Geometric Attenuation Factor Research Articles

A Fully-correlated Anisotropic Micrograin BSDF Model

We introduce an improved version of the micrograin BSDF model [Lucas et al. 2023] for the rendering of anisotropic porous layers. Our approach leverages the properties of micrograins to take into account the correlation between their height and normal, as well as the correlation between the light and view directions. This allows us to derive an exact analytical expression for the Geometrical Attenuation Factor (GAF), summarizing shadowing and masking inside the porous layer. This fully-correlated GAF is then used to define appropriate mixing weights to blend the BSDFs of the porous and base layers. Furthermore, by generalizing the micrograins shape to anisotropy, combined with their fully-correlated GAF, our improved BSDF model produces effects specific to porous layers such as retro-reflection visible on dust layers at grazing angles or height and color correlation that can be found on rusty materials. Finally, we demonstrate very close matches between our BSDF model and light transport simulations realized with explicit instances of micrograins, thus validating our model.

Infrared polarization model optimization and radiation characteristics of camouflage coatings

To investigate the polarization characteristics of the infrared radiation form camouflage a coating surface, an improved model for the two-component polarized bidirectional reflectance distribution function (pBRDF) is established. A new form of the geometric attenuation factor is used instead of the traditional Blinn shielding function, and diffuse scattering component caused by the rough surface is also taken into account in the micro mirro model. The expression of the degree of linear polarization (DOLP) of the infrared radiation is derived by using the optimized pBRDF, the valid of which is proved by experimental data. The numerical calculations results of DOLP of the three coatings are in good agreement with the experimental data. The expression is numerically evaluated and the influence of coating surface roughness, the effect of geometric attenuation diffuse scattering on the infrared DOLP is discussed. The greater the surface roughness of the coating is, the more obvious are the geometric attenuation effect and diffuse scattering effect caused by the roughness. These results provide theoretical and technical support for the realization of military camouflage, anti-camouflage, target recognition, and other fields.

Degree of polarization model based on a modified three-component pBRDF.

The polarized bidirectional reflectance distribution function (pBRDF) model not only can quantify the radiation intensity, but also can effectively describe the polarization characteristics of the scattered light on the target surface. In this paper, a modified three-component pBRDF model is proposed, which considers the reflection process to be composed of specular reflection, multiple reflection, and volume scattering. Key parameters such as the distribution of the microfacet, geometrical attenuation factor, multiple reflection, and volume scattering, are modified. The degree of polarization model is derived based on the new pBRDF, when the incident light is natural light. The degree of polarization of four coating fabric samples is measured by a multi-angle polarization instrument, and the undetermined coefficients in the model are inverted based on the experimental data. A comparison of the measured and modeled results at a wavelength of 720nm reveals that the model can accurately describe the spatial distribution of polarization characteristics of four samples and control the errors within 0.06, 0.1, 0.04, and 0.09, which provides a theoretical basis for polarization detection and polarization image simulation.

Calculating shadowing and masking on a rough surface

Existing research has confirmed that light attenuation has an intrinsic effect on light reflection from rough surfaces. In this study, a technique is developed to solve the shadowing and masking problems of visual representation on a rough surface. Using the developed technique, a novel framework is built using optics to ensure that shadowing and masking can be presented on a rough surface and then calculated accurately. Moreover, the above-described technique is validated on generated random rough Gaussian surfaces, and it is compared with a wide variety of GAF theories (geometrical attenuation factor, GAF). As revealed by the results of this study, both method and algorithm proposed in this study are confirmed to be more effective than previous ones.

Light attenuation characteristics on a rough surface

The geometric attenuation characteristics and geometric attenuation factor is significant for reflection on a rough surface, which describes the masking and shadowing effect on rough surfaces. When studying the attenuation of light on random Perfect Electrical Conductor (PEC) Gaussian rough surfaces using the integral equation of electromagnetics and the scattering theory, the incident state and wavelength are taken into account in this paper. The Finite Difference Time Domain (FDTD) simulation results show that light attenuation strongly related to wavelength, incident state, and rough surface topography. As a result, light attenuation can be precisely calculated, simulated, and characterized by the incident parameter and surface topography.

Analysis and Improvement on Integral Geometrical Attenuation Factor of Bidirectional Reflection Distribution Function

Analysis and Improvement on Integral Geometrical Attenuation Factor of Bidirectional Reflection Distribution Function

Geometric attenuation factor based on scattering theory from randomly rough surface.

The geometrical attenuation factor (GAF) describes the effect of shadowing and masking on surfaces. The GAF is a crucial factor in achieving a high degree of realism in computer graphics and is important for the evaluation of the accuracy of the bidirectional reflectance distribution function (BRDF). The Smith GAF is a simplified algorithm that is calculated on some assumptions and by using the root mean square. The Sun GAF is a brute-force algorithm that is calculated on the given surface; however, the Sun GAF does not consider the incident wavelength and its interaction with the surface. We propose a GAF algorithm that is designed based on Maxwell's equations and the scattering. We consider the incident wavelength, the shape of the rough surface, and the scattering, and validated on generated Gaussian surfaces. The results demonstrated that, to a large extent, the proposed algorithm eliminated the undesired behavior of the Cook-Torrance BRDF model near the grazing angle.

An algorithm of computing 3D geometric attenuation factor.

Precisely evaluating the geometrical attenuation factor is critical for constructing a more complete bidirectional reflectance distribution function (BRDF) model. Conventional theories for determining the geometrical attenuation factor neglect the correlation between height and slope and the self-shadowing or self-masking effects on microsurfaces, leading to results that are discrepant from reality, apparently. This paper presents a three-dimensional (3D) geometrical attenuation factor formulation on 3D Gaussian random rough surfaces. The proposed numerical analysis of 3D geometrical attenuation factor is much more precise for a practical application, especially near grazing angles. Our proposed numerical analysis of 3D geometrical attenuation factor can precisely evaluate the BRDF model.

STD: Student's t-Distribution of Slopes for Microfacet Based BSDFs

This paper focuses on microfacet reflectance models, and more precisely on the definition of a new and more general distribution function, which includes both Beckmann's and GGX distributions widely used in the computer graphics community. Therefore, our model makes use of an additional parameter γ, which controls the distribution function slope and tail height. It actually corresponds to a bivariate Student's t-distribution in slopes space and it is presented with the associated analytical formulation of the geometric attenuation factor derived from Smith representation. We also provide the analytical derivations for importance sampling isotropic and anisotropic materials. As shown in the results, this new representation offers a finer control of a wide range of materials, while extending the capabilities of fitting parameters with captured data.

Modification of geometrical attenuation factor of bidirectional reflection distribution function based on random surface microfacet theory

The reflection attenuation factor given by Blinn has been widely used as an important factor in the bidirectional reflectance distribution function (BRDF) model based on geometrical optics theory for nearly half a century. However, Blinn's attenuation factor is based on microfacet theory and geometry of equicrural V-grooves caused sharp turning points and obvious error in its function curves. In this paper, a modified geometry attenuation factor based on random surface microfacet theory is presented. We assume that the surface is composed of a large number of microfacets, and the slope of each microfacet is independent of each other and follows Gaussian distribution. The attenuation effect is caused by the masking and shadowing factors in adjacent microfacets. Depending on the slope angles of microfacets, reflection falls in three submodels, i.e., passing model, semi-passing model, and masking/shadowing model when discussing masking/shadowing factor. The modified attenuation factor is given in an integral expression. The modified geometry attenuation factor is simulated and compared with Blinn's geometry attenuation factor. The sharp turning point in Blinn's attenuation factor curve is eliminated and the error of the BRDF curve is reduced. The result shows that the modified geometry attenuation factor reaches better physical rationality and significantly improves the accuracy of BRDF model. Compared with Blinn's geometry attenuation factor, the modification reduces the standard error between BRDF model and existing data from 0.0636 to 0.0084. The cause of the error in Blinn's geometry attenuation factor is analyzed, the equicrural V-grooves assumption of Blinn's geometry attenuation model considers too much reflection attenuation in the condition of small incident angle and large reflect angle. The modification in this paper is based on random surface microfacet theory, in which the angular dependence of adjacent microfacet is eliminated, for this reason the accuracies of geometry attenuation model and BRDF model are improved.

Regional differences in attenuation modelling for Eastern China

This paper describes the development of seismological models for three sub-regions within Eastern China. An important feature of the modelling is that two main types of local data were used to determine parameters for input into the seismological model. Shear wave velocity data was used in Step One of the procedure for deriving the upper crustal factors which are part of the seismological model. Two further steps were involved in incorporating the historical Intensity ( MMI) data into the modelling. In Step Two, the simulated peak ground velocity ( PGV) values were converted to MMI values, and site factor was calculated by dividing the inferred PGV value by the respective simulated PGV value for each given (short distance) earthquake scenario. In Step Three, the quality ( Q) factor of the seismological model for each sub-region was calibrated in accordance with the criterion that site factors inferred from records of long distance earthquakes in the database match with the median site factor obtained in Step Two for short distance earthquakes. Importantly, the Q values obtained by this calibration method were highly consistent with Coda Q values (obtained for each sub-region from a previous study by Jin and Aki based on analysing records of local earth tremors). The calibrated Q values in combination with the developed crustal factors and geometrical attenuation factor constitute the regional seismological model for Eastern China. The seismological model so developed takes into account intra-regional differences and has been used to simulate strong ground motions by the stochastic method for assessing the potential seismic hazards in the region.

Analysis of the Emitted Wavelet of High-Resolution Bowtie GPR Antennas

Most Ground Penetrating Radars (GPR) cover a wide frequency range by emitting very short time wavelets. In this work, we study in detail the wavelet emitted by two bowtie GPR antennas with nominal frequencies of 800 MHz and 1 GHz. Knowledge of this emitted wavelet allows us to extract as much information as possible from recorded signals, using advanced processing techniques and computer simulations. Following previously published methodology used by Rial et al. [1], which ensures system stability and reliability in data acquisition, a thorough analysis of the wavelet in both time and frequency domain is performed. Most of tests were carried out with air as propagation medium, allowing a proper analysis of the geometrical attenuation factor. Furthermore, we attempt to determine, for each antenna, a time zero in the records to allow us to correctly assign a position to the reflectors detected by the radar. Obtained results indicate that the time zero is not a constant value for the evaluated antennas, but instead depends on the characteristics of the material in contact with the antenna.

2005年8月16日の宮城県沖地震の震源スペクトル特性ならびに宮城県周辺の減衰特性およびサイト特性の推定

We estimated source spectra of the 2005 Miyagi-oki earthquake (MJMA 7.2) and 11 events (4.0< MJMA<5.0) consisting of inter-plate and inland earthquakes occurred around Miyagi region applying the spectral inversion method to seismic records observed at KiK-net stations in Miyagi prefecture. Attenuation and site amplification factors were also estimated. Before applying the method, geometrical spreading factor was estimated as a function of frequency using the twofold spectral ratios. It was successfully estimated at a frequency range from 3 to 20 Hz. The average over this frequency range is represented as 1.12±0.27. Applying this average value to the geometrical spreading factors for all frequency ranges (0.5 to 20 Hz), we performed the spectral inversion for the data recorded at 12 KiK-net stations in Miyagi prefecture. As a result the attenuation factor (1/Qs) of shear waves was successfully estimated at frequency ranges above 3 Hz. The frequency dependent 1/Qs can be approximated by Qs(f)-1=(5.0×10-3)ƒ-0.8 at a frequency range of 3 to 12 Hz. We found that total attenuation effect including geometrical spreading and attenuation factor contribute little to the observed strong acceleration at high frequency range. Short-period spectral level of the 2005 Miyagi-oki earthquake estimated from the source spectrum is roughly two times as large as that expected from the empirical rule for the event with same seismic moment. These results indicate that high level of high frequency source spectrum of the 2005 Miyagi-oki earthquake contributed to the observed strong acceleration at high frequency range in Miyagi region.

Bidirectional reflection functions from surface bump maps

The Torrance-Sparrow model for calculating bidirectional reflection functions contains a geometrical attenuation factor to account for shadowing and occlusions in a hypothetical distribution of grooves on a rough surface. Using an efficient table-based method for determining the shadows and occlusions, we calculate the geometric attenuation factor for surfaces defined by a specific table of bump heights.Diffuse and glossy specular reflection of the environment can be handled in a unified manner by using an integral of the bidirectional reflection function times the environmental illumination, over the hemisphere of solid angle above a surface. We present a method of estimating the integral, by expanding the bidirectional reflection coefficient in spherical harmonics, and show how the coefficients in this expansion can be determined efficiently by reorganizing our geometric attenuation calculation.

Scattering of Light by an Air Bubble in Water

The angular distribution of intensity of light scattered from a collimated beam incident upon a spherical air bubble in water is determined for any bubble with radius greater than a few wavelengths of the incident light. The computations are for wavelength 5893 A and n=1.3334, the relative index of refraction of water at 15°C. One external reflection, five internal reflections, and six refractions are considered. A general equation for the geometric attenuation factor is developed, with special forms for external reflection and for zero angle of incidence. The limits of accuracy of the equations for angles of scattering in the neighborhood of 0° and 180° are evaluated. The effects of diffraction and interference are assumed to be negligible. The fractions of the incident light scattered from each of the six “surfaces” (successive points of incidence of any ray on the spherical surface) are shown by accurate curves for all angles of deviation. The corresponding geometric attenutation factors are similarly shown. Final intensity values are tabulated and are plotted both with rectangular and with polar coordinates.