Phase recovery from Fresnel incoherent correlation holography using differential Zernike fitting

Fresnel incoherent correlation holography (FINCH) was created to improve imaging resolution and 3D imaging capabilities using spatially incoherent illumination. The optical setup of a FINCH-based interferometer is closely related to a radial shearing interferometer, which measures the radial phase difference of an input wavefront. By using phase retrieval methodologies from lateral shearing interferometry, namely, differential Zernike fitting (DZF), we show that FINCH-based and radial shearing interferometry can be used for phase retrieval and adaptive optics (AO). In this paper, we describe the phase retrieval algorithm using least squares-based DZF and demonstrate a simple adaptive optics loop with an aberrated point spread function using wave optics simulation. We find that FINCH-based phase retrieval has the advantages of fast phase retrieval measurements, thanks to well-studied least squares-based phase reconstruction methods, improved resolution compared to the Shack-Hartmann-based wavefront sensing, and the simplified optical setup of radial shearing interferometry.