Aberration-free synthetic aperture phase microscopy based on alternating direction method

•An effective and straightforward global phase aberration-free synthetic-aperture phase microscopy is proposed.•The optical field is decomposed into two solutions with object terms and aberration terms by using alternating direction method (ADM) in the variable splitting strategy.•The background aberration of synthetic aperture in different angle of oblique illumination can be directly decomposed with the Zernike polynomials.•Faithful high-resolved phase reconstruction by non-iterative synthetic-aperture can be obtained to relax the strict alignment requirements for system aberrations. Objective measurements of the morphology and dynamics of label-free cells and tissues can be achieved by quantitative phase with low phototoxicity and no photobleaching. Modern quantitative phase imaging is developing toward high throughput and a huge amount of data. The quantitative nature makes it susceptible to optical aberrations when high spatial-frequency content of the object spectrum is recorded by using synthetic aperture. We present an effective and straightforward global phase aberration-free synthetic-aperture phase microscopy (AF-SAPM). We introduce alternating direction method (ADM) in the variable splitting strategy. The optimization in optical fields is decomposed into two solutions with object terms and aberration terms. The inverse problem of aberration extraction is solved by imposing the sparsity regularization on the object and coefficients of polynomial bases. The background aberration in different angle of oblique illumination can be directly decomposed with the Zernike polynomials. Global phase aberration can be suppressed for faithful synthetic aperture reconstruction, which outperforms the existing solutions. We demonstrate the availability of the proposed method in quantitative monitoring of endocrine tumor with highly variable phases.