KEYWORDS: Bidirectional reflectance transmission function, Reflection, Monte Carlo methods, Radio optics, Radiometry, 3D modeling, Stochastic processes, Ray tracing, Instrument modeling, Spherical lenses
The accuracy of Monte Carlo calculations in optical radiometry is often limited by the reflection model employed
(usually, diffuse (Lambertian), or simplified specular-diffuse). There are many cases when these models cannot
adequately simulate the bidirectional reflection distribution functions (BRDFs) of real materials, which can call into
question the results of the calculations. The features and the methods of modeling with the use of importance sampling
for various materials are considered with a focus on an acceptance-rejection technique and on a procedural ab initio
method. The Monte Carlo algorithms for modeling non-Lambertian reflection are discussed. The simulated and
measured BRDFs for several materials are compared.
KEYWORDS: Bidirectional reflectance transmission function, Reflection, Monte Carlo methods, 3D modeling, Reflectivity, Data modeling, Geometrical optics, Mathematical modeling, Radio optics, Spherical lenses
The TETRA bi-directional reflectance distribution function (BRDF) model was developed to simulate the reflection
from random rough surfaces in optical radiation transfer modeling by the Monte Carlo method (MCM). This procedural
model is based on geometrical optics, has as a prototype the two-dimensional model proposed by Torrance and Sparrow,
and allows generating, for each ray, a random tetrahedral pit with walls that reflect according to Fresnel's law. An
incident ray undergoes one or several reflections from the tetrahedron's walls, and then continues to participate in the
radiation transfer on the macro-level. The properties of the TETRA BRDF are studied using numerical experiments.
KEYWORDS: Reflection, Reflectivity, Data modeling, Calibration, Black bodies, Infrared radiation, Sensors, Radiometry, Numerical modeling, Monte Carlo methods
Use of linear or concentric grooves is a well-known approach for increasing the surface emissivity to enable the construction of compact blackbody radiators, improve absorptance of stray radiation traps, baffles and thermal radiation detectors, as well as enhance thermal radiation transfer. Emitters with V-grooved surfaces are widely used as reference sources in radiation thermometry and radiometry. In the design phase of such devices, it is important to predict their performance. Most existing models are devoted to modeling isothermal linear grooves with purely diffuse or specular reflectance. Radiation behavior of concentric grooves differs from linear ones and becomes similar only for large values of the ratio of the radial coordinate to the groove period. This paper covers numerical modeling of isothermal and nonisothermal concentric grooves with mixed specular-diffuse reflection for various viewing conditions using Monte Carlo specialized software. It is shown that the temperature drop towards the peak of a groove might lead to a substantial decrease of the grooves' effective emissivity.
We summarize recent progress in our infrared (IR) spectral radiance metrology effort. In support of customer blackbody characterization, a realization of the spectral radiance scale has been undertaken in the temperature range of 232 °C to 962 °C and spectral range of 2.5 μm to 20 μm. We discuss the scale realization process that includes the use of Sn, Zn, Al and Ag fixed-point blackbodies (BB), as well as the transfer of the spectral radiance scale to transfer standard BBs based on water, Cs and Na heat pipes. Further we discuss the procedures for customer source calibration with several examples of the spectral radiance and emissivity measurements of secondary standard BB sources. For one of the BBs, a substantial deviation of emissivity values from the manufacturer specifications was found. Further plans include expansion of the adopted methodology for temperatures down to 15 °C and building a dedicated facility for spectral characterization of IR radiation sources.
Incomplete hemispherical irradiation of the sample (or collection of radiation, in the reverse geometry) in an integrating sphere reflectometer is unavoidable due to sample viewing (or illumination) requirements. This means that one measures with nearly hemispherical irradiation and obtains a quantity that is not identical to the hemispherical/directional (or directional/hemispherical) reflectance factor (HDR) of the sample. The assumption that this quantity is identical to the HDR can lead to error in the measurement result, which is not generally corrected for.
The error, a.k.a. "port loss error", is minimal for comparative measurements of samples with similar reflective properties, but can easily amount to several percent for a diffuse vs. specular comparison and could be even higher for samples that exhibit strong forward scattering. Few papers in the literature have dealt with this issue, perhaps due to the existence of other larger sources of error.
Our approach to this problem has three elements: (1) establish a definition and set of equations that quantify the error due to incomplete irradiation of the sample due to the presence of the viewing port ("port loss" uncertainty); (2) develop algorithms and computer models to predict port loss effects for a specular-diffuse sphere coating and specular-diffuse (or more general bi-directional reflectance distribution function (BRDF)) sample; (3) design a technique and instrumentation to allow routine direct measurements of port loss to correct the error; using reference standards such as an Al mirror and a polytetraflouroethylene (PTFE).
KEYWORDS: Bidirectional reflectance transmission function, Reflectivity, Reflection, Ray tracing, Monte Carlo methods, Data modeling, Geometrical optics, Specular reflections, Mathematical modeling, Radio optics
An algorithmic model of bi-directional reflectance distribution function (BRDF) based on the ray optics approximation and microfacet model of randomly rough surface is proposed. Its central idea is that for every incident ray, the normal vector to the surface undergoes a random perturbation, and the direction of specular reflection is calculated using this perturbed normal. Such behavior of the normal can be treated within the framework of a microfacet model of randomly
rough surfaces. The algorithm allows one to model reflection from both isotropic and anisotropic surfaces, with two-dimensional
Gaussian and other probability density functions for the normal vector perturbations, and various geometrical attenuation functions. The proposed "perturbed normal microfacet (PNMF) model" exhibits experimentally observed effects such as increased reflectance near grazing incidence and off-specular peaks, and allows fast
importance sampling. A weighted sum of Lambertian and PNMF BRDFs can be fitted to experimental data by varying the appropriate parameters. Adherence to the reciprocity principle and energy conservation law is demonstrated via results of forward and backward ray tracing. The PNMF model can be used in Monte Carlo calculations of radiative
heat exchange among rough surfaces, in realistic image synthesis, lighting engineering, for modeling of such radiometric devices as blackbody radiation sources, integrating spheres in the infrared spectral range, cavity detectors of radiation, diffusely reflected panels, etc.
Baffles are often placed in integrating spheres to accommodate the non-ideal aspects of other sphere components. These include detectors, sources, sphere wall surface shape and coatings. Baffles intentionally prevent light interchange between these and other important sphere components and regions such as entrance/exit ports, sample, reference and detector field-of-view. The challenge for an integrating sphere designer is to position and construct baffles that achieve the primary goal of shadowing specific elements from each other, while at the same time minimizing all other “side” effects that the baffles may have. Perhaps the most important side effect is the additional signal loss for light arriving at or leaving the sample from or to the baffle due to its absorptance. This is especially true for coatings and spectral ranges where the wall reflectance is relatively low such as for BaSO4 above 1.5 mm and diffuse gold. A potential improvement that we have investigated in an infrared reflectometer sphere is the use of a specular coating that has significantly higher reflectance than any other available diffuse coating. In our case we have used specular gold versus the diffuse gold-coated plasma-sprayed metal coating that is on the sphere wall. Although this provides for lower loss of light reflected from the sample onto the baffle, the side effects must also be considered and reduced in the design. Specifically one needs to consider the mirroring that will take place in the sphere. In this paper we discuss the important design issues along with some integrating sphere characterization results that demonstrate improved sphere performance by use of specular baffles.
Integrating spheres are often used as calibration sources providing uniform radiance within a solid angle and/or uniform irradiance at a distance. The best performance in such a system can be achieved if one is able to evaluate as well as predict the important characteristics of the sphere system's output, such as the spatial and angular distributions of radiance over the exit port, or the distribution of irradiance at the external plane of calibration. We have developed the algorithms and specialized software based on Monte Carlo techniques to solve the problem of radiation transfer inside an integrating sphere containing several point sources and conical annular baffle. The new algorithm employs backward ray tracing coupled with the shadow rays technique. As a timesaving procedure, the axial symmetry of the sphere and the superposition principle are used to substitute the sum of single source radiation fields rotated through a specific angle, for the radiation field of the complete multiple source sphere. The random (due to the stochastic character of the Monte Carlo method) component of uncertainty for the radiance or irradiance results is less than 0.1%. The results of numerical experiments are used to establish the performance variation as a function of the reflectance and specularity of the sphere wall, the number of radiation sources, the type of baffle used, and the angular distribution of their radiant intensity.
KEYWORDS: Black bodies, Temperature metrology, Solar concentrators, Nitrogen, Calibration, Liquids, Reflectors, Reflectivity, Monte Carlo methods, Mirrors
Radiation temperature calibrations of IR radiometers and imaging systems, pre-launch characterization of spaceborne optical sensors require low and medium-background test facilities, equipped with reference blackbodies for full aperture calibration. Such extended area blackbodies have been recently developed and characterized by VNIIOFI and Vega International, Inc. Target technical specifications for the low temperature blackbody include 100 mm full aperture, plus or minus 12 degrees viewing angles, 0.999 effective spectral emissivity in 3 micrometer to 15 micrometer band, 100 K to 450 K temperature range, 50 mK temperature uniformity across aperture and, finally, 30 mK temperature setting/measurement accuracy. Monte Carlo technique and finite element method were employed for computer modeling of temperature distributions and effective emissivities of radiating cavities consisting of V-grooved flat bottom and particularly profiled reflector. The design features and technical specifications of blackbodies, developed for operation in high vacuum conditions in the temperature range from 100 K to 900 K, are presented. Results of investigation confirm applicability of the selected approach, though leaving space for improvement of blackbodies performance. Main directions of further research and development are discussed.
KEYWORDS: Black bodies, Temperature metrology, Calibration, Solar concentrators, Nitrogen, Reflectivity, Liquids, Monte Carlo methods, Reflectors, Control systems
Two extended area reference blackbodies, covering temperature range from 100 K to 900 K, have been designed and built by VNIIOFI and Vega International, Inc., for German Institute of Space Sensor Technology. The design objectives were to develop Plankian sources for high accuracy IR calibrations; provide, where possible, both high vacuum and atmospheric operation capabilities for easier achievable calibration traceability; and attain compact design to serve as a portable transfer standard. Target technical specifications for the low temperature blackbody BB100 include 100 mm full aperture, +/- 12 degree viewing angles, 0.999 effective spectral emissivity in 3 micrometers to 15 micrometers band, 100 K to 450 K temperature range, 50 mK temperature uniformity across aperture and, finally, 30 mK temperature setting/measurement accuracy. An employed design was selected after conceptual design study, which involved extensive thermophysical modeling and optimization. A finite element method has been applied to calculation of temperature distribution. Effective emissivity simulation was realized by the Monte Carlo method. The result of computer modeling of temperature distributions and effective emissivity are presented. Both target specifications and results of BB characterization are provided. Results of investigation confirm validity of selected approach and assumptions. Possibilities of further improvement of blackbodies performance are discussed.
The present state of the art of temperature blackbody (HTBB) sources development at the All-Russian Institute for Optical and Physical Measurements (VNIIOFI, Russia) and their characteristics are analyzed. The precision graphite blackbody BB22p, operating now at NIST, PTB, NPL and VNIIOFI, large area blackbody BB2000 and super high temperature pyrolitic graphite blackbody BB3200pg are described. Results of their theoretical and experimental investigation are given.
The design of filters with specific spectral characteristics is a requirement not only for the design of filter radiometers, but also for many applications in optical measurements. The most general type of absorptive filters are composite subtractive-additive filters and the general problem of filter radiometer spectral response optimization using such filters is formulated. The algorithm and software realization of constrained optimization for various objective functions with arbitrary weight functions are described. Successive random search and Hooke-Jeeves methods are employed in the optimization and several goodness-of-fit criteria are used for evaluation of the results. Illustrative numerical examples are presented.
The Monte Carlo method was applied to statistical modeling of radiometric properties of integrating spheres. According to employed model of reflectance, specular and diffuse components are approximated by polynomial function of incident angle cosine. Developed software allows to simulate the irradiance distribution over internal surfaces of sphere with relative uncertainty of 0.1%. Sphere geometries with arbitrary number of apertures and baffles of circular shapes are admitted. To illustrate capabilities of software, an irradiance distribution over internal surfaces of the integrating sphere is plotted for several cases of practical importance.
KEYWORDS: Monte Carlo methods, Sensors, Radiometry, Black bodies, Reflection, Radiative energy transfer, Algorithm development, Detection and tracking algorithms, Cryogenics, Radiation effects
The Monte Carlo technique is applied to model the radiation transfer in a radiometric system, consisting of a cavity radiator, a stray radiation trap with two apertures, and a cavity radiometer. The algorithms for the statistical simulation of the non-isothermal black body, the cavity detector, and the radiation trap are described. The method is used for the numerical simulation of the radiative heat transfer in the radiometric system for the precise determination of the Stefan-Boltzmann constant.
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