Automatic compensation of phase aberrations in digital holographic microscopy based on sparse optimization

In digital holographic microscopy, phase aberrations, which are usually caused by the imperfections of components and nontelecentric configuration of the optical system, severely affect the visualization and quantitative measurement for phase-contrast imaging. Here, we propose a purely numerical and automatic method to compensate for phase aberrations. Without any manual involvement of selecting a sample-free background, the compensation is cast as a surface fitting problem, in which the aberration surface is approximated by formulating an inverse problem. By adopting the ℓ₁-norm as the loss function and by minimizing an objective function, aberrations can be accurately fitted and thus removed numerically. Synthetic and experimental results are demonstrated to verify the efficacy of this method over the least squares method.