The analytical expression for total integrated scatter (defined as diffuse reflectance divided by total reflectance) has been around for almost six decades TIS = 1 - exp[-(4π cosθ_i σ/λ)²]. Most surface scatter analysts now realize that the expression is ambiguous unless spatial frequency band-limits are specified for the rms roughness, σ, in the expression. However, there still exists uncertainty about the domain of validity of the expression with regard to both surface characteristics and incident angle. In this paper we will quantitatively illustrate this domain of validity for both Gaussian and fractal one-dimensional surfaces as determined by the rigorous integral equation method (method of moments) of electromagnetic theory. Two dimensional error maps will be used to illustrate the domain of validity as a function of surface characteristics and incident angle. Graphical illustrations comparing the TIS predictions of several approximate surface scatter theories will also be presented.

The relationship between total integrated scatter and rms roughness was developed in the radar literature and enabled the first use of scatter measurements to monitor optical roughness. This relationship has been used and misused ever since. Its most common form makes use of a smooth surface approximation and has been applied to optical surfaces now for half a century. It has been suggested that Davies’ exponential form can be applied to much rougher surfaces. This paper investigates that issue through a combination of approximate and rigorous calculations made on optically deep sinusoidal gratings and a few measurements.

A new generalized Harvey-Shack (GHS) surface scatter theory is numerically compared to the classical small perturbation method (SPM), the Kirchhoff approximation method (KM) and the rigorous method of moment (MoM) for one-dimensional ideally conducting surfaces whose surface power spectral density function is Gaussian or abc-function. In spite of its simple analytic form, our numerical comparison shows that the new GHS theory is valid (with reasonable accuracy) over a broader range of surface parameter space than either of the two classical surface scatter theories.

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 primary image in microscopic devices is nothing else than the scatter image of the aperture under investigation, an imaging scatterometer could be used as a microscope as well. It is self-evident to seek a combination: in both domains only the power distribution can be obtained with low effort, so a direct conversion into each other via Fourier transform is not the way to go. On the other hand, both domains have their advantages: while the original image shows the large structures, in other words the lower frequencies, the scatter image resolves the high spatial frequencies. The current paper deals with theoretical and practical aspects of basic design concepts. A corresponding paper is dedicated to concepts of the combined data analysis.

In recent years the development of a system to detect and measure the trajectory of a projectile by its backscatter using a laser light source has been presented. The used principle of the described system requires a dark environment as given at night. In the current paper techniques will be discussed to enable above projectile trajectory measurements under daylight conditions. With this a new system setup under given hardware limitations is derived and described. Experimental results for measurements under daylight conditions will be presented.

In a corresponding paper the optical design of combined microscopic and scatterometrical imaging devices is extensively discussed. The current paper deals with concepts of the necessary combined data analysis. A major problem is the fact that usually only the power distributions of both original and scatter images can be measured with arguable effort, and so both domains have to offer certain non-redundant information. Basic concepts, theoretical investigations of limitations and examples from typical applications are presented.

An inter-laboratory comparison (ILC) between glazing manufacturers that submit data to the International Glazing Database (IGDB) is carried out every four years. This time a large number of independent laboratories were included in addition to the IGBD submitters, in total over 50 boxes of samples were sent out in parallel. Each box contained 5 specular samples, consisting of clear float glass, low-e coated glass, laminates, and an applied film on clear glass. New for the IGDB submitters were 5 diffuse samples, 2 fritted glass samples, a diffuse laminate, a light-redirecting daylighting film, and a shade fabric with an inhomogeneous pattern. The samples were characterized by each participant in the solar optical range, 300 nm - 2500 nm, as well as the thermal infrared from 5µm–25µm. Spectral data was inspected for anomalies such as systematic absorption and non-continuous steps due to instrument design and operation. Spectral averaged data was calculated and used to compare the results from the different laboratories. Such comparisons indicated that use of a diffuse reference for specular measurements marginally increased the measured result. For diffuse products the effects of sphere geometry and design influenced the results to a significant degree.

At the National Research Council of Canada (NRC), the scale of diffuse spectral reflectance in the UV and visible range is realized using an integrating sphere method known as the Modified Sharp-Little method and has been wellcharacterized and validated. More recently, a gonioreflectometer has been designed to capture the bidirectional reflectance of reflecting objects. This system incorporates a diode-array spectroradiometer and is prone to non-linearity errors. In this paper the magnitude of this non-linearity error is evaluated using several diffusely reflecting materials by comparing the angular-integrated reflection indicatrix measured with the gonioreflectometer with results obtained using a transfer spectrophotometer that is traceable to the sphere-based NRC Absolute Reflectometer.

In search of next-generation solar cells, silicon nanowire arrays have attracted great attention since they are costeffective and may absorb more light compared to thin-film silicon solar cells. Theoretical studies using finite-different time-domain and transfer matrix methods have been performed to investigate the optical properties of silicon nanowire (SiNW) arrays, however, they are computationally intensive and require periodic condition, which may not be satisfied with most fabricated samples. In the present study, an effective medium analysis is performed to study the optical properties of vertically-aligned SiNWs on Si substrate in the wavelength range from 310 nm to 1100 nm, which is of the most important interest for solar cells. The effective dielectric function of the SiNW layer is obtained from the Bruggeman approximation. Thin-film optics formulae are employed to calculate the reflectance, transmittance and absorptance of the SiNWs on silicon substrate at normal incidence. The effect of geometric parameters such as filling ratio and wire length will be investigated to understand the light absorption and to facilitate the optimal design of highperformance SiNW solar cells.

In the mid-1970’s it became apparent that incident plane scatter data could be represented by simple two or three parameter expressions. This realization made possible the generation of stray light estimation codes which are used on everything from military weapons, to telescopes, to car headlights to flat panel display systems. Almost all of these applications estimate hemispherical scatter from incident plane measurements. For most of these applications estimates that are good to within a factor of three - or even an order of magnitude - are acceptable and can result in dramatic product improvements. This paper takes a closer look at how the out-of-incident-plane estimates are made and evaluates how accurate the process is for the case of optically rough isotropic surfaces. The estimating process is reviewed and estimates are compared to hemispherical scatter measurements. It will be shown how the empirical observations that led to the procedures now widely used can be understood using well-known scatter models that link the surface roughness and scattering properties.

Scratch-dig is an acknowledged cosmetic specification that is often misused as a specification to limit scattered light. In spite of its shortcomings, the stray light analyst is often called upon to write this specification, or at least approve it. An analytic model that relates a bidirectional reflectance distribution function (BRDF) to a scratch-dig specification is proposed. Applying scalar diffraction theory and some idealizations for the shape, orientation, and number of scratches and digs; the magnitude and functional form of the BRDF is derived. The effective BRDF associated with the scratch dig specification is compared with the magnitude and functional form of the BRDF from surface roughness and contamination.

The electromagnetic response of an arbitrary array of multiple slits perforated on a metallic film and filled with different slit dielectric materials is studied in an analytical way. As a specific example, we consider a triple-slit structure perforated on a gold film, where the middle slit is used for the surface-plasmon excitation by a narrow Gaussian beam while the other two side slits are used for the detection of a transmitted surface-plasmon wave propagated from the middle opaque slit either at a particular wavelength or at double that wavelength, respectively. For this particular structure, we show that only one of the two side observation slits can be in a passing state for a particular wavelength, but the other blocked slit will change to a passing state at double that wavelength with a specific design for the slit depth, silt dielectric and inter-slit distance in the deep sub-wavelength regime. In this sense, we create a surface-plasmon mediated light diffraction in the near-filed regime.

The (heuristic) Kubelka-Munk theory of diffuse reflectance and transmittance of a film on a substrate, which is widely used because it gives simple analytic results, is compared to the rigorous radiative transfer model of Chandrasekhar. The rigorous model has to be numerically solved, thus is less intuitive. The Kubelka-Munk theory uses an absorption coefficient and scatter coefficient as inputs, similar to the rigorous model of Chandrasekhar. The relationship between these two sets of coefficients is addressed. It is shown that the Kubelka-Munk theory is remarkably accurate if one uses the proper albedo parameter.

STARR II is a planned NIST facility for spectral measurements of specular reflectance and diffuse bidirectional reflectance distribution function (BRDF) that is the follow-on to the current NIST STARR (Spectral Tri-function Automated Reference Reflectometer) facility. STARR II will improve and expand on the measurement capabilities of STARR, increasing spectral coverage in the short-wave infrared spectral region and adding out-of-plane BRDF measurement capability. We present characteristics of a tunable light source constructed for STARR II, which is based upon a supercontinuum fiber laser and has a tuning range from 500 nm to 2450 nm, alongside those of the current lampbased system in STARR. We then discuss considerations for measuring BRDF using this source. The STARR II goniometer will employ an articulated robotic arm to center and orient the sample, and we calculate the transformations from orientation of the sample and receiver to incident and scattering angles for measurements of in-plane and out-ofplane BRDF. We also present, for the first time, an analytic expression for the correction of measured BRDF to true BRDF due to the finite illumination area and collection aperture, and to the effects of uniformity of illumination. Finally, we present exploratory BRDF measurements on a diffuse sample made using the tunable supercontinnum source.

It is important to measure both reflectance (R ) and transmittance (T ) with the same accuracy. But many commercial accessories are exchanged by themselves or a sample is replaced on the other position in one accessory, when the reflection measurement is changed from the transmission measurement, so that it is impossible to measure reflectance and transmittance with the same accuracy. Accordingly the absorptance (A=1-R-T ) of the sample is not a sufficient index to evaluate the optical properties. A new scatterometer, which overcomes the defect, has been developed in AIST. It consists mainly of two ellipsoidal mirrors and a new detection system, which is composed of a hemispherical lens, a fiber optic taper and a CCD camera. These mirrors are a belt-shape and a quarter ellipsoidal mirrors with two focal points and are combined such that each focal point is a common focal point, on which the sample is placed. A rotating mirror is set on a remaining focal point of the belt-shape mirror. Each arrangement, where the rotating mirror looks at the upper or lower arm of the belt-shape mirror, is for the transmission or reflection measurement, respectively. The center of the hemispherical lens in the detection system is set on a remaining focal point of the quarter mirror, the incident plane of the fiber optic taper coincides with the image plane of the hemispherical lens and the outgoing plane of the fiber optic taper is in contact with the CCD camera. A clear image can be obtained using this detection system. The absolute values of the reflectance and transmittance and the light distributions of the reflection and transmission of the micro-ball-lenses, whose radii were 0.75, 1, 2.5 and 4.8mm, were measured. The systematic errors of our scatterometer are briefly discussed.

We designed and assembled a highly capable UV reflectometer chamber and data acquisition system to provide bidirectional scattering data of various surfaces and materials. This chamber was initially conceived to create laboratory-based UV reflectance measurements of water frost on lunar soil/regolith simulants, to support interpretation of UV reflectance data from the Lyman Alpha Mapping Project (“LAMP”) instrument on-board the NASA Lunar Reconnaissance Orbiter spacecraft. A deuterium lamp illuminates surfaces and materials at a fixed 45° incident beam angle over the 115 to 200 nm range via a monochromator, while a photomultiplier tube detector is scanned to cover emission angles -85° to +85° (with a gap from -60° to -30°, due to the detector blocking the incident beam). Liquid nitrogen cools the material/sample mount when desired. The chamber can be configured to test a wide range of samples and materials using sample trays and holders. Test surfaces to date include aluminum mirrors, water ice, reflectance standards, and frozen mixtures of water and lunar soil/regolith stimulant. Future UV measurements planned include Apollo lunar samples, meteorite samples, other ices, minerals, and optical surfaces. Since this chamber may well be able to provide useful research data for groups outside Southwest Research Institute, we plan to take requests from and collaborate with others in the UV and surface reflection research community.

“Indirect photography” was recently demonstrated for imaging hidden scene information through the collection and radiometric modeling of light reflecting off of visible reflecting surfaces. The ability to focus the beam that reflects off the visible surface to a tight spot on the hidden object is theorized to simulate a direct line of sight from the light source to the object, reducing the radiometric model to that of the previously demonstrated “dual photography.” Experiments involving the focusing of light transmitted through highly scattering media have been adapted to the case of reflection. The focusing of a HeNe laser reflected off diffusely scattering surfaces to a tight spot is demonstrated using phase control. A liquid crystal spatial light modulator assigns pixelated phase delay to the beam to conjugate the scattering properties of the reflector. Intensity enhancement values between 13.8 and 122.3 are achieved for the surfaces studied. Samples with relatively strong specular reflection achieve higher enhancement for a given geometry. More diffusely reflecting materials achieve higher enhancement in regions of nonspecular scatter, facilitating non-mechanical beam steering.

This paper addresses non-conventional three-dimensional imaging with laser systems which explores the advantages of laser imagery to form a three-dimensional image of the scene. In this paper, we present the 3D laser scattering simulation of objects hidden behind porous occluders, such as foliage or camouflage. The physics based model presented in this paper is designed to provide accurate results but also to include all the electromagnetic interaction mechanisms with the different elements of the scene. A 3D laser cross-section computer model is used to develop reconstruction algorithms to obtain a high-resolved three-dimensional image. Synthetic images of three-dimensional objects are based on extraction of laser backscattered signals. But 3D reconstruction must take into account sparse collected data and reconstruction algorithms must solve a complex multi-parameter inverse problem. The objective of our paper is also to present new algorithmic approaches for the generation of 3D surface data from 3D sparse point clouds corresponding to our reconstruction algorithm. The role of this type of algorithmic process is to complete the 3D image at satisfactory levels for reliable identification of concealed objects. Identifying targets or objects concealed by foliage or camouflage is a critical requirement for operations in public safety, law enforcement and defense.

Indirect photography was recently demonstrated as a technique for imaging hidden objects. A camera and laser are collocated, neither with line-of-sight to the object. Laser light is reflected off a visible surface onto the hidden object, then reflected back to the visible surface and collected by the camera. Varying laser spot position yields different camera images, which are used to construct an "indirect" image of the object. Here, camera images are processed by modeling the system as a set of radiometric transport and reflectance matrices. Matrix formulation and inversion, and those parameters demonstrated to improve indirect image quality, are discussed.

The Infrared Grazing Angle Reflectometer allows measurement of Directional Hemispherical Reflectance (DHR) at very high angles of incidence (30 to 85 degrees) and at wavelengths ranging from 4.3 to 10.8 microns. A hemi-ellipsoidal mirror redirects the reflected light and reflects it on to a novel five-sided pyroelectric detector. The incident light intensity is measured and used in calculating the DHR of the sample. In this paper, the theory of operation of this detector is derived, and used to simulate the operation of the system. This simulation of the detector shows errors of 3% or less for both diffuse and specular samples, compared to the theoretical DHR. The calibration method defined in this paper allows for high accuracy and ease of use without knowing the specific attributes of the optics used in the system. Finally, collected DHR data is compared with the simulated data for comparison. Comparing the measured data to the simulation shows that the model correctly predicts the locations and trends of the scattered energy.

Specular gloss is an important measurand used in quality control of manufacturing processes of highly reflective parts. In this work we present an in-process quality control system to evaluate the gloss of free-form surfaces to be used in an automated polishing process. Due to the geometry of our test objects the presented sensor is mounted on a robot arm and, therefore, needs to be robust against sensor misalignment. This robustness is achieved using a 2D CCD-camera as detector which allows us to properly handle sensor orientation deviations of up to 1⁰. The required dynamic range of the sensor is obtained based on the acquisition of high dynamic range images. We present first results of a sensor prototype and show its applicability to the target application.

Light scattering based characterization techniques are well suited to meet the challenging requirements for fast and sensitive finish assessment of optical surfaces. Further advantages are the high flexibility and robustness which enable the inspection of large geometries and freeform optics that are sometimes too complex for characterization techniques like atomic force microscopy or white light interferometry. In this paper, we report on the development of instruments for total and angle resolved light scattering measurements at wavelengths ranging from the vacuum ultraviolet to the infrared spectral regions. Extremely high sensitivities equivalent to surface roughness levels of below 0.1 nm and dynamic ranges of up to 15 orders of magnitude have been achieved. In addition to laboratory-based equipment, compact and table-top tools are discussed which enable the advantages of light scattering metrology to be used for characterization tasks close to or even in manufacturing processes. Instructive examples of applications are presented ranging from the characterization of diamond-turned and polished substrates to interference coatings, diffraction gratings, and IR window materials.

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 paper describes differential ray tracing and shows how it can be used to great advantage in stray light analysis. Tracing a differential ray from a source to a target yields a set of derivatives that contain a complete first-order description of a ray bundle surrounding the ray being traced. These derivatives provide the information needed for aiming rays and transforming a sample area on a target surface into a solid angle seen by the source. By using targeted differential rays, we eliminate the need for defining importance curves for generating scattered rays. Convergence is accelerated, and the resulting irradiance distributions end up smoother than what one usually obtains with the traditional Monte Carlo approach. This paper also shows how the derivatives from a single ray can be used to define and propagate Gaussian beams without the need for secondary rays.

In this paper, a novel optical approach is proposed and demonstrated for the non-contact measurement for the thickness of silica thick films. This approach is based on the principal of an optical based displacement sensor. The calibration curve for the measurement of the thickness of an unknown sample is obtained using four sample with known thicknesses of 6.90, 10.23, 19.69 and 25.47 μm respectively. As compared to a prism coupler, which is assumed to provide the most precise measurement of thick film thicknesses, the proposed system has an error of approximately 8%. The proposed method is able to provide a simple, low cost and time saving approach in measuring thick films thicknesses during fabrication.

Remote-sensing technology designed to exploit disturbed earth signatures has become extremely useful in the detection of disturbed soil in military areas of operation. Soil reflectance can be exploited for this purpose and is dependent on atmospheric conditions. An understanding of the in situ soil background is vital to any type of change detection. Researchers from the Engineering Research and Development Center (ERDC) conducted OCONUS soil spectral measurements at ten sites in Afghanistan from July to November, 2011. Sampling sites were chosen on the basis of geomorphic setting, surface-soil characteristics, and field-expedient conditions. Goniometric spectral measurements at these sites have provided high quality bi-directional reflectance data, and their analyses are presented in the context of threat recognition and discrimination. These data can also provide the basis for BDRF model validation. Most spectral data were acquired under ambient solar lighting, but other data were collected at night and under artificial illumination conditions. Bidirectional measurements of soil reflectance in the VIS/NIR and SWIR were taken using the University of Lethbridge Goniometer System (ULGS) at dawn, mid-day, dusk and after sunset with a light. Soil surface roughness and reflectance varied, depending on the presence of desert varnish and desert pavement at some sites. Sun angle and dust and smoke in the atmosphere impacted soil reflectance and noise in the SWIR part of the light spectrum, in particular. The presence of minerals such as calcium carbonate, gypsum, and oxidized iron in the subsurface directly impacted reflectance measurements in disturbed soil.

Optical component differentiation (diffusers and light processing elements) between reflective displays based on Interferometric Modulation (IMOD) and typical transmissive (LCD) displays is discussed. We characterize optimized diffusers for a front light of reflective displays and present the key differentiation data with important metrology tools to monitor the image quality. Drawing on our experience, we outline guidance going forward.

A roughness measurement method based on the application of a photodiode integrator for scattered radiation gathering as well as results of experiments concerning this method are presented in the paper. The new integrator, contrary to known optical integrating devices, provides the possibility to get much less expensive and smaller instruments than traditional ones. Unfortunately, a decrease of the integrator dimensions could restrict its spatial frequency bandwidth causing measurement errors. Therefore, experimental works have been performed to find the relation between the range-of-acceptance angle of the integrator and measured rms roughness. They have been done by constructing a model of the integrator and a complete TIS instrument as well as a precision experimental set. For the purpose of making a direct comparison between the new instrument and the existing one, the Ulbricht sphere has also been used in the set. For very smooth surfaces, the value of the lower angle range is very critical and should be smaller than 2 deg. The upper limit can be about 30 deg. for measurement of smooth and isotropic surfaces. At such limits, the influence of the integrator flatness is stated to be non-substantial. Results of surface roughness measurements obtained from the new unit and the Ulbricht sphere show that both methods have similar issues. Taking into account the dimensions of the photodiode integrator, a small and inexpensive TIS instrument can be designed for measuring roughness and reflectance of isotropic smooth surfaces in the optical and electronic industries.

We have examined the trial-to-trial variability of the reflectance spectra of surface coatings containing effect pigments. Principal component analysis of reflectances was done at each detection angle separately. A method for classification of principal components is applied based on the eigenvalue spectra. It was found that the eigenvalue spectra follow characteristic power laws and depend on the detection angle. Three different subsets of principal components were examined to separate the relevant spectral features related to the pigments from other noise sources. Reconstruction of the reflectance spectra by taking only the first subset indicated that reflectance variability was higher at near-specular reflection, suggesting a correlation with the trial-to-trial deposition of effect pigments. Reconstruction by using the second subset indicates that variability was higher at short wavelengths. Finally, reconstruction by using only the third subset indicates that reflectance variability was not totally random as a function of the wavelength. The methods employed can be useful in the evaluation of color variability in industrial paint application processes.

Inhomogeneity measurement is an important test of reference materials. In case of hardness reference blocks it consists of measurements at five distributed points on the surface with a test indenter. Unfortunately the test is destructive and it is not possible to use the same point for a new measurement. In this work we propose an optical method to measure the inhomogeneity of hardness standards. As we reported in a recent work, variations of hardness in a steel produces variations in their optical properties, this fact can be used to detect variations in the hardness of blocks with a non-destructive method.

In this work we propose a Surface Plasmon Resonance (SPR) system driven by Labview software which produces a fast, simple and accuracy measurements of samples. The system takes 2000 data in a range of 20 degrees in 20 seconds and 0.01 degrees of resolution. All the information is sent from the computer to the microcontroller as an array of bytes in hexadecimal format to be analyzed. Besides to using the system in SPR measurement is possible to make measurement of the critic angle, and Brewster angle using the Abeles method.

The study of open quantum billiards has gained popularity in the last decades, including different common and uncommon geometries such as the circular and stadium billiards. We study the electromagnetic scattering of a linearly polarized electric field in the elliptic quantum billiard with hyperbolic channels. We analyze the effect of different parameters on the scattering in a billiard configuration obtained by displacing both channels by the same angle. We observed that for the configuration proposed in this work the polarization of the electric field is conserved.