Investigation on the correlation between intensity and phase in monochromatic light

Within the scope of the scalar wave theory, a monochromatic light field can be described at every point in space by means of its amplitude and phase. Optical sensors are only capable to measure the intensity of the light. The amplitude can be directly determined by taking the square root, but it is difficult to obtain information about the phase from the measured intensity. By superposition with a coherent reference beam the spatial phase distribution can be visualized in the intensity of the resulting field. However, the necessity of a reference beam makes this interferometric approach unsuitable for certain applications. For those cases methods are required that allow the extraction of phase information from the original intensity distribution. In this thesis the correlation between intensity and phase is investigated in order to find out to what extend phase information can be extracted from the intensity distribution. Starting from the Helmholtz equation, analytical expressions are derived in which the phase gradient of a monochromatic light field is expressed by means of the three-dimensional intensity distribution. The resulting expressions are utilized to determine under which condititons the phase can be recoverd from the intensity of the light field. It is shown that the absolute value of the three-dimensional phase gradient can be fully determined from non-interferometric intensity measurements. It is also derived that the two-dimensional phase gradient, and thus the phase map in a sensor plane, can be recovered from the intensity distribution only if additional information about the light field are given. A full phase recovery in a sensor plane can be achieved e.g. if the light propagates strictly into one direction. The expressions derived in this thesis are verified and confirmed by means of numerical investigations on simulated speckle fields. The analytical results are compared to common deterministic phase retrieval approaches. It is pointed out that previous results from other researchers appear as a subset of the equations presented in this thesis. Therefore, the presented results can be considered as a generalization of former solutions for deterministic phase retrieval