The phase problem in scattering phenomena: the zeros of entire functions and their significance

Author:

Abstract

The paper outlines an approach to the calculation of the phase from intensity data based on the properties of the distribution of zeros of functions of exponential type. This leads to a reinterpretation of such phenomena as Gibbs’ or speckle, which underlines their intrinsic unity. The phase problem is solved for functions which present complex zeros by apodization, i.e. by creating a sufficiently large zero-free area. The method is based on a compromise between signal to noise ratio and resolution and is meaningful provided the apodization required is not too severe. Real zeros, for which the phase problem is trivial, occur only for the special case of eigenfunctions of the Fourier transform

Publisher

The Royal Society

Subject

Pharmacology (medical)

Reference23 articles.

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2. de Brange L. 1968 Hilbert spaces of entirefunctions. Englewood Cliffs New J ersey: Prentice-Hall.

3. Bremermann H. 1965 Distributions complex variables and Fourier transforms. Reading Massachusetts: Addison-Wesley.

4. The phase problem

5. Cartwright M. L. 1930 Q.

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