System model enabling fast tomographic phase microscopy with total variation regularisation.

Tomographic phase microscopy (TPM) facilitates three-dimensional imaging of live cells based on quantitative measurement of the distribution of the refractive index, but without the need for specific staining. However, the limited imaging speed and the anisotropic resolution of the reconstructed refractive index map remain major obstacles to the extension and further application of TPM. To address these obstacles, we first formulate a general measurement model that linearises the relationship between the measurement data and refractive index map based on a system matrix. In this way, the measurement system is interpreted as a linear system in a complete manner. Then we propose a reconstruction framework for retrieving the refractive index map from the measurement data with reduced angular sample frequency and limited angular coverage of illumination. The framework aims to transform the reconstruction task into an optimisation scheme based on total variation norm regularisation, followed by an efficient solution using the accelerated alternating direction method of multipliers algorithm. Using this method, only sparse angular illuminations need to be collected, thus speeding up the imaging process. We obtained experimental results from both cell-mimic phantom data and real measurement data, which showed that the proposed method can improve the imaging speed while still providing refractive index images with better quality compared with a conventional reconstruction method.