Polarization-modulated second harmonic generation ellipsometric microscopy at video rate

Polarisation optics for biomedical and clinical applications: a review

Many polarisation techniques have been harnessed for decades in biological and clinical research, each based upon measurement of the vectorial properties of light or the vectorial transformations imposed on light by objects. Various advanced vector measurement/sensing techniques, physical interpretation methods, and approaches to analyse biomedically relevant information have been developed and harnessed. In this review, we focus mainly on summarising methodologies and applications related to tissue polarimetry, with an emphasis on the adoption of the Stokes-Mueller formalism. Several recent breakthroughs, development trends, and potential multimodal uses in conjunction with other techniques are also presented. The primary goal of the review is to give the reader a general overview in the use of vectorial information that can be obtained by polarisation optics for applications in biomedical and clinical research.

Dual- and single-shot susceptibility ratio measurements with circular polarizations in second-harmonic generation microscopy

Polarization-resolved second-harmonic generation (P-SHG) microscopy is a technique capable of characterizing nonlinear optical properties of noncentrosymmetric biomaterials by extracting the nonlinear susceptibility tensor components ratio χzzz2'/χzxx2' , with z-axis parallel and x-axis perpendicular to the C₆ symmetry axis of molecular fiber, such as a myofibril or a collagen fiber. In this paper, we present two P-SHG techniques based on incoming and outgoing circular polarization states for a fast extraction of χzzz2'/χzxx2' : A dual-shot configuration where the SHG circular anisotropy generated using incident right- and left-handed circularly-polarized light is measured; and a single-shot configuration for which the SHG circular anisotropy is measured using only one incident circular polarization state. These techniques are used to extract the χzzz2'/χzxx2' of myosin fibrils in the body wall muscles of Drosophila melanogaster larva. The results are in good agreement with values obtained from the double Stokes-Mueller polarimetry. The dual- and single-shot circular anisotropy measurements can be used for fast imaging that is independent of the in-plane orientation of the sample. They can be used for imaging of contracting muscles, or for high throughput imaging of large sample areas.

Single-scan interferometric second harmonic generation microscopy using a kHz phase-scanner

In conventional laser-scanning microscopy, images are formed by acquiring the signal from pixel to pixel. Here, we report more than one order of magnitude reduction in acquisition time of Interferometric Second Harmonic Generation (I-SHG) by scanning the phase within each pixel, to characterize the relative polarity of various samples. Using an electro-optic phase-scanner, we show that the phase-shift patterns required for interferometry can be applied at each pixel during the scanning of the sample, allowing single-scan I-SHG (1S-ISHG) measurements. Requiring exposure times comparable to standard SHG intensity images, the additional phase information of the signal can thus be retrieved in parallel to its amplitude at the time-scale of seconds. Moreover, slower modulations can be used to enhance the precision of the phase measurement, without any spatial or temporal shift between interferograms, in contrast to conventional frame phase-shifting I-SHG (standard I-SHG). This continues to extend I-SHG to dynamical processes, and opens it to large-scale studies, as well as to imaging samples where the signal-to-noise ratio is an issue.

Mueller Tensor Nonlinear Optical Polarization Analysis in Turbid Media

A mathematical framework to treat partial polarization in second harmonic generation imaging of nonlinear optical susceptibility is described and applied to imaging tissue sections 5, 40, and 70 μm thick, sufficient to introduce significant depolarization of the incident field. Polarization analysis becomes complicated in turbid media, in which scattering can result in degradation of polarization purity. The simplest framework for describing the polarization of purely polarized light is the Jones framework, which has been applied to great effect in the polarization analysis of second harmonic generation. However, the Jones framework lacks the necessary generality to describe a partially polarized electric field, (i.e., ones positioned within the volume of the Poincaré sphere rather than on the surface). Recent work connecting the Jones framework to the Mueller-Stokes framework has enabled interpretation of results with the more intuitive Jones framework while maintaining generality of the Mueller-Stokes method. The magnitude and nature of linear interactions of the tissue with the incident infrared field are discussed. Despite substantial depolarization, the nonlinear optical susceptibility tensor elements of collagen was recoverable at each pixel images of thick tissue utilizing the described framework. For thick and thin tissues, values of the tensor element ratio ρ were recovered in good agreement with previous studies. Both hyperpolarizing and depolarizing effects of SHG were observed, and the mechanism of hyperpolarization was determined to rest upon the interplay of orientation and relative contribution of polarized and depolarized incident light to elicit SHG.

Monitoring dynamic collagen reorganization during skin stretching with fast polarization-resolved second harmonic generation imaging

The mechanical properties of biological tissues are strongly correlated to the specific distribution of their collagen fibers. Monitoring the dynamic reorganization of the collagen network during mechanical stretching is however a technical challenge, because it requires mapping orientation of collagen fibers in a thick and deforming sample. In this work, a fast polarization-resolved second harmonic generation microscope is implemented to map collagen orientation during mechanical assays. This system is based on line-to-line switching of polarization using an electro-optical modulator and works in epi-detection geometry. After proper calibration, it successfully highlights the collagen dynamic alignment along the traction direction in ex vivo murine skin dermis. This microstructure reorganization is quantified by the entropy of the collagen orientation distribution as a function of the stretch ratio. It exhibits a linear behavior, whose slope is measured with a good accuracy. This approach can be generalized to probe a variety of dynamic processes in thick tissues.

Characterization of Pancreatic Cancer Tissue Using Multiphoton Excitation Fluorescence and Polarization-Sensitive Harmonic Generation Microscopy

Thin tissue sections of normal and tumorous pancreatic tissues stained with hematoxylin and eosin were investigated using multiphoton excitation fluorescence (MPF), second harmonic generation (SHG), and third harmonic generation (THG) microscopies. The cytoplasm, connective tissue, collagen and extracellular structures are visualized with MPF due to the eosin stain, whereas collagen is imaged with endogenous SHG contrast that does not require staining. Cellular structures, including membranous interfaces and nuclear components, are seen with THG due to the aggregation of hematoxylin dye. Changes in the collagen ultrastructure in pancreatic cancer were investigated by a polarization-sensitive SHG microscopy technique, polarization-in, polarization-out (PIPO) SHG. This involves measuring the orientation of the linear polarization of the SHG signal as a function of the linear polarization orientation of the incident laser radiation. From the PIPO SHG data, the second-order non-linear optical susceptibility ratio, χ(2) zzz '/χ(2) zxx ', was obtained that serves as a structural parameter for characterizing the tissue. Furthermore, by assuming C6 symmetry, an additional second-order non-linear optical susceptibility ratio, χ(2) xyz '/χ(2) zxx ', was obtained, which is a measure of the chirality of the collagen fibers. Statistically-significant differences in the χ(2) zzz '/χ(2) zxx ' values were found between tumor and normal pancreatic tissues in periductal, lobular, and parenchymal regions, whereas statistically-significant differences in the full width at half maximum (FWHM) of χ(2) xyz '/χ(2) zxx ' occurrence histograms were found between tumor and normal pancreatic tissues in periductal and parenchymal regions. Additionally, the PIPO SHG data were used to determine the degree of linear polarization (DOLP) of the SHG signal, which indicates the relative linear depolarization of the signal. Statistically-significant differences in DOLP values were found between tumor and normal pancreatic tissues in periductal and parenchymal regions. Hence, the differences observed in the χ(2) zzz '/χ(2) zxx ' values, the FWHM of χ(2) xyz '/χ(2) zxx ' values and the DOLP values could potentially be used to aid pathologists in diagnosing pancreatic cancer.

Spatially encoded polarization-dependent nonlinear optics

A single fixed optic is combined with the sample translation capabilities inherent to most microscopes to achieve precise polarization-dependent second harmonic generation microscopy measurements of thin tissue sections. Although polarization measurements have enabled detailed structural analysis of collagen, challenges in integrating rotation stages or fast electro-optic/photoelastic modulation have complicated the retrofitting of existing systems for precise polarization analysis. Placing a static microretarder array in the rear conjugate plane resulted in spatially encoded polarization modulation across the field of view. A complete set of polarization rotation measurements was acquired at each pixel by sample translation, recovering local-frame tensors relating to structure within collagenous tissue.

Triboluminescence from Pharmaceutical Formulations

Triboluminescence (TL) is shown to enable selective detection of trace crystallinity within nominally amorphous solid dispersions (ASDs). ASDs are increasingly used for the preparation of pharmaceutical formulations, the physical stability of which can be negatively impacted by trace crystallinity introduced during manufacturing or storage. In the present study, TL measurements of a model ASD consisting of griseofulvin in polyethylene glycol produced limits of detection of 140 ppm. Separate studies of the particle size dependence of sucrose crystals and the dependence on polymorphism in clopidogrel bisulfate particles are both consistent with a mechanism for TL closely linked to the piezoelectric response of the crystalline fraction. Whereas disordered polymeric materials cannot support piezoelectric activity, molecular crystals produced from homochiral molecules adopt crystal structures that are overwhelmingly symmetry-allowed for piezoelectricity. Consequently, TL may provide a broadly applicable and simple experimental route for sensitive detection of trace crystallinity within nominally amorphous materials.

Ultrahigh-resolution nonlinear optical imaging of the armchair orientation in 2D transition metal dichalcogenides

We used nonlinear laser scanning optical microscopy to study atomically thin transition metal dichalcogenides (TMDs) and revealed, with unprecedented resolution, the orientational distribution of armchair directions and their degree of organization in the two-dimensional (2D) crystal lattice. In particular, we carried out polarization-resolved second-harmonic generation (PSHG) imaging for monolayer WS2 and obtained, with high-precision, the orientation of the main crystallographic axis (armchair orientation) for each individual 120 × 120 nm2 pixel of the 2D crystal area. Such nanoscale resolution was realized by fitting the experimental PSHG images, obtained with sub-micron precision, to a new generalized theoretical model that accounts for the nonlinear optical properties of TMDs. This enabled us to distinguish between different crystallographic domains, locate boundaries and reveal fine structure. As a consequence, we can calculate the mean orientational average of armchair angle distributions in specific regions of interest and define the corresponding standard deviation as a figure-of-merit for the 2D crystal quality.

Snapshot second-harmonic generation polarimeter based on spectral analysis

A new high-speed second-harmonic generation (SHG) polarimetric method is reported. It is based on the spectral analysis of the SHG radiation emitted by a nonlinear medium excited with circularly polarized femtosecond laser pulses. The setup uses only passive components for polarization encoding and a fast spectrometer for spectral analysis. The method is validated on a z-cut quartz plate, then on a collagen-rich biological tissue with a view to single image polarization-resolved SHG microscopy.

Second Harmonic Generation of Unpolarized Light

A Mueller tensor mathematical framework was applied for predicting and interpreting the second harmonic generation (SHG) produced with an unpolarized fundamental beam. In deep tissue imaging through SHG and multiphoton fluorescence, partial or complete depolarization of the incident light complicates polarization analysis. The proposed framework has the distinct advantage of seamlessly merging the purely polarized theory based on the Jones or Cartesian susceptibility tensors with a more general Mueller tensor framework capable of handling partial depolarized fundamental and/or SHG produced. The predictions of the model are in excellent agreement with experimental measurements of z-cut quartz and mouse tail tendon obtained with polarized and depolarized incident light. The polarization-dependent SHG produced with unpolarized fundamental allowed determination of collagen fiber orientation in agreement with orthogonal methods based on image analysis. This method has the distinct advantage of being immune to birefringence or depolarization of the fundamental beam for structural analysis of tissues.

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. 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.

Recent Advances in Nonlinear Optical Analyses of Pharmaceutical Materials in the Solid State

The past decade has seen an increase in the use of nonlinear optical (NLO) techniques such as second harmonic generation, coherent antistokes Raman scattering, stimulated Raman scattering, and two-photon fluorescence for the solid-state characterization of pharmaceutical materials. These combined techniques offer several advantages (e.g., speed, selectivity, quantitation) of potential interest to the pharmaceutical community, as decreased characterization times in formulation development and testing could help decrease the time required to bring new, higher quality drugs to market. The large body of literature recently published in this field merits a review. Literature will be discussed in order of drug development, starting with applications in initial therapeutic molecule crystallization and polymorphic analysis, followed by final dosage form characterization, and ending with drug product performance testing.

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. Polarization-dependent second harmonic generation measurement was performed on Z-cut quartz and the local-frame tensor elements were calculated. The recovered tensor elements agree with the expected values dictated by symmetry.

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. SHG-CS was applied to the analysis of BaTiO3 nanoparticles ranging from 200 to ∼500 nm and of photosystem I nanocrystals. A size distribution was recovered for each sample and compared with the size histogram measured by scanning electron microscopy (SEM). Good agreement was observed between the two independent measurements. The intrinsic selectivity of the second-order nonlinear optical process provides SHG-CS with the ability to distinguish well ordered nanocrystals from conglomerates and amorphous aggregates. Combining the recovered distribution of particle diameters with the histogram of measured SHG intensities provides the inherent hyperpolarizability per unit volume of the SHG-active nanoparticles. Simulations suggest that the SHG activity per unit volume is likely to exhibit relatively low sensitivity to the subtle distortions within the lattice that contribute to resolution loss in X-ray diffraction, but high sensitivity to the presence of multi-domain crystals.

Polarized light interaction with tissues

This tutorial-review introduces the fundamentals of polarized light interaction with biological tissues and presents some of the recent key polarization optical methods that have made possible the quantitative studies essential for biomedical diagnostics. Tissue structures and the corresponding models showing linear and circular birefringence, dichroism, and chirality are analyzed. As the basis for a quantitative description of the interaction of polarized light with tissues, the theory of polarization transfer in a random medium is used. This theory employs the modified transfer equation for Stokes parameters to predict the polarization properties of single- and multiple-scattered optical fields. The near-order of scatterers in tissues is accounted for to provide an adequate description of tissue polarization properties. Biomedical diagnostic techniques based on polarized light detection, including polarization imaging and spectroscopy, amplitude and intensity light scattering matrix measurements, and polarization-sensitive optical coherence tomography are described. Examples of biomedical applications of these techniques for early diagnostics of cataracts, detection of precancer, and prediction of skin disease are presented. The substantial reduction of light scattering multiplicity at tissue optical clearing that leads to a lesser influence of scattering on the measured intrinsic polarization properties of the tissue and allows for more precise quantification of these properties is demonstrated.

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 99.99% confidence interval was achieved by standard statistical tests of the recovered probability density functions for the measured observables following two class linear discriminant analysis. These measurements target bottlenecks in small-volume, high-throughput solid form screening experiments for polymorph discovery in the development of emerging active pharmaceutical ingredients.

Connection of Jones and Mueller Tensors in Second Harmonic Generation and Multi-Photon Fluorescence Measurements

Despite the rapidly growing use of second harmonic generation (SHG) and two-photon excited fluorescence (TPEF) microscopy, opportunities for relating polarization-dependent measurements back to local structure and molecular orientation are often confounded by losses in polarization purity. In this work, connections linking Mueller tensor and Jones tensor descriptions of polarization-dependent SHG and TPEF are shown to substantially simplify partially depolarized microscopy measurements. These connections were facilitated by the derivation of several new tensor identity relations, based on generalization of established transformations of matrices and vectors. Methods are described for integrating local-frame symmetry and azimuthal rotation angle for simplifying the Mueller tensor. Through simple expressions bridging the Mueller and Jones formalisms, mathematical models for partial depolarization can greatly simplify interpretation of SHG and TPEF measurements to reconstruct the more general Mueller tensors using the much more concise Jones descriptions for the purely polarized components. Integrating the Mueller architecture allows polarization-dependent SHG and TPEF measurements to be connected back to a relatively small set of free parameters related to local structure and orientation.

Full control of polarization state with a pair of electro-optic modulators for polarization-resolved optical microscopy

Full and arbitrary control of polarization states of light using two independent electro-optic modulators is presented. The mechanism of the controllability is theoretically described using the Jones vector and matrix, and the polarization state change with control parameters is geometrically illustrated in the Stokes parameter space. Our theoretical framework involves possible distortions of the polarization state due to optical elements between the polarization controller and measurement point and presents a mechanism for pre-compensating the polarization distortion. The theory's validity and controllability of the polarization state are experimentally demonstrated with a test optical setup using a dichroic mirror as a polarization distorter. The inevitable intensity variation during polarization sweeps and a strategy for pre- and post-compensation of the variations are discussed. The technique's applicability to bioimaging is also discussed.

Intercalating dyes for enhanced contrast in second-harmonic generation imaging of protein crystals

The second-harmonic generation (SHG) activity of protein crystals was found to be enhanced by up to ∼1000-fold by the intercalation of SHG phores within the crystal lattice. Unlike the intercalation of fluorophores, the SHG phores produced no significant background SHG from solvated dye or from dye intercalated into amorphous aggregates. The polarization-dependent SHG is consistent with the chromophores adopting the symmetry of the crystal lattice. In addition, the degree of enhancement for different symmetries of dyes is consistent with theoretical predictions based on the molecular nonlinear optical response. Kinetics studies indicate that intercalation arises over a timeframe of several minutes in lysozyme, with detectable enhancements within seconds. These results provide a potential means to increase the overall diversity of protein crystals and crystal sizes amenable to characterization by SHG microscopy.

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. Processing of this image set by linear fitting contracts down each set of 10 images to a set of 5 parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the fundamental laser beam. Using these parameters, it is possible to recover the Jones tensor elements of the sample at video rate. Video rate imaging is enabled by performing synchronous digitization (SD), in which a PCIe digital oscilloscope card is synchronized to the laser (the laser is the master clock.) Fast polarization modulation was achieved by modulating an electro-optic modulator synchronously with the laser and digitizer, with a simple sine-wave at 1/10th the period of the laser, producing a repeating pattern of 10 polarization states. This approach was validated using Z-cut quartz, and NOSE microscopy was performed for micro-crystals of naproxen.

Flexible digital signal processing architecture for narrowband and spread-spectrum lock-in detection in multiphoton microscopy and time-resolved spectroscopy

The lock-in amplifier is a critical component in many different types of experiments, because of its ability to reduce spurious or environmental noise components by restricting detection to a single frequency and phase. One example application is pump-probe microscopy, a multiphoton technique that leverages excited-state dynamics for imaging contrast. With this application in mind, we present here the design and implementation of a high-speed lock-in amplifier on the field-programmable gate array (FPGA) coprocessor of a data acquisition board. The most important advantage is the inherent ability to filter signals based on more complex modulation patterns. As an example, we use the flexibility of the FPGA approach to enable a novel pump-probe detection scheme based on spread-spectrum communications techniques.