This paper deals with an inverse source problem starting from the knowledge of the radiated field in Fresnel and near zone. In particular, here we are concerned with a 2D geometry characterized by a rectilinear magnetic source and measurement rectilinear domains in Fresnel and near zone. The effect of the added knowledge of the radiated field over a second observation domain is investigated via the Singular Values Decomposition of the radiation operator and we point out how the addition of a second observation domain allows us always to achieve a better noise rejection. Also, we determine conditions under which the knowledge of the field over the second domain increases the information content (as the number of singular values of the radiation operator before their asymptotic decay) for both the Fresnel and near zone cases. Finally reconstruction examples with noise-free and noisy data are presented.
2. Solimene, R. and R. Pierri, "Number of degrees of freedom of the radiated field over multiple bounded domains," Opt. Lett., Vol. 32, 3113-3115, 2007.
3. Bucci, O. M., C. Gennarelli, G. Riccio, and C. Savarese, "Sampling representation of electromagnetic fields over three-dimensional domains," Radio Science, Vol. 34, 567-574, 1999.
4. Sten, J. C.-E. and E. A. Marengo, "Inverse source problem in an oblate spheroidal geometry," IEEE Transactions on Antennas and Propagation, Vol. 54, 3418-3428, 2006.
5. D'Agostino, F., F. Ferrara, C. Gennarelli, R. Guerriero, and M. Migliozzi, "Near field-far field transformation technique with helicoidal scanning for elongated antennas," Progress In Electromagnetics Research B, Vol. 4, 249-261, 2008.
6. Bertero, M. and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics, Bristol, UK, 1998.
7. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons Publishers, Inc., New York, 1989.
8. Barakat, R. and G. Newsam, "Algorithms for reconstruction of partially known, band-limited Fourier-transform pairs from noisy data," J. Opt. Soc. Am. A, Vol. 2, 2027-2039, 1985.
9. Frieden, B. R., "Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions," Progress in Optics, Vol. 4, 311-407, E. Wolf (ed.), North-Holland, Amsterdam, 1971.
10. Miller, D. A. B., "Communicating with waves between volumes: Evaluating orthogonal spatial channels and limits on coupling strengths," Optics Letters, Vol. 39, No. 11, 1681-1699, 2000.