Fast 8 MHz polarization modulation coupled with analytical modeling, fast beam-scanning, and synchronous digitization (SD) have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and polarized laser transmittance imaging with image acquisition rates up to video rate. In contrast to polarimetry, in which the polarization state of the exiting beam is recorded, NOSE enables recovery of the complex-valued Jones tensor of the sample that describes all polarization-dependent observables of the measurement. Every video-rate scan produces a set of 30 images (10 for each detector with three detectors operating in parallel), each of which corresponds to a different polarization-dependent result. Linear fitting of this image set contracts it down to a set of five parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the incident beam. These parameters can in turn be used to recover the Jones tensor elements of the sample. Following validation of the approach using z-cut quartz, NOSE microscopy was performed for microcrystals of both naproxen and glucose isomerase. When weighted by the measurement time, NOSE microscopy was found to provide a substantial (>7 decades) improvement in the signal-to-noise ratio relative to our previous measurements based on the rotation of optical elements and a 3-fold improvement relative to previous single-point NOSE approaches.

Two-photon excited ultraviolet fluorescence (TPE-UVF) microscopy is explored for sensitive protein-crystal detection as a complement to second-order nonlinear optical imaging of chiral crystals (SONICC). Like conventional ultraviolet fluorescence (UVF), TPE-UVF generates image contrast based on the intrinsic fluorescence of aromatic residues, generally producing higher fluorescence emission within crystals than the mother liquor by nature of the higher local protein concentration. However, TPE-UVF has several advantages over conventional UVF, including (i) insensitivity to optical scattering, allowing imaging in turbid matrices, (ii) direct compatibility with conventional optical plates and windows by using visible light for excitation, (iii) elimination of potentially damaging out-of-plane UV excitation, (iv) improved signal to noise through background reduction from out-of-plane excitation and (v) relatively simple integration into instrumentation developed for SONICC.

Polarization-resolved second-harmonic generation (PR-SHG) microscopy is described and applied to identify the presence of multiple crystallographic domains within protein-crystal conglomerates, which was confirmed by synchrotron X-ray diffraction. Principal component analysis (PCA) of PR-SHG images resulted in principal component 2 (PC2) images with areas of contrasting negative and positive values for conglomerated crystals and PC2 images exhibiting uniformly positive or uniformly negative values for single crystals. Qualitative assessment of PC2 images allowed the identification of domains of different internal ordering within protein-crystal samples as well as differentiation between multi-domain conglomerated crystals and single crystals. PR-SHG assessments of crystalline domains were in good agreement with spatially resolved synchrotron X-ray diffraction measurements. These results have implications for improving the productive throughput of protein structure determination through early identification of multi-domain crystals.

Nonlinear optical Stokes ellipsometric (NOSE) microscopy was demonstrated for the analysis of collagen-rich biological tissues. NOSE is based on polarization-dependent second harmonic generation imaging. NOSE was used to access the molecular-level distribution of collagen fibril orientation relative to the local fiber axis at every position within the field of view. Fibril tilt-angle distribution was investigated by combining the NOSE measurements with ab initio calculations of the predicted molecular nonlinear optical response of a single collagen triple helix. The results were compared with results obtained previously by scanning electron microscopy, nuclear magnetic resonance imaging, and electron tomography. These results were enabled by first measuring the laboratory-frame Jones nonlinear susceptibility tensor, then extending to the local-frame tensor through pixel-by-pixel corrections based on local orientation.

A symmetry-additive ab initio model for second-harmonic generation (SHG) activity of protein crystals was applied to assess the likely protein-crystal coverage of SHG microscopy. Calculations were performed for 250 proteins in nine pointgroup symmetries: a total of 2250 crystals. The model suggests that the crystal symmetry and the limit of detection of the instrument are expected to be the strongest predictors of coverage of the factors considered, which also included secondary-structural content and protein size. Much of the diversity in SHG activity is expected to arise primarily from the variability in the intrinsic protein response as well as the orientation within the crystal lattice. Two or more ordersof-magnitude variation in intensity are expected even within protein crystals of the same symmetry. SHG measurements of tetragonal lysozyme crystals confirmed detection, from which a protein coverage of $84% was estimated based on the proportion of proteins calculated to produce SHG responses greater than that of tetragonal lysozyme. Good agreement was observed between the measured and calculated ratios of the SHG intensity from lysozyme in tetragonal and monoclinic lattices.