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International audience; We investigate the optical absorption in a thin Cu(In,Ga)Se2 solar cell with a Lambertian white paint beneath a transparent back contact. Although this configuration has been proposed more than 30 years ago, it turns out that rigorous simulation of Maxwell's equations demand powerful numerical calculations. This type of approach is time consuming and does not provide a physical insight in the absorption mechanisms. Here, we use the radiative transfer equation to deal with multiple scattering of the diffuse part of the light. The collimated part is treated accounting for wave effects. Our model is in good agreement with optical measurements.

This paper presents an analysis of light scattering by surface particles on the sensor window of a missile during ascent flight. The particulate contaminant distribution on the window is calculated by tallying the number of particles in a set of size ranges. The particulate contamination at the end of the mission is predicted by adding the contributions from the events of ground and flight operations. The surface particle redistribution caused by vibroacoustic-induced surface acceleration was found to contribute the most to particulate surface contamination. The analytical surface obscuration calculation with a set of particle counts was compared with the results of the image analyzer measurement. The analytical results, which were calculated with a given function of particle shape depending on size, were more conservative than the measurement. A scattering calculation using a verified BSDF model showed that the scattering was less than 0.001 at 20 deg off the direction of the incident light in the mid IR wavelength when the surfaces were at Level 300 initially.

Dose perturbations at tissue interfaces have been of significant concern since the beginning of this century. However, comprehensive studies related to the backscatter perturbation in kilovoltage beams are still limited. The dose perturbation depends on various parameters, including beam energy, field size, and the thickness, width, position, and atomic number, Z, of the inhomogeneity creating the interface with soft tissue. Using a thin window parallel plate ion chamber having relatively flat response at low energies, the dose perturbation was measured as backscatter dose perturbation factor, BSDF, at various interfaces in kilovoltage x-ray beams. The BSDF is defined as the ratio of doses with and without an interface for identical setup conditions. Results indicate that the BSDF is strongly dependent on beam energy, like the backscatter factor. Contrary to its behavior in megavoltage beams, BSDF in kilovoltage beams does depend on the field size, suggesting a contribution from scattered photons and fluorescent radiation, originating in the high-Z material. The thickness of the high-Z medium is not critical, since a fraction of a millimeter is sufficient to provide full backscatter. The interface effect with wide inhomogeneity has two distinct regions: the high dose region (BSDF > 1.0), which is very localized and disappears within a fraction of a millimeter, and the low dose region (BSDF < 1.0), which is observed up to 10 cm. The dependence of BSDF is neither a quadratic function of Z nor a cube root of beam energy, indicating that the interface effect is complex and not predominantly due to photoelectron transport.

Purpose: To quantify the backscatter dose factors near the interfaces for clinically relevant high atomic number materials using GPUMCD for the Elekta MRI Linac. Methods: Backscatter dose factors (BSDF) were calculated as the ratio of the dose with and without the presence of the heterogeneity. The BSDF's were calculated either in the absence or presence of an orthogonal 1.5 T magnetic field. Doses were scored in small voxels of side 1 mm in a water phantom with dimensions of 20×20×20 cm using GPUMCD (Elekta). The minimum uncertainty in dose calculations was kept to 0.5%. A slab of thickness 2 cm, representing the inhomogeneity, was placed inside the phantom with variable position from the surface of the phantom. The slab was filled with either bone, aluminum, titanium, stainless steel, or dental amalgam. The phantom was irradiated using particles sampled from a histogram which represented the true MRI Linac spectrum. Results: With the application of the 1.5 T magnetic field (B-On), all of the BSDF's were reduced by at least 8% compared to the no magnetic field (B-Off) cases. For the B-Off case, the BSDF decreases exponentially with the upstream distance away from the interface. With B-On, the BSDF decreases exponentially for titanium, SS, and amalgam. However, it remains constant for Aluminum. In the case of bone, the BSDF increases up to a distance of 4 mm away from the interface in the presence of the magnetic field. Conclusion: The BSDF does not depend upon the thickness of the homogeneous material above the inhomogeneity for either the B-Off or B-On cases. For all the materials investigated, the BSDF is lower at the interface for the B-On case. The exponential fall-off of the BSDF away from the interface is not valid for all the materials when the magnetic field is turned ON. Funding support for this research was provided by Elekta

Purpose: To establish a simple relation of backscatter dose enhancement around a high-Z dental alloy in head and neck radiation therapy to its average atomic number based on Monte Carlo calculations. Methods: The PHITS Monte Carlo code was used to calculate dose enhancement, which is quantified by the backscatter dose factor (BSDF). The accuracy of the beam modeling with PHITS was verified by comparing with basic measured data namely PDDs and dose profiles. In the simulation, a high-Z alloy of 1 cm cube was embedded into a tough water phantom irradiated by a 6-MV (nominal) X-ray beam of 10 cm × 10 cm field size of Novalis TX (Brainlab). The ten different materials of high-Z alloys (Al, Ti, Cu, Ag, Au-Pd-Ag, I, Ba, W, Au, Pb) were considered. The accuracy of calculated BSDF was verified by comparing with measured data by Gafchromic EBT3 films placed at from 0 to 10 mm away from a high-Z alloy (Au-Pd-Ag). We derived an approximate equation to determine the relation of BSDF and range of backscatter to average atomic number of high-Z alloy. Results: The calculated BSDF showed excellent agreement with measured one by Gafchromic EBT3 films at from 0 to 10 mm away from the high-Z alloy. We found the simple linear relation of BSDF and range of backscatter to average atomic number of dental alloys. The latter relation was proven by the fact that energy spectrum of backscatter electrons strongly depend on average atomic number. Conclusion: We found a simple relation of backscatter dose enhancement around high-Z alloys to its average atomic number based on Monte Carlo calculations. This work provides a simple and useful method to estimate backscatter dose enhancement from dental alloys and corresponding optimal thickness of dental spacer to prevent mucositis effectively.

The free-form optical quasilens surface technology was utilized to develop and design a solid transparent plastic optical lens for the LED down light with the narrow angular light distribution requirement in the LED lighting applications. In order to successfully complete the mission, the precise mid-field angular distribution model of the LED light source was established and built. And also the optical scattering surface property of the Harvey BSDF scattering model was designed, measured, and established. Then, the optical simulation for the entire optical system was performed to develop and design this solid transparent plastic optical lens system. Finally, the goals of 40 deg angular light distribution pattern defined at full width half maximum with glare reduced in the areas of interest and the optical performance of nearly 82% light energy transmission optics were achieved for the LED down light illumination.

For simulating light guide lighting systems, we have developed a ray-tracing model for an ink layer extracting light from a light guide. The model consists of the volume and the rough surface scattering calculated on the basis of Mie theory and the facet model, respectively. The model of an ink layer was required to conserve energy for analyzing how much light loss occurs in each component in the lighting system. Though a single-scattering rough surface model with a shadowing/masking function successfully describes the scattering distribution, shadowing light violates the energy conservation law because of a lack of multiple scattering. We developed the rough surface ray-tracing model (RSRT model), which includes the multiple scattering instead of the shadowing/masking effect. We investigated the applicability of the RSRT model for an ink layer by comparing the RSRT model with recent physical and facet models. Finally, we compared the calculated and measured scattering distributions of an ink layer, applied the developed ink layer model to the lighting system, and confirmed the developed model to be valid.

For the systematic development of a small-scale daylight-redirecting louver system the impact of manufacturing on light scattering characteristics has to be quantified, localized and understood. In this research, the accordance of the measured scattering distributions of a de-facto production sample V1 with the computed predictions based on its design geometry V2 are quantified for selected incident light directions. A metric describing the global accordance of distributions is adapted to quantify their overall difference. A novel metric of local accordance allows further analysis. A particular low global accordance between V1 and V2 is found for an incident elevation θ i = 35 ∘ . To test the hypothesis that this result can be explained by observed geometric deviations, a simulation model V3 replicating these is compared to the design. The hypothesis is supported by the resulting high degree of accordance. The low local accordance for individual outgoing light directions indicates geometric non-uniformity of the sample V1. This method has been found useful for product development and quality assurance. Beyond their application in the proposed method, global and local accordance have potential applications in all fields of light scattering measurements.

Optical design tools allow more and more complete physical phenomena simulation and illumination design itself becomes more and more complex. A big part of these designs uses volume scattering materials. However, those are not yet implemented in such tools. For this reason we worked on a way to characterize volume scattering materials. How can we characterize and implement volume scattering materials in optical design tool for illumination design? We worked on two ways of characterizing volume scattering materials based on real Bidirectional Scatter Distribution Function (BSDF) measurements made with Reflet bench. LightTools software with its Henyey-Greenstein and Mie scattering model was also used in the process of material characterization. The study showed that the results with both Henyey and Mie characterization, allow simulation of volume scattering materials within of 5% precision compare to real measurements. Thanks to such simulations it is now possible to have custom shape illumination design using volume scattering materials from a library. Sony Ericson was the first user to benefit from these study’s results.

Back-surface acrylic mirrors can be used in low concentration and mirror augmented photovoltaics (LCPV, MAPV) to increase the irradiance on a module. Back-surface mirrors can spectrally filter incoming solar radiation reducing the ultraviolet (UV) and infrared (IR) load on the module, while useful radiation is coupled into a module or photovoltaic cell. Degradation of these mirrors can occur from UV induced photodegradative processes and metallization corrosion. Environmental stresses such as humidity, thermal cycling and exposure to corrosive substances can cause an increase in scattering, reducing mirror performance. In order to increase the lifetime and durability of back-surface acrylic mirrors a better understanding of the degradation modes is necessary. In a study of acrylic back-surface mirrors for LCPV and MAPV applications, optical properties and bidirectional scattering distribution functions (BSDF) were investigated and correlated to simulated exposure protocols. Formulations of Poly(methyl methacrylate) (PMMA) with differing concentration of UV absorbers were used for the aluminum backsurface acrylic mirrors. The formulations of aluminum back-surface acrylic mirrors were exposed in a QUV accelerated weathering tester (QLabs) to ASTM G154 Cycle 4. Total and diffuse reflectance spectra were measured for each mirror under exposure using a diffuse reflectance accessory (DRA) from 180-1800 nm on a Varian Cary 6000i at defined dose intervals. The total reflectance losses in the 250-400 nm region were greater and diffuse-only reflectance increased for formulations of acrylic mirrors that contained the least amount of UV stabilizer after each dose of QUV exposure. Acrylic back-surface mirrors were exposed to salt fog corrosion and QUV and were analyzed using BSDF. There was an increase in scattering from roughening of the mirror surface after exposure to the corrosive environment.

The studies on planetary radiative transfer computation have become important elements to disk-averaged spectral characterization of potential exoplanets. In this paper, we report an improved ray-tracing based atmospheric simulation model as a part of 3-D earth-like planet model with 3 principle sub-components i.e. land, sea and atmosphere. Any changes in ray paths and their characteristics such as radiative power and direction are computed as they experience reflection, refraction, transmission, absorption and scattering. Improved atmospheric BSDF algorithms uses Q.Liu's combined Rayleigh and aerosol Henrey-Greenstein scattering phase function. The input cloud-free atmosphere model consists of 48 layers with vertical absorption profiles and a scattering layer with their input characteristics using the GIOVANNI database. Total Solar Irradiance data are obtained from Solar Radiation and Climate Experiment (SORCE) mission. Using aerosol scattering computation, we first tested the atmospheric scattering effects with imaging simulation with HRIV, EPOXI. Then we examined the computational validity of atmospheric model with the measurements of global, direct and diffuse radiation taken from NREL(National Renewable Energy Laboratory)s pyranometers and pyrheliometers on a ground station for cases of single incident angle and for simultaneous multiple incident angles of the solar beam.

The process to convert raw profilometer data describing surface roughness into PSD and BSDF is discussed, but not well-documented in the open optical engineering literature, and is therefore prone to procedural mistakes. This paper describes the step-by-step numerical process as well as the three "check points" that insure that errors have not been introduced into the calculation. A numerical example is discussed.

Since the bidirectional scatter distribution function (BSDF) is proportional to the intensity of the scattered light, a BSDF system with the addition of a dual rotating retarder system can be used to calculate the Mueller matrix of a scatterer. An advantage of a BSDF system is the large dynamic range which allows the measurement of scattered light both near to and far from the specular region. In some cases as measurements move away from the specular and into the scatter region, the measured signal decreases and the system reaches a measurement floor. Therefore, any BSDF and Mueller matrix measurements are dependent on the scatter from the sample and on the noise floor of the system. Since the noise floor of an electro-optical system is near constant, the Mueller matrix measurement of the noise floor will be that of a perfect depolarizer. As the measurement space moves away from the high-signal region, the scattered signal decreases and the floor of the system is approached so the Mueller matrix measurements can shift towards a perfect depolarizer. The rate and location of this shift will be dependent on how Lambertian the sample is and the ratio of signal to noise in the system. Because of this tendency, caution must be taken when drawing conclusions about the Mueller matrix of scattered light, particularly in the scatter measurement region where the measured signal approaches the system floor.

This text has gone into considerable detail on the analysis and measurement of BSDF data. The importance of using a data set that truly matches a specific should be very clear. There are times when knowing general BSDF levels can be of considerable help. For example, if you have determined via analysis that a ZnSe window will work in your application if its mid-IR scatter can be kept below 10 -3 sr -1 at 30 deg from specular, then knowing that windows are routinely made at 10 -5 sr -1 in this region lets you proceed with your design. If you needed 10 -6 sr -1 , then the situation would be a little more difficult. You might actually want your component measured, or you might want to change your design. Another problem with practical use of BSDF data sets is categorizing the variables associated with the sample, the measuring instrument, and the laboratory-reporting methods. The two BRDF standards (SEMI 1392 and ASTM E2387) described in Section 12.2 provide formats for reporting BRDF data as well as complete definitions of terms. These documents provide a means for laboratories to compare, trade, and purchase reliable measurements on samples of interest. It is also expected that a relational database, probably PC based, will become available that will allow a fast search of hundreds of files to obtain data that fit a particular requirement. The 32 BSDF scans in this appendix are offered in the spirit of giving merely a sense of values measured from a few samples. Hopefully, it will be useful in the short term. Once an accessible national database is available there will be little need for the microscopic, difficult-to-use windows on BSDF data provided by data sets similar to those in this appendix.

It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman This chapter reviews the methods and equipment used to take scatter measurements. As pointed out in Section 1.5, the BSDF is defined in differential form but is measured with the incremental limitations imposed by real instrumentation. The finite detector aperture, scatter created by the instrument, calibration inaccuracies, and other practical equipment limitations, such as noise, detector nonlinearity, and mechanical errors, all produce noticeable deviations between the true BSDF and the measured BSDF. In order to generate meaningful scatter specifications and fully utilize the data, it is important to understand the source and magnitude of these deviations. System calibration, an often-discussed issue, is described in detail. The chapter progresses from these basic concepts to discussions of other measurement techniques (curved samples, area raster scans, retroscatter, TIS, and out-of-plane scatter) and concludes with a section on error analysis. Chapter 1 provides necessary background information for understanding this material. 7.1 Scatterometer Components The simple plane-of-incidence scatterometer outlined in Fig. 7.1 contains most of the components typically found in more-sophisticated systems. These are easily grouped into four categories: light source, sample mount, receiver (detection system), and computer/electronics package. A fifth important element is the controlling software package. This section outlines the need for and general operation of these modules.

Image analysis in the presence of surface scatter due to residual optical fabrication errors is often perceived to be complicated, nonintuitive, and achieved only by computationally intensive nonsequential ray tracing with commercial optical analysis codes such as ASAP, Zemax, Code V, TracePro, or FRED. However, we show that surface scatter can be treated very similarly to conventional wavefront aberrations. For multielement imaging systems degraded by both surface scatter and aberrations, the composite point spread function is obtained in explicit analytic form in terms of convolutions of the geometrical point spread function and scaled bidirectional scattering distribution functions of the individual surfaces of the imaging system. The approximations and assumptions in this formulation are discussed, and the result is compared to the irradiance distribution obtained using commercial software for the case of a two-mirror telescope operating at an extreme ultraviolet wavelength. The two results are virtually identical.

Light-emitting diodes are common light sources in modern lighting. The optical distribution of an LED package and the bidirectional scattering distribution function (BSDF) of diffusing optical components are important factors in lighting design. This paper proposes an innovative method of measuring both the optical distribution of LEDs and BSDF quickly. The proposed method uses a 2-D screen and a camera to capture the illumination on a screen, and acquires the whole-field optical distribution by synthesizing the images on the screen in different angles. This paper presents theoretical calculations and experimental results demonstrating the construction of the BSDF.

Light scattering measurements are used to determine surface PSD functions and application-specific roughness values in different relevant spatial frequency ranges. A new method is presented for area covering investigations of the high-spatial frequency roughness.

We present an importance sampling method for the bidirectional scattering distribution function (bsdf) of hair. Our method is based on the multi-lobe hair scattering model presented by Sadeghi et al. [SPJT10]. We reduce noise by drawing samples from a distribution that approximates the bsdf well. Our algorithm is efficient and easy to implement, since the sampling process requires only the evaluation of a few analytic functions, with no significant memory overhead or need for precomputation. We tested our method in a research raytracer and a production renderer based on micropolygon rasterization. We show significant improvements for rendering direct illumination using multiple importance sampling and for rendering indirect illumination using path tracing. © 2012 Wiley Periodicals, Inc.

The Bidirectional scattering distribution function (BSDF) is used to describe the multidimensional aspect of light scattering properties of a surface. Often, the BSDF is broken into the two parts: the bidirectional reflectance distribution function (BRDF), and the bidirectional transmittance distribution function (BTDF). In this paper, we investigate the onaxis BTDF at a dielectric surface (i.e., a surface where the index of refraction is different on the two sides of the surface) and show how it relates to the off-axis BRDF and BTDF of textured surfaces that are commonly used in illumination modeling and design. Numerous interesting Monte Carlo simulation results are provided.

To examine the polarimetric Bidirectional Scatter Distribution Function (BSDF) of samples in the mid-wave infrared (MWIR) and long-wave infrared (LWIR), a full Stokes polarimetric optical scatter instrument has been developed which is tunable from 4.3-9.7 microns through the use of six external-cavity quantum-cascade lasers. The polarimeter is realized through a dual-rotating-retarder configuration, which allows full Mueller-matrix extraction over the tunable wavelengths. Optical characterization of the polarimeter components was conducted to establish performance baselines for the system. The dynamic range of the system is nine orders of magnitude.

The need for rendering woven fabrics arises frequently in computer graphics. Woven fabrics have a specific appearance, luster, and transparency. We have proposed a BTDF model using the Henyey-Greenstein Function (HGF)[Uno et al. 2008]. However, since the HGF is a phenomenologically based model, to make the model more accurate, a physically based model is introduced. This paper proposes a new microfacet BTDF model for woven fabrics. we embed a multi-band structure with a fluorescent property into the model, and the results of the rendering show the powerful influence of fluorescence on the appearance of the visible band.

The Bidirectional Scattering Distribution Function (BSDF) of a surface depicts how it scatters the optical radiation, being therefore fundamental in order to explain the visual appearance of the objects. This work assesses the effect that the use of non-zero solid angles of illumination and detection has in the BSDF measurement, and it proposes a matrix-based formalism to allow this effect to be compensated from the measured BSDF and from the previous knowledge of the solid angles involved in the measurements. This deconvolution is important to obtain a better insight of the surface gloss, since it provides a more accurate absolute peak measurement and a better angular resolution in the directional scattering determination.

For the phosphor-converted light-emitting diodes (pcLEDs), the interaction of the illuminating energy with the phosphor would not just behave as a simple wavelength-converting phenomenon, but also a function of various combinations of illumination and viewing geometries. This paper presents a methodology to characterize the converting and scattering mechanisms of the phosphor layer in the pcLEDs by the measured bidirectional scattering distribution functions (BSDFs). A commercially available pcLED with conformal phosphor coating was used to examine the validity of the proposed model. The close agreement with the measurement illustrates that the proposed characterization opens new perspectives for phosphor-based conversion and scattering feature for white lighting uses.

In this paper, a method is proposed for highly precisely simulating the optical behavior of a light guide plate, which has microstructures of rough texture and rugged edges thereon. By adopting the 'equivalent medium-immersed measurement' to establish precise optical characteristic of the light guide plate, the simulated results of luminance distribution are much accordant with experimental measurement. This method will be useful in luminance uniformity evaluation and hot-spot check in advance, and it will greatly contribute to save time and cost of product development.

Visual ranking of optical surfaces with a Nomarski differential interference contrast microscope correlates well with a modified fractallike dimension and the average intensity of their scattered light field.

Non-sequential ray tracing for stray light analyses have demonstrated value, but are over-constrained when high sampling and speed are both needed. In cases where real geometry and mechanical surface properties are critical, such analyses are certainly required. But the goal of these analyses is often to attempt to approach the performance that would be achieved if only the optics contributed scatter and only through the sequential optical path. In other words, optical element scatter is the limiting case for system performance. An analysis technique is therefore presented that enables approximate but rapid sequential stray light estimates through deterministic modeling. Results of correlation to nonsequential analyses demonstrate the large range of applicability of this approach. Examples of parametric studies show the value of rapid paraxial estimates for understanding system performance sensitivities.

Image degradation due to scattered radiation form residual optical fabrication errors is a serious problem in many short wavelengths imaging system. Most currently-available image analysis codes require the bidirectional scattering distribution function (BSDF) data as an input in order to calculate the image quality from such systems. This BSDF data is difficult to measure and rarely available for the operational wavelengths of interest. Since the smooth-surface approximation is often not satisfied at these short wavelengths, the classical Rayleigh-Rice expression that indicates the BSDF is directly proportional to the surface PSD cannot be used to calculate BSDFs from surface metrology data for even slightly rough surfaces. An FFTLog numerical Hankel transform algorithm enables the practical use of the computationally intensive Generalized Harvey-Shack surface scatter theory to calculate BRDFs for increasingly short wavelengths that violate the smooth surface approximation implicit in the Rayleigh-Rice surface scatter theory. A generalized Peterson analytical scatter model is then used to make accurate image quality predictions. The generalized Peterson model is numerically validated by both ASAP and ZEMAX.

A semi-empirical reflectance/scatterance model has evolved over the years to represent a diverse set of materials from coated substrates to optical windows. This model separates the BRDF/BSDF into four basic components, specular, near-specular, diffuse, and Lambertian (random diffuse) terms. The specular and near-specular components employ a Gaussian phase function and the Fresnel power reflection coefficient. The Lambertian component uses Kubelka-Munk theory for the total integrated reflectance and transmittance. The model features wavelength, angle, and full hemispherical dependencies. It is applied to a variety of samples, from painted surfaces to transparent windows, with good success. This parameterized modeling approach is attractive because algorithms that use the model can be computationally efficient. Previous work has only considered in-plane effects. The present paper now explicitly takes into account the out-of-plane contribution and improves the total integrated factors.

The optical scattering signature and the absorbance of a material are of interest in a variety of engineering applications, particularly for those pertaining to optical remote sensing. The John Hopkins University Applied Physics Laboratory has developed an experimental capability to measure in-plane bidirectional scattering distribution functions to retrieve optical properties of materials. These measurements are supported at high angular resolution with wavelengths that span the ultra-violet to the long-wave infrared. Models have been developed to fit Lambertian, diffuse, near-specular, and specular scattering at a range of incident angles. Useful material properties can then be determined through analysis of the modeled BSDF. Optical characterization results are shown for a variety of materials, including paints, metals, optical windows, and leaves.

Understanding the Earth spectral bio-signatures provides an important reference datum for accurate de-convolution of collapsed spectral signals from potential earth-like planets of other star systems. This study presents a new ray tracing computation method including an improved 3D optical earth model constructed with the coastal line and vegetation distribution data from the Global Ecological Zone (GEZ) map. Using non-Lambertian bidirectional scattering distribution function (BSDF) models, the input earth surface model is characterized with three different scattering properties and their annual variations depending on monthly changes in vegetation distribution, sea ice coverage and illumination angle. The input atmosphere model consists of one layer with Rayleigh scattering model from the sea level to 100 km in altitude and its radiative transfer characteristics is computed for four seasons using the SMART codes. The ocean scattering model is a combination of sun-glint scattering and Lambertian scattering models. The land surface scattering is defined with the semi empirical parametric kernel method used for MODIS and POLDER missions. These three component models were integrated into the final Earth model that was then incorporated into the in-house built integrated ray tracing (IRT) model capable of computing both spectral imaging and radiative transfer performance of a hypothetical space instrument as it observes the Earth from its designated orbit. The IRT model simulation inputs include variation in earth orientation, illuminated phases, and seasonal sea ice and vegetation distribution. The trial simulation runs result in the annual variations in phase dependent disk averaged spectra (DAS) and its associated bio-signatures such as NDVI. The full computational details are presented together with the resulting annual variation in DAS and its associated bio-signatures.

Stray light modeling and analysis play a key role in new technology assessment, system engineering, and the overall performance assessment of telescope/instrument systems under real use conditions. It also is a key tool in risk reduction as stray light problems that appear late in the program are usually severe, expensive to fix, and often compromise final system performance. This paper will review the current stray light software and testing tools of value to the astronomical community and their capabilities/ limitations for general and specialized telescope systems. We will describe the role of stray light analysis in end-to-end modeling and integrated modeling for a number of systems we have analyzed and discuss in detail the stray light modeling and analysis cycle for different types of programs. A key issue is how managers might deal with the issues revealed by an analysis as well as the risks of an incomplete or improperly-timed analysis. The importance of stray light analysis for end-to-end performance assessment and whether such an analysis can reduce life-cycle costs will also be discussed. The paper will use examples from ground and space-based astronomical telescope/instrument systems.

Black and spectrally selective surfaces are important in optical systems. The proper selection of these surfaces is essential to create or maintain system performance. A critical first step in selection of surfaces is to understand the performance requirements for contrast and stray light. A well-defined performance specification accompanied by stray light modeling is important to understand how the system behaves. Without both of these, the selection of surfaces is very difficult. Practical considerations in choosing spectrally selective and tailored emissivity surfaces for a range of ultraviolet/optical/infrared telescopes and instruments are given. The Bidirectional Reflectance Data Function (BRDF) of a surface is the most useful characterization in assessing the optical properties of surfaces. Data on long-term surface durability characteristics necessary for end of life optical predictions are also critical.

A simple model for transmittance measurements with an integrating sphere is presented. The scattered light is divided into three components, each resulting in its own separate contribution to the detector signal. These contributions depend on the scattering angle and mode of operation. The true specular, diffuse, and total transmittance values are obtained as functions of the signal outputs from a reference reading, a total transmittance reading, and a diffuse transmittance reading. Two different modes of operation are distinguished involving a BaSO(4) plate and an Al mirror. Experimental results are presented illustrating the model for two samples with different scattering characteristics.

Scattering properties of nineteen single layer titania films are presented. These films are among those prepared for the 1986 Optical Society of America Annual Meeting and were made using six different deposition techniques. The properties are given in terms of total integrated scattering and the bidirectional reflectance distribution function. We looked for a relationship between scattering properties and microstructure. Our measurements indicate a strong influence by the substrate which greatly limits the conclusions that can be drawn. Measurements and theoretical analysis demonstrate that some samples have short period defects incorporated in the film.

A computer controlled facility for measurement of the bidirectional scattering distribution function is described, with application to the evaluation of spacecraft surface contamination in optical and thermal control systems. An automatic detector/sampleholder allows a 360-deg detector scan around the sample for a complete bidirectional reflectance and transmittance distribution function characterization. The system demonstrates reduced data acquisition and reduction cycle time, and improved accuracy.

Bidirectional reflection and transmission distribution functions are measured for healthy green soybean and corn leaves in vivo, for nineteen narrow wavelength bands from 375 nm to 1000 nm. Off-normal incidence reflection distribution functions show considerable specular contributions at wavelengths of strong absorption, while transmission distribution functions show a near-lambertian shape for all wavelengths employed. An empirical m-layer leaf model affords a reasonable qualitative understanding of these scattering distributions.

A generalization of Peterson’s surface scatter model results in an improved capability to predict image degradation from optical surface metrology data. A new surface scatter theory for moderately rough surfaces provides the necessary BSDF data.

This chapter looks back at some of the details of the complete pbrt system, discusses some design alternatives, and also discusses some potential major extensions to the system. pbrt represents one single point in the space of rendering system designs. pbrt represents one single point in the space of rendering system designs. The basic decisions win pbrt are that ray tracing would be the geometric visibility algorithm used, that physical correctness would be a cornerstone of the system, and that Monte Carlo would be the main approach used for numerical integration; all these have pervasive implications for the system's design. One of the basic assumptions in pbrt's design was that the most interesting types of images to render are images with complex geometry and lighting. One result of these assumptions is that pbrt is relatively inefficient at rendering simple images. Another performance implication of this design approach is that finding the BSDF at a ray intersection is more computationally intensive than it is in renderers that do not expend as much effort filtering textures and computing ray differentials. Another instance where the chosen abstractions impact the overall system efficiency is the range of geometric primitives that the renderer supports. While ray tracing's ability to handle a wide variety of shapes is elegant, this property is not as useful in practice as one might initially expect. Not many shapes that are commonly encountered in real-world scenes can be described well with spheres and cones. An alternative approach to design a ray tracer around a single low-level shape representation like triangles and only operating on this representation throughout much of the pipeline has several advantages which increase performance and remove complexity from the system.

Publisher Summary The BSDF class in pbrt software represents a collection of the bidirectional reflectance distribution functions (BRDFs) and bidirectional transmittance distribution functions (BTDFs). Grouping them in this manner allows the rest of the system to work with composite BSDFs directly, rather than having to consider all of the components they may have been built from. Although low-level BRDFs and BTDFs describe how light is scattered at a particular point on a surface, the renderer needs to determine which BRDFs and BTDFs to use at that point and how to set their parameters. This chapter describes a procedural shading mechanism that determines the BRDF and BTDF to use at points on surfaces. The basic idea is that a surface shader is bound to each primitive in the scene. The surface shader is represented by an instance of the Material interface class, which has a method that takes a point to be shaded and returns a BSDF object. The BSDF class holds a set of BxDFs that collectively describe scattering at a point. Materials, in turn, use instances of the Texture class to determine the material properties at particular points on surfaces. The abstract Material class defines two methods that material implementations must provide, Material::GetBSDF() and Material::GetBSSRDF(). Implementations of these methods are responsible for determining the reflective properties at the given point on the surface and returning an instance of the BSDF class that describes them. The Material class is defined in the files core/material.h and core/material.cpp.

Publisher Summary This chapter introduces the mathematics to describe how light is affected as it passes through participating media—particles distributed throughout a region of 3D space. Simulating the effect of participating media makes it possible to render images with atmospheric haze, beams of light through clouds, light passing through cloudy water, and subsurface scattering, where light exits a solid object at a different place than where it entered. The chapter begins by describing the basic physical processes that affect the radiance along rays passing through participating media. It then introduces the VolumeRegion base class, an interface for modeling different types of media. Like a BSDF, the volume description characterizes how light is scattered at individual points. In order to determine the global effect on the distribution of light in the scene, VolumeIntegrators are necessary. Furthermore, the chapter describes the abstraction that represents the subsurface scattering properties of objects, the BSSRDF, as well a number of Materials for translucent objects.

Publisher Summary This chapter defines a set of classes that are used in pbrt for describing the way light scatters at surfaces. Reflection from surfaces can be split into four broad categories: diffuse, glossy specular, perfect specular, and retro-reflective. Most real surfaces exhibit reflection that is a mixture of these four types. The bidirectional reflectance distribution function (BRDF) abstraction describes light reflection at a surface, the BTDF describes transmission at a surface, and the BSDF encompasses both of these effects. The chapter defines a generic interface to these surface reflection and transmission functions. Scattering from realistic surfaces is often best described as a mixture of multiple BRDFs and BTDFs. Surface reflection models come from a number of sources: measured data, phenomenological models, simulation, physical (wave) optics, and geometric optics. The chapter describes implementations of reflection models based on measured data, phenomenological models, and geometric optics.

Detecting objects hidden beneath forest canopies is a difficult task for optical remote sensing systems. Rather than relying upon the existence of gaps between leaves, as other researchers have done, our ultimate goal is to use light scattered by leaves to image through dense foliage. Herein we describe the development of a Monte Carlo model for simulating the scattering of light as it propagates through the leaves of an extended tree canopy. We measured several parameters, including the gap fraction and maximum leaf-area density, of a nearby sugar maple tree grove and applied them to our model. We report the results of our simulation in both the ground and the receiver planes for an assumed illumination angle of 80 degrees. To validate our model, we then illuminated the sugar maple tree grove at 80 degrees and collected data both on the canopy floor and at our monostatic receiver aperture. Experimental results were found to correlate well with our simulated expectations.

This chapter reviews the processes and equipment for taking scatter measurements. As pointed out in Sec. 1.5, the BSDF is defined in differential form, but is measured with the incremental limitations imposed by real instrumentation. The finite detector aperture, scatter created within the instrument, calibration inaccuracies, and other practical equipment limitations such as noise, detector nonlinearity, and mechanical errors, all produce noticeable deviations between the true BSDF and the measured BSDF. In order to generate meaningful scatter specifications and fully utilize the data, it is important to understand the source and magnitude of these deviations. System calibration, an often-discussed issue, is described in detail. The chapter progresses from these basic concepts to discussions of other measurement techniques (curved samples, area raster scans, retroscatter, TIS, and out-of-plane scatter) and concludes with a section on error analysis. Chapter 1 provides necessary background information for understanding this material. 6.1 Scatterometer Components The simple plane-of-incidence scatterometer outlined in Fig. 6.1 contains most of the components typically found in more-sophisticated systems. These may be grouped into four categories: light source, sample mount, receiver (detection system), and computer/electronics package. This section outlines the need for and general operation of these modules. The light source is shown as a laser beam that is chopped, spatially filtered, expanded, and finally brought to a focus on the detector path. Lasers are convenient, but not necessary, sources for scatter measurements. The beam is chopped to reduce both optical and electronic noise. This is accomplished through the use of lock-in detection in the electronics package that suppresses all signals except those at the chopping frequency.

Accurate identification and understanding of spectral bio-signatures from possible extra terrestrial planets have received an ever increasing attention from both astronomy and space science communities in recent years. In pursuance of this subject, one of the most important scientific breakthroughs would be to obtain the detailed understanding on spectral biosignatures of the Earth, as it serves as a reference datum for accurate interpretation of collapsed (in temporal and spatial domains) information from the spectral measurement using TPF instruments. We report a new Integrated Ray Tracing (IRT) model capable of computing various spectral bio-signatures as they are observed from the Earth surface. The model includes the Sun, the full 3-D Earth, and an optical instrument, all combined into single ray tracing environment in real scale. In particular, the full 3-D Earth surface is constructed from high resolution coastal line data and defined with realistic reflectance and BSDF characteristics depending on wavelength, vegetation types and their distributions. We first examined the model validity by confirming the imaging and radiometric performance of the AmonRa visible channel camera, simulating the Earth observation from the L1 halo orbit. We then computed disk averaged spectra, light curves and NDVI indexes, leading to the construction of the observed disk averaged spectra at the AmonRa instrument detector plane. The model, computational procedure and the simulation results are presented. The future plan for the detailed spectral signature simulation runs for various input conditions including seasonal vegetation changes and variable cloud covers is discussed.

This paper presents a methodology for including the photometric raw data sets into the diffuse illumination design process. The method is based on computing the luminance distribution on the outgoing side of diffusing elements from measured bidirectional scattering distribution functions (BSDFs). The model is limited to specimens that create rotationally symmetric scattering distribution. The calculation procedure includes the linear superposition and the correcting feedback. As an application example, the method is verified by a commercially available diffusing sheet illuminated by a 32-inch backlighting module. Close agreement (correlation coefficient = 98.6%) with the experimental measurement confirmed the validity of the proposed procedure.

Spectral features are introduced by the diffuser that is used during on-board sun calibration. New findings are presented on how to reduce the size of these spectral features. Reduction can be obtained via optical design of the calibration unit, but also in creating a better diffuser. A novel diffuser design will be presented and its performance will be compared to standard diffusers like an Aluminum diffuser, a Spectralon diffuser, and the QVD (Quasi Volume Diffuser). For the in-house spectral features testing setup an improvement of about a factor of eight was obtained for the new diffuser type when compared to QVD. QVD in its turn is already better than an Aluminum diffuser by a factor of ten. Spectralon and QVD are found to be about equally good when measured in terms of spectral features reduction. The novel diffuser is referred to as SanDiff since it is a sandwich of QVD and PTFE material. For the SanDiff also the BSDF was measured and will be presented here. © 2009 SPIE.

In conjunction with the development of a bidirectional scattering metrology project, a large number of papers pertaining to the theory and measurement of bidirectional scattering from optical surfaces were collected and categorized. This collection includes papers that deal with various aspects of the bidirectional scattering distribution function (BSDF), its measurement, interpretation, use, and implications. Each paper is classified in one or more subject categories on the basis of its technical content. The subject categories are included just to serve as a key to the most salient characteristics of each paper cited. Because of the interest in this field, this bibliography is being published as a service to the public.

A theoretical model of optical scattering in materials consisting of densely packed spherical particles is developed that can be used to predict its optical properties given its physical characteristics. The inputs to this model are the waveband of interest, the complex refractive indices and particle size distribution of the materials that comprise the media (including any contaminants), the density and sizes of any contaminants in the media, and the dimensions of the media slab. The outputs of this model are the specular transmittance and emissivity vs. wavelength of the media, and it's Bidirectional Scattering Distribution Function (BSDF) vs. scatter angle vs. wavelength. The results of this model are compared to measured transmittance and BSDF data from optical ceramics comprised of densified nanopowders (nanocomposite optical ceramics).

Shade-screens are widely used in commercial buildings as a way to limit the amount of direct sunlight that can disturb people in the building. The shade screens also reduce the solar heat-gain through glazing the system. Modern energy and daylighting analysis software such as EnergyPlus and Radiance require complete scattering properties of the scattering materials in the system. In this paper a shade screen used in the LBNL daylighting testbed is characterized using a photogoniometer and a normal angle of incidence integrating sphere. The data is used to create a complete bi-directional scattering distribution function (BSDF) that can be used in simulation programs. The resulting BSDF is compared to a model BADFs, both directly and by calculating the solar heat-gain coefficient for a dual pane system using Window 6.