IXPE Mirror Module Assemblies

Expected to launch in 2021 Spring, the Imaging X-ray Polarimetry Explorer (IXPE) is a NASA Astrophysics Small Explorer Mission with significant contributions from the Italian space agency (ASI). The IXPE observatory features three identical x-ray telescopes, each comprised of a 4-m-focal-length mirror module assembly (MMA, provided by NASA Marshall Space Flight Center) that focuses x rays onto a polarization-sensitive, imaging detector (contributed by ASI-funded institutions). This paper summarizes the MMAs design, fabrication, alignment and assembly, expected performance, and calibration plans

First Images from HERO: A Hard-X-Ray Focusing Telescope

We are developing a balloon-borne hard-x-ray telescope that utilizes grazing incidence optics. Termed HERO, for High-Energy Replicated Optics, the instrument will provide unprecented sensitivity in the hard-x-ray region and will achieve milliCrab-level sensitivity in a typical 3-hour balloon-flight observation and 50 microCrab sensitivity on ultra-long-duration flights. A recent proof-of-concept flight, featuring a small number of mirror shells captured the first focused hard-x-ray images of galactic x-ray sources. Full details of the payload, its expected future performance and its recent measurements are provided

The Imaging X-ray Polarimetry Explorer (IXPE): Technical Overview

The Imaging X-ray Polarimetry Explorer (IXPE) will expand the information space for study of cosmic sources, by adding linear polarization to the properties (time, energy, and position) observed in x-ray astronomy. Selected in 2017 January as a NASA Astrophysics Small Explorer (SMEX) mission, IXPE will be launched into an equatorial orbit in 2021. The IXPE mission will provide scientifically meaningful measurements of the x-ray polarization of a few dozen sources in the 2-8 keV band, including polarization maps of several x-ray-bright extended sources and phase-resolved polarimetry of many bright pulsating x-ray sources

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS)

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) is a sounding rocket instrument that flew on July 30, 2021 from the White Sands Missile Range, NM. The instrument was designed to address specific science questions that require differential emission measures of the solar soft X-ray spectrum from 6 – 25[Formula: see text]Å(0.5 – 2.1[Formula: see text]keV). MaGIXS comprises a Wolter-I telescope, a slit-jaw imaging system, an identical pair of grazing incidence paraboloid mirrors, a planar grating and a CCD camera. While implementing this design, some limitations were encountered in the production of the X-ray mirrors, which ended up as a catalyst for the development of a deterministic polishing approach and an improved meteorological technique that utilizes a computer-generated hologram (CGH). The opto-mechanical design approach addressed the need to have adjustable and highly repeatable interfaces to allow for the complex alignment between the optical sub-assemblies. The alignment techniques employed when mounting the mirrors and throughout instrument integration and end-to-end testing are discussed. Also presented are spatial resolution measurements of the end-to-end point-spread-function that were obtained during testing in the X-ray Cryogenic Facility (XRCF) at NASA Marshall Space Flight Center. Lastly, unresolved issues and off-nominal performance are discussed

The Mathematical Theory of Wavelets

ABSTRACT. We present an overview of some aspects of the mathematical theory of wavelets. These notes are addressed to an audience of mathematicians familiar with only the most basic elements of Fourier Analysis. The material discussed is quite broad and covers several topics involving wavelets. Though most of the larger and more involved proofs are not included, complete references to them are provided. We do, however, present complete proofs for results that are new (in particular, this applies to a recently obtained characterization of “all ” wavelets in section 4). 1

On the existence of wavelets for non-expansive dilation matrices

Sets which simultaneously tile $\mathbb{R}^n$ by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices $A$ for which there exist sets that tile by powers of $A$ and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essentialway on the interplay between the \textit{eigenvectors} of the dilation matrix and the translation lattice rather than the usual dependence on the eigenvalues. For example, it is shown that for any values $\vert a\vert > 1 > \vert b\vert$ , there is a $(2\times 2)$ matrix $A$ with eigenvalues $a$ and $b$ for which such a set exists, and a matrix $A'$ with eigenvalues $a$ and $b$ for which no such set exists. Finally, these results are related to the existence of wavelets for non-expansive dilations