On the design of wide-field x-ray telescopes
X-ray telescopes having a relatively wide field-of-view and spatial resolution vs. polar off-axis angle curves much flatter than the parabolic dependence characteristic of Wolter I designs are of great interest for surveys of the X-ray sky and potentially for study of the Sun's X-ray emission. We discuss the various considerations affecting the design of such telescopes, including the possible use of polynomial mirror surface prescriptions, a method of optimizing the polynomial coefficients, scaling laws for mirror segment length vs. intersection radius, the loss of on-axis spatial resolution, and the positioning of focal plane detectors.
Grazing incidence optics for wide-field x-ray survey imaging: a comparison of optimization techniques
Discussions of optimizing wide-field x-ray optics, with field-of-view less-than 1.1 degree-squared, have been made previously in the literature. However, very little has been published about the optimization of wide-field x-ray optics with larger field-of-views, which technology could greatly enhanced x-ray surveys. We have been working on the design of a wide-field (3.1 degree-squared field-of-view), short focal length (190.5 cm), grazing incidence mirror shell set, with a desired rms image spot size of 15 arcsec. The baseline design consists of Wolter 1 type mirror shells with polynomial perturbations applied to the baseline design. The overall optimization technique is to efficiently optimize the polynomial coefficients that directly influence the angular resolution, without stepping through the entire multi-dimensional coefficient space. We have investigated optimization techniques such as the downhill simplex method, fractional factorial, and response surface (including Box- Behnken and central composite) design. We have also investigated the use of neural networks, such as backpropagation, general regression, and group method of data handling neural networks. We report our findings to date.
APPLICATION OF THE FINITE ELEMENT METHOD TO ROTARY-WING AEROELASTICITY.
Recent research in rotary-wing aeroelasticity has indicated that all fundamental problems in this area are inherently nonlinear. The non-linearities in this problem are due to the inclusion of finite slopes, due to moderate deflections, in the structural, inertia and aerodynamic operators associated with this aeroelastic problem. In this paper the equations of motion, which are both time and space dependent, for the aeroelastic problem are first formulated in P.D.E. form. Next the equations are linearized about a suitable equilibrium position. The spatial dependence in these equations is discretized using a local Galerkin method of weighted residuals resulting in a finite element formulation of the aeroelastic problem. As an illustration the method is applied to the coupled flap-lag problem of a helicopter rotor blade in hover. Comparison of the solutions with previously published solutions establishes the convergence properties of the method. It is concluded that this formulation is a practical tool for solving rotary-wing aeroelastic stability or response problems.