Color-multiplexed 3D differential phase contrast microscopy with optimal annular illumination

Quantitative phase imaging (QPI) has become a valuable tool in the field of biomedical research due to its ability to quantify refractive index variations of live cells and tissues. For example, three-dimensional differential phase contrast (3D DPC) imaging uses through-focus images captured under different illumination patterns deconvoluted with a computed 3D phase transfer function (PTF) to reconstruct the 3D refractive index. In conventional 3D DPC with semi-circular illumination, partially spatially coherent illumination often diminishes phase contrast, exacerbating inherent noise, and can lead to a large number of zero values in the 3D PTF, resulting in strong low-frequency artifacts and deteriorating imaging resolution. To overcome the above drawbacks, we obtain the conditions for acquiring the optimal 3D PTF based on the analysis of the 3D imaging model and the derivation of the 3D PTF calculation process and propose a 3D DPC microscopy based on optimal annular illumination. The proposed optimal annular illumination pattern minimizes the missing frequency components in the 3D Fourier space, resulting in the best noise-robustness and significantly increased phase contrast. To expedite imaging speed, we utilize a 1/2 annular multiplexed illumination, reducing data acquisition volume by 75%. The 3D refractive index tomography of a simulated 3D phase object, unstained tongue sections, and oral epithelial cells demonstrates that our proposed method achieves the above advantages. In conclusion, we demonstrate a novel 3D DPC microscope that only requires replacing the illumination of a commercial microscope with a programmable LED array. The accurate 3D refractive index tomography and the compactness of the system setup allow the method to play a significant role in the biomedical field.