ALBERT

Description: A formula for the rms blur circle for Wolter telescopes has been derived using the transverse ray aberration expressions of Saha (1985), Saha (1984), and Saha (1986). The resulting formula for the rms blur circle radius over an image plane and a formula for the surface of best focus based on third-, fifth-, and seventh-order aberration theory predict results in good agreement with exact ray tracing. It has also been shown that one of the two terms in the empirical formula of VanSpeybroeck and Chase (1972), for the rms blur circle radius of a Wolter I telescope can be justified by the aberration theory results. Numerical results are given comparing the rms blur radius and the surface of best focus vs the half-field angle computed by skew ray tracing and from analytical formulas for grazing incidence Wolter I-II telescopes and a normal incidence Cassegrain telescope.

Description: The wavefront aberration polynomial and transverse ray aberration expansions will be derived for grazing incidence two-mirror Wolter telescopes including all paraboloid-hyperboloid and paraboloid-ellipsoid combinations. The reference sphere is determined with the help of the principal surface of the telescope, and the aberration polynomials will be given as functions of the coordinates of the ray intersection with the reference sphere. Third -and some of the fifth-order and seventh-order aberration terms will be analyzed. Also, the well-known relationship between wavefront aberration polynomials and transverse ray aberration polynomials will be verified.

Description: 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.

Description: 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.

Description: A generalized set of equations are derived for two mirror glancing incidence telescopes using Fermat's principle, a differential form of the law of reflection, the generalized sine condition, and a ray propagation equation described in vector form as a theoretical basis. The resulting formulation groups the possible telescope configurations into three distinct classes which are the Wolter, Wolter-Schwarzschild, and higher-order telescopes in which the Hettrick-Bowyer types are a subset. Eight configurations are possible within each class depending on the sign and magnitude of the parameters.

Description: Large number of grazing incidence telescope configurations have been designed and studied. Wolte1 telescopes are commonly used in astronomical applications. Wolter telescopes consist of a paraboloidal primary mirror and a hyperboloidal or an ellipsoidal secondary mirror. There are 8 possible combinations of Wolter telescopes. Out of these possible designs only type 1 and type 2 telescopes are widely used. Type 1 telescope is typically used for x-ray applications and type 2 telescopes are used for EUV applications. Wolter-Schwarzshild (WS) telescopes offer improved image quality over a small field of view. The WS designs are stigmatic and free of third order coma and, therefore, the PSF is significantly better over a small field of view. Typically the image is more symmetric about its centroid. As for the Wolter telescopes there are 8 possible combinations of WS telescopes. These designs have not been widely used because the surface equations are complex parametric equations complicating the analysis and typically the resolution requirements are too low to take full advantage of the WS designs. There are several other design options. Most notable are wide field x-ray telescope designs. Polynomial designs were originally suggested by Burrows4 and hyperboloid-hyperboloid designs for solar physics applications were designed by Harvey5. No general aberration theory exists for grazing incidence telescopes that would cover all the design options. Several authors have studied the aberrations of grazing incidence telescopes. A comprehensive theory of Wolter type 1 and 2 telescopes has been developed. Later this theory was expanded to include all possible combinations of grazing incidence and also normal incidence paraboloid-hyperboloid and paraboloid-ellipsoid telescopes. In this article the aberration theory of Wolter type telescopes is briefly reviewed.

Description: We describe an approach to build an x-ray mirror assembly that can meet Lynxs requirements of high-angular resolution, large effective area, light weight, short production schedule, and low-production cost. Adopting a modular hierarchy, the assembly is composed of 37,492 mirror segments, each of which measures 100 mm 100 mm 0.5 mm. These segments are integrated into 611 modules, which are individually tested and qualified to meet both science performance and spaceflight environment requirements before they in turn are integrated into 12 metashells. The 12 metashells are then integrated to form the mirror assembly. This approach combines the latest precision polishing technology and the monocrystalline silicon material to fabricate the thin and lightweight mirror segments. Because of the use of commercially available equipment and material and because of its highly modular and hierarchical building-up process, this approach is highly amenable to automation and mass production to maximize production throughput and to minimize production schedule and cost. As of fall 2018, the basic elements of this approach, including substrate fabrication, coating, alignment, and bonding, have been validated by the successful building and testing of single-pair mirror modules. In the next few years, the many steps of the approach will be refined and perfected by repeatedly building and testing mirror modules containing progressively more mirror segments to fully meet science performance, spaceflight environments, as well as programmatic requirements of the Lynx mission and other proposed missions, such as AXIS.

Description: We introduce a new type of x-ray telescope design; an Equal-Curvature telescope. We simply add a second order axial sag to the base grazing incidence cone-cone telescope. The radius of curvature of the sag terms is the same on the primary surface and on the secondary surface. The design is optimized so that the on-axis image spot at the focal plane is minimized. The on-axis RMS (root mean square) spot diameter of two studied telescopes is less than 0.2 arc-seconds. The off-axis performance is comparable to equivalent Wolter type 1 telescopes.

Description: The Constellation-X Spectroscopy X-ray Telescope (SXT) is a large diameter, high throughput, grazing incidence imaging mirror system, designed to perform high sensitivity spectroscopy of cosmic X-ray sources in the 0.2-10.0 keV band. The baseline effective area requirement is -3 m# at 1 keV. The system-level angular-resolution requirement is a 15-arcseconds half-power diameter, with a 5-arcsecond goal. The effective area is attained through a modular design, involving the nesting of many confocal, thin-walled Wolter I mirror segments. Considerable progress has been made in developing thin, thermally formed, glass mirror substrates that meet or better the angular-resolution requirement. Several approaches to mounting and aligning reflector segments into a mirror system are under investigation. We report here on the progress of the SXT technology development program toward reaching the performance goals.

Description: In support of Goddard's Constellation-X mandrel manufacturing effort a series of fabrication experiments are being performed to determine a best approach. Currently, polishing immediately after diamond turning, produces a RMS surface roughness of 0.31 nm, on a nickel plated aluminum mandrel. Studies currently under way will incorporate an abrasive figuring step followed by a polishing operation. The current diamond turning, figuring and polishing procedures will be described and the results presented.