Diffraction effects of X-ray optical systems are often (justifiably) ignored due to the small wavelength of the X-ray radiation. However, the extremely large obscuration ratio inherent to grazing incidence optical systems produces a profound degradation of the diffraction image over that produced by a moderately obscured aperture of the same diameter. The contradictory requirements of large collecting area and relatively short length of optical elements has tended to result in proposed designs containing many concentric shells with increasingly higher obscuration ratios. In this paper we show that diffraction effects in such systems can significantly affect the achievable optical performance at the low energy (long wavelength) end of the intended operating spectral range. Parametric diffraction-limited performance predictions for both imaging and spectrographic applications will be presented and compared to AXAF performance goals and/or BBXRT fabrication techniques.

Transverse ray aberration expansions are derived for Wolter type 1 telescopes. The analysis gives third order aberration terms, most of the fifth order terms and two seventh order terms as functions of system parameters and entrance aperture coordinates. The third order distortion is negligible and, therefore, this term is omitted in the expansions. The spot diagrams derived from exact ray tracing and aberration expansions agree well. The importance of fifth and seventh order terms is discussed. The derived aberration expansions are also valid for Wolter type 2 telescopes.

The high quality of some experimental x-ray images formed at grazing incidence by a single reflecting surface raises some questions about the interpretation of Abbe's sine condition. In standard textbooks Abbe's sine condition is usually derived for the refractive case. What if any changes in its form or interpretation occur in the case of reflection and in particular grazing incidence reflection. A commonly encountered form of Abbe's sine condition is n'y' sin θ' - ny sin θ = 0 where n and n' are the refractive indices of object and image space respectively. Since the product of refractive index and geometrical length is defined as an optical path-length, one sees in the statement of Abbe's sine condition essentially a restatement of Fermat's principle. Any application of the zero form of Abbe's sine condition would rule out the single reflector as a good imaging device free of coma at grazing incidence because θ increases as e' decreases. By making use of a geometrical construction dating back to a Thomas Young publication, circa 1807, a modified sine relationship applicable to reflection at grazing incidence can be formulated as n'y' sin θ' - ny sin θ = yy'/f where f is the focal length. Using an error analysis procedure the modified sine relationship can be put into a more practical form and the results tabulated for a range of focal lengths f in cm, objects heights y in microns and magnifications M. Experimental results for a single reflector adjusted to satisfy the modified sine condition at grazing incidence will be shown.

It has been known for some time that glancing incidence x-ray optics have sharply peaked point response functions. The spatial resolution of Wolter x-ray telescope systems is frequently limited by the performance characteristics of the x-ray detector rather than by the optics, even when high resolution detectors such as photographic emulsions are used. This problem becomes even more severe when it is desirable to take advantage of the high sensitivity and broad wavelength response afforded by modern solid state detectors such as charge coupled devices or multi-anode microchannel arrays. We will report results of theoretical investigations of methods for increasing the telescope plate scale by the use of glancing incidence hyperboloid/ellipsoid x-ray microscope optics and normal incidence contoured layered synthetic microstructure optics for coupling the Wolter mirrors to the detector. The relative merits of the different hybrid x-ray telescope systems which result will be discussed. Considerations will be made concerning applications of these systems to high resolution imagery and spectroscopy of astronomical x-ray/XUV sources.

In order to demonstrate optical technology readiness for the Advanced X-ray Astrophysical Facility (AXAF), a Wolter Type I telescope was built. This telescope, called the Technology Mirror Assembly (TMA), was designed to have a system resolution of 0.6 arc second and a tight encircled energy performance specification. In order to meet these goals for encircled energy and resolution, an error budget was established, and specifications applied to each optical parameter. These tolerances are nearly an order of magnitude tighter than those required for HEAO-B, the highly successful forerunner of AXAF, which represents the present state of the art. Such stringent tolerances required a considerable advance in the metrology and polishing process. This paper describes the TMA error budget generation, details the metrology instrumentation and performance levels achieved, and discusses the computer controlled polishing process and equipment used to fabricate these X-ray optics. Finally, we illustrate how polishing progress was measured using a mathematical performance prediction model. Subsequent measurement of TMA focal plane performance shows a resolution of less than 0.5 arc second at X-ray wavelengths, which is in good agreement with these predictions and which represents the highest level of X-ray telescope performance ever achieved.

Roughness and waviness on mirrors for use in grazing-incidence optical systems intended for the extreme ultraviolet and x-ray regions affect both the focusing properties of the mirrors and the scattered light they produce. The most important surface spatial wave-lengths of the roughness are in the 1- to 100-μm range and are easily measurable using conventional optical and mechanical techniques. Descriptions of some of these techniques will be given along with examples of measurements made on very smooth polished optical surfaces that are comparable to those used as grazing-incidence optics.

Measurements of surface roughness were made on a large number of grazing incidence mirrors delivered for use at the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory. The measurements were made with a WYKO optical profiler using a 2.5X and a 10X objective and analyzed with our PROFILE code to generate an average periodogram representation for each surface. The data is presented in the form of representative profiles with all of the periodogram curves arranged according to figure type. Analysis of the periodograms allows one to compute bandwidth-limited values for RMS roughness and slope, to provide valuable feedback information to manufacturers regarding compliance with specifications, and to predict the performance of the optic at x-ray wavelengths.

An investigation is made of the sensitivity of the image quality for the proposed FUSE telescope to mirror misalignments and a wide spatial frequency range of figure errors. Representative figure error data was obtained for the analysis from measurements made on the SEUTS (Solar Extreme Ultraviolet Telescope Spectrograph) telescope mirrors. The tolerancing analysis was carried out with the aid of the Optical Surface Analysis Code (OSAC) program.

Vertical honing is in use at Itek for free-abrasive grinding of grazing-incidence mirrors for the Advanced X-Ray Astronomical Observatory (AXAF) Technology Mirror Assembly (TMA) program as a demonstration for the High-Resolution Mirror Assembly (HRMA) flight hardware. Software has been developed to enable exploring, by numerical simulation, the consequences of various options of this fabrication technique. The tolerances allowed for these mirrors are such that the flexibilities of the workpiece, of the vertical-honing blades, and of the mechanism that supports the blades and the work-piece must be taken into account, as well as the hydrodynamic properties of the slurry and the relative wear of the blades and the workpiece. Two policies of formation of the blades are considered: (1) an initially flat profile with face width proportional to the desired figure, or (2) a curved profile proportional to the desired figure with straight-edged face. It is shown that both policies can form the desired figure, but that the latter has more attractive properties as the end of grinding approaches. Using the latter policy, it is demonstrated by simulation that it is possible to preform vertical-honing blades to take into account the system flexibility and the effects of wear (both of the blades and the workpiece) so that grinding in principle ends with a workpiece ready for polishing. The principles of the software model will be outlined. Some of the results to date and grinding control policies that become possible will be discussed.

Flight mirrors for the Extreme Ultraviolet Explorer satellite are currently under fabrication. The grazing incidence metal mirrors are Wolter-Schwarzschild Type I and II and are figured by diamond turning. Imaging performance is excellent, with the figure after polishing for the best mirror being such that the full width-half maximum is 1.0 arc seconds and the half energy width is 8 arc seconds measured at visible wavelengths. Surface finish, as determined from scattering measurements in the extreme ultraviolet, is about 20Å rms.

The conical X-ray imaging mirror represents the long focal length limit of the Wolter type I grazing incidence mirror, in which the curved surfaces have been replaced by simple cones. When many thin-walled cones are nested, such a mirror affords the relatively high aperture filling factor needed for telescopes well suited to broadband X-ray astronomy. A conical mirror also features a constant spatial resolution across the field of view and can be designed to have an arbitrarily high intrinsic spatial resolution. We describe the general principles involved in the design of conical optics, as revealed by ray tracing studies. We also discuss the progress we have made toward the development of an arc-minute quality conical mirror, as part of the Broad-Band X-Ray Telescope experiment, which will fly as an attached Shuttle payload in late 1988. The approach we have developed for producing extremely smooth reflecting surfaces, application of a thin layer of acrylic lacquer to a metallic substrate, has produced X-ray reflecting surfaces whose microroughness is comparable with that of the highest quality polished grazing incidence mirrors. We review the efforts being made by a number of groups to produce a conical mirror with improved spatial resolution.

The reduction of scattering, especially near-specular scattering, constitutes one of the major challenges to the grazing-incidence optics community for either x-ray astronomy or synchrotron-radiation applications. In this paper, the theoretical predictions of angular scattering by microfacets in the surface (facet-model scattering), and by diffraction from surface microirregularities (diffractive-model scattering) are examined. The differences between these two theories is discussed for the case of grazing-incidence optics. By using a simple normalization to minimize the effects of the approximations made in the first-order diffractive-scattering theory, three approximate scaling or invariance rules are derived for the near-specular angular distribution of scattering. If verified experimentally, these rules will facilitate the extrapolation of near-specular angular scattering from one set of operational conditions to another.

Grazing incidence mirrors used to focus synchrotron radiation beams through small distant apertures have severe optical require-ments. The surface distortion due to heat loading of the first mirror in a bending magnet beam line is of particular concern when a large fraction of the incident beam is absorbed. In this paper we discuss mirror design considerations involved in minimizing the thermal/ mechanical loading on vertically deflecting first surface mirrors required for SPEAR synchrotron radiation beam lines. Topics include selection of mirror material and cooling method, the choice of SiC for the substrate, optimization of the thickness, and the design of the mirror holder and cooling mechanism. Results obtained using two-dimensional, finite-element thermal/mechanical distortion analysis are presented for the case of a 6° grazing incidence SiC mirror absorbing up to 260 W at Beam Line VIII on the SPEAR ring. Test descriptions and results are given for the material used to thermally couple this SiC mirror to a water-cooled block. The interface material is limited to applications for which the equivalent normal heat load is less than 20 W/cm².

The practical testing and specification of x-ray and UV mirrors requires a scattering theory to link topographic finish errors and functional performance. This paper examines various smooth-surface theories that have been proposed for this purpose, with particular attention to their behavior near the critical angle where the surface reflectivity is a rapid function of angle. Of the various diffraction theories considered, Rayleigh-Rice vector perturbation theory is the most realistic; and predicts scattering distributions that are characteristically different fram those of the canonical model. In sane cases these differences or anomalies are similar to those observed by Yoneda and by Matsushita et al., which have previously been interpreted using geametrical-optics models. But there are differences. For example, the Rayleigh-Rice theory predicts anomalous scattering near the critical angle above the glancing angle of incidence ("anti-Yoneda effect"). Results are illustrated by calculations for strawman scattering experiments.

The development of visible region free electron lasers (FELs) and their prospective extension into the UV and the XUV regions has created an additional source of demand for high performance optics in these wavelength regions. I review the new damage phenomenon (UV-induced absorption) observed in short wavelength FELs, discuss the optics requirements in this application, and examine the additional data required to ascertain the scaling characteristics of this process.

Techniques for surface finishing figured X-ray optics by a lacquer coating process are described. This lacquer coating can be applied with an optical quality of λ/8 at 6328Å and very effectively covers surface roughness with spatial frequencies more than ^~ 5 mm^-1 . Tungsten films have been deposited on the lacquer coatings so that the surface provides highly efficient X-ray reflectivity.

The temperature stability of metal (W, WRe, Co, Cr)-carbon multilayers has been studied using X-ray diffraction (θ-2θ and Debye-Scherrer) and electron microscopy. The results show that in all cases a crystallization occurs in the temperature range 650-750°C. As a consequence of this crystallization, the layered structure is destroyed, the surface of the film becomes rough and the X-ray reflectivity is considerably reduced. These results imply that efficient cooling or new multilayer structures will have to be developed for use at high temperatures or under high X-ray incident flux.

The replication of grazing incidence optics is reviewed. Electroform and epoxy replication are described and compared. It is concluded that for light weight and deep nesting, replication has a distinct advantage over direct production. The resolution of optics produced in this manner is however, limited to about 10 arc seconds; a typical value is 40 arc seconds. Epoxy replicated pieces tend to have better optical figures than electroformed optics, but the latter can be made thinner to make more deeply nested systems.

The Advanced X-Ray Astrophysics Facility (AXAF), a NASA project scheduled for launch in the 1990s, is a nested set of six Wolter Type I, x-ray telescopes with a 1.2 meter aperture, and associated scientific instruments. AXAF will perform up to two orders of magnitude better than the highly successful High Energy Astrophysics Observatory (HEAO-II), or the Einstein Observatory, in terms of resolution and effective area. To achieve this goal, the specification on the mirror figure quality must be up to approximately ten times more stringent than that for the HEAO-II. To demonstrate that such high figure quality could be achieved, NASA's Marshall Space Flight Center (MSFC) and the Smithsonian Astrophysical Observatory (SAO) undertook the Technology Mirror Assembly (TMA) project. This paper is a summary of the assembly and alignment techniques that were successfully used on the TMA.

An automated figure formation system for Kirkpatrick-Baez geometry grazing incidence X-ray mirrors is described. The system is based on an IBM PC/XT microcomputer and utilizes primarily commercially available equipment. The mirror assemblies currently being manufactured for the LAMAR experiment attain an angular resolution of ~30" (50% power diameter) on axis. The angular resolution is limited by the float glass used for the mirror plates, not the figure formation process.

The ultimate test of an optical component is its performance under conditions similar to those that it will encounter in service. Prior to this stage, precision dimensional measurement is the key to achieving the specification, and a range of measuring instruments has been developed specifically for the metrology of grazing incidence optics. These instruments can be calibrated to uncertainties of about 10 picometres by X-ray interferometry.

Angle resolved X-ray scattering was measured from flat mirrors and synthetic wultilayers using crystal collimator and analyzer with a resolution of 4 arc sec at 1.54 A. The scattering a few hundreds arc sec below and above the specular reflection from the mirror was intepreted to arise from the slope errors of the surface. Strong correlations between the angular broadening of the Bragg-diffracted beam from the multilayer and the surface quality of the substrate suggested that the multilayer mimics the slope distribution of the substrate.

The optical tests described here were performed after each step in the fabrication process of three Extreme Ultraviolet Explorer (EUVE) Type 1 telescope mirrors. The surface finish and irregularity was determined by image analysis and the geometrical figure was tested interferometrically. Images of a collimated point source were relayed to obtain magnifications and photographic exposures were adjusted to include all the scattered light while still resolving the smallest bright image core. By linearizing film sensitivity and taking digitized lineouts of the photographed image, less than 1 arc second full width half maximum (FWHM) intensities were measured. The integrated energy density was measured photometrically, and diffraction limited curves of 5 arc second half energy widths (HEW) were obtained. The test purpose, instruments employed, alignment methods, and test results are detailed.