Retinex-qDPC: Automatic background-rectified quantitative differential phase contrast imaging

The quality of quantitative differential phase contrast reconstruction (qDPC) can be severely degenerated by the mismatch of the background of two oblique illuminated images, yielding problematic phase recovery results. These background mismatches may result from illumination patterns, inhomogeneous media distribution, or other defocusing layers. In previous reports, the background is manually calibrated which is time-consuming, and unstable, since new calibrations are needed if any modification to the optical system was made. It is also impossible to calibrate the background from the defocusing layers, or for high dynamic observation as the background changes over time. The background mismatch reduces the experimental robustness of qDPC and largely limits its applications. To tackle the mismatch of background and increases the experimental robustness, we propose the Retinex-qDPC.

In Retinex-qDPC, we replace the data fidelity term of the previous cost function for qDPC inverse problem, by the images' edge features yielding L₂-Retinex-qDPC and L₁-Retinex-qDPC for high background-robustness qDPC reconstruction. The split Bregman method is used to solve the L₁-Retinex DPC. We compare both Retinex-qDPC models against state-of-the-art DPC reconstruction algorithms including total-variation regularized qDPC, and isotropic-qDPC using both simulated and experimental data.

Retinex qDPC can significantly improve the phase recovery quality by suppressing the impact of mismatch background. Within, the L₁-Retinex-qDPC is better than L₂-Retinex and other state-of-the-art qDPC algorithms.

The Retinex-qDPC increases the experimental robustness against background illumination without any modification of the optical system, which will benefit all qDPC applications.