 39-54 (1995). [CrossRef]
  11. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, "Quantitative optical phase microscopy," Opt. Lett. 23, 817-819 (1998). [CrossRef]
  12. G. Gbur and E. Wolf, "Hybrid diffraction tomography without phase information," J. Opt. Soc. Am. A 19, 2194-2202 (2002). [CrossRef]
  13. M. H. Maleki and A. J. Devaney, "Phase retrieval and intensity-only reconstruction algorithms for optical diffraction tomography," J. Opt. Soc. Am. A 10, 1086-1092 (1993). [CrossRef]
  14. J. Cheng and S. Han, "Diffraction tomography reconstruction algorithms for quantitative imaging of phase objects," J. Opt. Soc. Am. A 18, 1460-1464 (2001). [CrossRef]
  15. M. H. Maleki, A. J. Devaney, and A. Schatzberg, "Tomographic reconstruction from optical scattered intensities," J. Opt. Soc. Am. A 9, 1356-1363 (1992). [CrossRef]
  16. M. R. Teague, "Deterministic phase retrieval: a Green's function solution," J. Opt. Soc. Am. 73, 1434-1441 (1983). [CrossRef]
  17. G. Vdovin, "Reconstrution of an object shape from the near-field intensity of a reflected paraxial beam," Appl. Opt. 36, 5508-5513 (1997). [CrossRef] [PubMed]
  18. N. Jayashree, G. Keshava Datta, and R. M. Vasu, "Optical tomographic microscope for quantitaive imaging of phase objects," Appl. Opt. 39, 277-283 (2000). [CrossRef]
  19. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," Phys. Rev. Lett. 77, 2961-2964 (1996). [CrossRef] [PubMed]
  20. A. Semichaevsky and M. Testorf, "Phase-space interpretation of deterministic phase retrieval," J. Opt. Soc. Am. A 21, 2173-2179 (2004). [CrossRef]
  21. A. H. Hielscher, A. D. Klose, and K. M. Hansen, "Gradient-based iterative image reconstruction scheme for time-resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999). [CrossRef] [PubMed]
  22. S. R. Arridge and M. Schweiger, "A gradient based optimization scheme for optical tomography," Opt. Express 6, 213-226 (1998). [CrossRef]
  23. S. R. Arridge, "Topical review: optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999). [CrossRef]
  24. S. R. Arridge, "Photon-measurement density functions. Part 1: analytical forms," Appl. Opt. 34, 7395-7409 (1995). [CrossRef] [PubMed]
  25. S. R. Arridge, "Photon-measurement density functions. Part 2: finite-element-method calculations," Appl. Opt. 34, 8026-8037 (1995). [CrossRef] [PubMed]
  26. B. Kanmani and R. M. Vasu, "Diffuse optical tomography through solving a system of quadratic equation: theory and simulation," Phys. Med. Biol. 51, 981-998 (2006). [CrossRef] [PubMed]
  27. J. Shen and L. L. Wang, "Spectral approximation of the Helmholtz equation with high wave numbers," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 43, 623-644 (2005). [CrossRef]
  28. S. Chandler-Wilde and S. Langdon, "A wave number independent boundary element method for an acoustic scattering problem," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 43, 2450-2477 (2006). [CrossRef]
  29. S. Kim, C. S. Shin, and J. B. Keller, "High-frequency asymptotics for the numerical solution of Helmholtz equation," Appl. Math. Lett. 18, 797-804 (2005). [CrossRef]
  30. F. Natterer, "Marching schemes for inverse Helmholtz and Maxwell problems," http://arachne.uni-muenster.de:8000/num/Preprints.
  31. W. Dahmen, "Wavelet and multiscale methods for operator equations," Acta Numerica 6, 55-228 (1997). [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