We propose a method of designing and fabricating one- dimensional random surfaces that scatter light uniformly within a specified range of angles and produce no scattering outside this range. The proposed method is tested by means of computer simulations, and preliminary experimental results are also presented.

We investigate theoretically changes in the spectrum of light scattered from a system with a random surface (the Wolf effect). The system we consider is the Otto attenuated total reflection configuration that is widely used to couple the incident light to surface polaritons. The angular dependence of the intensity of the light scattered incoherently from this system exhibits sharp, intense peaks at the angles of optimum excitation/radiation of the surface polaritons supported by it. In the vicinity of each of these resonance angles the spectrum of the scattered light is red-shifted for scattering angles larger than this angle, and is blue-shifted for scattering angles smaller than this angle. The magnitude of the shift is three to four orders of magnitude larger than that predicted for disordered volume media. We conclude that the Otto attenuated total reflection configuration is another example of bounded systems with random surfaces which are more attractive subjects for experimental studies of the Wolf effect than systems with a single random surface or disordered volume systems.

The like and cross polarized single and double scattered fields are derived using a full wave approach. This approach is based on the complete expansion of the electromagnetic fields, the imposition of exact boundary conditions and the conversion of Maxwell's equations into generalized telegraphists equations for the scattered wave amplitudes. Thus, the zero order iterative solutions for the generalized telegraphists equations yield the primary electromagnetic (source) fields impressed upon the rough surface. The first and second order iterative solutions to the generalized telegropherts' equations yield the single and double scattered fields. This can be clearly demonstrated by taking the geometric optics limit of the full wave solutions. To obtain the corresponding like and cross polarized scatter cross sections, as in the case of scattering from one dimensional rough surfaces, it is necessary to account for contributions from the quasi parallel double scatter paths as well as the quasi antiparallel double scatter paths. However, for scattering from two dimensional rough surfaces, these paths are not restricted to the plane of incidence. The full wave solutions for the double scattered fields are expressed as six dimensional integrals, that account for the complete wave spectra of scattered fields and the coordinate variables at a pair of points on the rough surface. These expressions are used to obtain the multidimensional integrals for the like and cross polarized cross sections. To make these solutions tractable for computational purposes, a high frequency approximation of the full wave double scatter cross sections are expressed as four dimensional integrals involving scatter wave vector variables. These results can be evaluated in significantly less time than standard numerical solutions of the integral equations. Moreover, the physical interpretation of the results shed light on the impact, of different statistical parameters of the random rough surfaces, upon the backscatter enhancement.

We apply the method of ordered multiple interactions (MOMI) to solve the magnetic and electric field integral equations pertinent to electromagnetic scattering from a randomly rough dielectric-dielectric interface. We consider a two-dimensional geometry (invariance in the y-direction) and investigate convergence of the MOMI algorithm for a TM polarized incident plane wave and Gaussian tapered beam. It is known that the Neumann iteration does not converge for a dielectric system. The MOMI, which is basically a Neumann iteration on an extensive modification of the original integral equation, also does not converge. We show a new combination of the relevant integral equations for which the MOMI converges.

The Beckmann-Kirchoff (B-K) classical scalar diffraction theory is commonly used in the scatter community to model and predict scattering behavior when surfaces are 'rough.' However, although the B-K theory can be used to model surfaces that are much rougher than other theories can handle, the B-K theory has a small-angle assumption inherent in its derivation. The paper illustrates a modified B-K theory that shows excellent agreement with experimental scattering data from rough surfaces for both large angles of incidence and scatter angles.

We apply an iterative solution approach, the method of ordered multiple interactions (MOMI), to solve the magnetic and electric field integral equations which are pertinent to scattering by a thin dielectric film bounded by a semi- infinite dielectric substrate and by a semi-infinite dielectric superstrate. The thin film boundaries are randomly rough, which is numerically generated. We consider two- dimensional geometry (invariance in the y-direction) and investigate convergence for a TM polarized incident Gaussian tapered beam.

A connection is established between the degree of surface roughness and the diffuse maximum of light scattering indicatrix in the direction of mirror reflection. It is proposed to consider its mean contribution, p, to the total scattered intensity as the quantitative measure of the surface roughness degree. It is shown that the effective mirror constituent p determines the character of light transfer in the space, bounded by the rough reflecting surface, and must be allowed for when calculating relevant optical devices, e.g. scintillation detectors. For that purpose, a constructive calculation method was developed and verified by the quantitative comparison with experimental data on spectrometric characteristics of scintillation crystals. The surface roughness parameter p dictates the character of their dependence on geometric and optic parameters of a crystal.

Experiments with different types of near-field microscopes have demonstrated that the classical diffraction limit of conventional optical systems can be beaten. In these experiments, the resolution of the images is determined, primarily, by the size of the probe. One of these techniques consists of using scatterers in the near field of the sample. High resolutions have been demonstrated with this kind of scheme, although the signals are weak and the image formation is rather complex. Systematic studies are required to understand the properties and capabilities of the technique. Efforts are being made by many groups to understand the relation between the probe, the object and the image. In this work we present an experimental study of the image formation properties of different types of scatter-probe near-field optical microscopes.

Because their electromagnetic fields are localized to the surfaces that support them, surface electromagnetic waves are more sensitive to topographical and dielectric perturbations in their propagation path than are volume electromagnetic waves incident on the same surface perturbations. This suggests that a near-field optical microscopy based on surface electromagnetic waves could reconstruct surface profiles with greater resolution than one based on the scattering of volume electromagnetic waves from surfaces with the same profiles. In this work we examine this possibility by studying the scattering of a surface plasmon polariton propagating along a vacuum-metal interface and incident on a surface defect. We calculate the intensity of the total field in the vacuum region at constant height above the unperturbed surface to first order in the surface profile function. The result can be written in the form of a convolution of the surface profile function and a function that depends only on the properties of the metal surface. We invert this result by a Fourier transform method to obtain the surface profile function. As experimental intensity data we use the results of a rigorous numerical solution of the corresponding reduced Rayleigh equation for the scattering amplitude. We show that surface structures with lateral dimensions of the order of or smaller than one-tenth the wavelength of the incident surface plasmon polariton can be reconstructed in this way, as well as extended segments of a randomly rough surface profile.

The speckle correlations in the light scattered from a volume disordered dielectric medium are studied theoretically. A scalar wave treatment is used for the motion of the light in the system, and the dielectric constant of the volume disordered medium is taken to be of the form (epsilon) (vector r) equals (epsilon) ((omega) ) plus (delta) (epsilon) (vector r), where (epsilon) ((omega) ) is a homogeneous isotropic frequency- dependent dielectric constant and (delta) (epsilon) (vector r) is a zero-mean Gaussian random process. A diagrammatic perturbation theory approach is used to compute the speckle correlation function defined by C(vector q, vector kvector q', vector k') equals <{I(vector qvector k) - [I(vector qvector k)]} {I(vector q'vector k') - [I(vector q'vector k')]}> where I(vector qvector k) is proportional to the differential scattering coefficient for the elastic scattering of light of incident wavevector vector k into light of wavevector vector q. Contributions associated with ladder, maximally crossed, and more complicated higher order diagrams are summed in the determination of the speckle correlation function. In addition we make the approximation of including only s- scattering in the evaluation of the various diagrams contributing to the speckle correlation function. Results are presented for C(vector q, vector kvector q', vector k') in the approximation C equals C⁽¹) plus C⁽¹⁰) plus C^(1.5) where C⁽¹), C⁽¹⁰) and C^(1.5) are terms arising from three distinct classes of diagrams. The contribution C⁽¹), which contains the memory and time-reversed memory effect terms, has been studied before and is proportional to (delta) (vector q minus vector k minus vector q' plus vector k'). C⁽¹⁰) is a new term (of the same order of magnitude as C⁽¹)) in the scattering of light from volume disorder which is found to be proportional to (delta) (vector q minus vector k plus vector q' minus vector k'). C^(1.5) is a new term in the scattering of light from volume disorder which exhibits an unrestricted dependence on vector q, vector k, vector q', vector k' and a series of interesting intensity peaks related to the resonant scattering of light by the volume disorder. The contributions C⁽¹⁰) and C^(1.5) have been considered in the study of the speckle correlation function for the scattering of light from rough surfaces, but this is the first consideration of these terms in the scattering of light from volume disorder.

The decorrelation of the characteristic speckle pattern, produced by the scattering of coherent light from a random rough surface, is used to monitor changes in the microtopography of the surface. In a basic optical setup minute alterations down to a few nanometers can be measured. To enlighten the basic relations between the speckle field decorrelation and the surface changes a theoretical model is developed, numerical calculations are carried out and comparisons with high resolution AFM measurements on two frozen states of a surface process are undertaken. Whereas the reproducibility of the AFM measurement turns out to be not precise enough to measure nanometer changes on a micrometer scale rough surface, the theoretical model is consistent with results gained from experimental variation of wavelength and angle of illumination and a-priori knowledge about the surface. It is then used to obtain information about magnitude, time constants and statistical parameters of a corrosion process.

A method for determining surface roughness of engineering surfaces that is applicable to in-process measurements under harsh circumstances of industrial production plants (e.g. vibrations, humidity) is introduced. The rough surface is illuminated with polychromatic laser light. The angular distribution of scattered light intensities, i.e. a polychromatic speckle pattern, is the result of an incoherent superposition of monochromatic speckle intensities. The angular dispersion leads to increasing speckle widths with an increasing distance to the optical axis an effect called speckle elongation. This gives rise to a radial structure of the speckle pattern. However, with increasing surface roughness the radial structure vanishes because of a decreasing similarity of the monochromatic speckle patterns of the different wavelengths. The markedness of this effect is analyzed by digital image processing algorithms, e.g. the procedure of polychromatic speckle autocorrelation. The latest approach to an in-process roughness measurement device was made by the use of singlemode fiber-pigtailed laser diodes in order to supply a trichromatic, temporally partially coherent laser beam. A brief introduction to the theoretical background is followed by the presentation of the experimental setup. The image processing algorithms for calculating an optical roughness measure from digitalized speckle patterns are explained, and first results of surface roughness determination are presented.

The speckle correlations in the light scattered from a volume disordered dielectric medium consisting of a random array of dielectric spheres are studied using computer simulation techniques. The random medium is formed by placing dielectric spheres of radius R and dielectric constant (epsilon) randomly on the vertices of a simple cubic lattice, so that a fixed fraction (rho) of the vertices is occupied by the spheres. The region outside the spheres is vacuum, and the radius of the spheres is assumed to be much smaller than the lattice constant of the cubic lattice. For simplicity the electromagnetic fields are treated in a scalar wave approximation. The scalar wave field equations of this system are integrated numerically to determine the scattered fields, and these fields are used to calculate the speckle correlation function defined by C(vector q, vector kvector q', vector k') equals <{I(vector qvector k) - [I(vector qvector k)]} {I(vector q'vector k') - [I(vector q'vector k')]}>, where I(vector qvector k) is proportional to the differential scattering coefficient for the elastic scattering of light of wavevector vector k into light of wavevector vector q. In implementing our computer simulation we have considered a 9 X 9 X 9 cubic lattice that is occupied by 178 dielectric spheres of dielectric constant (epsilon) equals 9. The lattice constant a of the cubic lattice was taken to satisfy a/(lambda) equals 0.7 where (lambda) is the wavelength of the light in vacuum, and the radius of the dielectric spheres was taken such that R equals 0.0159 (lambda) . Results are presented for C(vector q, vector kvector q', vector k') in the approximation C equals C⁽¹) plus C⁽¹⁰) plus C^(1.5), where C⁽¹), C⁽¹⁰) and C^(1.5) are terms arising from three distinct scattering processes. The contribution C⁽¹), which contains the memory and time-reversed memory effect terms, has been studied before, and is proportional to (delta) (vector q minus vector k minus vector q' plus vector k'). C⁽¹⁰) is a new term (of the same order of magnitude as C⁽¹)) in the scattering of light from volume disorder, that is found to be proportional to (delta) (vector q minus vector k plus vector q' minus vector k'). C^(1.5) is a new term in the scattering of light from volume disorder that exhibits an unrestricted dependence on vector q, vector k, vector q', vector k' and a series of interesting intensity peaks related to the resonant scattering of light by the volume disorder. The contributions C⁽¹⁰) and C^(1.5) were considered in the earlier study of the speckle correlation function for the scattering of light from randomly rough surfaces, but have only recently been considered in the scattering of light from volume disorder.

Polarization is indicative of small scale surface roughness and photometry indicates large scale surface roughness. These phenomenon are evident from measurements on natural and contrived surfaces. The original surface scattering research was based on laboratory simulation of the lunar surface from astronomical observations prior to the lunar landing. It was found that large scale irregularities on a surface causes shadowing to exert a major influence on the surface photometric scattering, as well as polarization. A dust coating on a coarse surface modifies the photometric as well as the polarimetric scattering function. The dust coating causes depolarization and generally increased surface brightness. Percent polarization is found to be inversely proportional to surface optical albedo. In remote sensing, the fine structure on targets is related to percent polarization. Polarized retroreflectance is found to be related to both coarse and fine structure of surfaces and valuable key to assessing contributing factors. Also, polarization can be used to advantage in military applications to distinguish targets from backgrounds.

An experimental investigation of the hemispherical distribution of the light scattered by randomly rough isotropic dielectric surfaces is presented. The surfaces, whose profiles constitute good approximations to Gaussian random processes with Gaussian correlation functions are fabricated in photoresist. The substrates employed in the fabrication of the samples consist of thick parallel plates of filter glass that absorb the incident light and whose refractive index is close to that of photoresist. This allows us to approximate experimentally a situation in which the light is scattered by a randomly rough interface separating two semi-infinite dielectric media. The results display features that can be attributed to multiple scattering. In particular, a well-defined enhanced backscattering peak is observed in both, the co- and cross-polarized scattering measurements.

Bidirectional ellipsometry results are presented for scatter from SiO₂ films grown on photolithographically produced microrough silicon surfaces. The principle direction of the polarization and the degree of linear polarization for scatter directions out of the plane of incidence are compared to results of theoretical modeling for interfacial microroughness in the presence of dielectric layers. The results indicate that light scattered from these surfaces does not behave like that from two truly random rough correlated interfaces. Possible reasons for the lack of agreement between the model and the data are discussed.

Ellipsometric parameters, depolarization and directional reflectance of reflection and scattering by a rough stainless steel surface are measured. Linear and circular polarizations, and principal Mueller matrix can be obtained from the above quantities. Measurements were made at fixed incident and detection directions and variable sample's orientation. For one-dimensional rough surfaces, it was found that depolarization and circular polarization increase with the off-specular angle of scattering while linear polarization does the opposite. Measurements were also made for specular direction. The effective refractive index, extinction coefficient and rms roughness for the rough sample were derived from these data.

We present the experimental results of the detection of subsurface defects which show that the memory effect (or the far-field correlation function) of speckle patterns is sensitive to a small local change under the rough surface geometry. We envision this property can be applied to inspection of a target buried in the background by speckle mapping.

Polytetrafluoroethylene (PTFE) is widely used in applications requiring a material with a diffuse reflectance factor close to unity. The bidirectional reflectance distribution function (BRDF) of both pressed and sintered samples was measured as a function of wavelength, polarization, and incident and viewing angles. The results for both samples show that the BRDF is constant at wavelengths from 400 nm to 1000 nm and depends on the polarization of the incident beam of radiant flux, that the BRDF varies with viewing angle, and that Helmholtz reciprocity holds for angles from 10 degrees to 60 degrees.

The effipsometry parameters is calculated for the light reflection from porous surface with the pores which go vertically in the volume and have transverse size near the wavelength, the longitudinal size much more the wavelength and the size ofthe width ofthe partition much less the wavelength. The pore is considered as the waveguide and the porous surface is appcoximated by the periOdiCal system of the coupled vertical waveguides. The results of calculations show that the porous siructures with the pore size near the wavelength can redistrib.. ute mirror component ofreflected energy sufficiently increasing it in the nanow region ofangles of incidence. Keywords: reflection, scattering, porous surfaces, ellipsometry, rough surfaces

Scatterometry, the analysis of light diffraction from periodic structures, is shown to be a versatile metrology technique applicable to a number of processes involved in the production of microelectronic devices, flat panel displays, and other technologies which involve precise dimensional control of micron and sub-micron features. This paper reviews metrology issues and requirements of these technologies and gives details on one application of scatterometry for illustration. Scatterometer results are compared to measurements of the same samples using other metrology techniques, including cross- section SEM, top-down SEM, AFM, and ellipsometry.

The NIST (National Institute of Standards and Technology) virtual/physical surface roughness calibration standard consists of physical specimens whose surfaces are manufactured by a numerically controlled diamond-turning process using digitized profiles. These standards are designed for checking the characteristics and algorithms of surface measuring systems, and for sensing the amount of distortion of the surface information flow though different measuring systems. The digitized profiles can also be used for remote instrument calibration and surface measurement unification. The design, manufacture, test results, and potential uses of the NIST prototype specimens are discussed.

Angular dependent total reflection x-ray fluorescence (TRXF) is used to characterize the surface roughness or the extent of planarization of a thin polymer coating on a stainless steel surface with significant roughness. The objective of this work is to explore the use of TRXF as a non-contact and quantitative technique for characterizing surface roughness of thin film coatings. Once developed, this technique is expected to perform equally well on other surface coating materials other than polymers. Unlike optical methods, whether the thin films are transparent or not is not expected to affect the outcome of this measurement. TRXF data were collected with incident angle in the region around the polymer critical angle and were analyzed in conjunction with the results deduced from specular x-ray reflectivity (XR). Comparison between the TRXF results and those obtained from atomic force microscope (AFM) was also made in order to evaluate this TRXF method critically.

The microelectronics fab need the manufacturing in ultraclean environments. The actual and future requirements of new generation of semiconductor devices become more stringent that which demand the reduction of tolerances to particles in cleanroom air and in processing liquids, gases and vacuum. The purity of process chemicals, water and gases is one area under scruting the systems for distribution. These fluids must also be examined so that their contamination charge to be minimal. For examining functional surfaces of fluid distribution systems by using more surface analysis tools such as electron spectroscopy for chemical analysis (ESCA), auger electron spectroscopy for chemical analysis (AES), scanning electron spectroscopy (SEM), brush analyzer or 3D laser scanner provide specification of a material identity, a measure of its surface contaminant, and a measurement record of surface roughness. In our paper we will analyze two case studies of investigation results of surface roughness measurement for electropolished 316L stainless steel and molded polyvinylidene fluoride (PVDF).

Many applications require quantitative measurements of surface light scattering, including quality control on production lines, inspection of painted surfaces, inspection of field repairs, etc. Instruments for measuring surface scattering typically fall into two main categories, namely bidirectional reflectometers, which measure the angular distribution of scattering, and hemispherical directional reflectometers, which measure the total scattering into the hemisphere above the surface. Measurement of the bi-directional reflectance distribution function (BRDF) gives the greatest insight into how light is scattered from a surface. Measurements of BRDF, however, are typically very lengthy measurements taken by moving a source and detector to map the scattering. Since BRDF has four angular degrees of freedom, such measurements can require hours to days to complete. Instruments for measuring BRDF are also typically laboratory devices, although a field- portable bi-directional reflectometer does exist. Hemispherical directional reflectance (HDR) is a much easier measurement to make, although care must be taken to use the proper methodology when measuring at wavelengths beyond 10 micrometer, since integrating spheres (typically used to make such measurements) are very energy inefficient and lose their integrating properties at very long wavelengths. A few field- portable hemispherical directional reflectometers do exist, but typically measure HDR only at near-normal angles. Boeing Defense and Space Group and Surface Optics Corporation, under a contract from the Air Force Research Laboratory, have developed a new hand-held instrument capable of measuring both BRDF and HDR using a unique, patented angular imaging technique. A combination of an hemi-ellipsoidal mirror and an additional lens translate the angular scatter from a surface into a two-dimensional spatial distribution, which is recorded by an imaging array. This configuration fully maps the scattering from a half-hemisphere above the surface with more than 30,000 angularly-resolved points and update rates to 60 measurements per second. The instrument then computes HDR from the measured BDR. For ease of use, the instrument can also compare both the BRDF and HDR to preset limits, generating a Pass/Fail indicator for HDR and a high-acceptable-low image display of BRDF. Beam incidence elevation is variable from normal incidence ((theta) equals 0 degrees) to 5 degrees off grazing ((theta) equals 85 degrees), while scattering is measured to nearly 90 degrees off normal. Such capability is extremely important for any application requiring knowledge of surface appearance at oblique viewing angles. The current instrument operates over the range of 3 micrometer to 12 micrometer, with extension into the visible band possible.

A major problem of in-situ surface characterization by using angle resolved light scattering (ARS) is the contradiction of speed and accurate detection of the scatter signal. During the last years several fast and compact ARS sensors have been developed, namely a fiber optic stray light sensor (FOSSIL) with 516 fibers in 3 azimuths, an integrated optics stray light sensor with 120 waveguides in one azimuth and a planar silicon scatter sensor (PSS) with 8013 detector elements. This paper deals with the evaluation of these sensors and their employment to characterize smooth and rough surfaces. After introducing the sensor setups the theoretical performance of the various sensors is compared. This is done by modeling the properties of the radiation detectors and the arrangements of the sampling points. The real performance is obtained by applying the sensors to surfaces with a known BRDF and comparing the measurements with the expected scatter distributions, i.e. from Lambertian reflection standards and preliminary scatter standards of NIST. Furthermore a set of smooth surfaces (polished silicon and steel) was scanned by an atomic force microscope (AFM) and the computed surface statistics is compared to the values obtained from scatter measurements. Finally, the sensors ability to characterize rough surfaces is shown by using pattern recognition methods.

Calibration of laser scanner is usually a complicated procedure and is only carried out in the manufacture site. Here we report a new statistical calibration method that is simple and easy. It can be carried out in either customer or manufacture site. This new approach is much more accurate than the current factory calibration method.

Characterization of the transmission and scattering of ultraviolet light through thin carbon foils is central to the operation of high-energy neutral atom (HENA) images. When unwanted external UV enters a HENA imager through its carbon foil window, some of this radiation is scattered toward the internal side mounted detectors. These detectors may then produce a 'false count' which is unrelated to any neutral particle inspection. It is against the background of ultraviolet produced false counts that the true counts of high-energy neutral particles must be made. This report describes the UV transmission and scattering through thin carbon foils at the Lyman-(alpha) wavelength of 1216 angstroms; the dominant ultraviolet wavelength in the solar system. The films tested were flight hardware from the HENA imager of the IMAGE (Imager for Magnetopause-to-Aurora Global Exploration) spacecraft. The imager ultimately produces a two dimensional map by measuring the neutral atom flux in different directions. The IMAGE spacecraft is scheduled for launch on Jan 1, 2000. A twin HENA was also placed aboard the Cassini mission to Saturn spacecraft, which was successfully launched on Dec. 5, 1997.

The Optical Monitor Camera (OMC) is a part of the scientific payload being developed for the INTEGRAL mission, scheduled to be launched in 2001. The OMC is an imager that will monitor star variations in the V-band in a 5 X 5 degree field of view. An optical system based on 6 lenses has been developed in order to meet the optical requirements in specific environmental conditions. The concept of the optical system and the optical performances are discussed in this paper. The optical design was mainly driven by the high radiation levels and the very wide temperature range of the instrument. The system has been optimized with specific constrains: limited radiation resistant glasses availability and lens barrel material. The filter section is designed in order to improve the optical performances and to withstand the high radiation environment. Great care is taken for the tolerance analysis that is a key factor for the manufacturing process. Specific stray light analyses including ghost effects are included in the optical design.

A user friendly, ASTM-formatted, 2-D and 3-D Bidirectional Scattering Distribution Function software data tool for PC- based computers has been developed which quickly archives, sorts, retrieves, plots, and analyzes the data for thousands of surfaces and materials. Many of these materials are black, white, and reflective surfaces for thermo-optical applications for ground and space-based instrumentation. The software can be used as a standalone CD-ROM or in conjunction with existing, commercially available optical design software analysis/design packages. This paper describes the reasons the database was able to be completed, the features, the sources of data, and the many participants from the scattering and general optics community.

At short wavelengths, optical systems can be designed such that a single aperture defines the beam that is used (system light gathering power), and another (the system field stop) defines the field-of-view (FOV). These components define the beam envelope and all other components are oversized so that they do not 'clip' or vignette this envelope. At longer wavelengths the diffraction caused by such clipping can seriously degrade the FOV response function and cause an increase in stray-light background. It is thus even more desirable to avoid clipping the beam as it passes through an instrument by oversizing all the optical elements. In space borne instruments, however, accommodation constraints can turn such oversizing into an unaffordable luxury. Instrument design must therefore consider the impact of multiple beam clipping and in particular any degradation in the FOV function. In this paper we describe such an analysis, based on advanced ray- tracing software, and give results for its application to two instruments: (1) The infra-red space observatory Long Wavelength Spectrometer (ISO-LWS, wavelength range 46 - 198 micrometer), where the FOV response is modeled for use with on-board calibration and data retrieval. (2) The imaging photometer in the Far Infra-Red Space Telescope SPIRE instrument (Spectral & Photometric Imaging Receiver, wavelength range 200 - 650 micrometer), where the analysis is needed for (a) Trade-off studies between instrument sensitivity (aperture size) and FOV degradation by clipping (b) Predicting the FOV performance of the final proposed design.

The Rayleigh-Rice (R-R) vector perturbation theory agrees well with experimental wide-angle scatter measurements from 'smooth' surfaces for arbitrary incident angles. However, not all applications of interest satisfy the smooth surface approximation. The Beckmann-Kirchoff (B-K) scalar diffraction theory of surface scatter phenomena is valid for rougher surfaces; but contains a paraxial (small-angle) assumption that limits its ability to accurately handle wide-angle scattering and large angles of incidence. In 1979 Harvey and Shack formulated a scattering theory in a linear systems format. Harvey later generalized this Harvey-Shack (H-S) theory to include the effects of small-angle scatter caused by 'mid' spatial frequency surface irregularities, and the extremely large incident angles inherent to grazing incidence Wolter Type I x-ray telescopes. In this paper we extend the H- S theory to include large incidence angles and scatter angles. We demonstrate that the customary paraxial limitation imposed in most scalar diffraction treatments is completely unnecessary and the resulting calculations for diffracted radiance (not irradiance or radiant intensity) are shift- invariant in direction cosine space

A common-path heterodyne interferometer for on-line non- contact measurement of surface profile has been developed. A single-mode frequency-stabilized laser diode (780 nm) serves as the light source to make whole system compact (total volume 250L X 200W X 100Dmm). The optical common-path configuration remarkably minimizes the effects caused by vibration, air turbulence and other environmental variations. Multiperiodical phase measuring technique, which is based on the combination of fractional periodic phase measurement and integer periodic phase counting, is employed in signal processing, so the system features not only high vertical resolution but wide measuring range as well. In addition, the automatic focusing system greatly facilitates the measurement especially on-line profiling. This paper gives the brief principles, the arrangement of the interferometer and some test results. The system has vertical resolution of 0.39 nm and lateral resolution of 0.73 micrometer. The stability is 1.95 nm (3(sigma) ) during about 1 hour and the accuracy of automatic focusing system is 0.1 micrometer within plus or minus 25 micrometer of the focus.

A theoretical formalism to study the scattering by reflection from a vitreous film on a planar medium with graded refraction index is developed. It is employed the impedance function, which characterizes the interface between two media and the diffuse diffraction pattern is obtained The medium is characterized using the function sech(x) in the refraction index and then, general and particular conclusions can be obtained starting from the surface impedance function.

A description is given of the scatterometer which has been developed at KRISS for BRDF and diffraction pattern measurement. Light source, goniometer, and receiver is described. As a light source, the collimated HeNe and argon ion laser is used, with which the wavelengths of 632.8, 514.5, and 488.0 nm are available. The goniometer has 6 degrees of freedom. The precision of scattering polar angle is enhanced by choosing long rotation arm (length: 1.2 meter) placed on the stepmotor-controlled rotary table whose angle is read by the angle encoder with the resolution of 0.0001 degree and accuracy 0.001 degree. The receiver has a wide dynamic range greater than 10¹⁴ in intensity without intensity attenuation and receiver aperture change, which is made by cascading three kinds of detectors: photodiode (PD), photo- multiplier in direct current mode (DC), and photo-multiplier in pulse counting mode (PC). The measured instrument signature and the sinusoidal grating BRDF at the wavelength of 488 nm is presented.

A new coating, whose specular reflectance at far-infrared wavelengths is considerably less than that of either Ames 24E2 or Martin Infrablack and whose diffuse IR reflectance is less than that of Ames 24E2, has been developed through cooperation of NASA-Ames Research Center and Ball Aerospace & Technologies Corporation. The new coating is called Ball IR Black. This new coating is harder and more robust than Ames 24E2 and has a lower tendency to shed particles. It is also rougher and thicker than Ames 24E2. At least two lines of evidence point toward multiple scatter among the huge surface facets of this coating as the principal mechanism behind its lower IR reflectance. A special technique to permit spray application of the coating (which contains SiC grinding compound) has been developed at Ball ATC and may be responsible for the unusually large surface facets.

The subject of scattering of electromagnetic waves from a rough surface has been an active research area for a long time. Among them, one of the most interesting phenomena associated with the scattering of the light from a rough surface is the enhanced backscattering. We have reported a giant enhanced backscattering peak for a weakly rough dielectric film on a reflecting metal substrate. Recently, we have measured larger enhanced backscattering from different samples of paints, paper, and metal surfaces. When the incident angle is large, a significant enhanced backscattering peak is measured from grazing angle. Not all manifestations of localization in the interaction of light with rough surfaces are in backscattering. We have also measured much larger enhanced reflection and enhanced transmission for a rough surface with even symmetry. This may be due to the multiple interference of diffused light.

For monitoring processes of semi conductor or optical industry automatically, stray light sensors are employed for a fast surface san to measure rms, defects, and contamination on surfaces. Surfaces can be characterized by the BRDF. The BRDF is parametrized to classify different surfaces. Classification may be done with various pattern recognition tools, but up to now no proof exists that justifies any choice of classes found empirically. Of course, a basic quantitative, i.e. metrological understanding of stray light sensors is necessary, which could successfully be obtained after comparing BRDFs evaluated from AFM topography scans with smooth surfaces. The power spectrum of surface topographies sufficiently smooth to obey Rayleigh-Rice approximation is proportional to the BRDF. Surfaces obeying this approximation, however, may not include defects and contamination with lateral sizes smaller than the wavelength of the illuminating light employed in the stray light sensor. Thus the comparison was only carried out with specially prepared samples. We have measured the topography of large areas up to 600 micrometer X 100 micrometer with an AFM by patching several scans (up to 8) with overlap. BRDFs evaluated from AFM measurements agree well with BRDFs measured with a stray light sensor.

The Optical Monitor Camera (OMC) is a part of the scientific payload of the INTEGRAL spacecraft, scheduled to be launched in 2001. The OMC is an imager that will monitor star variations in the V-band in a 5 X 5 degree field of view. It is required that the instrument detects object of plus 19.7 magnitude within the FOV. This requires highly sophisticated baffling techniques to provide attenuation up to 10^-45. To obtain such performances, the design of each sub-element is optimized to fulfill very stringent stray-light requirements. The stray-light sources are discussed and performances are simulated with a 3D ray-tracing model.