Accurate one-dimensional inverse scattering using a nonlinear renormalization technique

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 2, Issue 11, 1985, Pages 1922-1930

  Jaggard, D L ^a   Kim, Y ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747842430     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.2.001922     Document Type: Article

References (21)

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4. J. R. Pierce, "A note on the transmission line equation in terms of impedance," Bell Syst. Tech. J. 22, 263-265 (1943). (In this short note, the Riccati differential equation is derived using circuit concepts and physical insight. It is noted that the same equation describes the electron-optics equation for paraxial trajectories.)
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7. For a modern derivation of the Riccati equation, see, e.g., F. T. Ulaby, R. K. Moore, and A. K. Fung, Fundamentals and Radiometry, Vol. 1 of Microwave Remote Sensing (Addison-Wesley, Reading, Mass., 1981), pp. 82-84.
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13. The techniques include invariant embedding, use of the impedance concept and a direct manipulation of Maxwell's equations or the Helmholtz equation.
14. The dispersive case for a cold plasma is treated by D. B. Ge, D. L. Jaggard, and H. N. Kritikos, "Perturbational and high frequency profile inversion," IEEE Trans. Antennas Propag. AP-31, 804-803 (1983), while the nondispersive case is discussed
15. Note that r(p) must satisfy energy conservation and causality. However, r(p) is a mathematical transformation that does not necessarily satisfy the restriction |r(p)| < 1.
16. Lord Rayleigh (J. W. Strutt), "On the reflection of light from a regularly stratified medium," Proc. R. Soc. London Ser. A 93, 565-577 (1917).
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19. D. L. Jaggard and K. E. Olson, "Numerical reconstruction of dispersionless refractive profiles," J. Opt. Soc. Am. A 2, 1931-1936 (1985).
20. D. L. Jaggard and P. V. Frangos, "Profile reconstruction for dispersionless layered dielectrics with imprecise and band-limited data," IEEE Trans. Antennas Propag. (to be published).
21. H. D. Ladouceur and A. K. Jordan, "Renormalization of an inverse-scattering theory for inhomogeneous dielectrics," J. Opt. Soc. Am. A 2, 1916-1921 (1985).