Abstract: Advanced long-range imaging systems are often equipped with adaptive optics to compensate for the phase distortions caused by atmospheric effects. At the core of this compensation process is the wavefront estimation problem where we need to know the phase of the distortion from the magnitude of a complex signal. While this in many senses is similar to a phase retrieval problem, a phase retrieval method can accept trivial ambiguity in a solution (e.g., conjugate flip) whereas a wavefront estimation needs a unique solution. I will discuss our recent findings about the conditions under which a wavefront estimation will have a unique global solution. I will also demonstrate conceptually how wavefront estimation can be achieved using a single measurement, without any iterative algorithm.