Phase diversity: math, methods and prospects, including sequential diversity imaging

Phase Diversity (PD) is an unconventional imaging technique which uses two or more distorted views of an object to perform wavefront sensing and/or to clarify the object. In 1990 it was used to remove the flaw in the Hubble Space Telescope. A major advantage of PD is that it needs no auxiliary hardware, like a guide star or a Shack-Hartmann wavefront sensor. We review a personal path in the discovery and the use of phase diversity. That path started in 1974 with the removal of raster lines in digital-based satellite images and has led to the real-time removal of aberrations in high-performance, ground-based telescopes, among other applications. PD could be used in cell phones which maintain good image quality by changing the camera's optics. The recorded video and the changes in the camera's optics are the necessary observations needed to improve the video, with software called sequential diversity imaging.