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PubMed2006

Influence of the angular shape of the volume-scattering function and multiple scattering on remote sensing reflectance.

Scattering phase functions derived from measured (volume-scattering meter, VSM) volume-scattering functions (VSFs) from Crimean coastal waters were found to have systematic differences in angular structure from Fournier-Forand (FF) functions with equivalent backscattering ratios. Hydrolight simulations demonstrated that differences in the angular structure of the VSF could result in variations in modeled subsurface radiance reflectances of up to +/-20%. Furthermore, differences between VSM and FF simulated reflectances were found to be nonlinear as a function of scattering and could not be explained with the single-scattering approximation. Additional radiance transfer modeling demonstrated that the contribution of multiple scattering to radiance reflectance increased exponentially from a minimum of 16% for pure water to a maximum of approximately 94% for turbid waters. Monte Carlo simulations demonstrated that multiple forward-scattering events were the dominant contributors to the generation of radiance reflectance signals for turbid waters and that angular structures in the shape of the VSF at forward angles could have a significant influence in determining reflectance signals for turbid waters.

Journal Article↗

PubMed2007

Reflection and refraction of narrow Gaussian beams with general astigmatism at tilted optical surfaces: a derivation oriented toward lens design.

The formulas for the reflection and refraction of a narrow Gaussian beam with general astigmatism at a tilted optical surface are derived by ray-tracing techniques. The propagation direction of the reflected and refracted beams is computed by tracing the central ray of the incident beam, and the characteristic parameters of the respective wavefronts are worked out by applying the formulas developed for the generalized ray tracing. Moreover, the Gaussian form of the reflected and refracted amplitude distributions along the transverse coordinates is determined by requiring the matching of the incident, reflected, and refracted light spots on the optical surface. No limiting assumptions are made regarding the form of the optical interface or the orientation of the incident astigmatic wavefront. In the end, to illustrate a simple application of these formulas, the reflection of a Gaussian beam at a conicoid is considered, and a simple property of the conicoidal mirrors is reported.

Journal Article↗

PubMed1977

Saturation of colored samples at various levels of reflectance.

The dependence of saturation on the level of reflectance of colored surfaces was measured by numerical estimation and by matching judgments. Four sets of chromatic samples, one for each hue--blue, 460 nm, green, 510 nm, yellow, 580 nm, and red, 620 nm--within a range between 4% and 65% reflectance, were presented to the observers. The largest changes of saturation were observed at the high and low values of reflectance. The effect is more pronounced for the yellows than for the reds and greens, and relatively less apparent for the blues. For each hue, saturation grows faster at intermediate values of reflectance. The four families of saturation functions permitted us to draw a map of equal-purity contours. There are values of colorimetric purity for which saturation remains constant for all levels of reflectance.

Color Perception↗

PubMed1997

Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium.

Improved solutions of the diffusion equation for time-resolved and steady-state spatially resolved reflectance are investigated for the determination of the optical coefficients of semi-infinite turbid media such as tissue. These solutions are derived for different boundary conditions at the turbid-medium-air interface and are compared with Monte Carlo simulations. Relative reflectance data are fitted in the time domain, whereas relative and absolute reflectance are investigated in the steady-state domain. It is shown that the error in deriving the optical coefficients is, especially for steady-state spatially resolved reflectance, considerably smaller for the solutions under study than for the commonly used solutions. Analysis of experimental measurements of absolute steady-state spatially resolved reflectance confirms these results.

Diffusion↗

PubMed2000

Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications

Longitudinal and transverse shifts of a light beam at total internal reflection was experimentally studied by far-field measurements on the reflected field. We propose to use a scanning tunneling optical microscope (STOM) to study these shifts in transmission, and we present a theoretical model of this proposed experiment to obtain a numerical estimation of these shifts. We study the reflection and the transmission of a three-dimensional polarized incident beam. We verify the validity of our formalism by studying the Goos-Hanchen shift in reflection and by comparing our results with published ones. Then we calculate STOM images of the transmitted field distribution. On the images the well-known Goos-Hanchen shift is easily observed. But we also encounter a smaller shift, perpendicular to the plane of incidence. This transverse shift was also observed in reflection by Imbert and Levy [Nouv. Rev. Opt. 6, 285 (1975)]. We study the variations of the two shifts versus various parameters such as the angle of incidence, the optical index, and the incident polarization. Then we discuss the feasibility of the near-field observation of these shifts.

Journal Article↗

PubMed2000

Design considerations for narrow-band dielectric resonant grating reflection filters of finite length

An interference-waveguide approach is developed to predict the response of a resonant grating reflection filter and to provide a better understanding of the resonant process. An expression for the reflected field that accounts for all internal boundary reflections within the filter is developed. Under the assumption of an anti-reflective design, expressions characterizing the line shape of a filter of infinite length are first developed; then the effects of finite length on the response are determined. Expressions relating the length of the filter to the peak reflection efficiency and line width are developed. The degradation of the response as a function of filter length is evaluated. An equivalent waveguide representation is used to determine the location of the resonance as well as the spectral and angular linewidths of the filter. The minimum obtainable spectral linewidth for a filter of given length is determined to be on the order of deltalambda approximately lambda2/L. Rigorous analysis is used to verify the interference-waveguide approach.

Journal Article↗

PubMed2002

Reflectance enhancement in the extreme ultraviolet and soft x rays by means of multilayers with more than two materials.

Sub-quarterwave multilayer coatings with more than two different materials are shown to provide a reflectance enhancement compared with the standard two-material multilayer coatings when reflectance is limited by material absorption. A remarkable reflectance enhancement is obtained when the materials in the multilayer are moderately absorbing. A simple rule based on the material optical constants is provided to select the most suitable materials for the multilayer and to arrange the materials in the correct sequence in order to obtain the highest possible reflectance. It is shown that sub-quarterwave multilayers generalize the concept of multilayers, of which the standard two-material multilayers are a particular case. Various examples illustrate the benefit of sub-quarter-wave multilayer coatings for highest reflectance in the extreme ultraviolet. Applications for sub-quarterwave multilayer coatings are envisaged for astronomy in the extreme ultraviolet (EUV) and soft x rays and also for future EUY lithography.

Journal Article↗

PubMed2003

Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach.

We consider the coherent reflection and transmission of electromagnetic waves from a slab of a dilute system of randomly located, polarizable, spherical particles. We focus our attention on the case where the size of the spheres is comparable to the wavelength of the incident radiation. First, using wave-scattering and Mie theories, we derive expressions for the coherent fields that are transmitted and reflected by a very thin slab. Then we find the effective-current distribution that would act as a source of these fields. We conclude that if the effective currents were induced in an effective medium, this medium must possess, besides an effective electric permittivity, also an effective magnetic permeability. We find that both of these optical coefficients become functions of the angle of incidence and the polarization of the incident wave. Then we calculate the reflection coefficient of a half-space by considering a semi-infinite pile of thin slabs and compare the result with Fresnel relations. Numerical results are presented for the optical coefficients as well as for the half-space reflectance as a function of several parameters. The reflectance is compared with that obtained without considering the magnetic response. Finally, we discuss the relevance and the physics behind our results and indicate as well the measurements that could be performed to obtain an experimental verification of our theory.

Journal Article↗

PubMed2004

Estimating visible through near-infrared spectral reflectance from a sensor radiance spectrum.

We show that surface spectral reflectance can be separated from illumination effects in visible through near-infrared (350 nm-1740 nm) hyperspectral data by using only the information in a single radiance spectrum. The separation method exploits the fact that reflectance and illumination spectra typically lie in distinct subspaces. We present a comparison of a linear and a nonlinear algorithm for the separation. These algorithms compute an estimate of the spectral reflectance up to a scaling factor. In addition, we present an iterative method that is used to determine the starting point for the nonlinear algorithm. We also develop a method for selecting the dimension of the reflectance and illumination subspaces that is appropriate for material identification applications. The accuracy of the separation methods is quantified by application to noisy visible through near-infrared spectral data with a database of 107 materials and 3000 illumination spectra. The utility of the separation method for material identification is demonstrated with the same database. The results show that accurate reflectance recovery and material identification is possible by use of visible through near-infrared spectral data over the outdoor environmental conditions represented in this data set.

Journal Article↗

PubMed2004

Absorption of the eye lens and macular pigment derived from the reflectance of cone photoreceptors.

We measured the amplitude of the directional component of the bleached fundus reflectance, the so-called optical Stiles-Crawford effect, as a function of wavelength. The directional reflectance originates from within the outer segments of the photoreceptors. Thus only two anterior absorbers are of importance: macular pigment and the crystalline lens. Analysis of spectra obtained in pseudophakes established that the cone photoreceptors act as spectrally neutral reflectors. The reflectance spectra, expressed in density units, resembled the macular pigment density spectrum. Studying age effects in the lens of normal subjects resulted in a description of the optical density of the lens in terms of a "young" and an "aged" template. The young template represents the pigment O-beta-glucoside of 3-hydroxykynurenine, which dominates the light absorption in young eyes and decreases with age. The aged template represents the pigments accumulating in the lens with age. The total optical density increased with age, but it was lower in the wavelength region 500-650 nm than was previously assumed on the basis of psychophysical studies. Analysis of the spectra also provided precise individual estimates of the optical density of macular pigment. Finally, we observed a decrease in the photoreceptor reflectivity with age, possibly reflecting a degradation of the photoreceptors.

Adolescent↗

PubMed2005

Influence of total reflection on the imaging quality of optical systems.

In the case of total reflection at a boundary surface between two different optical media, the ray reflected at the boundary is spatially shifted with respect to the point where the incident ray intersects the boundary. The light penetrates into the second medium, and the evanescent electromagnetic wave propagates along the boundary. The described effect is called the Goos-Hänchen effect. Our work describes the influence of the Goos-Hänchen effect on the imaging properties of planar optical systems, and a differential equation of a wave-front meridian that corresponds to a reflected bundle of rays is derived. It is shown that the wave front can be described by the d'Alambert differential equation. This equation makes it possible to determine the coordinates of individual points on the wave-front meridian. The influence of total reflection on the value of the Strehl definition of the reflected ray bundle, is also investigated.

Journal Article↗

PubMed2005

Design of reflection retarders by use of nonnegative film-substrate systems.

A reflection-type film-substrate retarder is an optical device that changes the relative phase but not the relative amplitude of light upon reflection from a film-substrate system. While there are several such device designs based on the common negative film-substrate system, very little has been done with the other two categories of systems, zero and positive. The system category is determine by the relationship between the refractive indices of the ambient N0, film N1 and substrate N2. If N1 < square root of N0N2, the system is negative; if N1 = square root of N0N2, the system is zero; and if N1 > square root of N0N2, the system is positive. The design procedure and characteristics of zero-system reflection retarders are discussed. The polarization and ellipsometric properties of the positive system preclude the existence of a reflection retarder. First, a brief characterization of the zero and positive systems by means of constant-angle-of-incidence contours and constant-thickness contours of the ellipsometric function is presented and discussed. Then an algorithm outlining the design procedures is presented, and the characteristics of the obtained designs are optimized, analyzed, and discussed. The exact retarder is valid for a single wavelength at a set angle of incidence. The design tolerance to changes in the design parameters is analyzed and discussed. In general, N1 < or = square root of N1N2 is the condition to be satisfied to realize reflection-type retarders with film-substrate systems.

Journal Article↗

PubMed2006

Reflectance optimization of inhomogeneous coatings with continuous variation of the complex refractive index.

A model is derived for the reflectance optimization of an inhomogeneous coating made of absorbing materials. The model is applicable mainly for spectral regions where no transparent materials are available, such as in the extreme ultraviolet. The complex refractive index is assumed to take values within a given continuous domain and in a given sequence. The coating design is generated through a series of layer elements with a small refractive-index contrast across interfaces; the thickness of the element is calculated in terms of the refractive-index increment at the interface. The coating is optimized element by element starting from the substrate. When the refractive index varies both continuously and smoothly, the thickness element is of first order in the refractive-index increment. Suggestions are given on how to optimize a more general coating that alternates continuous and smooth refractive-index domains along with discrete indices, which results in a succession of inhomogeneous coatings and finite layers. An example is given to illustrate the model. A new material selection rule is obtained to discriminate whether the addition of a material on top of a partly grown coating will increase or decrease the reflectance of the coating. As a consequence, the model, which is highlighted toward the maximization of reflectance, can be used analogously for reflectance minimization such as for anti-reflection coatings.

Journal Article↗

PubMed2006

Single-scale spectroscopy of structurally colored butterflies: measurements of quantified reflectance and transmittance.

Butterfly scales generally have very elaborate structures in submicrometer size, and some of them show distinctive optical effects through interaction with light. We describe two methods to quantitatively characterize the optical properties of the individual scales in those structurally colored butterflies. Owing to the small dimensions of the scale and to the fact that the reflection and transmission are very diffuse, it is generally difficult to accurately measure the reflectance and transmittance. To overcome these difficulties, we have carefully constructed an optical system including an integrating sphere and investigated variously colored nine kinds of scale. It is shown that the obtained spectra clearly characterize the optical differences among those structurally colored scales and also the differences between structural and pigmentary colors. Further, we have performed the angle-resolved measurement of the reflected light to characterize the spatial pattern of reflection, which is closely related to the mechanism of reflection.

Algorithms↗

PubMed2006

Phase shifts in frustrated total internal reflection and optical tunneling by an embedded low-index thin film.

Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission deltar, deltat are found to be identical, and the associated ellipsometric parameters psir, psit are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the p and s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film thickness. In the limit of zero film thickness (i.e., for an ultrathin embedded layer), the reflection phase shifts are also quarter-wave independent of polarization (p or s) or angle of incidence (except at grazing incidence). Finally, variable-angle FTIR ellipsometry is shown to be a sensitive technique for measuring the thickness of thin uniform air gaps between transparent bulk media.

Journal Article↗

PubMed2006

Rapid simulation of steady-state spatially resolved reflectance and transmittance profiles of multilayered turbid materials.

We present a technique for efficiently computing the reflection and transmission of light by arbitrary systems of turbid layers. To approximate the steady-state reflectance and transmittance without the need to solve difficult boundary conditions, we convolve the reflectance and transmittance profiles of individual layers. We extend single-slab boundary conditions to handle index-of-refraction mismatches between turbid slabs and account for interlayer scattering by applying methods similar to Kubelka-Munk theory in frequency space. We demonstrate good agreement between the reflectance and the transmittance predicted by our model and numerical Monte Carlo methods and show that the far-source reflectance and transmittance of multilayered turbid materials are dominated by interlayer scattering.

Algorithms↗

PubMed2006

Transient reflection of TE-polarized plane waves from a Lorentz-medium half-space.

The time-domain reflection coefficient for a plane wave obliquely incident on a Lorentz-medium half-space is determined analytically by inversion of the frequency-domain reflection coefficient. The resulting expression contains only simple functions and a single convolution of these functions. Owing to its simplicity, this form of the reflection coefficient provides insight into its temporal behavior, specifically how the relationship between the damping coefficient and the oscillation frequency determines the shape of the response. The simple form of the reflection coefficient is validated numerically through comparison with the inverse fast Fourier transform of the frequency-domain reflection coefficient.

Journal Article↗

PubMed2007

Analytic solution for separating spectra into illumination and surface reflectance components.

The measured light spectrum is the result of an illuminant interacting with a surface. The illuminant spectral power distribution multiplies the surface spectral reflectance function to form a color signal--the light spectrum that gives rise to our perception. Disambiguation of the two factors, illuminant and surface, is difficult without prior knowledge. Previously [IEEE Trans. Pattern Anal. Mach. Intell.12, 966 (1990); J. Opt. Soc. Am. A21, 1825 (2004)], one approach to this problem applied a finite-dimensional basis function model to recover the separate illuminant and surface reflectance components that make up the color signal, using principal component bases for lights and for reflectances. We introduce the idea of making use of finite-dimensional models of logarithms of spectra for this problem. Recognizing that multiplications turn into additions in such a formulation, we can replace the original iterative method with a direct, analytic algorithm with no iteration, resulting in a speedup of several orders of magnitude. Moreover, in the new, logarithm-based approach, it is straightforward to further design new basis functions, for both illuminant and reflectance simultaneously, such that the initial basis function coefficients derived from the input color signal are optimally mapped onto separate coefficients that produce spectra that more closely approximate the illuminant and the surface reflectance for any given dimensionality. This is accomplished by using an extra bias correction step that maps the analytically determined basis function coefficients onto the optimal coefficient set, separately for lights and surfaces, for the training set. The analytic equation plus the bias correction is then used for unknown input color signals.

Journal Article↗