Calibrated χ⁽²⁾-tensor polarization-resolved second harmonic generation microscopy for precise tissue imaging

Polarization-resolved second harmonic generation (P-SHG) microscopy is commonly used to analyze the second-order susceptibility, χ⁽²⁾, tensor, which enables the calculation of the molecular structure of harmonophores. However, despite extensive research on type I collagen, the measured χ⁽²⁾ ratios vary considerably among published values, which raises the question of whether P-SHG imaging is universally applicable to all tissues containing harmonophores. In this work, we propose that the deviation of χ⁽²⁾ ratios is primarily due to ignoring the molecular tilt angle and chirality in image analysis. To confirm our hypothesis, we present an analytical model based on C₆ symmetry that takes into account these two factors. We also introduce an imaging scheme that splits SHG into X- and Y-polarized image components for χ⁽²⁾ tensor analysis. Our approach effectively improves the precision of determining χ⁽²⁾ ratios, depending on how much the two factors affect the P-SHG signals.