Phase retrieval framework for direct reconstruction of the projected refractive index applied to ptychography and holography

The interaction of an object with a coherent probe often encodes its properties in a complex-valued function, which is then detected in an intensity-only measurement. Phase retrieval methods commonly infer this complex-valued function from the intensity. However, the decoding of the object from the complex-valued function often involves some ambiguity in the phase, e.g., when the phase shift in the object exceeds 2 π . Here, we present a phase retrieval framework to directly recover the amplitude and phase of the object. This refractive framework is straightforward to integrate into existing algorithms. As examples, we introduce refractive algorithms for ptychography and near-field holography and demonstrate this method using measured data.