Nonlinear polarization tensor measurement with a vectorial complex field in second-harmonic-generation microscopy

Abstract

Polarization-sensitive second-harmonic-generation microscopy (pSHGM) allows one to determine the molecular orientation of harmonophores. Conventional point scanning based pSHGM is time consuming and subject to the assumption of the cylinder symmetry of the sample. Here, we propose a wide-field pSHGM measurement scheme that is able to measure the second-order nonlinear polarization tensor. The measurement scheme is based on first-order Born approximation, from which the relation between incident fundamental wave, second harmonic wave, and nonlinear polarization tensor has been established. It suggests that the polarization tensor can be solved by measuring the vectorial second harmonic complex fields corresponding to three independent polarization states of the incident fundamental wave. An experiment on measuring the supramolecular orientations, in terms of their symmetric axis, of myosin in rat muscle tissue has been carried out to demonstrate the proposed measurement scheme. Benefiting from the ability of recording the second harmonic signal from different positions parallelly, the proposed method possesses a higher imaging frame rate compared to point scanning based pSHGM. With the present configuration, it takes 0.01 s to acquire a 128\ifmmode\times\else\texttimes\fi{}128 pixels image, which is mainly limited by the excitation power density for wide-field illumination. For the same data throughput using pixel-by-pixel scanning, 0.16 s acquisition time is required for a pixel dwell time of 10 \textmu{}s. Having the ability of wide-field imaging and polarization measurement, the present work also lays a foundation for high-resolution SHG microscopy using computed tomography.