High-Resolution Quantitative Phase Microscopy with Second-Harmonic Generation and Structured Illumination from a k -Space Formulation

We propose a high-resolution label-free two-dimensional imaging method by introducing second-harmonic generation (SHG) and structured illumination in quantitative phase microscopy (QPM), termed ${\mathrm{S}}^{2}\mathrm{QPM}$, which can achieve a fourfold lateral resolution improvement compared with normal incident illumination for noncentrosymmetric structures. Unlike traditional QPM only obtaining information about the optical path difference, ${\mathrm{S}}^{2}\mathrm{QPM}$ can additionally recover structural information from the ${\ensuremath{\chi}}^{(2)}$ distribution. Analytical solutions for SHG fields are obtained by solving the inhomogeneous and nonlinear Helmholtz equation in the $\mathit{k}$-space in a both concise and accurate way. With the $\mathit{k}$-space SHG field solutions for different structured illumination patterns, an object reconstruction model is developed to retrieve the high-resolution normalized ${\ensuremath{\chi}}^{(2)}$ distributions and quantitative phase maps. We simulate high-resolution reconstructions of the normalized ${\ensuremath{\chi}}^{(2)}$ distributions and quantitative phase maps using various resolution targets. The lateral resolution improvement is quantified by synthesizing the object spectrum function and profiling resolution targets.