Phase Retrieval for Multiple Undersampled Polychromatic Images

We previously developed gradient-search phase-retrieval algorithms and used them to determine the aberrations of the Hubble Space Telescope [1-4]. We were not able to apply these algorithms to all the available data because (i) our algorithms [3-4] required that the images of point objects be of narrow spectral bandwidth, limiting us to using images recorded through narrowband optical filters, and (ii) we required that the measured data in the focal plane be Nyquist sampled for the optical fields, limiting us to the longer wavelengths and the Planetary Camera.