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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.
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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.
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This research images trapped atoms in three dimensions, utilizing light field imaging. Such a system is of interest in the development of atom interferometer accelerometers in dynamic systems where strictly defined focal planes may be impractical. In this research, a light field microscope was constructed utilizing a Lytro Development Kit micro lens array and sensor. It was used to image fluorescing rubidium atoms in a magneto optical trap. The three-dimensional (3D) volume of the atoms is reconstructed using a modeled point spread function (PSF), taking into consideration that the low magnification (1.25) of the system changed typical assumptions used in the optics model for the PSF. The 3D reconstruction is analyzed with respect to a standard off-axis fluorescence image. Optical axis separation between two atom clouds is measured to a 100 µm accuracy in a 3 mm deep volume, with a 16 µm in-focus standard resolution with a 3.9 mm by 3.9 mm field of view. Optical axis spreading is observed in the reconstruction and discussed. The 3D information can be used to determine properties of the atom cloud with a single camera and single image, and can be applied anywhere 3D information is needed but optical access may be limited.
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Nanostructured optical materials, for example, metamaterials, have unique spectral, directional, and polarimetric properties. Samples designed and fabricated for infrared (IR) wavelengths have been characterized using broadband instruments to measure specular polarimetric transmittance or reflectance as in ellipsometry or integrated hemisphere transmittance or reflectance. We have developed a wavelength-tunable IR Mueller-matrix (Mm) polarimetric scatterometer which uses tunable external-cavity quantum-cascade lasers (EC-QCLs) to tune onto and off of the narrowband spectral resonances of nanostructured optical materials and performed full polarimeteric and directional evaluation to more fully characterize their behavior. Using a series of EC-QCLs, the instrument is tunable over 4.37-6.54 µm wavelengths in the mid-wave IR and 7.41-9.71 µm in the long-wave IR and makes measurements both at specular angles, acting as a Mm polarimeter, and at off-specular angles, acting as a Mm scatterometer. Example measurements of an IR thermal metamaterial are shown.
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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.
RESUMEN
Since a measurement of the bidirectional scatter distribution function (BSDF) of a material is proportional to the intensity of the scattered light, a BSDF measurement system with the addition of a dual rotating retarder polarimeter can be used to calculate the Mueller matrix of a scatterer. One advantage of a BSDF system using a laser source is its large dynamic range, which allows the measurement of scattered light both near to and away from the specular region. As BSDF measurements move away from the specular region and into a more diffuse-scatter region, the measured signal decreases and may approach the system's measurement floor. Therefore, BSDF and Mueller-matrix measurements are dependent not only on the scatter from the sample but also on the noise floor of the system. By analyzing numerically created bidirectional reflectance distribution function data, we show that since the noise floor of a system is typically constant, the Mueller-matrix measurement at the noise floor appears to be that of a perfect depolarizer. Therefore, as the BSDF measurement space moves away from the high-signal region and the noise floor is approached, the Mueller matrix assigned to the sample artificially approaches that of a perfect depolarizer. The rate and location in scatter-angle space of this shift is dependent on the BSDF of the material and on the signal-to-noise ratio in the system. Therefore, caution must be taken when drawing conclusions about measured Mueller matrices for scattered light, particularly in measurement regions where the measured signal approaches the system floor.
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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.
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Hemi-ellipsoidal mirrors are used in reflection-based measurements due to their ability to collect light scattered from one focal point at the other. In this paper, a radiometric model of this energy transfer is derived for arbitrary mirror and detector geometries. This model is used to examine the imaging characteristics of the mirror away from focus for both diffuse and specular light. The radiometric model is applied to several detector geometries for measuring the Directional Hemispherical Reflectance for both diffuse and specular samples. The angular absorption characteristics of the detector are then applied to the measurement to address measurement accuracy for diffuse and specular samples. Examining different detector configurations shows the effectiveness of flat detectors at angles ranging from normal to 50°, and that multifaceted detectors can function from normal incidence to grazing angles.
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As a finite cross-section laser beam propagates through the atmosphere, the beam spreads due to both diffraction and atmospheric turbulence effects. Using turbulence theory valid in both weak and strong optical turbulence regimes, a relationship between atmospheric beam spread and the resulting return power for an optical system and the refractive-index structure parameter or Cn2 can be established. A technique for estimating the path-averaged Cn2 using a laser-and-corner-cube system based on this relationship is described. Experimental results using near-infrared laser wavelengths show good agreement between theoretical predictions and scintillometer-measured Cn2 values for near-ground line-of-sight propagation paths.