Cepstrum-based interferometric microscopy (CIM) for quantitative phase imaging (2501.10022v1)

Abstract: A universal methodology for coding-decoding the complex amplitude field of an imaged sample in coherent microscopy is presented, where no restrictions on any of the two interferometric beams are required. Thus, the imaging beam can be overlapped with, in general, any other complex amplitude distribution and, in particular, with a coherent and shifted version of itself considering two orthogonal directions. The complex field values are retrieved by a novel Cepstrum-based algorithm, named as Spatial-Shifting Cepstrum (SSC), based on a weighted subtraction of the Cepstrum transform in the cross-correlation term of the object field spectrum in addition with the generation of a complex pupil from the combination of the information retrieved from different holographic recordings (one in horizontal and one in vertical direction) where one of the interferometric beams is shifted 1 pixel. As a result, the field of view is tripled since the complex amplitudes of the three interferometric fields involved in the process are retrieved. Proof-of-concept validation of this methodology, named as Cepstrum-based Interferometric Microscopy (CIM), is provided considering an off-axis holographic configuration for retrieving the cross-correlation of the two interferometric complex amplitude fields in a compact quasi-common path Michelson interferometric configuration. Experimental results for different types of phase samples (resolution test targets for step-by-step calibration and demonstration as well as fixed biosamples) are included.