  In order to efficiently image a non-absorbing sample (a phase object),
dedicated phase contrast optics are required. Typically, these optics are
designed with the assumption that the sample is weakly scattering, implying a
linear relation between a sample's phase and its transmission function. In the
strongly scattering, non-linear case, the standard optics are ineffective and
the transfer functions used to characterize them are uninformative. We use the
Fisher Information (FI) to assess the efficiency of various phase imaging
schemes and to calculate an Information Transfer Function (ITF). We show that a
generalized version of Zernike phase contrast is efficient given sufficient
foreknowledge of the sample. We show that with no foreknowledge, a random
sensing measurement yields a significant fraction of the available information.
Finally, we introduce a generalized approach to common path interferometry
which can be optimized to prioritize sensitivity to particular sample features.
Each of these measurements can be performed using Fourier lenses and phase
masks.
