The U.S. Air and Space Forces require optical expertise among their personnel. The Air Force Institute of Technology offers a graduate optics curriculum, which includes a three-course sequence to educate students in the optical concepts of radiometry and radiometric instrumentation. We find radiometry is often a deceptively difficult concept for students to master. To address this, we have developed an experiment in our optics-laboratory coursework to help them gain this mastery. A Fourier-transform infrared spectrometer (FTS) is used to collect spectral data from an unknown sample. FTS calibration and data collection are discussed here, as are the two specific samples used, one with specular reflectance properties, the other with diffuse. The analysis methodology used on the data is also discussed. This is a good radiometry exercise to reveal to the student what can be learned about an unknown material's optical properties in a remote-sensing scenario and is the basis upon which the limiting simplifications of this initial experiment may be generalized to address more difficult, but more realistic, remote-sensing analyses.

Light curve analysis is often used to understand satellite activity in geosynchronous orbits which are too far away for resolved imagery from ground-based optical systems. Glinting features can provide identifiable information, but large sources of error have been documented. The bidirectional reflectance distribution function (BRDF) describes the spatial distribution of a material's reflectance by relating incident irradiance to scattered radiance, and BRDFs play an integral role in light curve observation, simulation, and interpretation. Microfacet models are a popular class of BRDF, which assume geometric optics and typically trade accuracy for computing speed in both scene generation and computer graphics. Another popular class of BRDF is comprised of physical optics models which account for wave optics effects, but their main drawbacks are complexity and computing power. For materials that exhibit wave optics effects, if a known wave optics solution can be combined with a microfacet model, perhaps computing speed can be retained while improving accuracy of the model. In this work, new models are suggested as inputs into light curve analysis to reduce glinting error by accounting for distinctive solar cell diffraction features. Previous work extended out-of-plane measurements to identify and then model a clear diffraction effect from a solar cell, and this work conducts validation of the model using alternative laser sources and additional solar cell samples. While prior work focused on the specular region, in this work, the theoretical modification is analyzed using high-fidelity, low-density, out-ofplane measurements gained from a modified Complete Angle Scatter Instrument (CASI) capturing BRDF data at scattered angles not just on the specular direction. This data informs a model used to show out-of-plane behavior resulting in otherwise unexpected reflection patterns. The results suggest that for remote sensing scenarios involving materials with diffractive properties, such as solar cells, incorporating a fundamental known solution for wave optics phenomena with a microfacet model foundation can improve the radiometric accuracy as well as retain computing speed.

Light curve analysis is often used to discern information about satellites in geosynchronous orbits. Solar panels, comprising a large part of the satellite’s body, contribute significantly to these light curves. Historically, theoretical bidirectional reflectance distribution functions (BRDFs) have failed to capture key features in the scattered light from solar panels. In recently published work, a new solar cell BRDF was developed by combining specular microfacet and “two-slit” diffraction terms to capture specular and periodic/array scattering, respectively. This BRDF was experimentally motivated and predicted many features of the solar cell scattered irradiance. However, the experiments that informed the BRDF were limited to a single laser wavelength, single beam size, and single solar cell sample. In addition, the BRDF was not physics based and therefore, physical insight into what causes certain features in the scattered irradiance was not evident. In this work, we examine solar cell scattering from first principles and derive a simple physics-based expression for the scattered irradiance. We analyze this expression and physically link terms to important scattering features, e.g., out-of-plane phenomena. In addition, we compare our model with experimental data and find good agreement in the locations and behaviors of these features. Our new model, being more predictive by nature, will allow for greater flexibility and accuracy when modeling reflection from solar cells in both real-world and experimental situations.

This paper develops a 3D vector solution for the scattering of partially coherent laser-beam illumination from statistically rough surfaces. Such a solution enables a rigorous comparison to the well-known Priest and Meier polarimetric bidirectional reflectance distribution function (pBRDF) [Opt. Eng.41(5), 988 (2002)10.1117/1.1467360]. Overall, the comparison shows excellent agreement for the normalized spectral density and the degree of polarization. Based on this agreement, the 3D vector solution also enables an extension to the Priest and Meier pBRDF that accounts for the effects of active illumination. In particular, the 3D vector solution enables the development of a closed-form expression for the spectral degree of coherence. This expression provides a gauge for the average speckle size based on the spatial-coherence properties of the laser source. Such an extension is of broad interest to long-range applications that deal with speckle phenomena.

Hyperbolic metamaterials have been demonstrated to have special potential in their linear response, but the extent of their non-linear response has not been extensively modeled or measured. In this work, novel non-linear behavior of an ITO/SiO2 layered hyperbolic metamaterial is modeled and experimentally confirmed, specifically a change in the sign of the non-linear absorption with intensity. This behavior is tunable and can be achieved with a simple one-dimensional layered design. Fabrication was performed with physical vapor deposition, and measurements were conducted using the Z-scan technique. Potential applications include tunable optical switches, optical limiters, and tunable components of laser sources.

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.

The continued technology push towards smaller pitch devices, the growing application of strained-layer-superlattice devices and the associated lateral carrier diffusion challenges with both trends make infrared (IR) detector resolution evaluation vital to the IR imaging community. Established methods for direct infrared detector modulation transfer function evaluation, namely laser speckle-based power spectral density methods, are reliant on Fresnel electric field propagation equations and are only applicable in regimes where small angle approximations are valid. This limitation prevents analysis of longer wavelength, smaller pixel pitch focal plane arrays (FPA). An alternative methodology is proposed, utilizing speckle autocorrelation functions to estimate the FPA impulse response. The major technique advantage is the input autocorrelation function is derived via Rayleigh-Sommerfeld propagation equations, making this method valid in a wider array of test geometries than conventional speckle-based methods. Therefore, this technique supports resolution estimation of smaller pixel pitch devices than previously possible with established techniques. This effort outlines an iterative maximum likelihood function-based approach proposed for impulse response estimation, demonstrates the proposed technique's effectiveness via simulation and discusses the challenges associated with implementing the technique experimentally.

The future of photonic devices involves harnessing non-linear effects, for applications such as frequency upconversion and down-conversion, optical switching, and emission control. To effectively do this, the optical properties of designed material systems are needed. Hyperbolic metamaterials that use both conductors and dielectrics have been shown to have enhanced non-linear properties near the topological transition point. Creating that topological transition point in a layered hyperbolic metamaterial offers a way to control the non-linear properties without a complicated 3D design. Layered 1D metamaterials still have a large enough design space to achieve various non-linear effects across a large frequency range and have a relative ease of fabrication. For this research, ITO was chosen as the conductor, which has advantages due to its ready availability and CMOS compatibility. The chosen dielectric, SiO2, is also easily available. The non-linear properties of the hyperbolic metamaterials were modeled with an efficient Matlab code, and the results show the capability of controlling the non-linear properties and optimizing for many different possible applications.

The Bidirectional Reflectance Distribution Function (BRDF) is of substantial use in remote sensing, scene generation, and computer graphics, to describe optical scatter off realistic surfaces. This paper begins by summarizing our prior work in relating wave optics and geometric optics models, culminating with the Modified Cook-Torrance (MCT) model. The MCT model is evaluated here against aluminum, Infragold, and silver paint at various wavelengths in the IR. In each case, the MCT model is shown to outperform a standard microfacet model. Then, this paper shows a non-trivial method of computing the primary new term, the polarization factor Q. This optimization requires manipulation of the polarization factor in the complex plane, and results in code that runs nearly 2 times faster when compared to the more straightforward implementation of Q. The code presented here is easily adapted to languages other than Matlab, as the code does not use complex variables and uses only cosines of relevant angles (which can trivially be computed by the dot product of unit vectors in scene rendering). It is anticipated that these results will lead to more widespread use of the polarization factor in scene rendering, to produce more accurate optical scatter results.

The infrared (IR) imaging community has a need for direct IR detector evaluation due to the continued demand for small pixel pitch detectors, the emergence of strained-layer-superlattice devices, and the associated lateral carrier diffusion issues. Conventional laser speckle-based modulation transfer function estimation is dependent on Fresnel propagation and limited to paraxial geometries, preventing the utilization of this approach on small pixel pitch IR devices. This paper presents a generalized approach for determining a focal plane array (FPA) system input power spectral density, utilizing numerical evaluation of Rayleigh-Sommerfeld speckle irradiance autocorrelation functions, speckle irradiance spectral analysis using the Wigner distribution function, and experimental error quantification incurred from making wide-sense-stationary assumptions regarding the associated laser speckle random process. The effort's final result is an experimental demonstration of an FPA resolution estimation technique valid in nonparaxial test scenarios. (C) 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)

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.

In this work, a CCD-augmented complete angle scatter instrument (CASI) with a visible red laser source was used to measure the BRDF of a commercially available solar cell designed for small satellites, simultaneously capturing both in-plane and out-of-plane data with high angular resolution surrounding the specular direction. The measurements exhibited three distinct scatter features: a central specular peak, an offset specular peak, and a diffraction pattern. The two peaks were caused by different material surfaces with slightly different normal directions, and the diffraction pattern arose from periodically-spaced metal conducting bars running in one direction across the solar cell surface. The diffraction pattern measurements were verified in-plane with an original single-pixel CASI detector and then used to inform the creation of a single closed-form BRDF model capable of describing the out-of-plane features. Both specular peaks were modeled using a traditional microfacet formulation, but the offset peak model implemented a rotation of the incident and scatter directions to account for the difference in surface normal direction. The diffraction pattern-which is not typically described with microfacet models-was described based on Fraunhofer diffraction through two rectangular stripes, adjusted in terms of microfacet coordinates. Parameters for the model were chosen manually, based largely on physical material properties when possible, rather than using optimized fitting algorithms. Model results were compared to the measurements by using the same CCD pixel scatter coordinates. Qualitatively, the model successfully replicated the observed features, and quantitatively, the modeled peak values agree with the measurements within an order of magnitude.

Measurement and analysis of planar elements is used to predict optical system performance and impact of planar optical component type. This is extended to optical, imaging performance, and thermal characteristics with modeling, analysis, and measurement.

Incorporating planar optics such as metalenses or metacorrectors into optical designs can drastically improve the performance of imaging systems with additional benefits such as cost, size and weight improvements. However, modeling of such hybrid lenses is challenging because of the multi-scale nature of the simulation. We demonstrate that one can combine ray optic simulations with full wave electromagnetic simulations and Fourier optics approaches to model a whole compound/hybrid lens considering all metasurface unit cell interactions and to study the effect of possible fabrication errors.

Abstract. 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.

We have proposed, designed, simulated and fabricated a holographic, low loss focusing lens with engineered nano-scaled features. This metastructure was designed to converge off-axis infrared (IR) radiation and created by patterning a dielectric surface. To leverage previous efforts for baseline data, we chose an array of nano-pillars which varied in widths although were fixed in both height and periodicity. We achieved the desired Gradient Index (GRIN) and resulting focus length, by engineering the effective index of refraction across the metasurface which was achieved from varying the material-to-air ratio. This allowed us to create a parabolic phase gradient, thereby generating an effective optical density that peaks in the appropriate sector of the lens while gradually degrading towards the perimeter of the lens in Figure 1. Lenslets with varying patterns, dependent upon their position in the array, were designed, simulated and fabricated.

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 (R)) 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 (R) 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. (C) The Authors.

Abstract. 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%.

The future of photonic devices involves harnessing non-linear effects, for applications such as frequency upconversion and down-conversion, optical switching, and emission control. To effectively do this, the optical properties of designed material systems are needed. Metamaterials can be fabricated in a layered form to operate in many wavelength bands, and they exhibit strong non-linear effects. To make the layered metamaterial, alternating layers of metal and dielectric were used. Samples were fabricated using physical vapor deposition for the material system ITO-SiO2, with varying layer thicknesses for each sample. First, the linear properties of the samples were measured using variable angle spectral ellipsometry, and then the non-linear properties were measured using the Z-scan technique. The linear results show a good agreement with effective medium theory, which signifies that the metamaterials are suited for computer-aided design. Also, the non-linear results show strong non-linear properties, of n2 = 1 ∗ 1014 cm2/W, and β = 2 ∗ 1010 cm/W, which is larger than many natural materials. This demonstrates the potential for use in non-linear applications.

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-focal-length 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.