Bidirectional Transmittance Distribution Function Research Articles

Survey of bidirectional transmittance distribution function measurement facilities by multilateral scale comparisons

In recent years, a growing demand for the capability of performing accurate measurements of the bidirectional transmittance distribution function (BTDF) has been observed in industry, research and development, and aerospace applications. However, there exists no calibration and measurement capabilities-entry for BTDF in the database of the Bureau International des Poids et Mesures and to date no BTDF comparison has been conducted between different national metrology institutes (NMIs) or designated institutes (DIs). As a first step to a possible future key comparison and to test the existing capabilities of determining this measurand, two interlaboratory comparisons were performed. In comparison one, five samples of three different types of optical transmissive diffusers were measured by five NMIs and one DI. By specific sample choice, the focus for this study lay more on orientation-dependent scatter properties. In comparison two, where one NMI, one DI, one university, and three industrial partners investigated their measurement capabilities, the dependence on the orientation was not assessed, but two additional samples of the same material and different thickness were measured. Results of the two comparisons are presented, giving a good overview of existing experimental solutions, and showing specific sample-related problems to be solved for improved future BTDF measurements.

Development of primary reference facilities and measurement comparison of standard artifacts for the bidirectional transmittance distribution function

To determine the bidirectional transmittance distribution function (BTDF) of diffusely transmitting materials, two new primary facilities have been developed at the Physikalisch-Technische Bundesanstalt (PTB) and Aalto University (Aalto). A detailed description of both facilities and the different approaches used are presented in this paper. The performance of both facilities is compared by determining the BTDF of two different diffuser types in both in-plane and out-of-plane bidirectional geometries at four different wavelengths in the visible spectral range. Due to delayed completion of PTB’s primary facility, the measured BTDF values are compared between Aalto’s primary facility and another PTB setup, whose measurement scales are successfully transferred to PTB’s primary facility by an internal comparison. A thorough analysis of the measurement uncertainty is presented, leading to a combined k = 1 standard uncertainty of 0.8%–1.2% for PTB’s primary facility and 1.3%–1.7% for Aalto’s primary facility. The BTDF results obtained agree well within their expanded k = 2 uncertainty. This indirect bilateral comparison shows that Aalto’s and PTB’s new facilities are suited as primary reference setups for the determination of the BTDF. These studies also reveal action points to improved measurement capabilities and for a reduction of the measurement uncertainty, depending on the type of diffuser under test.

Use of bidirectional transmittance distribution function measurements to determine transmittance haze

Accurate and traceable measurements of transmittance haze are required for quality control in various different industries, such as optoelectronics, automobiles, and agriculture. Transmittance haze is defined as the fraction of light transmitted through a material that deviates from the incident beam by more than 2.5∘. Various documentary standards specify the use of an integrating sphere with a prescribed geometry for the measurement of transmittance haze. This paper uses goniometric measurements of the bidirectional transmittance distribution function (BTDF) to calculate transmittance haze according to the definition and demonstrates that the sphere-based realisation of transmittance haze specified in the documentary standards does not agree with the definition, with the difference being up to 20% for some samples. The BTDF measurements are also used to simulate the integrating sphere haze, allowing the sensitivity of the sphere haze to errors in the integrating sphere geometry to be calculated.

Design, fabrication, test, and analysis of an out-of-plane plasmonic optical metasurface

Plasmonic metasurfaces with in-plane phase elements have a limit in transmission because they only affect the electric field of incident EM radiation. Recently, a set of out-of-plane plasmonic phase elements was designed using a genetic algorithm to work in the infrared as a Huygens metasurface with significantly improved transmission efficiency. A beam-steering metasurface (i.e., blazed transmissive diffraction grating) was fabricated from this design using membrane projection lithography (MPL) and characterized for its bidirectional transmittance distribution function as a function of scatter angle for normally incident light, and linear incident and transmitted polarizations. Measurements were compared with the designed behavior as predicted by finite element method (FEM) simulations that generated near fields for each phase element and propagated them to the far field as a metasurface using a Stratton–Chu formulation, but measurements showed strong zero-order diffraction not present in the simulation along with the designed +1-diffraction order. We analyze this disagreement between measured and ideal results. Further FEM modeling included the introduction of defects into the phase elements consistent with defects expected from the fabrication process and identified lateral displacement of the plasmonic decoration in the MPL structure as a potential cause for the reduced performance of the fabricated device.

Imaging Scatterometry with Extrapolation of Missing BRDF Data for Materials Used in Laser Material Processing.

Imaging scatterometry is a method for determining the reflection distribution based on bidirectional reflectance distribution function (BRDF) measurements. However, it has a well-known limitation that results obtained by imaging scatterometry for small illumination angles are practically useless. Therefore, we propose an approach for reconstruction of the reflection distribution based on a series of measurements at different illumination angles and extrapolation of the missing results to overcome this limitation. The developed algorithm was validated using bidirectional transmittance distribution function (BTDF) measurements. The BRDF measurements were carried out for materials that are commonly used in laser material processing, i.e. substrates and functional coatings. The obtained data were subsequently used to determine the total reflection intensity from all considered materials, which were characterized by reconstructed distributions.

Fundamental scattering quantities for the determination of reflectance and transmittance.

The bidirectional reflectance distribution function (BRDF) and the bidirectional scattering - surface reflectance distribution function (BSSRDF), which relate radiance at the surface to irradiance and radiant flux, respectively, are regarded as the most fundamental scattering quantities used to determine the reflectance of objects. However, for materials where the optical radiation is transmitted under the surface, this radiance depends not only on irradiance and radiant flux, but also on the size of the irradiated area of the surface. This article provides insight into such dependence under the special condition in which the radiance is evaluated within the irradiated area and, consequently, is produced by both the insurface reflection and the subsurface scattering, in contrast to the situation in which the radiance is evaluated at non-irradiated areas and only subsurface scattering contributes. By explicitly considering both contributions, two other scattering quantities are defined: one that accounts exclusively for the insurface reflection and the other that accounts for subsurface scattering. In this regard, these quantities might be considered more fundamental than the BRDF and the BSSRDF, although they are coincident with these two functions apart from the above-mentioned special condition and for materials with negligible subsurface scattering. In this work, the relevance of the proposed scattering quantities is supported by experimental data, practical considerations are given for measuring them, and their relation to the bidirectional transmittance distribution function (BTDF) is discussed.

New phase function development and complete spectral radiative properties measurements of aerogel infused fibrous blanket based on simulated annealing algorithm

Aerogel infused fibrous blankets have been regarded as one the most promising superinsulation materials for application of thermal subsystems with severe limitations in weight, volume, and thermal insulation efficiency in space missions. Aiming at accurate description of radiation transport within such multiscale, multicomponent composites with absorbing, emitting, and anisotropic scattering features, this research is interested in experimental characterization of complete series of spectral radiative parameters on basis of theoretical solution and optical measurements for the composites. To overcome the convergence difficulty in ill-posed problem, simulated annealing algorithm was employed for inverse identification of multiple radiative parameters of the aerogel-based samples. A new phase function with two Henyey-Greenstein (HG) and Rayleigh scattering functions was proposed to describe the radiation scattering distribution inside the composites. It was found that the developed method successfully achieved high precision measurements of radiative parameters of anisotropic scattering medium. The proposed phase function gives more exact expression of angular distribution behavior of scattering occurring inside the multiscale composites, in comparison with the commonly-used phase functions. The information collected from sensitivity analysis of Bidirectional Reflectance Distribution Function (BRDF) and Bidirectional Transmittance Distribution Function (BTDF) facilitated highly accurate and more efficient identification and optimization of experimental tests in measurements of complete radiative parameters of aerogel infused fibrous blankets for space applications.

Bidirectional reflection of semitransparent polytetrafluoroethylene (PTFE) sheets on a silver film

In our recent work, record-high solar reflectance (exceeding 99%) has been demonstrated by placing a layer of highly scattering, semitransparent polytetrafluoroethylene (PTFE) sheet on top of a silver film. This can significantly improve the performance of daytime radiative cooling system. Although a PTFE slab of 10-mm thick acts as an excellent diffuse reflector, it is unclear how this dual-layer structure made of a thin PTFE on a mirror-like reflector will alter the bidirectional reflection. Here, we report measurements of the bidirectional reflectance distribution function (BRDF) of the dual-layer structure using a laser scatterometer at the wavelength of 635 nm. Measurements of the BRDF and the bidirectional transmittance distribution function (BTDF) of free-standing PTFE sheets are also performed. The measured BRDF for a PTFE sheet as thin as 236 μm on Ag is essentially diffuse except at large incidence angles. A Monte Carlo ray-tracing method incorporating both surface scattering and volumetric scattering is developed to theoretically model the BRDF in order to elucidate the underlying mechanisms. The numerical model captures the main features and can be used to study the bidirectional properties for PTFE sheets thinner than what is experimentally available.

Comparison of bidirectional transmittance distribution function (BTDF) measurements on fused silica and sintered polytetrafluoroethylene diffusers

Accurate determination of the bidirectional transmittance distribution function (BTDF) of transmissive diffusers is critical for the on-orbit spectral radiance calibration of several satellite-based, Earth remote sensing instruments. This study presents the results of the comparison of BTDF measurements by NASA Goddard Space Flight Center’s Diffuser Calibration Laboratory and the National Institute of Standards and Technology’s Spectral Tri-function Automated Reference Reflectometer facility on two transmissive diffusers: HOD-500, a synthetic fused silica sample manufactured by Hereaus Quarzglas, and Spectralon-250, a sintered polytetrafluoroethylene sample manufactured by Labsphere, Incorporated. BTDF measurements were acquired at seven wavelengths from 290 nm to 740 nm, at incident elevation angles of 0° and 30°, and at scatter elevation angles from 1° to 15°. Comparison of the measurements made by the two facilities revealed excellent agreement within their combined standard uncertainties. NASA chose the parameters for the BTDF measurements to be identical to those NASA used when measuring the BTDF of the flight diffusers to be flown onboard the Tropospheric Emissions: Monitoring of Pollution (TEMPO) and the Geostationary Environment Monitoring Spectrometer (GEMS) satellite instruments. Successful agreement between NASA and NIST of BTDF results, therefore, effectively validates the BTDF measurements NASA made for these satellite flight programs.

Performance assessment of the BTDF data compression based on wavelet transforms in daylighting simulation

The bidirectional transmittance distribution function (BTDF), which is used to characterize the light transmission of a complex fenestration system (CFS), commonly involves bulky volume of data that can be a challenge to data storage and transmission in lighting simulation tools and on compact platforms. This paper introduces a compression scheme that is based on planar wavelet transforms with three levels of decomposition to efficiently compress the BTDF data of CFSs and maintain fidelity in daylighting simulation. The root-mean-square error (RMSE) and transmittance error (TE) of compressed medium-resolution BTDF data using three different wavelet bases were evaluated for five different CFS samples at various compression ratio. Based on the results, the generic error from compression did not exceed 20% with CDF9.7 basis for compression ratio up to 200. In the case of rendering an image of a scene in which a CFS was installed at the upper daylighting section of an unilateral façade, errors began to be noticeable at a compression ratio above 70. The uniformity factor g1 was discovered to be relatively sensitive to compression (below 15% error), while the average horizontal illuminance and daylight glare probability (below 10% error) were immune to compression ratio below 100. Compression was also evaluated for a high-resolution BTDF data of external Venetian blinds in the simulation of work-plane illuminance (WPI). With a HDR imaging technique based sky luminance map, the WPI simulation had unnoticeable errors for compressed BTDF data within a compression ratio of 100.

Estimation of the channel characteristics of a vertically downward optical wireless communication link in realistic oceanic waters

Light propagation in a downlink Optical Wireless Communication (OWC) system from above the sea surface to the underwater medium is influenced by wind generated surface waves, associated bubble layer, particulate absorption and scattering, and medium inhomogeneity. The present study aims to model the combined effects of these factors on the channel characteristics, power budget and channel impulse response of the OWC system using Monte-Carlo numerical simulation technique for two different water types (open-oceanic and coastal). The transmission of light across the air-sea interface is modelled by using a Bidirectional Transmittance Distribution Function (BTDF), whereas the medium inhomogeneity is taken into consideration by stratifying the underwater channel based on the in-situ measured IOPs. In order to examine the effect of stratification, the channel characteristics are estimated by considering the medium as homogenous as well as stratified and compared. Comparison results suggest that the medium stratification provides significant improvement in power estimation in comparison to a case where the medium is considered as homogeneous, for all depths. Similarly, the channel impulse responses estimated for these two conditions are notably different in terms of delay spread, suggesting that the medium stratification in clear and moderately turbid waters may be a vital necessity for precise estimation of channel characteristics. These results will be useful for design and implementation of a physical downlink optical wireless communication system.

A Fast All-sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS-NIT): Part I. The clear-sky model

The solar energy industry often uses individual steps to empirically compute plane-of-array (POA) irradiance from horizontal irradiance and decompose it to narrow-wavelength bands. Conventional radiative transfer models designed for meteorological applications requires significant computing efforts in practice; however, they provide a physics-based solution of radiance and therefore are capable of computing spectral POA irradiances in a single step. In this study, we integrate the advantages of the current models and develop an innovative radiative transfer model, the Fast All-sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS-NIT), to efficiently compute irradiances on inclined photovoltaics (PV) panels for 2002 narrow-wavelength bands from 0.28 to 4.0 µm. This study is reported in two parts. Part I presents the methodology and performance evaluation of the new model under clear-sky conditions. The Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS), which was designed to compute clear-sky irradiances, is employed to rapidly provide the optical properties of a given clear-sky atmosphere. The clear-sky radiances in the narrow-wavelength bands are computed by considering three paths of photon transmission and solving the radiative transfer equation with the single-scattering approximation. The Bi-directional Transmittance Distribution Function (BTDF) of aerosols is given by their single-scattering phase function with a correction using a two-stream approximation. The validation analysis confirms that FARMS-NIT has improved accuracy compared to TMYSPEC as evaluated by both surface observations and a state-of-the-art radiative transfer model. This model substantially improves computational efficiency compared to other radiative transfer models though it uses slightly more computing time than TMYSPEC. Part II of this study addresses the model in cloud-sky conditions and will be published as a companion paper.

Modeling and simulating the bidirectional reflectance distribution function (BRDF) of seawater polluted by oil emulsion

Based on bidirectional reflectance distribution function (BRDF), we proposed a concept of bidirectional transmittance distribution function (BTDF). By using subsurface scattering theory, the single scattering and multiple scattering of light beams transmitted in the oil-emulsion seawater were discussed. Then a high-efficiency model for BRDF of oil-emulsion seawater was built. Finally, the comparison of simulation results between our model and Monte Carlo method were also discussed.

PRELIMINARY RESULTS OF BTDF CALIBRATION OF TRANSMISSIVE SOLAR DIFFUSERS FOR REMOTE SENSING.

Satellite instruments operating in the reflected solar wavelength region require accurate and precise determination of the optical properties of their diffusers used in pre-flight and post-flight calibrations. The majority of recent and current space instruments use reflective diffusers. As a result, numerous Bidirectional Reflectance Distribution Function (BRDF) calibration comparisons have been conducted between the National Institute of Standards and Technology (NIST) and other industry and university-based metrology laboratories. However, based on literature searches and communications with NIST and other laboratories, no Bidirectional Transmittance Distribution Function (BTDF) measurement comparisons have been conducted between National Measurement Laboratories (NMLs) and other metrology laboratories. On the other hand, there is a growing interest in the use of transmissive diffusers in the calibration of satellite, air-borne, and ground-based remote sensing instruments. Current remote sensing instruments employing transmissive diffusers include the Ozone Mapping and Profiler Suite instrument (OMPS) Limb instrument on the Suomi-National Polar-orbiting Partnership (S-NPP) platform,, the Geostationary Ocean Color Imager (GOCI) on the Korea Aerospace Research Institute's (KARI) Communication, Ocean, and Meteorological Satellite (COMS), the Ozone Monitoring Instrument (OMI) on NASA's Earth Observing System (EOS) Aura platform, the Tropospheric Emissions: Monitoring of Pollution (TEMPO) instrument and the Geostationary Environmental Monitoring Spectrometer (GEMS).. This ensemble of instruments requires validated BTDF measurements of their on-board transmissive diffusers from the ultraviolet through the near infrared. This paper presents the preliminary results of a BTDF comparison between the NASA Diffuser Calibration Laboratory (DCL) and NIST on quartz and thin Spectralon samples.

Study of radiative transfer in 1D densely packed bed layer containing absorbing–scattering spherical particles

In this study, transmission process of diffused and collimated beam in a 1D densely packed bed is investigated. Absorbing–scattering spherical particles with the same radius are distributed randomly in transparent and absorbing host media. The refractive indexes of the spheres are different from that of the host medium. The size parameter χ of these spheres is sufficiently large to simulate their interaction with radiation through a Monte Carlo ray-tracing technique based on the geometrical optics approximation. Using the validation of the code for radiative transfer in a single absorbing–scattering sphere and in a packed bed filled with opaque or absorbing spheres, the effects of albedo, optical thickness, refractive index, and incident angle on the transmission process are examined in detail. The information of transmittance, reflectance, bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BTDF) are employed to describe the role of absorbing–scattering spheres in transparent and absorbing host media.

Evaluation of diffusing properties of greenhouse covering materials

Modern greenhouse covering and screen materials are able to transform direct sunlight into diffuse light. After entering the greenhouse the sunlight is scattered and penetrates the crop where it is absorbed and used for photosynthesis. Diffuse light has been shown to increase light interception of crops, increase crop photosynthesis and results in higher yields. Many different types of diffuse covering materials are available, and growers select materials based on crop, outside climate where the greenhouse is located and market situation. Earlier measurement methods to evaluate diffuse covering materials have been proposed (Hemming et al., 2008) and are mainly based on the measurement and evaluation of the hemispherical light transmittance, the average amount of light coming into the greenhouse (Nijskens et al., 1985; Papadakis et al., 2000) and the Haze (e.g., ASTM-D1003-07), the average amount of scattered light reaching the crop. A more detailed evaluation of the angular and spectral light transmittance of materials is needed (Hemming et al., 2014), including the spatial distribution of scattered light, or the way light is scattered by a material. In this paper we propose a new method of measuring the spatial distribution of scattered light by a bi-directional transmittance distribution function (BTDF) measurement. By comparing the BTDF values of a diffuse covering or screen material with the BTDF values of a Lambertian diffuser, we calculate one simple value for material characterisation, the F-scatter. F-scatter is a more representative value for the scattering properties of a material than Haze. The detailed material scatter properties can be used for further raytracing analysis of materials in greenhouses with a specific roof construction, at a specific location for any moment of the year. It can also be used for 3D functional crop models in the future.

National Institute of Standards and Technology measurement service of the optical properties of biomedical phantoms: Current status.

The National Institute of Standards and Technology (NIST) has maintained scales for reflectance and transmittance over several decades. The scales are primarily intended for regular transmittance, mirrors, and solid surface scattering diffusers. The rapidly growing area of optical medical imaging needs a scale for volume scattering of diffuse materials that are used to mimic the optical properties of tissue. Such materials are used as phantoms to evaluate and validate instruments under development intended for clinical use. To address this need, a double-integrating sphere based instrument has been installed to measure the optical properties of tissue-mimicking phantoms. The basic system and methods have been described in previous papers. An important attribute in establishing a viable calibration service is the estimation of measurement uncertainties. The use of custom models and comparisons with other established scales enabled uncertainty measurements. Here, we describe the continuation of those efforts to advance the understanding of the uncertainties through two independent measurements: the bidirectional reflectance distribution function and the bidirectional transmittance distribution function of a commercially available solid biomedical phantom. A Monte Carlo-based model is used and the resulting optical properties are compared to the values provided by the phantom manufacturer.

Characterization of the Optical Properties of 2D-to-3D Conversion Imaging Screens Using Bidirectional Transmittance Distribution Function

Characterization of the Optical Properties of 2D-to-3D Conversion Imaging Screens Using Bidirectional Transmittance Distribution Function

Automatic measurement of spectral bidirectional transmittance distribution function on translucent optical materials

A measurement platform of spectral bidirectional transmittance distribution function (BTDF) with a full three dimensional spatial coverage is developed based on a fiber spectrometer, a tungsten–halogen lamp and a 3D mechanical rotation angle system. The measurement software and the control software are integrated to realize the automatic measurement. The measurement equipment has a broad spectral coverage, a large angle range, a wide dynamic response and a short acquisition time. The measured spectral range is 380–760nm with 0.04nm spectral resolution. The measured angle range is 0–80° in zenith angle and 0–360° in azimuth angle with 0.01° angle resolution. The dynamic range is 107 and the minimal integration time is 1ms. The measurement of spectral BTDF on translucent frosted glass is performed and a large amount of measured data is obtained with the measurement error no more than 3.28%. It provides a reliable description facility for spectral and spatial transmission characteristics of the translucent materials.

Calibration function for an experimental setup for the measurement of irradiance distributions via a transmitting diffuser.

We describe a procedure to estimate the calibration function for an experimental setup that contains a transmitting diffuser whose bidirectional transmittance distribution function for light transmitted in normal direction is nearly independent of the incidence angle. This type of diffusing screen may be used in experimental setups to measure the irradiance distribution in the focal plane of concentrator optics that have large angles of incidence in the focal plane. It is shown that the influence of this screen and of the remaining components on the irradiance distribution may be described empirically by a Gaussian function and thus may be corrected for. Furthermore, it is demonstrated that the correction is necessary to avoid an underestimation of the concentrator optics' ability to concentrate the incoming radiation.