Specular Angle Research Articles

Analysis of Gloss Unevenness and Bidirectional Reflectance Distribution Function in Specular Reflection.

Gloss is associated significantly with material appearance, and observers often focus on gloss unevenness. Gloss unevenness is the intensity distribution of reflected light observed within a highlight area, that is, the variability. However, it cannot be analyzed easily because it exists only within the highlight area and varies in appearance across the reflection angles. In recent years, gloss has been analyzed in terms of the intensity of specular reflection and its angular spread, or the bidirectional reflectance distribution function (BRDF). In this study, we develop an apparatus to measure gloss unevenness that can alter the angle with an angular resolution of 0.02°. Additionally, we analyze the gloss unevenness and BRDF in terms of specular reflection. Using a high angular resolution, we measure and analyze high-gloss materials, such as mirrors and plastics, and glossy materials, such as photo-like inkjet paper and coated paper. Our results show that the magnitude of gloss unevenness is the largest at angles marginally off the center of the specular reflection angle. We discuss an approach for physically defining gloss unevenness based on the BRDF.

Theoretical derivation and application of empirical Harvey scatter model.

Starting from the Rayleigh-Rice perturbation theory, this paper derives the empirical Harvey scatter model and ABg scatter model applied extensively in optical analysis software packages and verifies the shift-invariant behavior of the scattered radiance in direction cosine space. Using data obtained from multi-wavelength laser scatterometer on carbon nanotube black coating and pineblack coating, we establish the polynomial model based on the sine of the scattering angle plus the sine of the specular reflection angle, i.e., sin θs+sin θ0 and the dual-Harvey model based on sin θs-sin θ0 , respectively. The models are in good accordance with the experimental data and further extend the valid range of empirical models.

A Modified BRDF Model Based on Cauchy-Lorentz Distribution Theory for Metal and Coating Materials

This paper presents a modified Bidirectional Reflectance Distribution Function (BRDF) model based on the Cauchy–Lorentz distribution that accurately characterizes the reflected energy distribution of typical materials, such as metals and coatings in hemispherical space. The proposed model overcomes the problem of large errors in classical models when detecting angles far away from the specular reflection angle by dividing the reflected light into specular reflection, directional diffuse reflection, and ideal diffuse reflection components. The newly added directional diffuse reflection component is represented by the Cauchy–Lorentz distribution, and its parameters are directly obtained from experimental measurement curves without distribution fitting. Surface morphology and model parameters are determined through measurements, and the comparison between simulation and actual measurement results shows that the modified BRDF model is in excellent agreement with the measured data. The proposed model not only achieves higher accuracy and universality, but it also represents a significant advancement in the field of BRDF modeling research. Its contributions have profound implications for advancing the state of the art in BRDF modeling, as well as having a broader impact on computer graphics and computer vision domains.

A 3D shape measurement method for high-reflective surface based on dual-view multi-intensity projection

Phase shifting profilometry has been commonly used in three-dimensional shape measurement with the advantages of high-precision and non-contact. However, it is still challenging to measure high-reflective surface because image saturation will lead to absolute phase errors and reconstruction errors. In this paper, a dual-view multi-intensity projection method was proposed. Compared with the single-view method, the proposed method can reconstruct more points at each projection intensity especially for pixels around the specular angle and reduce the number of projections to reduce the time consumption. First, we established the dual-view structured light system consisting of two monocular systems that share the same projector. Subsequently, a dual-view saturated pixel judging method was proposed that enables the reconstruction results under two views to be combined without duplicate points. The multi-intensity projection method was adopted by reducing the input projection intensity step by step and reconstructing the remaining pixels around the specular angle. Finally, the reconstruction result can be obtained by stitching point clouds at each projection intensity. Experiments verified that the proposed method could improve the integrity of reconstructed point clouds and measurement efficiency.

Self-Assembling Systems for Optical Out-of-Plane Coupling Devices.

Micromirrors are used in integrated photonics to couple extraplanar light into the planar structure of a device by redirecting light via specular reflection. Compared with grating or prism-based couplers, micromirrors allow for coupling of light over a broader range of wavelengths, provided that the micromirror is fabricated with a specific 3D shape to ensure proper reflection angles. In principle, self-assembly methods could enable reliable, parallelizable fabrication of such devices with a high degree of precision by designing self-assembling components that produce the desired microscale geometry as their thermodynamic products. In this work, we use DNA-functionalized nanoparticles to assemble faceted crystallites with predetermined crystal shapes, and demonstrate with microscale retroreflectance measurements that these self-assembled nanoparticle arrays do indeed behave like optically flat mirrors. Furthermore, we show that the tilt angle of the micromirrors can be intentionally controlled by altering the crystallographic symmetry and preferred crystal orientations as a function of the self-assembly process, thereby altering the resulting specular angle in a programmable manner. Measurements of optical coupling from normal incidence into the substrate plane via an optical fiber confirm that the faceted structures can function as optical out-of-plane coupling devices, and coating these structures with reflective materials allows for high efficiency of light reflection in addition to the angular control. Together, these experiments demonstrate how self-assembled nanoparticle materials can be used to generate optically relevant architectures, enabling a significant step in the development of self-assembly as a materials fabrication tool for integrated optical devices.

Time-series polarimetric bistatic scattering decomposition using comprehensive modified first-order radiative transfer model at C-band for vegetative terrain and validation

ABSTRACT The sensitivity of the bistatic scattered signal to both the soil and vegetation physical properties in microwave sensing of vegetation is subject to uncertainties. A multi-angular and fully polarimetric data acquisition from a bistatic system increases the number of observations. Thus, optimum bistatic system parameters for vegetation monitoring are necessary to develop an understating of microwave interactions with the surface and vegetation properties. In this study, C-band fully polarimetric bistatic scatterometer (BiSCAT) system was designed to measure the scattering response of vegetated terrain in the forward specular plane. The correlation analysis between the measured bistatic scattering coefficient () and in-situ soil/vegetation properties, such as plant water content (PWC) and soil moisture (), was used to find the optimum specular incidence angle of the BiSCAT system. The optimum parameters of the BiSCAT system were used as input to the modified first-order radiative transfer model (MRTM) for the simulation for vegetation. Kirchhoff’s approximate (KA) model for soil surface in forward specular plane was simplified for soil contribution within MRTM. Additionally, the temporal patterns of are modelled by employing the empirical formulation between the vegetation optical depth and PWC. The MRTM offers an understanding of co-polarized electromagnetic signal interaction with the temporal change in vegetation constituents and soil surface parameters. The model is limited to providing insights into co-polarized radar return from the target due to the incapability of yielding the cross-polarization factor from the KA model in the forward specular direction. The contributions of surface, vegetation, surface-vegetation, vegetation-surface and surface-vegetation-surface were quantified to better understand microwave’s interaction with the vegetation. The model is calibrated using a constrained non-linear least-square optimization algorithm. The performance indices of simulating yields good agreement with the BiSCAT measurements.

Measurement of Gloss Unevenness with Different Reflection Angles

In this study, we introduced a measurement method for gloss unevenness as a function of reflectance angles. Gloss is one of the most important qualities of materials, and it is evaluated subjectively by the intensity of reflected light and gloss unevenness. People can estimate the texture of a material using gloss unevenness, which is found in the small peripheral part of the gloss area and can easily be recognized by observing the reflected light while moving the object or eyes. However, it is not easy to photograph and quantify gloss unevenness. One reason is the area where gloss unevenness is observed is a small area near specular reflection. Second, the appearance of gloss unevenness changes depending on the reflection angle. We developed a measurement apparatus to measure gonio-photometric gloss unevenness. We introduced two solutions: a wide-area gloss unevenness measurement technology using telecentric imaging and a rotating mirror optical system that defects reflected light at an angular resolution of 0.02°. We analyzed three materials—mirror, plastic, and paper—and proposed three indicators as a quantitative evaluation method for gloss: intensity of reflected light at the specular angle, full width at half maximum (FWHM) of Bidirectional Reflectance Distribution Function (BRDF), and gloss unevenness image at the FWHM.

Wave-equation diffraction imaging using pseudo dip-angle gather

Diffraction images can directly indicate local heterogeneities, such as faults, fracture zones, and erosional surfaces, that are of high interest in seismic interpretation and unconventional reservoir development. We have adopted a new tool called pseudo dip-angle gather (PDAG) for imaging diffractors using the wave equation. PDAG has significantly lower computational cost compared to the classic dip-angle gather (DAG) due to the use of plane-wave gathers, a fast local Radon transform algorithm, and a one-side decomposition assumption. Pseudo dip angle is measured from the vertical axis to the bisector of the plane-wave surface incident angle and scattered wave-propagation angle. PDAG is generated by choosing the zero lag of the correlation of the plane-wave source wavefields and the decomposed receiver wavefields. It reveals diffraction and reflection patterns similar to DAG, that is, diffractions spreading as a flat event and reflections focused on a specular angle, whereas they may have dissimilar coverage for diffraction and different focused locations for reflection compared to that of DAG. A windowed median filter is then applied to each PDAG for extracting the diffraction energy and suppressing the focused reflection energy. In addition, the stacked PDAG can be used to evaluate the migration accuracy by measuring the flatness of the image gathers. Numerical tests on synthetic and field data sets demonstrate that our method can efficiently produce accurate results for diffraction images.

Far-field bistatic scattering simulation for rice crop biophysical parameters retrieval using modified radiative transfer model at X- and C-band

Dual-polarimetric (i.e., HH and VV) scattering responses at X- and C-bands from indigenously designed far-field bistatic specular (bi-spec) scatterometer acquired over the entire rice crop phenology have been analyzed using a modified parametric radiative transfer model (MRTM). The scattering responses are examined over a wide-ranging bi-spec incidence angle varying from 20° to 60° at 10° intervals. Furthermore, optimization of the bi-spec scatterometer system showed high sensitivity at 40° specular angle of incidence based on the correlation analysis between the measured value of bi-spec scattering coefficient (σMeasured0) and vegetation biophysical parameters such as leaf area index (LAI) and plant water content (PWC). The MRTM implied to investigate the dominance of surface (σSurface0) and vegetation(σVegetation0) specular scattering components within the total value of simulated bi-spec scattering coefficient (σSimulated0) in forward scattering alignment (FSA) convention. The vegetation phase function (VPF) and a bi-directional reflectance distribution function (BRDF) are parameterized to approximate scattering responses from the vegetation volume layer and the surface beneath vegetation. In addition, empirical frequency-specific parameters (i.e., b1and b2) are used to simulate temporal dynamics of σSimulated0 using a linear relationship between vegetation optical depth (VOD) with LAI and PWC. The model and empirical frequency-specific parameters are calibrated using a constrained non-linear least square optimization algorithm, and the results are validated against the value of σMeasured0. According to the simulation findings, the total specular scattering decomposition offers a robust model for interpreting time-series microwave scattering scenarios through vegetation in the FSA convention. Moreover, as compared to C-band, the inverse modeling of MRTM showed high retrieval accuracies of LAI at VV polarization and PWC at HH polarization for the X-band.

Effects of Weakly Nonlinear Waves on Acoustic Scattering from the Ocean Surface

The elevation of ocean waves is always modeled in linear theory as a superposition of the sinusoidal components with crests and troughs of identical heights. However, under some circumstances, the wave amplitude is outside the linear range and presents as a weakly nonlinear asymmetrical waveform with sharper crests and shallower troughs. We studied the impact of the weakly nonlinear effect of ocean waves in deep and intermediate waters on acoustic scattering from the surface of the ocean using two rough surface models with fractal geometry and power law spectral behavior in the equilibrium range. The classic Weierstrass–Mandelbrot function was used to model the linear waves and a new fractal function, the fractional Weierstrass function developed in studies of electromagnetism, was used to model the weakly nonlinear waves. We evaluated these two models using the Pierson–Moskowitz spectrum and the incident wavelength. The bistatic scattering strength was obtained via a numerical method based on the “exact” solution of the integral equation. The weakly nonlinear phenomenon led to a very small reduction in the narrow area around the specular reflection angle and a small increase in the remaining wide area, including the backpropagation area with a scattering angle [Formula: see text]. The differences in backscattering strength between the two models were similar to the bistatic scattering strength in the backpropagation area and did not depend on the incident grazing angle.

Angular reflectance of a highly forward scattering medium at grazing incidence of light.

We study the angular distribution of light diffusely reflected from a turbid medium with large (compared to the light wavelength) inhomogeneities. Using Monte Carlo radiative transfer simulations, we calculate the azimuthally averaged bidirectional reflectance for an optically thick plane-parallel medium and analyze its dependence on the parameters of the scattering phase function. To model single scattering in the medium, we take advantage of the Reynolds-McCormick phase function. For grazing angles of incidence, we find that the angular distribution of reflected light becomes very sensitive to the angular profile of the scattering phase function. The more elongated the phase function, the more pronounced the peak that arises around the specular reflection angle. Comparison of our numerical results with an analytic solution of the radiative transfer equation is performed, and it is shown that the bidirectional reflectance can be decomposed into two contributions, namely, the diffusion contribution and the contribution from light experiencing multiple scattering through small angles. The latter relates directly to the angular profile of the scattering phase function and is responsible for the peak in the angular distribution of reflected light. An explicit analytic formula for the azimuthally averaged bidirectional reflectance is obtained.

Hair surface quality: Laser scattering as a tool for characterizing the surface condition and deposits from shampoos and conditioners.

The hair surface condition underlies many visually perceived attributes such as shine, colour and the 3D perception of a curly hair style. Many factors can alter the hair surface such as cumulated cleansing/styling regimens or chemical treatments which can lead to degradation of the cuticle edges and surface. Similarly, pollutants, sebum, and shampoo/conditioners can build up on the hair surface which are also perceivable to an observer. The highly directive light of a laser is reflected and scattered by the surface of hair fibres into a circular pattern. The angular and spatial characteristics of this pattern reflect the hair geometry and the quality of the hair surface, i.e. the outer cuticle layer. Dark flat hair tresses were used to measure the impact of artificial sebum and shampoo/conditioner regimens on the cuticle surfaces. Also, longer single hair fibres from 4 volunteers were characterized for their surface changes from roots to tips, i.e. over the chronological age of the hair. The laser scattering shows clear changes in specular reflection characteristics from treatments and allows for the extraction of the cuticle inclination angle with respect to the hair axis. Deep cleansing or clarifying shampoos do partially restore the cuticle angle by removing residues on the hair surface whereas more conditioning systems can lead to changes in specular reflection angle and scattering, especially for multiple cycles of shampoo+conditioner treatments. Lastly, changes in hair surface can be traced over time of hair age by this approach and are consistent with frequency and nature of hair treatments. The method shows great potential for characterizing cleansing regimens in terms of their impact on the hair surface, either as single or multiple washes. Coverage or damage to the hair cuticles appears readily as an angle shift of the specular reflection whereas the quality of the surface topology has a direct impact on the angular width of the specular reflection thus affecting the shine band on a person's head. Hair ageing from root to tip can be quantified by laser scattering and correlates well with treatment events in time.

Investigation of converging and collimated beam instrument geometry on specular gloss measurements

Specular gloss is an important appearance property of a wide variety of manufactured goods. Depending upon the application, e.g. paints, paper, ceramics, etc. different instrument designs and measurement geometries are specified in standard test methods. For a given specular angle, these instrument designs can be broadly classified as converging beam (TAPPI method) and collimated beam (DIN method). In recent comparisons of specular gloss measurements using different glossmeters, very large standard deviations have been reported, well exceeding the manufacturers claims. In this paper, we investigate the effect of instrument beam geometry on gloss measurements. These results indicate that this difference in beam geometry can give the magnitude of gloss differences reported in these comparisons and highlights the importance of educating the user community of best measurement practices and obtaining appropriate traceability for their glossmeters.

Bistatic Coherent Polarimetric Scattering of Randomly Corrugated Layered Snow Surfaces

We analyzed the bistatic coherent scattering mechanism of a layered randomly corrugated snow surface, a typical rough surface, with radar polarimetry theory whose scattering matrix was obtained from a physical-based full wave numerical simulation by solving Maxwell's equations. The effects of top–bottom structure, layer thickness, frequency response, and angular dependence are illustrated by observing stokes vector, coherence matrix, and Kennaugh matrix. The results show that top–bottom structure and snow thickness change the state of polarization depending on frequency and bistatic configuration. Analyzing the bistatic polarimetric scattering mechanism based on numerical simulation and the polarimetry theory can be an efficacious source for configuring bistatic observation to detect and classify radar targets. For example, observation at a specular angle of 55° comparatively contains more information on surface structure, and wave entropy is more preferable over degree of polarization as a snow surface structure estimator. Moreover, parameters from Kennaugh decomposition can indicate top–bottom structure better than layer thickness. Last but not the least, we also found that the symmetry assumption commonly used in classical theory of polarization is generally not valid for bistatic observation, and the combination of some Huynen parameters can be reasonably good indicators of snow surface structural symmetry. We expect this paper to offer deeper understanding of the coherent imaging of snow surfaces and to help design a novel bistatic imaging system for layered snow surface.

Kinematic artifacts in the subsurface-offset extended image and their elimination by a dip-domain specularity filter

Common-image gathers in the dip-angle domain may be computed in relation to wave-equation migration methods, extended by the subsurface offset. They involve the application of a postmigration local Radon transform on the subsurface-offset extended image. In the dip-angle domain, seismic reflections are focused around the specular dip angle of reflection. This focusing distinguishes them from any other event in the image space. We have incorporated the dip-angle information about the presence of specular reflections into the computation of the conventional scattering-angle-dependent reflection coefficient. We have designed a specularity filter in the dip-angle domain based on a local semblance formula that recognizes and passes events associated with specular reflections, while suppressing other sorts of nonspecular signal. The filter is remarkably effective at eliminating either random or coherent noises that contaminates the prestack image. In particular, our dip-angle filter provides a method for the suppression of kinematic artifacts, commonly generated by migration in the subsurface-offset domain. These artifacts are due to an abrupt truncation of the data acquisition geometry on the recording surface. We have studied their appearance and devised an appropriate formation mechanism in the subsurface-offset and scattering-angle domains. The prominent presence of the kinematic artifacts in image gathers usually impairs the quality of the postmigration analysis and decelerates the convergence of wave-equation inversion techniques. We have determined from testing on synthetic and field data that using the proposed dip-angle-domain specularity filter efficiently eliminates the kinematic artifacts in the delivered gathers. We expect involvement of the specularity filter to increase the reliability and quality of the seismic processing chain and provide a faster convergence of iterative methods for seismic inversion.

Diffuse scattered field of elastic waves from randomly rough surfaces using an analytical Kirchhoff theory

We develop an elastodynamic theory to predict the diffuse scattered field of elastic waves by randomly rough surfaces, for the first time, with the aid of the Kirchhoff approximation (KA). Analytical expressions are derived incorporating surface statistics, to represent the expectation of the angular distribution of the diffuse intensity for different modes. The analytical solutions are successfully verified with numerical Monte Carlo simulations, and also validated by comparison with experiments. We then apply the theory to quantitatively investigate the effects of the roughness and the shear-to-compressional wave speed ratio on the mode conversion and the scattering intensity, from low to high roughness within the valid region of KA. Both the direct and the mode converted intensities are significantly affected by the roughness, which leads to distinct scattering patterns for different wave modes. The mode conversion effect is very strong around the specular angle and it is found to increase as the surface appears to be more rough. In addition, the 3D roughness induced coupling between the out-of-plane shear horizontal (SH) mode and the in-plane modes is studied. The intensity of the SH mode is shown to be very sensitive to the out-of-plane correlation length, being influenced more by this than by the RMS value of the roughness. However, it is found that the depolarization pattern for the diffuse field is independent of the actual value of the roughness.

Inversion-Based Sensitivity Analysis of Snow-Covered Sea Ice Electromagnetic Profiles

For the microwave remote sensing of snow-covered sea ice dielectric profiles, the sensitivity of the normalized radar cross-section data with respect to the complex permittivity and thickness values is investigated. Our results show that the data collected closer to the nadir in monostatic setups, and the data collected closer to the specular angle in bistatic setups represent higher sensitivity values. Using both synthetically and experimentally collected data sets, we demonstrate that the inversion of data sets having higher sensitivity values results in enhanced reconstruction accuracy.

Balanced inversion of simulated bistatic radar cross-section data for remote sensing of snow-covered sea ice

The reconstruction of the dielectric profile of snow-covered sea ice from simulated bistatic radar cross-section data is investigated. To this end, a cost function representing the discrepancy between the true radar cross-section data and the calculated radar cross-section data due to a predicted dielectric profile is formed. This cost function is iteratively minimized using the differential evolution algorithm so as to reconstruct the unknown dielectric profile. Herein, four different formulations for this cost function are considered. These formulations are distinguished by their utilized weighting factors for each data point within the bistatic radar cross-section data set. Although these cost functions use the same simulated bistatic normalized radar cross-section data set, it will be shown that the reconstruction accuracy achievable from each of them will be different. Finally, an appropriate weighting scheme for bistatic data sets, which emphasizes the scattering data points collected at the vicinity of the specular angle, is presented. It will be shown that the use of this weighting scheme results in enhanced reconstruction accuracy as compared to the other formulations. It is speculated that the proposed weighting scheme balances the individual data points more properly, thus, resulting in enhanced accuracy.

J0540105 シリコン表面における水分子の散乱機構解析

The scattering behavior of water molecules on silicon(100) surface was investigated by the molecular beam experiment and molecular dynamics (MD) simulation. We changed the incident energy between 35 and 130 meV which corresponds to the energy of thermal motion of gas molecules at the room temperature, and measured the scattering distribution and the mean translational energy of scattered molecules in each scattering angle. The experimental results indicated that the scattering distribution was diffusive and close to that of the cosine scattering due to the roughness of the silicon surface when the incident energy was 130 meV. Generally, incident molecules would accommodate with a surface when the incident energy is low. That is because the incident molecules would interact with atoms on surface longer. However, when the incident energy was 35 meV, the scattering distribution had a directivity toward a certain angle close to the specular reflection angle. In order to investigate the reason of this directivity, we are analyzing the motion of water molecules on the silicon surface using MD method.

Point Spread Function of Specular Reflection and Gonio-Reflectance Distribution

In this article, the specular reflection phenomenon is analyzed by the concept of the point spread function (PSF). The conventional PSF, which is a sharpness criterion, is used for the transfer function in image science. In general, print (an ink image on paper) is observed as diffuse reflection light, and the light source image, i.e., gloss, is observed as specular reflection. We first introduce the point spread function of specular reflection (SR-PSF). A measurement principle for the SR-PSF is proposed, and a measurement apparatus for the SR-PSF is developed by using a collimator optical system. The experimental results show that the measured SR-PSF works as a transfer function for a specular reflection image. Each detected position is in agreement with the angle of reflected light. The apparatus works as a goniophotometer within a narrow solid angle. The relation between the SR-PSF and the specular reflection angle distribution is discussed in terms of surface geometry. It is concluded that the measured data are the SR-PSF and they have a gonio-reflectance distribution. The reflection angle is caused by the surface normal, and the surface normal distribution can be calculated from the gonio-reflectance distribution by using the mathematical model. We plan to apply our proposed principle to the development of an evaluation technique for the visual gloss. In addition, the high-resolution goniophotometer can be further developed by this measuring technique.