The phase of a signal at a plane is reconstructed from the intensity profiles at two close parallel screens connected by a small <i>abcd</i> canonical transform; this applies to propagation along harmonic and repulsive fibers and in free media. We analyze the relationship between the local spatial frequency (the signal phase derivative) and the derivative of the squared modulus of the signal under a one-parameter canonical transform with respect to the parameter. We thus generalize to all linear systems the results that have been obtained separately for Fresnel and fractional Fourier transforms.
© 2003 Optical Society of America
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(100.5070) Image processing : Phase retrieval
Martin J. Bastiaans and Kurt Bernardo Wolf, "Phase reconstruction from intensity measurements in linear systems," J. Opt. Soc. Am. A 20, 1046-1049 (2003)