Measuring x-ray polarization in the presence of systematic effects: Known background

The prospects for accomplishing x-ray polarization measurements of astronomical sources have grown in recent years, after a hiatus of more than 37 years. Unfortunately, accompanying this long hiatus has been some confusion over the statistical uncertainties associated with x-ray polarization measurements of these sources. We have initiated a program to perform the detailed calculations that will offer insights into the uncertainties associated with x-ray polarization measurements. Here we describe a mathematical formalism for determining the 1- and 2-parameter errors in the magnitude and position angle of x-ray (linear) polarization in the presence of a (polarized or unpolarized) background. We further review relevant statistics-including clearly distinguishing between the Minimum Detectable Polarization (MDP) and the accuracy of a polarization measurement.Comment: 12 pages, 4 figures, for SPIE conference proceeding

On understanding the figures of merit for detection and measurement of x-ray polarization

The prospects for accomplishing X-ray polarization measurements appear to have grown in recent years after a more than 35-year hiatus. Unfortunately, this long hiatus has brought with it some confusion over the statistical uncertainties associated with polarization measurements of astronomical sources. The heart of this confusion stems from a misunderstanding (or potential misunderstanding) of a standard figure of merit-the minimum detectable polarization (MDP)-that one of us introduced many years ago. We review the relevant statistics, and quantify the differences between the MDP and the uncertainty of an actual polarization measurement. We discuss the implications for future missions.Comment: 5 pages, 2 figures, to be presented at SPIE conference 7732 (paper 13), corrected typo

Methods of optimizing X-ray optical prescriptions for wide-field applications

We are working on the development of a method for optimizing wide-field X-ray telescope mirror prescriptions, including polynomial coefficients, mirror shell relative displacements, and (assuming 4 focal plane detectors) detector placement along the optical axis and detector tilt. With our methods, we hope to reduce number of Monte-Carlo ray traces required to search the multi-dimensional design parameter space, and to lessen the complexity of finding the optimum design parameters in that space. Regarding higher order polynomial terms as small perturbations of an underlying Wolter I optic design, we begin by using the results of Monte-Carlo ray traces to devise trial analytic functions, for an individual Wolter I mirror shell, that can be used to represent the spatial resolution on an arbitrary focal surface. We then introduce a notation and tools for Monte-Carlo ray tracing of a polynomial mirror shell prescription which permits the polynomial coefficients to remain symbolic. In principle, given a set of parameters defining the underlying Wolter I optics, a single set of Monte-Carlo ray traces are then sufficient to determine the polymonial coefficients through the solution of a large set of linear equations in the symbolic coefficients. We describe the present status of this development effort.Comment: 14 pages, to be presented at SPIE conference 7732 (paper 93

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

Techniques for Achieving Zero Stress in Thin Films of Iridium, Chromium, and Nickel

We examine techniques for achieving zero intrinsic stress in thin films of iridium, chromium, and nickel deposited by magnetron sputter deposition. The intrinsic stress is further correlated to the microstructural features and physical properties such as surface roughness and optical density at a scale appropriate to soft X-ray wavelengths. The examination of the stress in these materials is motivated by efforts to advance the optical performance of light-weight X-ray space telescopes into the regime of sub-arcsecond resolution through various deposition techniques that rely on control of the film stress to values within 10-100 MPa. A characteristic feature of the intrinsic stress behavior in chromium and nickel is their sensitivity to the magnitude and sign of the intrinsic stress with argon gas pressure and deposition rate, including the existence of a critical argon process pressure that results in zero film stress which scales linearly with the atomic mass of the sputtered species. While the effect of stress reversal with argon pressure has been previously reported by Hoffman and others for nickel and chromium, we report this effect for iridium. In addition to stress reversal, we identify zero stress in the optical functioning iridium layer shortly after island coalescence for low process pressures at a film thickness of approximately 35nm. The measurement of the low values of stress during deposition was achieved with the aid of a sensitive in-situ instrument capable of a minimum detectable level of stress, assuming a 35nm thick film, in the range of 0.40-6.0 MPa for oriented crystalline silicon substrate thicknesses of 70-280 microns, respectively

Chandra Contaminant Migration Model

No abstract availabl

The Imaging X-Ray Polarimetry Explorer: An Overview

No abstract availabl