Characterizing chromatin packing scaling in whole nuclei using interferometric microscopy.

Chromatin is the macromolecular assembly containing the cell's genetic information, and its architectural conformation facilitates accessibility to activation sites and thus gene expression. We have developed an analytical framework to quantify chromatin structure with spectral microscopy. Chromatin structure can be described as a mass fractal, with packing scaling D up to specific genomic length scales. Considering various system geometries, we established a model to measure D with the interferometric technique partial wave spectroscopy (PWS) and validated the analysis using finite difference time domain to simulate the PWS system. Calculations of D were consistent with ground truth electron microscopy measurements, enabling a high-throughput, label-free approach to quantifying chromatin structure in the nanometer length scale regime.

Spectroscopic microscopy can quantify the statistics of subdiffractional refractive-index fluctuations in media with random rough surfaces.

We previously established that spectroscopic microscopy can quantify subdiffraction-scale refractive index (RI) fluctuations in a label-free dielectric medium with a smooth surface. However, to study more realistic samples, such as biological cells, the effect of rough surface should be considered. In this Letter, we first report an analytical theory to synthesize microscopic images of a rough surface, validate this theory by finite-difference time-domain (FDTD) solutions of Maxwell's equations, and characterize the spectral properties of light reflected from a rough surface. Then, we report a technique to quantify the RI fluctuations beneath a rough surface and demonstrate its efficacy on FDTD-synthesized spectroscopic microscopy images, as well as experimental data obtained from biological cells.

Computation of tightly-focused laser beams in the FDTD method.

We demonstrate how a tightly-focused coherent TEMmn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field around the focus is decomposed into a plane-wave spectrum, and approximated by a finite number of plane waves injected into the FDTD grid using the total-field/scattered-field (TF/SF) method. We provide an error analysis, and guidelines for the discrete approximation. We analyze the scattering of the beam from layered spaces and individual scatterers. The described method should be useful for the simulation of confocal microscopy and optical data storage. An implementation of the method can be found in our free and open source FDTD software ("Angora").

Can OCT be sensitive to nanoscale structural alterations in biological tissue?

Exploration of nanoscale tissue structures is crucial in understanding biological processes. Although novel optical microscopy methods have been developed to probe cellular features beyond the diffraction limit, nanometer-scale quantification remains still inaccessible for in situ tissue. Here we demonstrate that, without actually resolving specific geometrical feature, OCT can be sensitive to tissue structural properties at the nanometer length scale. The statistical mass-density distribution in tissue is quantified by its autocorrelation function modeled by the Whittle-Matern functional family. By measuring the wavelength-dependent backscattering coefficient µb(λ) and the scattering coefficient µs, we introduce a technique called inverse spectroscopic OCT (ISOCT) to quantify the mass-density correlation function. We find that the length scale of sensitivity of ISOCT ranges from ~30 to ~450 nm. Although these sub-diffractional length scales are below the spatial resolution of OCT and therefore not resolvable, they are nonetheless detectable. The sub-diffractional sensitivity is validated by 1) numerical simulations; 2) tissue phantom studies; and 3) ex vivo colon tissue measurements cross-validated by scanning electron microscopy (SEM). Finally, the 3D imaging capability of ISOCT is demonstrated with ex vivo rat buccal and human colon samples.

Single realization stochastic FDTD for weak scattering waves in biological random media.

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result.

Near-field penetrating optical microscopy: a live cell nanoscale refractive index measurement technique for quantification of internal macromolecular density.

Quantification of intracellular nanoscale macromolecular density distribution is a fundamental aspect to understanding cellular processes. We report a near-field penetrating optical microscopy (NPOM) technique to directly probe the internal nanoscale macromolecular density of biological cells through quantification of intracellular refractive index (RI). NPOM inserts a tapered optical fiber probe to successive depths into an illuminated sample. A 50 nm diameter probe tip collects signal that exhibits a linear relationship with the sample RI at a spatial resolution of approximately 50 nm for biologically relevant measurements, one order of magnitude finer than the Abbe diffraction limit. Live and fixed cell data illustrate the mechanical ability of a 50 nm probe to penetrate biological samples.

Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis.

Most cancers are curable if they are diagnosed and treated at an early stage. Recent studies suggest that nanoarchitectural changes occur within cells during early carcinogenesis and that such changes precede microscopically evident tissue alterations. It follows that the ability to comprehensively interrogate cell nanoarchitecture (e.g., macromolecular complexes, DNA, RNA, proteins and lipid membranes) could be critical to the diagnosis of early carcinogenesis. We present a study of the nanoscale mass-density fluctuations of biological tissues by quantifying their degree of disorder at the nanoscale. Transmission electron microscopy images of human tissues are used to construct corresponding effective disordered optical lattices. The properties of nanoscale disorder are then studied by statistical analysis of the inverse participation ratio (IPR) of the spatially localized eigenfunctions of these optical lattices at the nanoscale. Our results show an increase in the disorder of human colonic epithelial cells in subjects harboring early stages of colon neoplasia. Furthermore, our findings strongly suggest that increased nanoscale disorder correlates with the degree of tumorigenicity. Therefore, the IPR technique provides a practicable tool for the detection of nanoarchitectural alterations in the earliest stages of carcinogenesis. Potential applications of the technique for early cancer screening and detection are also discussed.

Experimental confirmation at visible light wavelengths of the backscattering enhancement phenomenon of the photonic nanojet.

We report what we believe is the first experimental confirmation at visible light wavelengths of the backscattering enhancement phenomenon of the photonic nanojet. A specially designed sample stage consisting of a multilayered sandwich of glass, solid polydimethylsiloxane (PDMS), and liquid PDMS, permitted the precise positioning of a gold nanoparticle of diameter between 50 and 100 nm within the nanojet emitted by a 4.4 µm diameter BaTiO(3) microsphere embedded within the PDMS. We determined that, when the gold nanoparticle is optimally positioned within the nanojet, the backscattering of the microsphere can greatly increase: for example, by 3:1 (200%) for the 50 nm gold nanoparticle. The increased backscattering is strongly dependent upon the illumination wavelength and the numerical aperture of the imaging system, and occurs for nonresonant illuminations of the isolated microsphere. Low objective numerical apertures of approximately 0.075 yield the maximum observed increases in backscattering. The measured data agree well with numerical calculations incorporating Mie-based theory and Fourier optics.

Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method.

Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results.

Measurement of the spatial backscattering impulse-response at short length scales with polarized enhanced backscattering.

In this Letter, we describe an easy to implement technique to measure the spatial backscattering impulse-response at length scales shorter than a transport mean free path with resolution of better than 10 µm using the enhanced backscattering phenomenon. This technique enables spectroscopic measurements throughout the visible range and sensitivity to all polarization channels. Through a combination of Monte Carlo simulations and experimental measurements of latex microspheres, we explore the various sensitivities of our technique to both intrinsic sample properties and extrinsic instrumental properties. We conclude by demonstrating the extraordinary sensitivity of our technique to the shape of the scattering phase function, including higher order shape parameters than the anisotropy factor (or first moment).

Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells.

Recently, there has been a major thrust to understand biological processes at the nanoscale. Optical microscopy has been exceedingly useful in imaging cell microarchitecture. Characterization of cell organization at the nanoscale, however, has been stymied by the lack of practical means of cell analysis at these small scales. To address this need, we developed a microscopic spectroscopy technique, single-cell partial-wave spectroscopy (PWS), which provides insights into the statistical properties of the nanoscale architecture of biological cells beyond what conventional microscopy reveals. Coupled with the mesoscopic light transport theory, PWS quantifies the disorder strength of intracellular architecture. As an illustration of the potential of the technique, in the experiments with cell lines and an animal model of colon carcinogenesis we show that increase in the degree of disorder in cell nanoarchitecture parallels genetic events in the early stages of carcinogenesis in otherwise microscopically/histologically normal-appearing cells. These data indicate that this advance in single-cell optics represented by PWS may have significant biomedical applications.

Origins of subdiffractional contrast in optical coherence tomography.

We demonstrate that OCT images quantify subdiffractional tissue structure. Optical coherence tomography (OCT) measures stratified tissue morphology with spatial resolution limited by the temporal coherence length. Spectroscopic OCT processing, on the other hand, has enabled nanoscale sensitive analysis, presenting an unexplored question: how does subdiffractional information get folded into the OCT image and how does one best analyze to allow for unambiguous quantification of ultrastructure? We first develop an FDTD simulation to model spectral domain OCT with nanometer resolution. Using this, we validate an analytical relationship between the sample statistics through the power spectral density (PSD) of refractive index fluctuations and three measurable quantities (image mean, image variance, and spectral slope), and have found that each probes different aspects of the PSD (amplitude, integral and slope, respectively). Finally, we found that only the spectral slope, quantifying mass scaling, is monotonic with the sample autocorrelation shape.

Quasi one-dimensional light beam generated by a graded-index microsphere.

An optically illuminated micron-scale dielectric sphere can generate a photonic nanojet - a nonresonant propagating beam phenomenon of high amplitude, narrow waist, and substantial sensitivity to the presence of nanometer-scale particles and geometric features located within the beam. Via three-dimensional finite-difference time-domain computational electrodynamics modeling of illuminated graded-index microspheres, we have found that the useful length of a photonic nanojet can be increased by an order-of-magnitude to approximately 20 wavelengths. This is effectively a quasi one-dimensional light beam which may be useful for optical detection of natural or artificially introduced nanostructures deeply embedded within biological cells. Of particular interest in this regard is a potential application to visible-light detection of nanometer-scale anomalies within biological cells indicative of early-stage cancer.

Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media.

A rigorous error analysis is presented for the scattering coefficient of biological random continuous media in the Born (or single-scattering) approximation. The analysis is done in two dimensions (2-D) for simplicity of numerical computation. Scattering coefficients of various tissue-like random media are numerically calculated via statistical finite-difference-time-domain analysis. The results are then checked against analytical formulas for the scattering coefficient in the Born approximation. The validity ranges for the correlation length and the refractive index fluctuation strength of the medium are clearly identified. These 2-D results show promise for future 3-D investigations.

Generation of an incident focused light pulse in FDTD.

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is introduced into the FDTD simulation grid using the total-field/scattered-field (TF/SF) approach. The accuracy of our results is demonstrated by comparison with exact theoretical formulas.

Photonic nanojet-enabled optical data storage.

We show that our recently reported microwave photonic jet technique for detection of deeply subwavelength pits in a metal substrate can be extended to optical wavelengths for purposes of high-density data storage. Three-dimensional finite-difference time-domain computational solutions of Maxwell's equations are used to optimize the photonic nanojet and pit configuration to account for the Drude dispersion of an aluminum substrate in the spectral range near lambda= 400 nm. Our results show that nanojet-illuminated pits having lateral dimensions of only 50 nm x 80 nm yield a contrast ratio 27 dB greater than previously reported using a lens system for pits of similar area. Such pits are much smaller than BluRay features. The high detection contrast afforded by the photonic nanojet could potentially yield significant increases in data density and throughput relative to current commercial optical data-storage systems while retaining the basic geometry of the storage medium.

Incorporation of the electrode-electrolyte interface into finite-element models of metal microelectrodes.

An accurate description of the electrode-electrolyte interfacial impedance is critical to the development of computational models of neural recording and stimulation that aim to improve understanding of neuro-electric interfaces and to expedite electrode design. This work examines the effect that the electrode-electrolyte interfacial impedance has upon the solutions generated from time-harmonic finite-element models of cone- and disk-shaped platinum microelectrodes submerged in physiological saline. A thin-layer approximation is utilized to incorporate a platinum-saline interfacial impedance into the finite-element models. This approximation is easy to implement and is not computationally costly. Using an iterative nonlinear solver, solutions were obtained for systems in which the electrode was driven at ac potentials with amplitudes from 10 mV to 500 mV and frequencies from 100 Hz to 100 kHz. The results of these simulations indicate that, under certain conditions, incorporation of the interface may strongly affect the solutions obtained. This effect, however, is dependent upon the amplitude of the driving potential and, to a lesser extent, its frequency. The solutions are most strongly affected at low amplitudes where the impedance of the interface is large. Here, the current density distribution that is calculated from models incorporating the interface is much more uniform than the current density distribution generated by models that neglect the interface. At higher potential amplitudes, however, the impedance of the interface decreases, and its effect on the solutions obtained is attenuated.

Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere.

We theoretically investigate light scattering from a bi-sphere system consisting of a gold nanosphere and a lossless dielectric microsphere illuminated at a resonant optical wavelength of the microsphere. Using generalized multisphere Mie theory, we find that a gold nanosphere 100 times smaller than the dielectric microsphere can be detected with a subdiffraction resolution as fine as one-third wavelength in the background medium when the microsphere is illuminated at a Mie resonance. Otherwise, off-resonance, the spatial resolution reverts to that of the nonresonant nanojet, approximately one-half wavelength in the background medium. An important potential biophotonics application is the detection of antibody-conjugated gold nanoparticles attached to the membranes of living cells in an aqueous environment.

Anomalous oscillations in the spectra of light backscattered by inhomogeneous microparticles.

We report anomalous oscillatory features in the spectra of cross-polarized backscattered light from inhomogeneous dielectric microparticles. Numerical experiments based on the finite-difference-time-domain method demonstrate that cross-polarized backscattered spectra exhibit oscillation frequencies with two a priori surprising features. First, the oscillation frequencies decrease as the correlation length (Lc) of the particle's refractive index increases. Second, high-frequency oscillations exist even for Lc much smaller than the optical wavelength. These findings are exactly opposite to what is observed in co-polarized backscattering spectra, and are not expected from conventional optical scattering theory. We explain this anomalous behavior by examining the path-length distributions of the backscattered photons in the cross polarization.

Review of interferometric spectroscopy of scattered light for the quantification of subdiffractional structure of biomaterials.

Optical microscopy is the staple technique in the examination of microscale material structure in basic science and applied research. Of particular importance to biology and medical research is the visualization and analysis of the weakly scattering biological cells and tissues. However, the resolution of optical microscopy is limited to ? 200 ?? nm due to the fundamental diffraction limit of light. We review one distinct form of the spectroscopic microscopy (SM) method, which is founded in the analysis of the second-order spectral statistic of a wavelength-dependent bright-field far-zone reflected-light microscope image. This technique offers clear advantages for biomedical research by alleviating two notorious challenges of the optical evaluation of biomaterials: the diffraction limit of light and the lack of sensitivity to biological, optically transparent structures. Addressing the first issue, it has been shown that the spectroscopic content of a bright-field microscope image quantifies structural composition of samples at arbitrarily small length scales, limited by the signal-to-noise ratio of the detector, without necessarily resolving them. Addressing the second issue, SM utilizes a reference arm, sample arm interference scheme, which allows us to elevate the weak scattering signal from biomaterials above the instrument noise floor.