Unified Theory for Polarization Analysis in Second Harmonic and Sum Frequency Microscopy.

A unified theoretical framework for the recovery of second-order nonlinear susceptibility tensors and sample orientations from polarization-dependent second harmonic generation and sum frequency generation microscopy was developed. Jones formalism was extended to nonlinear optics and was used to bridge the experimental observables and the local-frame tensor elements. Four commonly used experimental architectures were explicitly explored, including polarization rotation with no postsample optics, polarization-in polarization-out measurement, and polarization modulation with and without postsample optics.

Imaging the Nonlinear Susceptibility Tensor of Collagen by Nonlinear Optical Stokes Ellipsometry.

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.

Second harmonic generation correlation spectroscopy for characterizing translationally diffusing protein nanocrystals.

Second harmonic generation correlation spectroscopy (SHG-CS) is demonstrated as a new approach to protein nanocrystal characterization. A novel line-scanning approach was performed to enable autocorrelation analysis without sample damage from the intense incident beam. An analytical model for autocorrelation was developed, which includes a correction for the optical scattering forces arising when focusing intense, infrared beams.

Rapid Discrimination of Polymorphic Crystal Forms by Nonlinear Optical Stokes Ellipsometric Microscopy.

The use of nonlinear optical Stokes ellipsometric (NOSE) microscopy for rapid discrimination of two polymorphic forms of the small molecule d-mannitol is presented. Fast (8 MHz) polarization modulated beam-scanning microscopy and a recently developed iterative, nonlinear least-squares fitting algorithm were combined to allow discrimination of orthorhombic and monoclinic crystal structures of d-mannitol with data acquisition times of <7 s per field of view with a signal-to-noise ratio (SNR) of ∼300. Discrimination between polymorphic forms within the 99.

Synchronous-digitization for Video Rate Polarization Modulated Beam Scanning Second Harmonic Generation Microscopy.

Fast beam-scanning non-linear optical microscopy, coupled with fast (8 MHz) polarization modulation and analytical modeling have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and linear Stokes ellipsometry imaging at video rate (15 Hz). NOSE enables recovery of the complex-valued Jones tensor that describes the polarization-dependent observables, in contrast to polarimetry, in which the polarization stated of the exciting beam is recorded. Each data acquisition consists of 30 images (10 for each detector, with three detectors operating in parallel), each of which corresponds to polarization-dependent results.

Polarization-modulated second harmonic generation ellipsometric microscopy at video rate.

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.

Digital deconvolution filter derived from linear discriminant analysis and application for multiphoton fluorescence microscopy.

A digital filter derived from linear discriminant analysis (LDA) is developed for recovering impulse responses in photon counting from a high speed photodetector (rise time of ~1 ns) and applied to remove ringing distortions from impedance mismatch in multiphoton fluorescence microscopy. Training of the digital filter was achieved by defining temporally coincident and noncoincident transients and identifying the projection within filter-space that best separated the two classes. Once trained, data analysis by digital filtering can be performed quickly.

Polarization-resolved second-harmonic generation microscopy as a method to visualize protein-crystal domains.

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.

Modeling the SHG activities of diverse protein crystals.

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 point-group 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.

Two-photon excited UV fluorescence for protein crystal detection.

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.