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On the Validity of Born Approximation

By Jianbing Li, Xuesong Wang, and Tao Wang
Progress In Electromagnetics Research, Vol. 107, 219-237, 2010


Born approximation is widely used in (inverse) scattering problems to alleviate the computational di±culty, but its validity and applicability are not well defined. In this paper, a universal criterion to identify the validity of Born approximation is put forward based on applying the operator theory on the scattering integral equation. In comparison with the traditional criteria, the new one excels in its ability to give a wider and more rigorous valid frequency range, especially while non-uniform scatterers are under consideration. Numerical examples verify the validity and advantage of the new criterion.


Jianbing Li, Xuesong Wang, and Tao Wang, "On the Validity of Born Approximation," Progress In Electromagnetics Research, Vol. 107, 219-237, 2010.


    1. Ballentine, L. E., Quantum Mechanics: A Modern Development, 672, World Scientific Publishing Company, Singapore, 1998.

    2. Van Deb Berg, P. M., "Iterative computational techniques in scattering based upon the integrated square error criterion," IEEE Transactions on Antennas and Propagation, Vol. 32, No. 10, 1063-1071, 1984.

    3. Bohren, C. F. and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983.

    4. Born, M. and E. Wolf, Principles of Optics, 7 Ed., Cambridge University Press, Cambridge, 1999.

    5. Bucci, O. M., N. Cardace, L. Crocco, and T. Isernia, "Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems," J. Opt. Soc. Am. A, Vol. 18, No. 8, 1832-1843, 2001.

    6. Chen, B. and J. J. Stamnes, "Validity of diffraction tomography based on the first Born and the first Rytov approximations," Appl. Opt., Vol. 37, No. 14, 2996-3006, 1998.

    7. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990.

    8. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 356, Springer, New York, 1998.

    9. Crocco, L. and M. D'Urso, "The contrast source-extended Born model for 2D subsurface scattering problems," Progress In Electromagnetics Research B, Vol. 17, 343-359, 2009.

    10. Cui, T. J., W. C. Chew, A. A. Aydiner, and S. Chen, "Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method," IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 2, 339-345, 2001.

    11. Durgun, A. C. and M. Kuzuoglu, "Computation of physical optics integral by Levin's integration algorithm," Progress In Electromagnetics Research M, Vol. 6, 59-74, 2009.

    12. Fan, Z., R.-S. Chen, H. Chen, and D.-Z. Ding, "Weak form nonuniform fast fourier transform method for solving volume integral equations," Progress In Electromagnetics Research, Vol. 89, 275-289, 2009.

    13. Harrington, R. F., Time-harmonic Electromagnetic Fields, IEEE Press, New York, 2001.

    14. Hatamzadeh-Varmazyar, S., M. Naser-Moghadasi, and Z. Masouri, "A moment method simulation of electromagnetic scattering from conducting bodies," Progress In Electromagnetics Research, Vol. 81, 99-119, 2008.

    15. Isernia, T., L. Crocco, and M. D'Urso, "New tools and series for forward and inverse scattering problems in lossy media," IEEE Geoscience and Remote Sensing Letters, Vol. 1, No. 4, 327-331, 2004.

    16. Ishimaru, A., Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978.

    17. Kak, A. C. and M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, Piscataway, 1988.

    18. Karris, S. T., Signals and Systems with MATLAB Computing and Simulink Modeling, 3 Ed., Orchard Publications, 2006.

    19. Kreyszig, E., Introductory Functional Analysis with Applications, John Wiley & Sons Inc, New York, 1978.

    20. Li, J., X. Wang, and T. Wang, "A universal solution to one-dimensional highly oscillatory integrals," Science in China, Vol. 51, No. 10, 1614-1622, 2008.

    21. Li, J., X.Wang, T.Wang, and C. Shen, "Delaminating quadrature method for multi-dimensional highly oscillatory integrals," Appl. Math. Comput., Vol. 209, No. 2, 327-338, 2009.

    22. Li, J., X. Wang, T. Wang, and S. Xiao, "An improved levin quadrature method for highly oscillatory integrals," Appl. Num. Math., Vol. 60, 833-842, 2010.

    23. Matzler, C., "Matlab functions for mie scattering and absorption,", Technical report, Institute of Applied Physics, University of Bern, 2001.

    24. Carruth McGehee, O., An Introduction to Complex Analysis, John Wiley & Sons Inc, New York, 2000.

    25. Mojabi, P. and J. LoVetri, "Adapting the normalized cumulative periodogram parameter-choice method to the tikhonov regularization of 2-D/TM electromagnetic inverse scattering using Born iterative method," Progress In Electromagnetics Research M, Vol. 1, 111-138, 2008.

    26. Nordebo, S. and M. Gustafsson, "A priori modeling for gradient based inverse scattering algorithms," Progress In Electromagnetics Research B, Vol. 16, 407-432, 2009.

    27. Leonard, L. S., Quantum Mechanics, McGraw-Hill, New York, 1968.

    28. Shariff, K. and A. Wray, "Analysis of the radar reflectivity of aircraft vortex wakes," J. Fluid Mech., Vol. 463, 121-161, 2002.

    29. Su, D. Y., D. M. Fu, and D. Yu, "Genetic algorithms and method of moments for the design of PIFAS," Progress In Electromagnetics Research Letters, Vol. 1, 9-18, 2008.

    30. Trattner, S., M. Feigin, H. Greenspan, and N. Sochen, "Validity criterion for the Born approximation convergence in microscopy imaging," J. Opt. Soc. Am. A, Vol. 26, No. 5, 1147-1156, 2009.

    31. Trattner, S., M. Feigin, H. Greenspan, and N. Sochen, "Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging," IEEE 11th International Conference on Computer Vision, Vol. 14, No. 21, 1-8, 2007.

    32. Trattner, S., M. Feigin, H. Greenspan, and N. Sochen, "The Born approximation for round and cubical objects in dic microscopy imaging," Proceeding of the Microscopic Image Analysis with Applications in Biology (MIAAB) Workshop, Piscataway, 2007.

    33. Wen, Y., "Improved recursive algorithm for light scattering by multilayered sphere," Appl. Opt., Vol. 42, No. 9, 1710-1720, 2003.

    34. Wu, Z., L. Guo, K. Ren, G. Gouesbet, and G. Grehan, "Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres," Appl. Opt., Vol. 36, No. 21, 5188-5198, 1997.

    35. Liu, Z. H., E. K. Chua, and K. Y. See, "Accurate and efficient evaluation of method of moments matrix based on a generalized analytical approach," Progress In Electromagnetics Research, Vol. 94, 367-382, 2009.