The Phase Problem in Object Reconstruction and Interferometry

In this contribution I shall review phase problems from different fields of optics which can be handled with similar techniques. In all cases the problem is to reconstruct the phase of a function from its modulus. In object reconstruction we have to know the complex image wave function (w.f.) while the intensity distribution only gives its modulus. In speckle interferometry only the autocorrelation of the brightness distribution of the source (or equivalently the modulus squared of its Fourier transform) is measurable. In interference microscopy often only the visibility of the interference fringes formed in a Michelson interferometer can be observed, yielding the absolute value of the complex degree of temporal coherence. But we also need its phase for the calculation of the spectral distribution of the source.