Optical phase retrieval using four rotated versions of a single binary mask - Simulation results

In signal processing one often faces the phase problem, i.e., when an image is formed information about the phase is lost so that only information about intensity is available. This is often an issue in astronomy, biology, crystallography, speckle imaging, diffractive imaging where the phase of the object must be known. While there have been many approaches how to find a solution to the phase problem, numerical algorithms recovering the phase from intensity measurements become more and more popular. One of such algorithms called PhaseLift has been recently proposed. In this study, we show that even 4 masks may be sufficient for reasonable recovery of the phase. The original wavefront and the recovered wavefront were visually indistinguishable and showed very high correlation. In addition, the four masks are essentially one and the same mask rotated around in steps of 90 degrees. By using just four rotated versions of a single mask, the PhaseLift could be easily implemented in real optical systems thus simplifying the wavefront sensing in astronomy, biology etc.