High Precision Single Beam Phase Retrieval Techniques

Single beam phase retrieval techniques [1-8] allow the reconstruction of the object phase information of a general volume speckle field for single beam devices such as optical microscopes. These techniques are well-suited for simple optical setups and recover the phase using the intensity recorded at a single or multiple planes. Deterministic Phase Retrieval techniques, as e.g. approaches based on the Transport of Intensity Equation [4-6] or the Contrast Transfer Function [7,8] allow recovering directly the phase of a wavefront, but are limited either to the paraxial case or impose restrictions on the phase to be estimated. Available Iterative Phase Retrieval (IPR) techniques as the Single-Beam-Multiple-Intensity-Reconstruction (SBMIR) algorithm [1-3] overcome this problem and are applicable to the non-paraxial case without imposing restrictions on the object to be investigated. However, this family of IPR techniques are subject to varying levels of performance or stagnate after few numbers of iterations. The stagnation is a result of the slow elimination of the remaining low frequency error components usually in form of a phase tilt, a bell-shaped error, or other low frequency artefacts. This problem results in a poor reconstruction for the case of slow-varying objects or the measurement of aberrations.