Stephen E. Nauyoks

Comparison of microfacet BRDF model to modified Beckmann-Kirchhoff BRDF model for rough and smooth surfaces.

A popular class of BRDF models is the microfacet models, where geometric optics is assumed. In contrast, more complex physical optics models may more accurately predict the BRDF, but the calculation is more resource intensive. These seemingly disparate approaches are compared in detail for the rough and smooth surface approximations of the modified Beckmann-Kirchhoff BRDF model, assuming Gaussian surface statistics. An approximation relating standard Fresnel reflection with the semi-rough surface polarization term, Q, is presented for unpolarized light. For rough surfaces, the angular dependence of direction cosine space is shown to be identical to the angular dependence in the microfacet distribution function. For polished surfaces, the same comparison shows a breakdown in the microfacet models. Similarities and differences between microfacet BRDF models and the modified Beckmann-Kirchhoff model are identified. The rationale for the original Beckmann-Kirchhoff F(bk)(2) geometric term relative to both microfacet models and generalized Harvey-Shack model is presented. A modification to the geometric F(bk)(2) term in original Beckmann-Kirchhoff BRDF theory is proposed.

Comparison of microfacet BRDF model elements to diffraction BRDF model elements

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.

Optimization of a dual-rotating-retarder polarimeter as applied to a tunable infrared Mueller-matrix scatterometer

The value of Mueller-matrix (Mm) scatterometers lies in their ability to simultaneously characterize the polarimetric and directional scatter properties of a sample. To extend their utility to characterizing modern optical materials in the infrared (IR), which often have very narrow resonances yet interesting polarization and directional properties, the addition of tunable IR lasers and an achromatic dual-rotating-retarder (DRR) polarimeter is necessary. An optimization method has been developed for use with the tunable IR Mm scatterometer. This method is rooted in the application of random error analysis to three different DRR retardances, λ/5, λ/4 and λ/3, for three different analyzer (A)-to-generator (G) retarder rotation ratios, θA:θG = 34:26, 25:5 and 37.5:7.5, and a variable number of intensity measurements. The product of the error analysis is in terms of the level of error that could be expected from a free-space Mm extraction for the various retardances, retarder rotation ratios and number of intensity measurements of the DRR. The optimal DRR specifications identified are a λ/3 retardance and a Fourier rotation ratio, with the number of required collected measurements dependent on the level of error acceptable to the user. Experimental results corroborate this error analysis using an achromatic 110-degree retardance-configured DRR polarimeter at 5 µm wavelength, which resulted in consistent 1% error in its free-space Mm extractions.

Development of tunable polarimetric optical scattering instrument from 4.3-9.7 microns

To examine the polarimetric Bidirectional Scatter Distribution Function (BSDF) of samples in the mid-wave infrared (MWIR) and long-wave infrared (LWIR), a full Stokes polarimetric optical scatter instrument has been developed which is tunable from 4.3-9.7 microns through the use of six external-cavity quantum-cascade lasers. The polarimeter is realized through a dual-rotating-retarder configuration, which allows full Mueller-matrix extraction over the tunable wavelengths. Optical characterization of the polarimeter components was conducted to establish performance baselines for the system. The dynamic range of the system is nine orders of magnitude.

Experimental analysis of bidirectional reflectance distribution function cross section conversion term in direction cosine space

Of the many classes of bidirectional reflectance distribution function (BRDF) models, two popular classes of models are the microfacet model and the linear systems diffraction model. The microfacet model has the benefit of speed and simplicity, as it uses geometric optics approximations, while linear systems theory uses a diffraction approach to compute the BRDF, at the expense of greater computational complexity. In this Letter, nongrazing BRDF measurements of rough and polished surface-reflecting materials at multiple incident angles are scaled by the microfacet cross section conversion term, but in the linear systems direction cosine space, resulting in great alignment of BRDF data at various incident angles in this space. This results in a predictive BRDF model for surface-reflecting materials at nongrazing angles, while avoiding some of the computational complexities in the linear systems diffraction model.

Development of a tunable polarimetric scatterometry system in the MWIR and LWIR

A unique tunable polarimetric scatterometry system has been developed by upgrading a Schmitt Measurement Systems Complete Angle Scatter Instrument (CASI) to produce a Dual-Rotating-Retarder full-Mueller-matrix polarimeter. The system has been enhanced by automation, addition of multiple, tunable, laser light sources, an improved sample positioning and orientation interface, and enhanced data-analysis software. A primary application of this system is the characterization of novel nano- and micro-structured materials, such as photonic crystals, plasmonic structures and optical meta-materials, which often display very narrow-band performance. The ability to characterize these materials both at and away-from their resonances is a clear advantage. The specific project goals are to demonstrate (1) a novel nano- and micro-structured-material-characterization full-polarimetric-diffuse-ellipsometry technique suitable to measure desired material properties with stated uncertainty limits for novel optical material structures of interest, and (2) the incorporation of predictive computational codes that estimate the electro-magnetic property values for novel nano- and micro-structured-material designs and concepts of interest.

Dynamic data driven bidirectional reflectance distribution function measurement system

The bidirectional reflectance distribution function (BRDF) is a fitted distribution function that defines the scatter of light off of a surface. The BRDF is dependent on the directions of both the incident and scattered light. Because of the vastness of the measurement space of all possible incident and reflected directions, the calculation of BRDF is usually performed using a minimal amount of measured data. This may lead to poor fits and uncertainty in certain regions of incidence or reflection. A dynamic data driven application system (DDDAS) is a concept that uses an algorithm on collected data to influence the collection space of future data acquisition. The authors propose a DDD-BRDF algorithm that fits BRDF data as it is being acquired and uses on-the-fly fittings of various BRDF models to adjust the potential measurement space. In doing so, it is hoped to find the best model to fit a surface and the best global fit of the BRDF with a minimum amount of collection space.

Experimentally validated modification to Cook-Torrance BRDF model for improved accuracy.

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.

Experimental measurement and analysis of wavelength-dependent properties of the BRDF

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.

Spectral coherent emission of thermal radiation in the far-field from a truncated resonator

The spectral radiative properties of coherent thermal emission in the mid- and far-IR from two metal-semiconductor resonating structures were demonstrated experimentally. Using an efficient implementation of Rigorous Coupled-Wave Analysis, a truncated resonator was designed to selectively emit at mid-IR and far-IR wavelengths. A High Impulse Power Magnetron Sputtering deposition technique was used to fabricate two Ag-Ge-Ag resonating structures with layer thicknesses of 6-240-160 nm for one sample and 6-700-200 nm for the other. Reflectance measurements demonstrated spectrally selective absorption at the designed mid- and far-IR wavelengths whose general behavior was largely unaffected by a wide range of incident angles. Further, radiance measurements were taken at various high temperatures, up to 601 K, where spectrally selective emission was achieved through wave interference effects due to thermally excited surface waves. From these radiance measurements, spectral emittance was directly derived and compared to the emittance inferred from reflectance measurements. It was established that inferring emittance through Kirchhoff’s law can help to approximate the expected emission from a structure, but it is not an exact method of determining the actual emittance of a thermal source at higher temperatures due to the temperature dependence of material parameters.