The techniques and status of the design approaches to system baffling, the comouter analysis, the BRDF measurements, and the theories of surface scattering are discussed.

A method is outlined for performing out-of-field rejection predictions using hand calculator methods and small computer programs. This method is useful in getting quick rejection estimates in the formative stages of a design, when detailed baffle design is not complete. General methods of obtaining point source scattering results in a reimaging optical system are outlined. Useful approximations are described, along with their derivation. The integration of point source values to obtain earth background values is then described.

Optical systems which have stringent reouirements on stray light levels often need optical baffles. Some basic design principles and goals for baffles are Presented. Four generic optical designs and their advantages for stray light control are discussed: all reflective and all refractive reimaging and nonreimaging systems. The desirable shape and location of baffle vanes are shown, based on various design criteria. Presuming that the designer has the ability to control specular reflections from baffle surfaces, absorptive coatings which reflect specularly are preferred over those which reflect diffusely. Stray energy from edge diffraction can be controlled in a nonreimaging optical system by forcing light to undergo multiple diffractions.

The general configuration of a satellite telescope is used to show how simple projections of the various limiting apertures onto a chosen plane can show the obscuration and vignetting at any selected position on the focal plane. The projections also indicate what por-tions of the walls, baffles, etc. are viewed from various positions on the focal plane. Again projections taken at the angle of external sources show what portions of the interior are illuminated by these sources and the two combined give a method of estimating stray rad-iation. Since most detectors in scanning systems are AC coupled, the ability to estimate the rate of change of stray light with time is demonstrated.

The determination of the stray radiation in a well-baffled optical system reduces to the calculation of the scattered energy propagated along a few distinct paths. Approximate formulas are derived that estimate the amount of unwanted energy reaching a focal plane detector from these paths. In order to simplify the calculations, single edge scatter, double internal scatter, and diffraction from any vane structure on the main baffle tube of the system is treated as a macroscopic process with a single effective BRDF. The predic-tions made by the formulas for a typical system compare favorably with more extensive calculations made by the APART stray radiation analysis computer program.

The APART/PADE (Arizona's Paraxial Analysis of Radiation Transfer/Program for the Analysis of Diffracted Energy) code is a deterministic stray radiation analysis program capable of yielding quantitative descriptions of systems along with providing insight about the propagation paths. The program can be used to determine the image plane distribution due to external point sources, external extended sources such as the Earth, and for internally emitted radiation. The inclusion of the PADE program allows not only pure diffraction paths to be evaluated but also mixed modes of diffraction and scatter in any order. The program handles a large class of asymmetrical optical sensors and is designed to be most efficient with rotationally symmetric systems. Many additional related features of the program are discussed.

A method that substantially reduces the computational effort required to determine diffraction (including wide-angle and near-field) from arbitrary apertures or obstacles is presented. The theoretical process involves rigorously transforming the two-dimensional Kirchoff diffraction integral over the area of the aperture into a one-dimensional integral along the edge of the aperture. The resulting integral is then approximated by the first two terms of an asymptotic expansion given by the method of stationary phase. Diffraction pattern predictions based on this method are compared with those of more conventional methods, e.g. Fourier techniques, for several different geometries. An algorithm derived from the theory has been incorporated into a computer program called PADE (Program for the Analysis of Diffracted Energy) which together with the APART stray radiation analysis program can be used to not only determine multiple diffraction effects but also combinations of both scattering and diffraction in complex opto-mechanical systems. An extension of the algorithm to apertures with serrated-edge or thin-film apodisation is also discussed.

The GUERAP III is a sophisticated stray light analysis computer program. It uses the Monte Carlo method with importance sampling to trace random real rays through an optical sensor model. The program is useful for calculating stray light in an existing optical sensor and for determining dominant paths of scattered light to aid in the improvement of an optical baffle. The accuracy of the program depends on the accuracy of the input data for geometry and surface scatter characteristics. The uncertainty in the random ray trace depends on the proper use of importance sampling.

The General Unwanted Energy Rejection Analysis Program (GUERAP-3) computer program is designed to predict instrument stray light performance. In this paper, we discuss an atypical application of the program as an illustration of a much wider variety of problems for which the program is useful. The application discussed here is light collection modeling in scintillation detectors. The optical attenuation of light scintillations produced by gamma rays and charged particles can be modeled, and the light collected by a photomultiplier tube (PMT) can be optimized as a function of geometry of the scintillator, its surface characteristics (polished, rough ground, reflective foil-covered, etc.), PMT placement, and volume absorption within the scintillator. Necessary modifications to the standard GUERAP-3 computer program are discussed. The modified program is used to predict the optical attenuation of a typical scintillation detector. These predicted results are shown to agree with experimental data, thus demonstrating the use of GUERAP-3 for such analyses.

A comparative study of the computer programs GUERAP III and APART/PADE has been made based on the stray radiation analysis of a typical heat-seeking missile. The programs are compared in terms of general approaches, execution, and results. Specific areas of comparison are input requirements, information provided by each program, intrinsic uncertainties, unique program capabilities, and cost.

The presence of nonimaging specular baffles in a radiation path between a source and collector surface precludes the use of traditional first order optics for mapping the collecting surface into the source space. A method is presented for constructing generalized first order and higher order mappings about a real base ray. These mappings allow one to calculate the view factor between the source and collector without the large number of real ray traces required in alternative techniques.

This paper describes a facility developed by SSG, Inc., that is capable of testing optical sensors for out of field of view rejection (OFVR) in the infrared. Included are descriptions of components, laboratory conditions and electronic instrumentation. Also included are measured results of two infrared optical telescopes, performed at this facility. The Air Force Geophysics Laboratory/Space Division Zodiacal Infrared Program (ZIP) telescope and the Air Force Geophysics Laboratory/Naval Research Laboratory Far Infrared Sky Survey Experiment (FIRSSE) telescope measurements are compared to theoretical predictions. A brief description of a stray radiation analysis computer program used to analyze the ZIP telescope design is included. In addition, effects of baffle design on performance of the ZIP telescope are described. A detailed error analysis of measurement techniques is described showing error bounds down to the noise floor of OFVR. Measurement to less than 10-12 OFVR rejection is achieved for sensors with microsteradian field of view.

Stray light control is a major consideration in the design of infrared cryogenically cooled telescopes such as the Infrared Astronomical Satellite (IRAS). The basic design of the baffle system, and the placement, shape, and coating of the secondary support struts for the are described. The intent of this paper is to highlight the stray light problems encountered while designing the system, and to illustrate how computer analysis can be a useful design aid.* Scattering measurements of the primary mirror, and a full system level scatter measurement are presented. Comparisons of predicted performance with the measured results are also presented.

NASA is developing two large space-based infrared astronomy telescopes, IRAS and SIRTF. Both of these systems will be functioning in the environment of a bright thermal emitting earth and sun while concurrently having baffle surfaces radiating thermal photons which combine to produce a stray radiation background. The APART program was used to analyze the stray radiation propagation paths of both the IRAS and SIRTF designs. The SIRTF design was found to be about 10³ superior in its stray radiation transmission, because several design options were able to be incorporated through different mechanical and optical constraints that were different, while being generically of a similar optical design. A comparison of the APART stray radiation analyses of the two systems will be presented illustrating how the design options altered stray-light performance.

The straylight rejection of the German Infrared Laboratory (GIRL) baffle system and telescope is investigated. GIRL is being developed to perform experiments in the fields of astronomy and atmospheric physics to wavelengths of 500im. The preliminary design submitted to Ball Aerospace Systems Division (BASD) for evaluation thus reflects some nonconventional attempts to minimize the effects of internal thermal emission and diffraction at these longer wavelengths in addition to suppression of scattered straylight. However, analysis indicates that some of these efforts, namely use of certain low emissivity surfaces, result in higher thermal straylight as well as sacrificing the scattered straylight rejection of the system.

The concepts of BRDF (Bidirectional Reflectance Distribution Function) and BTDF (Bidirectional Transmittance Distribution Function) are defined and discussed as being the ratios of differential outputs of radiance divided by differential inputs of irradiance. Appropriate measurement arrangements and procedures are presented, and the problems are described that are involved in going from the differentials of theory to the finite quantities of measurement. Finally appropriate data reduction schemes are given for determining BRDF and BTDF from these measurements.

A nonspecular reflectometer and its operation at far-infrared wavelengths are described. Large differences in nonspecular reflectance were found to exist between different optically black coatings. Normal incidence bidirectional reflectance distribution function (BRDF) measurements at wavelengths between 12 and 316 μm of three black coatings show that their mean BRDFs increase with wavelength. The specularity of two of these coatings also showed a strong wavelength dependence, while the specularity of one coating seemed independent of wavelength. The BRDF of one coating depended on the angle of incidence at 12 and 38 μm, but not at 316 μm. Beyond 200 μm, it was found necessary to correct the measurements for the beam spread of the instrument.

Methods of characterizing t roughness of and scattering from plane single-point diamond-turned surfaces include Nomarski mlcroscopy, microscopic double-beam and multiple-beam interferometry, mechanical profilometry, normalized scatter, and BRDF measurements. Size and curvature parameters limit the usefulness of some of these techniques in the study of nonflat, real-life hardware. A nartial solution to the problems of characterizing curved surfaces is t use replication methods. Polishing reduces the surface roughness and scattering from nonflat single-point diamond-turned surfaces.

A scattering instrument for making BRDF measurements is described. The instrument is microprocessor-controlled and is designed to obtain BRDF data at wavelengths of 0.6328, 1.15, 3.39, 10.6, 41.7, and eventually 118.8 microns.

The use of gold-plated sandpaper was investigated as a standard Lambertian reference reflector. Various grit sizes from 3 μm to 400 μm and material types (i.e., silicon carbide or aluminum oxide, were studied. The different gold-plated sandpaper grit sizes were measured in the same way using three laser wavelengths (0.6328 μm, 3.39 μm, and 10.6 μm) at five angles of incidence of the source (0', 10°, 20°, 30°, and 60'). All the scatter-ing measurements presented were taken in the plane of incidence. The best choice of sand-paper grit size was compared to other commonly used reflectors such as magnesium oxide, halon, sintered bronze, and flowers of sulfur. An attempt was made to correlate surface roughness (size of grit) to the degree of approximation to a good Lambertian reflector, but it was found that grit size is not as important as filling factor, or density of particles, over a given area. It was found that fairly good approximations to Lambertian behavior result when the angle of incidence is small, but not when the angle of incidence is as large as 60°.

Far-infrared optical sensors operating in the submillimeter wavelength region require baffle systems to suppress stray light. Because a high degree of rejection of the stray light is required, the baffle systems must use highly absorbent coatings. Most common optical baffle coatings are not functional at wavelengths greater than 100 μm. However, multilayer coatings have been developed that minimize front surface reflectance and maximize absorptance with a minimum required coating thickness. Data for a polyurethane binder and carbon-pigmented coating show that a multilayer coating with a thickness of approximately 5 mils has a reflectance of less than 10 percent over the wavelengths out to 300 μm.

The design of the barrel baffle of the Infrared Astronomical Satellite (IRAS) Optical Subsystem to minimize production of particulate contamination is described. The configuration of the 50-inch long, 28.5-inch diameter baffle required pop-rivet assembly after coating with Martin Optical Black for stray light suppression. An experiment to determine the contamination produced at assembly led to the modification of the baffle construction to preclude such damage to the coated surfaces.

Results of an analysis of surface profile measurements by J. Bennett on a set of very smooth flat surfaces is presented. Visible scattering profiles are predicted and compared with measured scatter profiles. The predicted scatter profiles are integrated for compari-son with total integrated scatter measurements (TIS). Using the model analysis at X-ray wavelengths illustrates the impact of various surface profiles on X-ray imaging.

As part of a technological effort for the AXAF program, visible light scatter measurements were made of various mirror samples to determine the surface roughness. The measurements were made to compare with x-ray scatter measurements of the same samples. The data is recorded in a HHDF format described in a doctorate dissertation by James Harvey at the University of Arizona. The total diffuse scatter is calculated using numerical integration techniques and used to estimate the HMS surface roupiness. The technology program is not complete but a summary of the data generated to date is presented.

Full beam X-ray tests of high angular resolution have been performed on two of MPI's 32 cm Wolter type I telescopes. Scattering levels are in agreement with those obtained earlier by pencil beam tests. Due to the higher angular resolution of the full beam tests the central core of the point spread function has been resolved. It shows a width of 6 arcsec FWHM and a half power radius of ≈ 30 arcsec. The large half power radius can be attributed to axial slope errors of the mirrors. 9 superpolished, flat mirror samples made of Zerodur have been subjected to extensive X-ray scattering measurements at λλ 13.3 Å, 8.3 Å, 2.8 Å, and 1.9 Å and grazing angles from 15 arcmin to 150 arcmin. The scattered intensity has been recorded out to 4- 20 arcmin off the specular direction. Two components differing in width can be distinguished in the line spread function: 1. a broad component, which can be understood in terms of standard scattering theories; 2. a narrow component, appearing within ± 5 areminofthe central peak. Some hypotheses for the origin of the narrow component will be discussed.

The Advanced X-ray Astrophysics Facility (AXAF) is to be an orbiting X-ray observatory with high resolution imaging capabilities. Specific goals of 0.5 arcsecond resolution, and an encircled energy of 60% within a 1.0 arcsecond diameter circle at 2.5 keV have been established for AXAF. Imaging X-ray optics are primarily limited by scattering of the X-rays from the mirror surfaces. To ensure that the AXAF goals can be met, comprehensive X-ray scattering measurements are being conducted on a large number of flat samples. Sub-arcsecond resolution is achieved in these measurements through use of the MSFC 1000 ft X-ray calibration facility and a high spatial resolution X-ray detector. Flats of various materials, various coatings, and a range of rms surface roughness are being evaluated. Direct evaluation of surface microroughness is also provided by a variety of optical and non-optical means. This paper describes the scattering measurement program, the instrumentation used to obtain the measurements and preliminary results of measurements on several of the sample flats.

A description of the performance of an X-ray imaging system can be formulated in several ways. The char-acterization can be given in terms of the point spread function (PSF), the line spread function (LSF), the modulation transfer function (MTF), or the edge spread function (ESF). While the different functions are mathematically related, they do not all emphasize the same performance features equally. In this paper we examine the character of each of the descriptions using a simple model of the telescope response which includes the effects of both figure and scattering and illustrate the conclusions using a numerical example. It is shown that the MTF and ESF are strongly affected by scattering and that the LSF and PSF are affected both by scattering and by the figure of the optics. To assess the spatial resolution of an X-ray imaging system, the PSF description is the most useful and the effects of scattering can be approximately isolated from effects due to the optical figure by using the MTF or ESF,

This paper discusses the interpretation of arc-second x-ray scattering of mirror surfaces in terms of the power spectral densities of their topographic roughness. Such scattering depends on surface spatial wave-lengths of the order of mm to cm; much longer than those involved in conventional visible-light scattering and profile measurements. Key features are: 1) Expressions are developed for analyzing smooth-surface scattering in the Fresnel regime at angles comparable with the point-spread function of the measuring apparatus. 2) A sampling-theorem representation is used to describe the scattering in terms of a discrete rather than a continuous convolution with the system point-spread function. 3) Corrections are included to account for finite-record-length effects. And 4), results are illustrated for simple power-law power spectra.