The phase problem in scattering phenomena  The zeros of entire functions and their significance
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 zerofree 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.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 March 1978
 DOI:
 10.1098/rspa.1978.0056
 Bibcode:
 1978RSPSA.360...25R
 Keywords:

 Electromagnetic Scattering;
 Entire Functions;
 Phases;
 De Broglie Wavelengths;
 Eigenvectors;
 Fourier Transformation;
 Roots Of Equations;
 Physics (General)