Directional-hemispherical Transmittance Research Articles

The correlation of the scattering coefficient and morphology‐based microstructure in yttria‐stabilized zirconia coatings

AbstractThe microstructure dependence of thermal radiative properties is critically needed to the design and operation of the thermal barrier coating systems. In this study, different yttria‐stabilized zirconia coating layers are fabricated by air plasma spray with three average porosities 5.9%, 14.5%, and 23.3% at coating thickness from 283 to 955 µm. The room‐temperature, spectral directional–hemispherical transmittance, and reflectance are measured over the wavelength range from 1.35 to 2.5 µm. The radiative properties of absorption and scattering coefficients are reduced by using a hybrid method of the discrete ordinate method and the Kubelka–Munk four‐flux method. Using the image processing tools developed in‐house, the porosity and pore size distribution (PSD) are obtained from SEM images for each coating. A numerical algorithm is used to convert the two‐dimensional PSD into a three‐dimensional PSD assuming that all pores are spheroid. The scattering coefficient is directly computed by the Mie theory based on the PSD. The new approach provides a predictive model of radiative properties based on the PSD, which is extracted from the coating cross‐section images. Comparison of radiative properties obtained by the direct Mie theory computation and those obtained by the reduction from spectral measurement is made and discrepancy is discussed.

Transmittance of transparent horizontal and tilted windows supporting large non-absorbing pendant droplets

This study establishes that the deviation of large pendant droplets from an ideal cap-shape due to gravity can have significant and complex impacts on the normal-hemispherical and directional-hemispherical transmittances of light through horizontal and tilted transparent windows. First, the shape of pendant droplets larger than the capillary length was predicted numerically by balancing gravitational and surface tension forces for various droplet volumes, contact angles, and window tilt angles. Then, light transfer through windows supporting such numerically generated droplets was simulated using the Monte Carlo ray-tracing method. The window transmittance for large droplets was found to be nearly independent of droplet spatial arrangement and size distribution for relatively narrow size distributions. Furthermore, the droplets could be assumed to be cap-shaped in predicting the normal-hemispherical transmittance for droplet volumes V< 10 µL and contact angles θc<θcr where θcr is the critical angle for total internal reflection at the droplet/air interface. However, for larger droplets and/or contact angles, assuming droplets to be cap-shaped caused the transmittance to be overestimated by as much as 37% for horizontal windows. This was due to gravity-induced deformation of the droplet shape resulting in increased reflection at the droplet/air interface. For tilted windows, the droplet deformation caused the normal-hemispherical transmittance to increase with increasing droplet volume and window tilt angle. For both horizontal and tilted windows, transmittance decreased linearly with increasing droplet surface area coverage. These results and numerical tools can be used to design energy efficient solar stills, greenhouses, and covered photobioreactors, for example.

Symbolic Monte Carlo method applied to the identification of radiative properties of a heterogeneous material

A Symbolic Monte Carlo method (SMC) is applied to the identification of radiative properties of a heterogeneous semitransparent insulating material from measurements of directional-hemispherical transmittance and reflectance at room temperature. The polynomials obtained with SMC allow the development of a complete inverse analysis which determines if the inverse problem solution exists, is unique and stable. Moreover, the numerical efficiency of the absorption and scattering coefficients identification is improved since the radiative transfer equation is only solved once in the overall inverse iterative procedure.

Light transfer through windows with external condensation

This study investigates systematically light transfer through windows supporting cap-shaped droplets on their external face. The presence of such droplets may have negative effects on the conversion efficiency of solar cells, distorts image quality of lenses, or hinders visibility through windows and windshields. Here, the directional-hemispherical transmittance was predicted by the Monte Carlo ray-tracing method. The droplets were monodisperse or polydisperse randomly distributed on the outside face of optically smooth windows. For nonabsorbing droplets, the diameter and size distribution did not have a significant effect on the window directional-hemispherical transmittance. The latter was nearly independent of contact angle for incident angle θi ≤ 30°. However, the directional-hemispherical transmittance decreased monotonously with increasing incident angle and droplet contact angle for contact angle θc ≤ 70° to reach a minimum at a contact angle θc,min beyond which it increased with increasing contact angle before reaching a plateau at large contact angles. This was attributed to total internal reflection at the back window/air and droplet/air interfaces. For absorbing droplets, the normal-hemispherical transmittance decreased significantly with increasing droplet contact angle, mean diameter, polydispersity, and projected surface area coverage due to strong absorption within the droplets. Moreover, the normal-hemispherical transmittance decreased with increasing contact angle for θc < 90° and remained constant and independent of the droplets’ absorption index, mean diameter, and contact angle for θc ≥ 90°. Finally, Analytical expressions for the upper and lower bounds of the normal-hemispherical transmittance as a function of droplet contact angle, optical properties, and projected surface area coverage were derived.

Assessing the consistency of optical properties measured in four integrating spheres

ABSTRACTLeaf optical properties (LOPs) determine the radiation regime of vegetation, thus being key input parameters in leaf and canopy radiative transfer models. It is of great importance to know the uncertainties originating from the LOP measurements. The most common approach to measure LOP uses integrating spheres. They allow measurements of both directional-hemispherical reflectance factor (R) and transmittance factor (T). However, sphere’s design, inner surface coating and measurement protocol differ among the spheres’ models and manufacturers. Our main goal was to evaluate the consistency of optical properties measured in four integrating spheres (Dualsphere, Labspehre, ASD, and Li-cor). Our test samples were three Spectralon® panels, four artificial materials and leaves from six common broadleaf tree species. Results showed that spectra measured in the four integrating spheres were generally similar in the spectral region between 400 and 1600 nm. The average standard deviation computed among the spectra of all samples measured in all spheres was around 0.023 (and varied between 0.005 and 0.044). Statistically significant differences were detected mainly between Dualsphere and Li-cor spheres.

Transmittance of transparent windows with non-absorbing cap-shaped droplets condensed on their backside

This study aims to quantify systematically the effect of non-absorbing cap-shaped droplets condensed on the backside of transparent windows on their directional-hemispherical transmittance and reflectance. Condensed water droplets have been blamed to reduce light transfer through windows in greenhouses, solar desalination plants, and photobioreactors. Here, the directional-hemispherical transmittance was predicted by Monte Carlo ray-tracing method. For the first time, both monodisperse and polydisperse droplets were considered, with contact angle between 0 and 180°, arranged either in an ordered hexagonal pattern or randomly distributed on the window backside with projected surface area coverage between 0 and 90%. The directional-hemispherical transmittance was found to be independent of the size and spatial distributions of the droplets. Instead, it depended on (i) the incident angle, (ii) the optical properties of the window and droplets, and on (iii) the droplet contact angle and (iv) projected surface area coverage. In fact, the directional-hemispherical transmittance decreased with increasing incident angle. Four optical regimes were identified in the normal-hemispherical transmittance. It was nearly constant for droplet contact angles either smaller than the critical angle θcr (predicted by Snell’s law) for total internal reflection at the droplet/air interface or larger than 180°-θcr. However, between these critical contact angles, the normal-hemispherical transmittance decreased rapidly to reach a minimum at 90° and increased rapidly with increasing contact angles up to 180°-θcr. This was attributed to total internal reflection at the droplet/air interface which led to increasing reflectance. In addition, the normal-hemispherical transmittance increased slightly with increasing projected surface area coverage for contact angle was smaller than θcr. However, it decreased monotonously with increasing droplet projected surface area coverage for contact angle larger than θcr. These results can be used to select the material or surface coating with advantageous surface properties for applications when dropwise condensation may otherwise have a negative effect on light transmittance.

COMBINED TWO-FLUX APPROXIMATION AND MONTE CARLO MODEL FOR IDENTIFICATION OF RADIATIVE PROPERTIES OF HIGHLY SCATTERING DISPERSED MATERIALS

An identification procedure is developed for obtaining spectral radiative properties of highly scattering dispersed materials such as porous ceramics. Traditional techniques based on measurements of the directional-hemispherical reflectance and transmittance are of limited use because of difficulties in fabricating sufficiently thin and mechanically stable samples to obtain reliable values of directional-hemispherical transmittance. However, one can use the directional-hemispherical reflectance measurements for optically thick samples to obtain the transport scattering albedo. A one-dimensional analytical solution employs the modified two-flux approximation for the identification of transport scattering albedo. An additional transmittance measurement is required to identify the transport extinction coefficient. Binormal narrow cone transmittance is measured for this purpose. Because the one-dimensional analytical solution is not applicable to model the binormal narrow cone transmittance, the Monte Carlo ray-tracing technique is used to identify the transport extinction coefficient. The identification procedure is applied to obtain near-infrared radiative properties of porous ceria ceramics used in solar thermochemical reactors. The identified transport scattering coefficient is shown to be in good agreement with theoretical estimates based on the Mie theory for polydisperse pores and grains. This verifies the applicability of a model based on independent scattering and Mie theory for theoretical predictions of radiative properties of two types of ceria ceramics with porosity of 0.08 and 0.72, and for extrapolating the properties of both ceramics in a limited near-infrared range to the range of significant absorption.

Validation of the performance of a new bidirectional video-goniophotometer

An accurate knowledge of the directional optical properties of advanced fenestration materials is necessary for them to be adequately integrated in buildings. These properties are expressed by the Bidirectional Transmission (or Reflection) Distribution Functions (BTDF, BRDF) of such elements, which are measured by specifically designed measuring equipment: an innovative, time-efficient bidirectional goniophotometer, based on digital imaging techniques, was designed and set up for that purpose. In this paper, the in-depth validation used for the bidirectional measurements performed with this apparatus is presented. It is based on different approaches including experimental error estimation, comparisons to analytical or ray-tracing based models and to other measured data, and calculation of the directional-hemispherical transmittance (reflectance) gauged against measurements of the same systems with Ulbricht (integrating) spheres. The high accuracy and reliability of this novel device were confirmed by this detailed investigation, and led to a maximum error for BT(R)DF data of only 10%.

Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles

An improved method used to determine the absorption and scattering characteristics of a weakly absorbing substance containing bubbles is suggested. The identification procedure is based on a combination of directional-hemispherical measurements and predictions of Mie-scattering theory including approximate relations for a medium with polydisperse bubbles. A modified two-flux approximation is suggested for the calculation of directional-hemispherical transmittance and reflectance of a refracting and scattering medium. The complete identification procedure gives not only the spectral radiative properties but also the volume fraction of bubbles and the characteristics of possible impurity of the medium. This procedure is used to obtain new data on near-infrared properties of fused-quartz samples containing bubbles.

Characterization of the Pore Structure of Ceramics via Propagation of Light and Infrared Radiation

The pore size distributions of alumina and magnesia ceramics were determined by measuring the directional-hemispherical transmittance and reflectance. These values are highly sensitive to changes of the pore structure. The partially sintered alumina samples were measured at room temperature in a wavelength range from 0.5 to 6 μm. The equation of radiative transfer can be solved for absorbing and scattering media by a three-flux solution. With this three-flux solution the scattering coefficients were derived from the measured directional-hemispherical transmittance and reflectance. The scattering coefficients can also be calculated theoretically by the Mie theory, if the pore size distribution is known. Finally, the quantitative pore size distribution was determined by fitting the theoretical scattering coefficients to the experimental scattering coefficients. To check the correctness of the derived pore-size distribution, scanning electron microscopy (SEM) and atomic force microscopy (AFM) pictures of the alumina samples were taken. The pore-size distribution was then derived by counting the pores and determining the diameters D of the spherical pores. Both results agree well and show that the new procedure is a valuable tool to extract structural information during the final sintering state.

Radiative Properties of Semitransparent Silicon Wafers With Rough Surfaces

This paper presents a Monte Carlo model for prediction of the radiative properties of semitransparent silicon wafers with rough surfaces. This research was motivated by the need of accurate temperature measurement in rapid thermal processing (RTP) systems. The methods developed in this paper, however, can be applied to various semitransparent materials, such as diamond films. The numerically obtained bidirectional reflectance distribution function (BRDF) showed a similar trend as the experimental data. Furthermore, a higher angular resolution can be achieved by simulation than by experiments. The bidirectional transmittance distribution function (BTDF) can also be computed in the same run for semitransparent wafers. Other spectral radiative properties (such as the directional-hemispherical transmittance and reflectance, the emittance and the absorptance) under various surface conditions were computed at various temperatures. The results can help gain a deeper understanding of the radiative behavior of semitransparent materials and may be applied to various fields.

Impact of water drops on the visible radiation transmittance of glazings under outside radiant conditions

Experimentally determined directional-hemispherical transmittances for visible radiation were used to calculate the effect of condensate on the hemispherical–hemispherical transmittance values under diffuse radiant conditions for single glass and polyethylene. The hemispherical–hemispherical transmittances were determined in the horizontal plane for different inclinations of both glazing materials assuming a completely overcast sky and a clear sky. In all cases, condensate was found to reduce the transmittance. Under an overcast sky, the transmittance of single glass was reduced by the presence of condensate from 8 up to 13% (on a relative scale) for increasing inclination angles of the glass plate, while for the polyethylene film, the transmittance reduction due to condensate decreased from 20 down to 13%. Under a clear sky, depending on date, time, and orientation of the glazing material, the transmittances of single glass and polyethylene were reduced by between 6 and 15% and by between 8 and 21%, respectively, due to the presence of condensate. These results revealed that the impact of the presence of condensate on the transmittance of a glazing cannot be omitted from design and performance calculations of solar energy systems.

Determination of spectral radiative properties of open-cell foam: hemispherical - directional spectral transmittance and directional - directional transmittance measurement

Spectral radiative properties (absorption coefficient, scattering coefficient, and phase function) of open-cell carbon foam have been determined experimentally. The identification method uses spectral transmittance and reflectance measurements and a prediction model based on a combination of geometric optics laws and diffraction theory. In the wavelength region 0.2-2 μm directional-hemispherical transmittance and reflectance measurements are used, and directional directional transmittance and reflectance measurements are used in the wavelength region 2-15 μm. Radiative properties are determined in the wavelength region from visible to infrared. Two approaches corresponding to two different types of measurements are compared for the determination of radiative properties. Moreover, experiments on a guarded hot-plate device are used to confirm that the proposed model is appropriate to predict the radiative heat transfer in such media.

SE—Structures and Environment: Condensation and Radiation Transmittance of Greenhouse Cladding Materials, Part 3: Results for Glass Plates and Plastic Films

The effect of condensate on the transmittances of single glass, low-emissivity glass, double glass, ordinary low-density polyethylene, anti-drop-condensation polyethylene and anti-dust polyethylene was investigated experimentally. The directional–hemispherical transmittances of the dry and the wet (i.e. covered with condensate) materials were measured under laboratory conditions using monochromatic radiation. Under dry conditions, the directional–hemispherical transmittances of the three plastic films and the single glass plate coincided within 3% for incidence angles up to 60°. The directional–hemispherical transmittances of dry low-emissivity glass and especially dry double glass were significantly lower than the three plastic films and the single glass plate. Depending on the cladding material and incidence angle, the effect of the presence of condensate on the directional–hemispherical transmittance was insignificant or negative (a reduction of up to 23% on plastic films without anti-drop agents). The presence of condensate caused similar transmittance reductions for single and double glass reaching 13–15% at incidence angles of 50–65°. The transmittance reductions determined for the wet low-emissivity glass were slightly smaller and limited to a maximum of 11% at an incidence angle of 70°. The addition of anti-drop agents to plastic films suppressed the transmittance reduction totally. The different influence of the condensate on the transmittance of different cladding materials was mainly due to shape of the condensate drops, which were much flatter on glass than on non-anti-drop plastics. Assuming uniformly diffuse radiation, condensate was found to lower the hemispherical–hemispherical transmittance by 8% for single and double glass, 5% for low-emissivity glass, 11% for low-density polyethylene and 13% for anti-dust polyethylene.

PAR TRANSMITTANCE OF DRY AND WET GLASS

A single, a low emissivity, and a double glass plate were investigated with respect to their transmittances in the photosynthetically active radiation (PAR) range. Directional-hemispherical transmittances of these glass plates were determined under laboratory conditions in the dry and the wet (i.e., condensate covered) states. The transmittance curve of the low emissivity glass plate lay below the one of the single glass plate and above the one of the double glass plate. The presence of a condensate layer caused a similar transmittance reduction for single and double glass. This reduction reached a maximum of 13 to 15% at incidence angles of 50-65 degrees. The transmittance reductions determined for the wet low emissivity glass were smaller and restricted to at most 11% at an incidence angle of 70 degrees. Assuming uniformly diffuse radiation, condensation was found to lower the transmittance by 8% for single and double glass and 5% for low emissivity glass.

Heat transfer coefficients of translucent glazing units for daylighting purposes

The Bavarian Centre for Applied Energy Research has developed a double-pane glazing unit containing a light-scattering translucent fleece mounted at half distance between two glass panes. The fleece, which consists of synthetic fibres with diameters in the range 1-4 μm, suppresses convection between the panes and reduces the infrared radiative heat transfer. The resulting heat transition coefficient, or U value, is as low as for a triple-pane window; the weight, however, is close to that of a double-pane window. A model based on the radiative, conductive, and convective components of heat transfer has been developed to calculate the U value as a function of the properties of the glass panes, fleeces, gas fillings, and gap widths used. The model was validated by measurements of the U values for several assembled glazings. With two low-e coated window panels (emissivity e = 0.04), a krypton gas filling, and a width of the two gaps of 12 mm, a U value of 0.47 W m -2 K -1 is obtained. Transmission of direct sunlight can be avoided as a result of the scattering properties of the fleece. Optimised fleeces provide a directional-hemispherical transmittance for the glazing unit of about 50% in the visible and a solar heat gain coefficient or g value of 20%-35%. Because of the scattering of sunlight within the fleece, the illumination level in the room was quite uniform.

Characterization of the pore structure of alumina ceramics by diffuse radiation propagation in the near infrared

Light scattering by pore/particle interfaces causes diffuse light propagation in ceramics. The diffuse light transmission is highly sensitive to structural changes in the last sintering state. The transmission increases more than one order of magnitude between 93% and 99% of the theoretically possible density. By using diffuse transmission and reflection measurements, a quantitative analysis of the pore size distribution can also be made. The directional-hemispherical transmittance and reflectance of partially sintered Al 2O 3-samples were measured at room temperature in the wavelength range from 700 nm to 2500 nm. A three-flux solution of the equation of radiative transfer is shown to be an adequate tool to derive the extinction coefficients from the directional-hemispherical transmittances. The pore size distribution was determined by fitting theoretical light scattering of spherical pores, which was calculated by the Mie theory, to the experimental extinction data.

Effective Sample Size in Diffuse Reflectance Near-IR Spectrometry

Two independent methods for determination of the effectively sampled mass per unit area are presented and compared. The first method combines directional-hemispherical transmittance and reflectance measurements. A three-flux approximation of the equation of radiative transfer is used, to separately determine the specific absorption and scattering coefficients of the powder material, which subsequently are used to determine the effective sample size. The second method uses a number of diffuse reflectance measurements on layers of controlled powder thickness in an empirical approach. The two methods are shown to agree well and thus confirm each other. From the determination of the effective sample size at each measured wavelength in the visible-NIR region for two different model powder materials, large differences was found, both between the two analyzed powders and between different wavelengths. As an example, the effective sample size ranges between 15 and 70 mg/cm(2) for microcrystalline cellulose and between 70 and 300 mg/cm(2) for film-coated pellets. However, the contribution to the spectral information obtained from a certain layer decreases rapidly with increasing distance from the powder surface. With both methods, the extent of contribution from various depths of a powder sample to the visible-NIR diffuse reflection signal is characterized. This information is valuable for validation of analytical applications of diffuse reflectance visible-NIR spectrometry.

An experimental investigation of thick-sample effects in the measurement of directional-hemispherical transmittance of advanced glazing materials

Samples that are thick with respect to the measuring apparatus can pose problems in the measurement of directional-hemispherical transmittance. Due to the lateral displacement of light that these samples induce, traditional small-beam techniques are often no longer applicable. Broad-area irradiation offers a solution to these problems, but, in practice, imperfections in the extent and the uniformity of the irradiation can create errors. This paper reports measurement of the “detector-integrated inscattering function”, which describes the lateral displacement of light, for a number of thick samples over a range of incidence angles. This function is used to determine the minimum area that must be irradiated for an accurate broad-area irradiation transmittance measurement. The errors caused by transverse non-uniformities in the irradiance distributions produced by a state-of-the-art broad-area irradiation spectrophotometer are also reported. Errors caused by transverse irradiation non-uniformities are estimated, and transmittance measurements made with small-area and broad-area irradiation are compared. It is shown that in most cases small-area irradiation transmittance measurements underestimate the transmittance of thick samples due to outscattering, and that broad-area irradiation measurements using state-of-the-art irradiation optics can contain large errors of up to 20%, due to irradiance non-uniformities, particularly at large angles of incidence.

The directional response error in integrating-sphere transmittance measurements at solar wavelengths

To correctly measure the solar transmittance of a material that scatters light, a detector with uniform directional response must be used, and the integrating sphere is often used in combination with an optical detector for this purpose. However, no real optical detector system has a completely uniform directional response, thus a directional response error will always exist. This note analyzes the directional response error in directional-hemispherical transmittance measurements at solar wavelengths and determines this error for transmittance measurements on materials that scatter light in different ways, made with a state-of-the-art integrating-sphere-spectrophotometer system. It is shown that for certain types of materials, the directional response error is the dominant error in the measurement of directional-hemispherical transmittance.