Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm

In this article we combine the well-known Ptychographical Iterative Engine (PIE) with the Hybrid Input-Output (HIO) algorithm. The important insight is that the HIO feedback function should be kept strictly separate from the reconstructed object, which is done by introducing a separate feedback function per probe position. We have also combined HIO with floating PIE (fPIE) and extended PIE (ePIE). Simulations indicate that the combined algorithm performs significantly better in many situations. Although we have limited our research to a combination with HIO, the same insight can be used to combine ptychographical algorithms with any phase retrieval algorithm that uses a feedback function.