For remote sensing purposes the ability to accurately model the light reflecting off of a solar panel is of great interest to the Department of Defense (DoD). The bidirectional reflectance distribution function (BRDF) describes material reflectance by describing how incident irradiance reflects into all possible scatter angles as a function of incident angle. Many such models of BRDF exist each consisting of their own advantages and tradeoffs when describing different kinds of materials. However, a solar panel has unique features that are not featured in any of these previously known models. A previous project at the Air Force Institute of Technology (AFIT)1 created a novel microfacet-like BRDF to model a solar panel with a prominent diffractive feature present which had not been previously modeled. This BRDF was coded into MATLAB and C++ for the purpose of trying to fit measured solar cell BRDF data to the model. This was accomplished by using the lsqcurvefit function in MATLAB which attempts to fit the model parameters, some of which are material parameters, to attempt to match the BRDF to plotted data. Current results have poor accuracy due to the presence of several parameters in each of the four terms in the novel BRDF function. As such further changes to code are needed to improve the fitting accuracy of the lsqcurvefit function.
This work presents a measurement uncertainty analysis for a system designed to simultaneously capture specular in-plane and out-of-plane bidirectional reflectance distribution function (BRDF) data with high spatial resolution by augmenting the Complete Angle Scatter Instrument (CASI®) with a charge-coupled device (CCD) camera. Various scatter flux, incident flux, scatter angle, and detector solid angle uncertainty contributions are considered and evaluated based on imperfectly known system parameters. In particular, incident flux temporal fluctuation, detector noise and non-linearity, and out-of-plane aperture misalignment considerations each require significant adjustment from original CASI® uncertainty analysis, and expressions for neutral density (ND) filter, scatter angle, and solid angle uncertainties each require new formulations. Ultimately, ND filter uncertainty produces the largest contribution for the augmented system—at least when using unrefined worst-case tolerances—followed by solid angle uncertainty and pixel non-linearity. Total BRDF uncertainty and its contributing terms are compiled for several measurement scenarios, and compared with those from original analyses for single-pixel detectors. In particular, when ND filter uncertainty can be ignored or mitigated, total BRDF uncertainty values are comparable to those for the original system.
The bidirectional reflectance distribution function (BRDF) is used to describe reflectances of materials by calculating the ratio of the reflected radiance to the incident irradiance. While it was found that the isotropic models maintained symmetry about ϕs = π, such symmetry was not maintained about the θs = θi axis, except for close to the specular peak. This led to the development of a data-driven metric for how isotropic a BRDF measurement is. Research efforts centered around developing an algorithm that could determine material anisotropy without having to fit to models. This algorithm was tested using high fidelity data (containing off-axis BRDFs), which was collected via a modified Complete Angle Scatter Instrument (CASI®) with a CCD array detector. The algorithm accurately characterized the degree of isotropy for four out of five materials and worked for cases where the BRDF is higher than 100 sr − 1. This algorithm is intended to improve BRDF characterization, and the applications of light curve analysis, scene generation, and remote sensing.
Accurate bidirectional reflectance distribution function (BRDF) models are essential for computer graphics and remote sensing performance. The popular microfacet class of BRDF models is geometric-optics-based and computationally inexpensive. Fitting microfacet models to scatterometry measurements is a common yet challenging requirement that can result in a model being fit as one of several unique local minima. Final model fit accuracy is therefore largely based on the quality of the initial parameter estimate. This makes for widely varying material parameter estimates and causes inconsistent performance comparisons across microfacet models, as will be shown with synthetic data. We proposed a recursive optimization method for accurate parameter determination. This method establishes an array of local minima best fits by initializing a fixed number of parameter conditions that span the parameter space. The identified solution associated with the best fit quality is extracted from the local array and stored as the relative global best fit. This method is first applied successfully to synthetic data, then it is applied to several materials and several illumination wavelengths. This method proves to reduce manual parameter adjustments, is equally weighted across incident angles, helps define parameter stability within a model, and consistently improves fit quality over the high-error local minimum best fit from lsqcurvefit by an average of 71%.
Optical metasurfaces are designed to control light similarly to conventional refractive optics, but with considerably less size and weight. They manipulate light based on the designed scattering from subwavelength resonant nanostructures within the surface. Such devices have only recently been fabricated. We characterized the performance of a 4-cm-focallength infrared dielectric metasurface lens using a scanning InSb detector array to record the intensity field behind the lens through its focal point and an optical scatterometer to measure its scatter. For the scatter measurements, a 5-mm-diameter beam illuminated a subsection of the metasurface at ten locations across the 40-mm extent of the lens to evaluate scattering in each subsection. The affected beam was steered through the lens’ focal point and expanded beyond it due to the 50-cm length of the scatterometer’s measurement arm. In general, the metasurface had scattering “shoulders” at angles outside the intended focal area about 2 orders of magnitude in transmission distribution space (Sr-1) higher than those of either a comparable infrared refractive optic or a flat polished silicon substrate; an additional forward-scattering lobe and a colinear peak caused by light travelling through the metasurface unaffected, which are not typically observed in a refractive lens, were also observed.
For a given material, a fully characterized bidirectional reflectance distribution function (BRDF) describes how light from any given incident direction reflects into all possible observed directions in space. For simplification, many BRDF measurement and modeling techniques assume isotropic material surface characteristics, focusing primarily on in-plane reflection along individual azimuthal directions. An augmented Complete Angle Scatter Instrument® (CASI®) with a scientific-grade charge-coupled device (CCD) provides the ability to simultaneously capture both in-plane and out-of-plane BRDF data with high spatial resolution, particularly surrounding the specular peak. For any individual CCD frame, each pixel measures the portion of total flux reflected into a unique scatter direction. To properly calculate, analyze, and annotate BRDF readings from raw measurements, each pixel must be mapped to its corresponding scatter direction. This work describes a methodology for mapping pixel location to scatter coordinates based on the geometry of the augmented CASI® system, assuming both the CCD and material surfaces are at. For now, material sample and CCD misalignments are neglected. A broadband metallic laboratory mirror, circularly polished aluminum, and unwrinkled Kapton® samples are then each measured at three incident angles. Measurement results and pixel scatter coordinate mapping are demonstrated for each incident angle, using the beam signature as a proxy for normal incidence. The mirror produces a symmetric specular peak, matching the beam signature, while the polished aluminum and Kapton® produce qualitatively asymmetric specular peaks. Ultimately, this work hopes to foster improvements in BRDF measurement and modeling of materials with anisotropic properties for a range of radiometric simulation, hyperspectral sensing, and scene generation applications.
For a given material, the bi-directional reflectance distribution function (BRDF) spatially describes how much light from any given incident direction reflects into each possible scattered direction. One common simplification in both BRDF measurement and modeling is to assume that material reflectance is isotropic throughout the scattered hemisphere with respect to the azimuthal direction. However, in reality, many materials with directionally-dependent surface characteristics, such as milled metals, are likely to exhibit anisotropic BRDFs, particularly noticeable near specular peaks. Scatter measurement devices similar to the modified Complete Angle Scatter Instrument® (CASI®) operated at the Air Force Institute of Technology (AFIT) are capable of direct specular measurements with high spatial resolution, but constrained within the plane of incidence. Anisotropic measurement techniques often sacrifice spatial resolution, particularly near specular peaks. In this work, AFIT's CASI® is augmented by installing a scientfic-grade monochrome charge-coupled device (CCD) camera on the detector arm, whose pixel array captures both in-plane and out-of-plane specular scatter measurements with high spatial resolution. Camera mounting and alignment processes are presented, including required beam attenuation for the visible red helium neon laser source used. The beam signature is measured and characterized, and the camera's effective dynamic range is extended using various exposure times. Beam signature is converted from raw digital counts to BRDF values, providing the baseline for an idealized perfectly specular material. Ultimately, this work is expected to lead towards improvements in measuring and modeling BRDFs for materials exhibiting anisotropic or out-of-plane reflectance properties for a range of radiometric remote sensing applications.
Microfacet BRDF models describe how light reflects off surfaces. Previous analysis found unpolarized data fitted to a microfacet BRDF model that approximated wave optics factor, Q for Fresnel reflectance and geometric attenuation terms was found to be more physically accurate. This work builds on those findings to examine pp and ss polarization cases individually, discovering that pp parameters fit the data better than ss parameters in 13/14 cases. This is accomplished for a variety of materials at different incident angles, and trends are determined to guide future work in refining microfacet pBRDF models.
Microfacet BRDF models based upon geometric optics and used in computer graphics and remote sensing commonly account for surface scatter and Lambertian volume scatter. These models agree well with forward scatter observations, but lack accuracy in backscatter observations. This work proposes directional volume scatter modeling for enhanced BRDF performance. Five directional volume models are incorporated into the modified Cook-Torrance model. A reduction in model error by as large as 53% overall, and 64% in backscatter modeling, is demonstrated. Using our novel semi-empirical model reduced error in 13/15 materials, and incorporating the Sandford-Robertson directional volumetric term reduced error in 14/15 materials.
Wavefront shaping is a technique that uses phase or amplitude modulation to create desired wavefronts on light in optical systems. Wavefronts which are properly conjugated will refocus after reflection from a rough surface. This refocusing effect is called reflective inverse diffusion. There currently are two different wavefront shaping techniques used to achieve reflective inverse diffusion: iterative methods and matrix methods. Iterative methods find one phase front which allows for reflected light to be focused at a single, specific position, with results that are immediately available and continuously improving. Matrix methods calculate the complex matrix which describes the rough surface and allow for reflected light to be be refocused at many positions after reflective inverse diffusion and at multiple spots simultaneously. However, matrix methods are susceptible to decreased performance in a noisy system, and their results are not available until the entire matrix is measured. A new alternative method for reflective inverse diffusion combines non-mechanical beam steering principles with an iterative method’s phase front, giving it the multiple-spot capabilities of matrix methods. Utilizing an optical Fourier transform relationship in the reflective inverse diffusion setup, the shift theorem of Fourier transforms creates phase tilts at the sample on top of the conjugating phasefront when the phasefront from the SLM is translated in position. The phase tilts at the sample steer the reflected focused beam. Translations of an iterative method’s phase front using circular shifts steer the reflected spot at the cost of decreased enhancement with a larger shift.
KEYWORDS: Error analysis, Data modeling, Mid-IR, Polarization, Long wavelength infrared, Near infrared, Statistical modeling, Solids, Signal attenuation, Bidirectional reflectance transmission function
The bidirectional reflectance distribution function (BRDF) describes optical scattering off realistic surfaces. The microfacet BRDF, while computationally simple, lacks accuracy especially for grazing angles. An approximation, which replaces mathematically problematic elements of the microfacet model with the polarization factor from wave optics, has proved useful in accurately modeling the grazing region. We now expand upon this analysis by additionally varying the microfacet distribution function—a fundamental part of microfacet BRDF models. We find that after choosing the best microfacet distribution, 12 of the 18 materials studied show a significant improvement in the BRDF fit at grazing angles using the proposed approximation. Additionally, there was one case for which the approximation produced a model statistically tied for best within the experimental uncertainty of the data. The remaining five materials have significant sources of error outside the grazing region and will be further studied in future work.
The bidirectional reflectance distribution function (BRDF) describes material reflectance by relating incident irradiance to scattered radiance. One popular class of BRDF models is the microfacet model, which assumes geometric optics but is more readily applicable to remote sensing. One drawback of this geometric optics model is the need for a cross section conversion term, which diverges at grazing angles. This problem is only partially addressed by adding a geometric attenuation term to conserve energy, while still neglecting wave optics effects. Based on previous work comparing microfacet and wave optics models, Butler proposed to replace the geometric attenuation and cross-section conversion terms with a theoretical approximation, the closed-form polarization factor, Q. Analysis presented both at Optics and Photonics by Butler in 2017 and SPIE Defense and Commercial Sensing (DCS) by Ewing in 2018 show this modification to be effective for both high density (but low fidelity) data, and low density (but high fidelity) data, particularly at grazing angles, but that analysis only examined unpolarized data. In this work, the theoretical modification is analyzed using high fidelity, low density, in-plane polarimetric oblique and grazing angle BRDF data. These polarimetric data are fit to the novel version of the microfacet model for each polarization separately, using the polarization factor Q, and the error in the fits are compared to the unpolarized fits that were presented at SPIE DCS. These results suggest incorporating the polarization factor to improve the quality of fit consistently for materials, including substantial improvement at grazing angles.
Studies of amorphous silica fibers bombarded with neutral particles indicate that both photons and neutrons have the same mechanism for creating defects, however rate of creation and affected wavelengths pertaining to each type remains unclear. It is difficult to positively attribute defects to one or the other when both are introduced in the sample concurrently. We sought to mitigate this issue in the current experiment by placing lead shielding of various thicknesses in the line of radiation from a nuclear reactor to the Yb-doped fiber, which is then exposed to neutrons and photons from a nuclear reactor source. Reducing photon fluence via various thicknesses of high-Z shielding materials, while maintaining the same neutron fluence, provides for a comparison of defect formation rates in YDF. In comparing neutron dominant and gamma dominant radiation sources for a similar total dose, the absorption spectrum of the 20/400 YDF deconvolves to several Gaussian peaks, with a 0.1 eV shift for the 1-1.5 eV peak and a 0.15 eV shift for the 2-2.5 eV peak (lower energies). Noticeably, the gamma radiation dominant source absorption spectrum shows a peak around 1.6 eV significantly more pronounced than in the neutron radiation dominant source dataset.
The BRDF describes optical scatter off realistic surfaces. The microfacet BRDF model assumes geometric optics but is computationally simple compared to wave optics models. Previously, densely-sampled MERL BRDF data for several materials was analyzed using a novel variation of a microfacet BRDF that used a polarization factor in place of the cross section conversion and geometric attenuation terms, demonstrating improved accuracy. This paper extends that analysis to examine high-fidelity grazing angle BRDF data measured in-plane with the novel BRDF modification. Results indicate that for many materials the novel BRDF modification is more accurate than the Traditional Cook-Torrance BRDF at near grazing angles. We show as much as an order of magnitude improvement in the fit error using this novel BRDF modification. These results are expected to lead to more accurate BRDF modeling for remote sensing, computer graphics, and scene generation.
The BRDF describes optical scatter off realistic surfaces. The microfacet BRDF model assumes geometric optics but is computationally simple compared to wave optics models. In this work, MERL BRDF data is fitted to the original Cook-Torrance microfacet model, and a modified Cook-Torrance model using the polarization factor in place of the mathematically problematic cross section conversion and geometric attenuation terms. The results provide experimental evidence that this modified Cook-Torrance model leads to improved fits, particularly for large incident and scattered angles. These results are expected to lead to more accurate BRDF modeling for remote sensing.
The bidirectional reflectance distribution function (BRDF) describes optical scatter from surfaces by relating the incident irradiance to the exiting radiance over the entire hemisphere. Laboratory verification of BRDF models and experimentally populated BRDF databases are hampered by sparsity of monochromatic sources and ability to statistically control the surface features. Numerical methods are able to control surface features, have wavelength agility, and via Fourier methods of wave propagation, may be used to fill the knowledge gap. Monte-Carlo techniques, adapted from turbulence simulations, generate Gaussian distributed and correlated surfaces with an area of 1 cm2 , RMS surface height of 2.5 μm, and correlation length of 100 μm. The surface is centered inside a Kirchhoff absorbing boundary with an area of 16 cm2 to prevent wrap around aliasing in the far field. These surfaces are uniformly illuminated at normal incidence with a unit amplitude plane-wave varying in wavelength from 3 μm to 5 μm. The resultant scatter is propagated to a detector in the far field utilizing multi-step Fresnel Convolution and observed at angles from −2 μrad to 2 μrad. The far field scatter is compared to both a physical wave optics BRDF model (Modified Beckmann Kirchhoff) and two microfacet BRDF Models (Priest, and Cook-Torrance). Modified Beckmann Kirchhoff, which accounts for diffraction, is consistent with simulated scatter for multiple wavelengths for RMS surface heights greater than λ/2. The microfacet models, which assume geometric optics, are less consistent across wavelengths. Both model types over predict far field scatter width for RMS surface heights less than λ/2.
Human skin detection is an important first step in search and rescue (SAR) scenarios. Previous research performed human skin detection through an application specific camera system that ex- ploits the spectral properties of human skin at two visible and two near-infrared (NIR) wavelengths. The current theory assumes human skin is diffuse; however, it is observed that human skin exhibits specular and diffuse reflectance properties. This paper presents a novel image-based bidirectional reflectance distribution function (BRDF) measurement system, and applies it to the collection of human skin BRDF. The system uses a grid projecting laser and a novel signal processing chain to extract the surface normal from each grid location. Human skin BRDF measurements are shown for a variety of melanin content and hair coverage at the four spectral channels needed for human skin detection. The NIR results represent a novel contribution to the existing body of human skin BRDF measurements.
The bidirectional reflectance distribution function (BRDF) describes realistic scattering of light off materials. Microfacet
BRDF’s often only describe one type of material and neglect wavelength effects. Wave-optics BRDF expressions,
however, can describe wavelength effects at the expense of being more computationally cumbersome. Previous work
relating wave-optics BRDF coordinates to micro-facet coordinates led to a complicated, but versatile, BRDF. In this
work, the infinite summation found in the previous derivation is investigated, leading toward a closed-form BRDF
model that describes wavelength-dependent effects for materials with various surface parameters, and which will be
usable in remote sensing applications.
The microfacet BRDF model is preferred to describe reflectance in many applications due to its closed-form approximation to the BRDF which is relatively easy to use; however, it almost entirely excludes wavelength-dependent scaling of the reflectance distribution. To rectify this, the BRDF was measured at multiple incident angles and for multiple materials at several wavelengths between 3.39 μm and 10.6 μm. Results quantify the dramatic change in the specular BRDF of a variety of materials even after accounting for overall reflectance, and suggests it is necessary to modify the wavelength dependence in the microfacet model.
A popular class of BRDF models is the microfacet model, where geometric optics is assumed, but where physical optics effects such as accurate wavelength scaling, important to Hyperspectral Imagery, are lost. More complex physical optics models may more accurately predict the BRDF, but the calculation is time-consuming. These seemingly disparate approaches are compared in detail. The linear systems direction cosine space is compared to microfacet coordinates, and the microfacet models Fresnel reflection in microfacet coordinates is compared to diffraction theory’s Fresnel-like term. Similarities and differences between these terms are highlighted to merge these two approaches to the BRDF.
KEYWORDS: Bidirectional reflectance transmission function, High dynamic range imaging, Data modeling, Long wavelength infrared, Atmospheric modeling, Solar radiation models, Nickel, Remote sensing, Databases, Reflectivity
In the LWIR, often one assumes a scene does not contain solar reflection. To test this assumption, a simple scene model is analyzed for two BRDFs: Lambertian and measured data. For certain geometries, non-negligible solar reflection is observed at 8, 10, and 12 microns when using the BRDF data. Additionally, the wavelength variation of the pupil plane radiance data differs from the Lambertian case when using a BRDF, not just the magnitude. These results suggest that even in the LWIR, BRDFs should be incorporated to account for solar radiance effects.
Since the development of the Torrance-Sparrow bidirectional re
ectance distribution function (BRDF) model
in 1967, several BRDF models have been created. Previous attempts to categorize BRDF models have relied
upon somewhat vague descriptors, such as empirical, semi-empirical, and experimental. Our approach is to
instead categorize BRDF models based on functional form: microfacet normal distribution, geometric attenua-
tion, directional-volumetric and Fresnel terms, and cross section conversion factor. Several popular microfacet
models are compared to a standardized notation for a microfacet BRDF model. A library of microfacet model
components is developed, allowing for creation of unique microfacet models driven by experimentally measured
BRDFs.
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