The functional relationship between the phase logarithm and the amplitude logarithm of a wave function near its real-plane zero point is found. This result takes the form of the dispersion relation that is deduced analytically and supported by the numerical simulation of the light-wave propagation in an inhomogeneous medium. The sufficient and necessary conditions of existence of this relationship are discussed, and their validity for infinite spectra is shown.
© 1998 Optical Society of America
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.5070) Image processing : Phase retrieval
Valeri A. Tartakovski and Nadežda N. Mayer, "Dispersion Relation for Real-Plane Zeros as a Concept of Wave-Front Measurement," Appl. Opt. 37, 7689-7697 (1998)