The Solution to the Inverse Scattering Problem, Based on Fast Zero Location from Two Measurements

The present paper presents a simple and fast method for solving the phase problem in scattering determinations. After defining the problem in the introduction, the paper outlines, in § 2, the main conventional approaches to solving the phase problem, which is due to the presence of complex zeros of the scattered field in the space of measurement. If N such zeros are present, the ambiguity in solving the inverse scattering problem in 2 N . Section 3 offers the mathematical foundations of the proposed new method. It discusses the properties of the distributions of zeros and in particular the way in which they encode the information in the object space. Using these properties as a basis, § 4 puts forward a method for zero location, which involves two conventional scattering measurements, without a priori information. The main advantage of the procedure consists of reducing the number of computations required for determining possible solutions from 2 N to 2N, by using an iterative procedure.

[1]  H. Ferwerda,et al.  The Phase Reconstruction Problem for Wave Amplitudes and Coherence Functions , 1978 .

[2]  M. Fiddy,et al.  The phase problem , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  The Speckle Effect: A Reappraisal , 1978 .

[4]  D. L. Misell.  An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations , 1973 .

[5]  M. A. Fiddy,et al.  Analytic Fourier Optics , 1979 .

[6]  G. Ross.  Scattering and information , 1970, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[7]  E. C. Titchmarsh.  Introduction to the Theory of Fourier Integrals , 1938 .

[8]  D. L. Misell,et al.  LETTER TO THE EDITOR: Phase determination from image intensity measurements in bright-field optics , 1974 .

[9]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[10]  H. Baltes.  Inverse source problems in optics , 1978 .

[11]  Michael A. Fiddy,et al.  The Propagation and Encoding of Information in the Scattered Field by Complex Zeros , 1979 .

[12]  A H Greenaway.  Proposal for phase recovery from a single intensity distribution. , 1977, Optics letters.

[13]  M. Fiddy,et al.  The phase problem in scattering phenomena: the zeros of entire functions and their significance , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.