Phase-diversity methods allow to estimate both the wavefront disturbance as well as the object that is being imaged and that is extended in space. Hence, in principle, phase-diversity methods can be used for wavefront sensing as well, without the need to spill part of the observed light to wavefront sensing with a dedicated wavefront sensor.
However, the use of phase-diversity in real-time applications is prevented by its high computational complexity, determined by the number of parameters quantifying the wavefront and the object.
To reduce the computational complexity, metrics have been proposed that are independent of the object, that allow to only estimate the wavefront, but still yield a nonlinear inverse problem.
To further reduce the computational complexity of the wavefront estimation methods we consider linear approximations of these metrics, that allow to update the estimate of the wavefront by solving a linear least squares problem.
We study the estimation error w.r.t. the presence of noise and the spectral content of the extended object, and compare metrics presented in literature.