Diffuse Reflection Model Research Articles

Surface radiance correction for shape from shading

It is well known that many surfaces exhibit reflectance that is not well modelled by Lambert's law. This is the case not only for surfaces that are rough or shiny, but also those that are matte and composed of materials that are particle suspensions. As a result, standard Lambertian shape from shading methods cannot be applied directly to the analysis of rough and shiny surfaces. In order to overcome this difficulty, in this paper, we consider how to reconstruct the Lambertian component for rough and shiny surfaces when the object is illuminated in the viewing direction (retroreflection). To do this we make use of the diffuse reflectance models described by Oren and Nayar, and by Wolff. Our experiments with synthetic and real-world data reveal the effectiveness of the correction method, leading to improved surface normal and height recovery.

The influence of reactant transport on the profiles of gas chopping etching processes: a simulation approach

A two-dimensional profile simulator [B.E. Volland et al., J. Vac. Sci. Technol. B 20 (6) (2002) 3111-3117] was applied to the simulation of the etching of high aspect ratio trenches into silicon by means of a gas chopping etching technique. Reactant transport is modeled by a two-dimensional diffuse reflection model in case of neutrals and by direct line-of-sight shadowing in case of ions. Good agreement of the simulated with the experimental profiles was observed for a wide range of aspect ratios and for different etching to deposition cycle timings. Variation of the reactant transport parameters of the simulation model leads to simulated profiles with nearly no RIE-Lag, which has to be experimentally confirmed in the future.

The influence of reactant transport on the profiles of gas chopping etching processes: a simulation approach

A two-dimensional profile simulator [B.E. Volland et al., J. Vac. Sci. Technol. B 20 (6) (2002) 3111–3117] was applied to the simulation of the etching of high aspect ratio trenches into silicon by means of a gas chopping etching technique. Reactant transport is modeled by a two-dimensional diffuse reflection model in case of neutrals and by direct line-of-sight shadowing in case of ions. Good agreement of the simulated with the experimental profiles was observed for a wide range of aspect ratios and for different etching to deposition cycle timings. Variation of the reactant transport parameters of the simulation model leads to simulated profiles with nearly no RIE-Lag, which has to be experimentally confirmed in the future.

Predicting speech metrics in a simulated classroom with varied sound absorption.

By systematically varying the amount of sound absorption, and the location of the sound-absorbing material in a simulated classroom, it was possible to assess the accuracy of the prediction of speech metrics in quite simple acoustical environments. Predictions of speech level, early-to-late sound ratios (C50) and speech transmission index (STI) values were obtained analytically and with two hybrid ray-based computer programs, RAYNOISE 3.0 and ODEON 4.1. The RAYNOISE predictions were accomplished with a purely specular reflection model and also with a calibrated diffuse reflection model. ODEON uses a parameter called transition order, TO, to change the reflection procedure from purely specular to diffuse for reflections that have orders higher than TO. A parametric study was conducted to determine the best transition order for the ODEON prediction of speech metrics. It was found that the analytical predictions of speech level and C50 were on average accurate to about 1 just-noticeable difference (jnd), whereas the analytical predictions of STI were on average within 2 jnd's. ODEON predictions of speech level, C50 and STI were on average within 2 jnd's. RAYNOISE predictions of C50 and STI with the specular model were on average within 2 jnd's. However, the RAYNOISE predictions of speech level, with both types of reflection models, and the RAYNOISE predictions of C50 and STI with the diffuse model had average errors greater than 2 jnd's. The effects of the sound-absorption treatments on the measured speech metric values are also discussed.

Broad spectrum diffusion model for room acoustics ray-tracing algorithms

Geometrical acoustics methods have already been transformed to account for diffusely reflecting boundaries. In randomized ray-tracing algorithms, the sound rays are either specularly reflected or scattered, according to the value of a random number which is compared with the diffusion factor. However, this method becomes inefficient if this factor depends on frequency, since the process must then be repeated for each frequency band. A method is proposed in this paper to compute all frequency components simultaneously in a single pass. The diffuse reflection model is based on the definition of a new concept: the "splitting coefficient," which can differ from the diffusion factor. First, the randomized ray-tracing method is described and the diffusion model is applied to a single diffusing surface in free field. It is shown that the results computed by the program are in accordance with theoretical results. Then, the method is shown to work properly when it is applied to more realistic enclosures: This is proved in theory and illustrated by some examples. A particular problem is the increase of the statistical error which has been solved by an appropriate control of the splitting coefficient.

Display reflectance model based on the BRDF

Many flat panel displays (FPDs) have anti-reflection surface treatments that differ in character from those of traditional cathode-ray-tube displays. Specular reflection models (mirror-like, producing a distinct image) combined with diffuse (Lambertian) reflection models can be entirely inadequate to characterize the reflection properties of such displays. A third reflection component, called haze, exists between specular and diffuse. Display metrology should account for the haze component of reflection. That is best done using the bidirectional reflectance distribution function (BRDF). The effects of using oversimplified reflectance models are discussed in contrast with a parameterized BRDF.

Rapid modeling of diffuse reflectance of light in turbid slabs.

An efficient and accurate hybrid model of the Monte Carlo technique and the diffusion theory was developed to simulate the diffuse reflectance of light in a turbid slab due to an infinitely narrow light beam. The narrow beam was normally incident on the top surface of the slab. The hybrid model was accurate in modeling the diffuse reflectance near the light source, where the diffusion theory was most inaccurate. The hybrid model was much faster than a pure Monte Carlo method by a factor as great as several hundred, depending on the optical properties, the thickness of the slab, and the settings of the hybrid and the Monte Carlo computations. The computation speed of the hybrid model was insensitive to the optical properties of the medium, in contrast to the pure Monte Carlo technique. The diffusion theory was accurate in modeling both the diffuse reflectance far from the source and the diffuse transmittance. The hybrid model and the diffusion theory should be used in conjunction for efficient and accurate computation of diffuse reflectance and diffuse transmittance.

Approximate model of diffuse reflectance from rough polymer surfaces

A simplified version of the Kirchhoff model for the overall reflectance from a rough conducting surface is presented and tested against data obtained on roughened polymer surfaces using a goniospectrophotometer. Samples were injection molded using textured molds having a range of roughness scales and then coated with 600 Å of aluminum. The surfaces were characterized by mechanical profilometry and relevant mathematical descriptors of the surface topographies were extracted by digital image analysis. The calculated and measured reflectance values agree well for incidence angles of 20° and 60° over a wide range of reflected intensities. At higher angles (82°), the measured reflectance values are more specular. Possible reasons for these discrepancies are discussed.

Computational and Experimental Studies of UV/Titania Photocatalytic Oxidation of VOCs in Honeycomb Monoliths

AbstractThe use of honeycombs as monolith supports for UV/Titania photocatalysis of volatile organic compounds (VOCs) has been investigated theoretically and experimentally. A theoretical model based on analysis of the UV intensity distribution, transport of gaseous contaminants to the catalyzed surface, and surface photocatalytic destruction has been developed. Both diffuse and specular reflection models have been developed for the UV illumination calculations. The model uses measured intrinsic photocatalytic destruction rates determined in a research reactor which gives the concentration-, humidity-, and UV intensity-dependences of the rates. Model predictions have been compared to measurements in a high-flow, staged monolith, demonstration purifier for several gaseous contaminants of interest. Agreement between modeling and experiment is generally quite good. The sensitivity of purifier efficiency to monolith pore size and illuminated contact time is discussed. The performance obtained with honeycombs is comparable to that with porous foams, but with much reduced weight, pressure drop, and cost. The conclusion of this research is that honeycomb monoliths are attractive for use in practical UV/Titania photocatalytic devices, particularly at very high flow rates where pressure drop is a concern, and for those situations where monolith weight is an important design constraint.

3D image reconstruction of bladder by nonlinear interpolation

In this paper, we propose a new 3D reconstruction method to produce the 3D shading image of the bladder from a series of 2D cross-sectional CT images. To achieve this goal, the deformable model method, based on the concept of energy driven and model matching, are employed to locate the contour of the bladder. After a series of 2D contours image is obtained, a 3D wire frame structure can be constructed by stacking these 2D contours in sequence. Next, a nonlinear interpolation scheme of the Hermite surface is used to interpolate the spatial data from the contours To create the depth effect and remove the hidden surface of the 3D image of the bladder, the diffuse reflection model, the Gourand shading technique, and the back-to-front display scheme are utilized, respectively. Experimental results that verify the effectiveness of this approach are given.

Flow-field properties under deposition of films from low-density jets

Statistical methods in the direct simulation Monte Carlo procedure and the electron-beam fluorescence technique were applied to investigate the distribution of density and temperature in a monatomic jet. Initial conditions of investigated flows corresponded to ones under deposition of films from low-density jets. In calculations, the variable hard-sphere model for molecular interaction potential and the diffuse reflection model with complete thermal accommodation were used. Distribution of density of Ar atoms in the jet and in the vicinity of the substrate were measured by the spontaneous radiation of Ar i 5912 Å (transition 4p[1/2]←4d[3/2]0,1←1′) and Ar ii 4610 Å (4s′2D←4p′2F0,5/2←7/2) induced by the electrons. The temperature was evaluated with the rotational temperature of N2, a small portion (5%) of which was added into Ar. The quantities of rotational temperature were found by measuring the intensity of the rotational lines of the first negative system N+2 band. The experimental data provide information about profiles of density along and across the center line of a jet over a range of 1×10−3≤Kn*≤4×10−2. On the whole, the computed profiles of density are in good agreement with the measurements. The calculated properties in the vicinity of the substrate allowed the performance of a detailed analysis of the gas-surface interaction process. A good comparison of the computed profile of the flux of molecules, incident on the substrate, and data on the film thickness of a-Si:H were obtained.

Diffuse-reflectance model for smooth dielectric surfaces

A reflectance model that accurately predicts diffuse reflection from smooth inhomogeneous dielectric surfaces as a function of both viewing angle and angle of incidence is proposed. Utilizing results of radiative-transfer theory for subsurface multiple scattering, this new model precisely accounts for how incident light and the distribution of subsurface scattered light are influenced by Fresnel attenuation and Snell refraction at a smooth air–dielectric surface boundary. Whereas similar assumptions about subsurface scattering and Fresnel attenuation have been made in previous research on diffuse-reflectance modeling, the proposed model combines these assumptions in a different way and yields a more accurate expression for diffuse reflection that is shown to account for a number of empirical observations not predicted by existing models. What is particularly new about this diffuse-reflectance model is the resulting significant dependence on the viewing angle with respect to the surface normal. This dependence on the viewing angle explains distinctive properties of the behavior of diffuse reflection from smooth dielectric objects, properties not accounted for by existing diffuse-reflection models. Among these properties are prominent diffuse-reflection maxima effects occurring on objects when incident point-source illumination is greater than 50° relative to viewing, including the range from 90° to 180°, where the light source is behind the object with respect to viewing. For this range of incident illumination there is significant deviation from Lambertian behavior over a large portion of most smooth dielectric object surfaces, which makes it important for the computer vision community to be aware of such effects during incorporation of reflectance models into implementation of algorithms such as shape-from-shading. A number of experimental results are presented that verify the proposed diffuse-reflectance model.

Quantitative Diffuse Reflectance and Transmittance Infrared Spectroscopy of Nondiluted Powders

An adaptation of Kubelka's general model of diffuse reflectance and diffuse transmittance of light to nonideal scattering samples is proposed. It is applied to quantitative Fourier transform infrared spectrometry of nondiluted surface-derivatized silica powders. Corrections of the measurements are introduced in order to take into account common problems that often prevent a truly quantitative application of the DRIFTS analytical method. Effects on the measured data due to the background absorption of the sample and to the specular reflection on its surface are discussed and quantitatively corrected for. The possible existence of gradients of the optical properties of the powder medium is taken into account by a numerical adaptation of the model to inhomogeneities of the phenomenological absorption and scattering coefficients K and S. Model systems constituted of two types of silica powders of very different morphology are prepared. Known concentrations of molecules carrying a cyano functional group as chromophore were covalently anchored on the powder surface. Application of the adapted model gives a quite good description of the measured diffuse reflectance and diffuse transmittance in these cases where the simple Kubelka-Munk function fails.

PERFORMANCE, ACCURACY, AND CONVERGENCE IN A THREE-DIMENSIONAL MONTE CARLO RADIATIVE HEAT TRANSFER SIMULATION

A general purpose Monte Carlo computer code for the calculation of radiative exchange factors in three-dimensional enclosures with a nonparticipating medium is described. Capabilities of the code include mixed specular and diffuse reflection models, banded spectral material properties, transmission through external surfaces, and simulation of beam radiation. The ray tracing and surface interaction routines are described, as well as the shading algorithms. The effect of input file parameters on computer lime usage is investigated, and rates of convergence are calculated. Results for run time and accuracy are in good agreement with predictions.

Quantitative Analysis of Powder Mixtures by Diffuse Reflectance

Previous tests of continuum diffuse reflectance models are extended in the current study to include powder mixtures in which one component is an intense absorbant and the other is a nonabsorbing scatterer. For model systems of this type, the Pitts-Giovanelli formula gives a very good fit over a large concentration range. However, the fitting procedure is very sensitive to the initial estimate of parameters, and it failed to converge in several cases. The Rozenberg formula, on the other hand, was very stable and gave a moderately good fit to the data, particularly for low reflectances. A simplified version of the Rozenberg formula, Ro/ R = 1 + β, was almost as good, and represents a very simple formula which should be quite useful for quantitative analyses.

LANDSAT test of diffuse reflectance models for aquatic suspended solids measurement

LANDSAT radiance data were used to test mathematical models relating diffuse reflectance to aquatic suspended solids concentration. Digital CCT data for LANDSAT passes over the Bay of Fundy, Nova Scotia were analyzed on a General Electric Co. Image 100 multispectral analysis system. Three data sets were studied separately and together in all combinations with and without solar angle correction. Statistical analysis and chromaticity analysis show that a nonlinear relationship between LANDSAT radiance and suspended solids concentration is better at curve-fitting than a linear relationship. In particular, the quasi-single-scattering diffuse reflectance model developed by Gordon and coworkers is corroborated. The Gordon model applied to 33 points of MSS 5 data combined from three dates produced r = 0.98.

Surface roughness effects on radiant transfer between surfaces

Radiative heat transfer between opaque interacting surfaces is formulated for equal temperature adjoint plates with a one-dimensional surface roughness profile. The rough surface bidirectional reflectance and directional emittance introduced in the analysis depend on material emittance, roughness element specularity and surface roughness slope. Numerical solutions to the giverning integral equation for radiant intensity yields local and total heat transfer for a range of each of the rough surface parameters. The heat transfer results indicate that roughness effects are relatively unimportant for high emittance materials while for low emittance materials roughness slope can change local flux and total radiant heat transfer by a factor of two. Comparison of rough surface heat transfer to that evaluated with simple surface property models demonstrates the superiority of the diffuse emission-diffuse reflection model employing rough surface apparent hemispherical emittance. The error incurred in local flux using this simple model, however, can be significant.