Mapping imaging transfer functions through holographic field correlations

Holographic microscopy recovers both the phase and amplitude of an optical field through a calibrated interferogram. We combine holographic imaging and {\it in-situ} microscopy to image elongated superfluids. By looking at the scattered field density correlations of an otherwise point correlated ensemble, we study an aberrated imaging transfer function. A regularized inversion digitally frees our images from the detected aberrations, improving our imaging performance with optimal signal-to-noise ratio.