Spatial Variation Of Refractive Index Research Articles

Evaluation of the spatial variation of the refractive index for biospecimens and dielectric samples using reflection and transmission of polarized light

As predicted by the Fresnel equations, the amplitude of light transmitted or reflected by a specimen is a function of the angle of incidence on the sample surface and the refractive indices of the incident medium and the sample. Of these three parameters, if the first two are known, the emerging light potentially contains information about the refractive index variations in the sample. Using this technique, the refractive index distribution in the human red blood cell is demonstrated, where the ratio of transmittivities for s- and p-polarized light is related to the refractive index of the sample through a calibration curve from which the refractive index is quantitatively evaluated for every pixel of the image. The same technique is followed for reflected samples such as a laser-etched glass plate in which the refractive indices of the plate and the etched regions are measured. In each case, the substrate is a glass prism surface so as to avoid having unwanted backreflections reach the detector. Experimental results are presented.

Two dimensional multifractal detrended fluctuation analysis of low coherence images for diagnosis of cervical pre-cancer

We report detection of cervical pre-cancer through their low coherence images by applying two dimensional multifractal detrended fluctuation analysis. Low coherent backscattered images of pre-cancerous cervical tissue sections were captured using a common path interferometric setup. The captured images contain both depth and lateral information of the spatial variation in refractive index (RI) occurring with progression of cervical pre-cancer. A two-dimensional multifractal detrended fluctuation analysis (2D MFDFA) was applied on these low coherent images to study the variations occurring in their fractal nature. Long-range correlations were observed in the RI fluctuations and the strength of multifractality was found to be stronger for higher grades of cervical pre-cancer. A combination of derived multifractal parameters, namely, the generalized Hurst exponent and width of singularity spectrum showed clear differences among the different grades of pre-cancers. Normal, CIN-I and CIN-II were clearly discriminated by application of support vector machine (SVM) using radial Bessel function (RBF) kernel. The specificities and sensitivities between normal and CIN-I, CIN-I and CIN-II and normal and CIN-II were found to be 94%, 88% and 93%, 96% and 98%, 100% respectively.

Surface plasmon resonance imaging of excitable cells

Surface plasmons (SPs) are surface charge density oscillations occuring at a metal/dieletric interface and are highly sensitive to refractive index variations adjacent to the surface. This sensitivity has been exploited successfully for chemical and biological assays. In these systems, a surface plasmon resonance (SPR)-based sensor detects temporal variations in the refractive index at a point. SPR has also been used in imaging systems where the spatial variations of refractive index in the sample provide the contrast mechanism. SPR imaging systems using high numerical aperture (NA) objective lenses have been designed to image adherent live cells with high magnification and near-diffraction limited spatial resolution. Addressing research questions in cell physiology and pharmacology often requires the development of a multimodal microscope where complementary information can be obtained.In this paper, we present the development of a multimodal microscope that combines SPR imaging with a number of additional imaging modalities including bright-field, epifluorescence, total internal reflection microscopy and SPR fluorescence microscopy. We used a high NA objective lens for SPR and TIR microscopy and the platform has been used to image live cell cultures demonstrating both fluorescent and label-free techniques. Both the SPR and TIR imaging systems feature a wide field of view (~300 µm) that allows measurements from multiple cells whilst maintaining a resolution sufficient to image fine cellular processes. The capability of the platform to perform label-free functional imaging of living cells was demonstrated by imaging the spatial variations in contractions from stem cell-derived cardiomyocytes. This technique shows promise for non-invasive imaging of cultured cells over very long periods of time during development.

Broadband focusing of underwater sound using a transparent pentamode lens.

An inhomogeneous acoustic metamaterial lens based on spatial variation of refractive index for broadband focusing of underwater sound is reported. The index gradient follows a modified hyperbolic secant profile designed to reduce aberration and suppress side lobes. The gradient index (GRIN) lens is comprised of transversely isotropic hexagonal microstructures with tunable quasi-static bulk modulus and mass density. In addition, the unit cells are impedance-matched to water and have in-plane shear modulus negligible compared to the effective bulk modulus. The flat GRIN lens is fabricated by cutting hexagonal centimeter scale hollow microstructures in aluminum plates, which are then stacked and sealed from the exterior water. Broadband focusing effects are observed within the homogenization regime of the lattice in both finite element simulations and underwater measurements (20-40 kHz). This design approach has potential applications in medical ultrasound imaging and underwater acoustic communications.

Mueller matrix approach for probing multifractality in the underlying anisotropic connective tissue.

Spatial variation of refractive index (RI) in connective tissues exhibits multifractality, which encodes useful morphological and ultrastructural information about the disease. We present a spectral Mueller matrix (MM)-based approach in combination with multifractal detrended fluctuation analysis (MFDFA) to exclusively pick out the signature of the underlying connective tissue multifractality through the superficial epithelium layer. The method is based on inverse analysis on selected spectral scattering MM elements encoding the birefringence information on the anisotropic connective tissue. The light scattering spectra corresponding to the birefringence carrying MM elements are then subjected to the Born approximation-based Fourier domain preprocessing to extract ultrastructural RI fluctuations of anisotropic tissue. The extracted RI fluctuations are subsequently analyzed via MFDFA to yield the multifractal tissue parameters. The approach was experimentally validated on a simple tissue model comprising of TiO2 as scatterers of the superficial isotropic layer and rat tail collagen as an underlying anisotropic layer. Finally, the method enabled probing of precancer-related subtle alterations in underlying connective tissue ultrastructural multifractality from intact tissues.

Tomographic imaging of transparent biological samples using the pyramid phase microscope.

We show how a pyramid phase microscope can be used to obtain tomographic information of the spatial variation of refractive index in biological samples using the Radon transform. A method that uses the information provided by the phase microscope for axial and lateral repositioning of the sample when it rotates is also described. Its application to the reconstruction of mouse embryos in the blastocyst stage is demonstrated.

On Galerkin method for solving radiative heat transfer in finite slabs with spatially-variable refractive index

The problem of radiative heat transfer through a finite plane-parallel medium which possesses a continuous transverse spatial variation in refractive index has been solved. Galerkin method is used to have the analytical solution of the integral form of the radiative heat transfer equation, which gives the analytical forms of both the radiation energy density and the net radiant heat flux through the medium. Numerical results are obtained for the reflection and transmission coefficients at the medium boundaries. These results are carried out for isotropic scattering with different thicknesses and different ranges of refractive index. Some obtained results are compared with those calculated by using the Pomraning-Eddington approximation which was previously published, and gave good agreement.

Contribution to the benchmark for ternary mixtures: Measurement of diffusion and Soret coefficients in 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane onboard the ISS.

The paper is devoted to processing the data of DCMIX 1 space experiment. In this experiment, the Optical digital interferometry was used to measure the diffusion and Soret coefficients in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene and n-dodecane at mass fractions of 0.8/0.1/0.1 and at 25°C. The raw interferometric images were processed to obtain the temporal and spatial evolution of refractive indices for two laser beams of different wavelengths. The method for extracting the diffusion and thermal diffusion coefficients originally developed for optical beam deflection was extended to optical digital interferometry allowing for the spatial variation of refractive index along the diffusion path. The method was validated and applied to processing the data for Soret and diffusion steps in 5 experimental runs. The obtained results for the Soret coefficients and one of the eigenvalues of diffusion matrix showed acceptable agreement within each step. The second eigenvalue was not determined with sufficient accuracy.

A closed-form solution of differential approximation for radiative transfer in a planar refractive medium

The closed-form solution of differential approximation (DA) for radiative transfer in a planar, scattering, refractive medium can be derived when the medium is in radiative equilibrium or purely scattering. In this work, linearly and exponentially spatial variations of refractive index are considered. The results obtained by the DA agree well with those obtained by the discrete ordinates method (DOM) and the Monte Carlo method (MCM) for the optically thick cases and the discrepancy between the DA results and the accurate numerical solutions obtained by the DOM and the MCM increases as the optical thickness decreases. The discrepancy between the results obtained by the DA and by the DOM also increases as the gradient of the linear refractive index increases. Besides, the influence of the scattering albedo and the scattering phase function coefficient on the accuracy of the analytical DA solution is less noticeable. Since the internal reflection due to the exponential decay of refractive index increases with the variation range of refractive index, the dimensionless radiative flux decreases with the increase of variation range of refractive index in a purely scattering medium. The present results show that the effect of the internal reflection is stronger in a thinner medium with an exponentially decaying refractive index.

Tropospheric effects on L‐band geosynchronous circular SAR imaging

Circular synthetic aperture radar (SAR) imaging on the geosynchronous orbit has significant potential advantages, such as high resolution three-dimensional imaging, large coverage, but it also has challenges to overcome. One major problem limiting the high-resolution geosynchronous circular SAR (GEOCSAR) performances is the atmospheric effects including the tropospheric and ionospheric effects. In this study, the authors mainly consider the tropospheric effects on L-band GEOCSAR imaging. Since the integration time of GEOCSAR may be as long as 24 h, and the coverage can reach 1/3 of the Earth's surface, the effects of the spatial and temporal variation of the tropospheric refractive index cannot be ignored if well focused images are to be obtained. The analysis shows that the temporal variation of the tropospheric refractive index may cause severe degradation of the SAR images; the spatial variation of the refractive index and the tropospheric turbulence are not the important factor limiting the GEOCSAR imaging performance.

Azimuthally dependent radiative transfer in a slab with variable refractive index

Applying Fourier series expansion and a discrete ordinates method, we obtain accurate solutions of azimuthally dependent radiative transfer in an anisotropically scattering slab with variable refractive index and oblique irradiation. It is found that in a slab with a positive gradient of refractive index the optical distance traveled by incident rays decreases, and thus the value of transmittance increases. Besides, the increase of gradient of refractive index enhances the above effect. Influence of the optical thickness, scattering albedo and phase function of the medium, the incident angle of irradiation and the spatial variation of refractive index on the angular distribution of bidirectional reflectance is also investigated.

Spatial refractive index measurement of porcine artery using differential phase optical coherence microscopy

We describe a methodology to record spatial variation of refractive index of porcine renal artery using differential phase optical coherence microscopy (DP-OCM). The DP-OCM provides quantitative measurement of thin specimen phase retardation and refractive index by measuring optical path-length changes on the order of a few nanometers and with a lateral resolution of 3 microm. The DP-OCM instrumentation is an all-fiber, dual-channel Michelson interferometer constructed using a polarization maintaining (PM) fiber. Two-dimensional en face dual-channel phase images are taken over a 150 x 200 microm region on a microscopic slide, and the images are reconstructed by plotting a two-dimensional refractive index map as the OCM beam is moved across the sample. Because the DP-OCM can record transient changes in the optical path-length, the system may be used to record quantitative optical path-length alterations of tissue in response to various stimuli. A fiber-based DP-OCM may have the potential to substantially improve in vivo imaging of individual cells for a variety of clinical diagnostics, and monitoring applications.

A Fourier Tool for the Analysis of Coherent Light Scattering by Bio-Optical Nanostructures

The fundamental dichotomy between incoherent (phase independent) and coherent (phase dependent) light scattering provides the best criterion for a classification of biological structural color production mechanisms. Incoherent scattering includes Rayleigh, Tyndall, and Mie scattering. Coherent scattering encompasses interference, reinforcement, thin-film reflection, and diffraction. There are three main classes of coherently scattering nanostructures-laminar, crystal-like, and quasi-ordered. Laminar and crystal-like nanostructures commonly produce iridescence, which is absent or less conspicuous in quasi-ordered nanostructures. Laminar and crystal-like arrays have been analyzed with methods from thin-film optics and Bragg's Law, respectively, but no traditional methods were available for the analysis of color production by quasi-ordered arrays. We have developed a tool using two-dimensional (2D) Fourier analysis of transmission electron micrographs (TEMs) that analyzes the spatial variation in refractive index (available from the authors). This Fourier tool can examine whether light scatterers are spatially independent, and test whether light scattering can be characterized as predominantly incoherent or coherent. The tool also provides a coherent scattering prediction of the back scattering reflectance spectrum of a biological nanostructure. Our applications of the Fourier tool have falsified the century old hypothesis that the non-iridescent structural colors of avian feather barbs and skin are produced by incoherent Rayleigh or Tyndall scattering. 2D Fourier analysis of these quasi-ordered arrays in bird feathers and skin demonstrate that these non-iridescent colors are produced by coherent scattering. No other previous examples of biological structural color production by incoherent scattering have been tested critically with either analysis of scatterer spatial independence or spectrophotometry. The Fourier tool is applied here for the first time to coherent scattering by a laminar array from iridescent bird feather barbules (Nectarinia) to demonstrate the efficacy of the technique on thin films. Unlike previous physical methods, the Fourier tool provides a single method for the analysis of coherent scattering by a diversity of nanostructural classes. This advance will facilitate the study of the evolution of nanostructural classes from one another and the evolution of nanostructure itself. The article concludes with comments on the emerging role of photonics in research on biological structural colors, and the future directions in development of the tool.

Spatial variation of refractive index in a pane of float glass.

In the statistical interpretation of forensic glass evidence it is standard practice to make the assumption of homogeneity of the refractive index (RI) of the source glass, or of localized homogeneity. However, the work of Locke and Hayes showed that, for toughened windscreen glass, this assumption might not be true. This work is well cited, but there appears to have been little follow-on published research. Furthermore, the toughening process is something known to affect the refractive index, and is a process that float glass does not undergo. Float glass is a major component of casework in New Zealand and for that reason it would be interesting to know whether the findings of Locke and Hayes apply when dealing with float glass. In this paper we describe an experiment similar to that of Locke and Hayes, systematically examining the variation of RI in a pane of float window glass. It was found that, although there were no systematic differences in refractive index, there were observable differences across the pane.

Transient temperature response in semitransparent variable refractive index medium subjected to a pulse irradiation

The transient temperature responses in a one-dimensional semitransparent slab with variable refractive index caused by a pulse irradiation are studied. The processes of the transient coupled radiative–conductive heat transfer in the semitransparent slab are analyzed numerically. An implicit central-difference scheme is employed for handling the energy equation, while a discrete curved ray-tracing method is used to solve the radiative transfer equation. The transient temperature responses in the case of constant refractive index are compared with those in the case of variable spatial refractive index. The results show that the spatial variation of refractive index has significant influences on the transient temperature responses of semitransparent slab. Omitting the spatial variation of refractive index may result in errors of transient temperature responses within semitransparent slab to some extent. The effects of optical thickness and refractive index gradient on the transient temperature responses are significant. Increasing the slab optical thickness, the effects of refractive index gradient on the transient temperature responses increase, especially for the non-incident surface.

Refractive-index profiling of embedded microstructures in optical materials.

We describe use of a phase-sensitive low-coherence reflectometer to measure spatial variation of refractive index in optical materials. The described interferometric technique is demonstrated to be a valuable tool to profile the refractive index of optical elements such as integrated waveguides and photowritten optical microstructures. As an example, a refractive-index profile is mapped of a microstructure written in a microscope glass slide with an ultrashort-pulse laser.

Coherent light scattering by nanostructured collagen arrays in the caruncles of the malagasy asities (Eurylaimidae: aves)

We investigated the anatomy, nanostructure and biophysics of the structurally coloured facial caruncles of three species in a clade of birds endemic to Madagascar (Philepittinae, Eurylaimidae: Aves). Caruncle tissues of all species had reflectance spectra with prominent, peak hues between 403 and 528 nm. Dark blue Neodrepanis tissues had substantial reflectance in the near ultraviolet (320-400 nm), which is visible to birds but not to humans, providing the first evidence of ultraviolet skin colours in birds and the first indications of the possible function of ultraviolet skin colours in avian communication. These structural colours are produced by coherent scattering from arrays of parallel collagen fibres in the dermis. Tissues of Philepitta castanea were organized into hexagonal, crystal-like arrays, whereas Neodrepanis tissues were quasiordered. Predictions of the peak hues of reflectance ( &lgr; (max)) using Bragg's law were relatively accurate, but Bragg's law requires physical assumptions that are obviously violated by these structures. A two-dimensional discrete Fourier analysis of the spatial variation in refractive index within the tissues documented that all the tissues are substantially nanostructured at the appropriate spatial scale to scatter visible light coherently. Predicted reflectance spectra based on the two-dimensional Fourier power spectra are relatively accurate at predicting the hue and shape of the reflectance spectra of the tissues. These results confirm that the nanostructure of the collagen arrays determines the colours that are coherently scattered by these tissues. The evolution of the anatomy and nanostructure of asity caruncles is discussed.

Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs

We conducted two-dimensional (2D) discrete Fourier analyses of the spatial variation in refractive index of the spongy medullary keratin from four different colours of structurally coloured feather barbs from three species of bird: the rose-faced lovebird, Agapornis roseicollis (Psittacidae), the budgerigar, Melopsittacus undulatus (Psittacidae), and the Gouldian finch, Poephila guttata (Estrildidae). These results indicate that the spongy medullary keratin is a nanostructured tissue that functions as an array of coherent scatterers. The nanostructure of the medullary keratin is nearly uniform in all directions. The largest Fourier components of spatial variation in refractive index in the tissue are of the appropriate size to produce the observed colours by constructive interference alone. The peaks of the predicted reflectance spectra calculated from the 2D Fourier power spectra are congruent with the reflectance spectra measured by using microspectrophotometry. The alternative physical models for the production of these colours, the Rayleigh and Mie theories, hypothesize that medullary keratin is an incoherent array and that scattered waves are independent in phase. This assumption is falsified by the ring-like Fourier power spectra of these feathers, and the spacing of the scattering air vacuoles in the medullary keratin. Structural colours of avian feather barbs are produced by constructive interference of coherently scattered light waves from the optically heterogeneous matrix of keratin and air in the spongy medullary layer.

Coherent light scattering by blue feather barbs

The structural colours of avian feather barbs are created by the scattering of light from the spongy matrix of keratin and air in the medullary layer of the barbs1,5. However, the precise physical mechanism for the production of these colours is still controversial1,3,4,6. Here we use a two-dimensional (2D) Fourier analysis of the spatial variation in refractive index of the blue feather barbs of the plum-throated cotinga (Cotinga maynana, Cotingidae) to show that the colour is produced by constructive interference between light waves scattered coherently by the nanostructured keratin-air matrix of the barbs.

Ground penetrating radar tomography: algorithms and case studies

Algorithms based on two inversion procedures suggested in a previous study are applied to the problem of imaging and target detection using ground penetrating radar data acquired at two sites. One inversion procedure, referred to as the Fourier transform method, employs the spatial Fourier transform of measured data and requires subsurface inhomogeneities to be relatively deep. The second inversion method does not require the data to be Fourier transformed; however, it does require the additional restriction that inhomogeneities be relatively small. This is referred to as the far-field method. These two inversion relationships are used to reconstruct images of both spatial variations-in refractive index and log likelihood function. It is found that both procedures perform well at a site where only a single isolated inhomogeneity exists. At a second site, where there are two adjacent inhomogeneities, the Fourier transform method proved superior. >