Determination of the complex amplitude of monochromatic light from a set of intensity observations

Determination of the complex amplitude of monochromatic light from a set of intensity measurements, without using interference based methods, is often referred to as phase retrieval. Within this approach, recovering the phase can be stated as an inverse problem, where the measured intensities represent the observed impact which has been caused by an unknown set of phase values. In regard to the state of the art, solutions of this inverse problem have been treated, so far, in two different ways; deterministic and iterative. These ways have certain disadvantages which limit their applicability to special cases. For example, the requirement of a priori knowledge about the wave field in deterministic approaches and on the other hand iterative methods do always converge but the physical correctness of the result is not assured. The aim of the present study is to develop a method which uses the physical properties of the light wave as boundary conditions for setting up a kind of iterative process in order to overcome these current problems in phase retrieval. Different to current iterative approaches each mathematical step, i.e. the start condition, the propagation between the planes and the assessment of the results, is going to be determined by applying equations derived from the wave equation. This means to involve the physical properties of light in each step. It is the aim to be able to retrieve the entire monochromatic light field’s complex amplitude from experimentally measured intensities. The new process combines the advantages of the deterministic methods, i.e. deterministic and physically correct results, and the robustness as well as the less complex mathematical structure of the iterative methods while eliminating their respective drawbacks. Eliminating the current need of a priori knowledge about the wave field in deterministic approaches a new flexibility in phase retrieval is obtained, which allows to extract the higher degree of physical information from the intensity of the wave field. Based on this method, the complex amplitude of diffusely scattered monochromatic light is experimentally determined. In comparison to the current phase retrieval methods only four intensity measurements, like in common temporal phase shifting, are required and additionally provides faster convergence.