\contentsline {chapter}{\hbox to\@tempdima {\hfil }Preface}{xiii}
\contentsline {chapter}{\numberline {1}Introduction}{1}
\contentsline {section}{\numberline {1.1}The HETG on AXAF}{1}
\contentsline {section}{\numberline {1.2}The HETG Itself}{2}
\contentsline {section}{\numberline {1.3}HETGS Calibration Definition and Goals}{3}
\contentsline {subsection}{\numberline {1.3.1}Effective Area and Efficiency Definitions}{3}
\contentsline {subsection}{\numberline {1.3.2}Effective Area Calibration Goals}{5}
\contentsline {subsection}{\numberline {1.3.3}LRF Definition}{7}
\contentsline {subsection}{\numberline {1.3.4}LRF Calibration Goals}{8}
\contentsline {section}{\numberline {1.4}Ground Calibration Overview}{8}
\contentsline {section}{\numberline {1.5}HETG Documentation}{9}
\contentsline {part}{\uppercase {i}\hspace {1em}Physics, Models, and Laboratory Measurements}{11}
\contentsline {chapter}{\numberline {2}LRF Physics and Model}{13}
\contentsline {section}{\numberline {2.1}Rowland Geometry and Astigmatism}{13}
\contentsline {section}{\numberline {2.2}LRF Approximation: Resolving Power Error Budget}{16}
\contentsline {subsection}{\numberline {2.2.1}HRMA PSF}{19}
\contentsline {subsection}{\numberline {2.2.2}Rowland Astigmatism}{21}
\contentsline {subsection}{\numberline {2.2.3}Grating Period and Roll Variations}{21}
\contentsline {subsection}{\numberline {2.2.4}Aspect and Dither Blurs}{21}
\contentsline {subsection}{\numberline {2.2.5}Detector Blur}{22}
\contentsline {section}{\numberline {2.3}Ray-trace Model: {\bf MARX\nobreakspace {}}\nobreakspace {}}{23}
\contentsline {chapter}{\numberline {3}Efficiency Physics and Model}{25}
\contentsline {section}{\numberline {3.1}Diffraction Theory and Models}{25}
\contentsline {subsection}{\numberline {3.1.1}Scalar Diffraction Theory}{25}
\contentsline {subsection}{\numberline {3.1.2}Rectangular Models}{26}
\contentsline {subsection}{\numberline {3.1.3}Vertex Model}{27}
\contentsline {subsection}{\numberline {3.1.4}Tilted Grating Model}{28}
\contentsline {subsection}{\numberline {3.1.5}Trapezoidal Model}{28}
\contentsline {section}{\numberline {3.2}Synchrotron Measurements}{30}
\contentsline {subsection}{\numberline {3.2.1}Synchrotron Measurements Summary}{30}
\contentsline {subsection}{\numberline {3.2.2}Synchrotron Data Analysis Techniques}{30}
\contentsline {subsection}{\numberline {3.2.3}Gold Optical Constants and Edge Structure}{30}
\contentsline {subsection}{\numberline {3.2.4}Polyimide Optical Constants and Edge Structure}{34}
\contentsline {subsection}{\numberline {3.2.5}Reference Grating Measurements}{37}
\contentsline {subsection}{\numberline {3.2.6}Error Estimates for X-GEF Predictions of Grating Efficiency}{41}
\contentsline {subsection}{\numberline {3.2.7}Synchrotron Analysis Status}{43}
\contentsline {section}{\numberline {3.3}Scattering Model}{44}
\contentsline {subsection}{\numberline {3.3.1}General Scattering Theory}{44}
\contentsline {subsection}{\numberline {3.3.2}Scattering Example: Grating Bar Shifts}{46}
\contentsline {chapter}{\numberline {4}Laboratory Measurements and Predictions}{49}
\contentsline {section}{\numberline {4.1}LR Measurements}{50}
\contentsline {subsection}{\numberline {4.1.1}LR Period and Roll Variations}{50}
\contentsline {subsection}{\numberline {4.1.2}LR Calibration using NIST Samples}{55}
\contentsline {section}{\numberline {4.2}X-GEF Measurements}{56}
\contentsline {subsection}{\numberline {4.2.1}Order Assymmetry and Tilt}{61}
\contentsline {subsection}{\numberline {4.2.2}Laboratory Efficiency Predictions}{61}
\contentsline {section}{\numberline {4.3}Alignment Measurements}{64}
\contentsline {section}{\numberline {4.4}Long-term: Vacuum Storage Gratings}{66}
\contentsline {part}{\uppercase {ii}\hspace {1em}X-Ray Calibration Facility Measurements and Analysis}{67}
\contentsline {chapter}{\numberline {5}XRCF and the HETG}{69}
\contentsline {section}{\numberline {5.1}XRCF Introduction}{69}
\contentsline {subsection}{\numberline {5.1.1}XSS}{70}
\contentsline {subsection}{\numberline {5.1.2}BNDs}{70}
\contentsline {subsection}{\numberline {5.1.3}HRMA, Gratings, and Shutters}{70}
\contentsline {subsection}{\numberline {5.1.4}HXDS Focal Plane System}{71}
\contentsline {subsubsection}{\numberline {5.1.4.1}HXDS translations}{71}
\contentsline {subsubsection}{\numberline {5.1.4.2}HSI in the Focal Plane}{71}
\contentsline {subsection}{\numberline {5.1.5}FPC and SSD in the Focal Plane}{71}
\contentsline {subsection}{\numberline {5.1.6}ACIS-2C}{71}
\contentsline {subsection}{\numberline {5.1.7}ACIS}{72}
\contentsline {subsection}{\numberline {5.1.8}HRC}{72}
\contentsline {section}{\numberline {5.2}Differences between XRCF and Flight}{73}
\contentsline {subsection}{\numberline {5.2.1}HETG Location at XRCF}{73}
\contentsline {subsection}{\numberline {5.2.2}HETG Orientation at XRCF}{74}
\contentsline {section}{\numberline {5.3}Summary of HETG XRCF Measurements}{75}
\contentsline {subsection}{\numberline {5.3.1}Efficiency Measurements}{75}
\contentsline {subsection}{\numberline {5.3.2}LRF Measurements}{75}
\contentsline {section}{\numberline {5.4}Examples of XRCF Data}{78}
\contentsline {section}{\numberline {5.5}Status of the HETG XRCF Analysis}{82}
\contentsline {chapter}{\numberline {6}XRCF LRF Measurements}{83}
\contentsline {section}{\numberline {6.1}Overview}{83}
\contentsline {section}{\numberline {6.2}Periods and Angles}{84}
\contentsline {subsection}{\numberline {6.2.1}Analysis Method}{84}
\contentsline {subsection}{\numberline {6.2.2}Results}{84}
\contentsline {section}{\numberline {6.3}LRF Core: Period and Roll Variations}{90}
\contentsline {subsection}{\numberline {6.3.1}Focus tests}{90}
\contentsline {subsection}{\numberline {6.3.2}1D Scans of LRF}{90}
\contentsline {subsection}{\numberline {6.3.3}Results}{90}
\contentsline {section}{\numberline {6.4}MEG Mis-Aligned Gratings}{94}
\contentsline {section}{\numberline {6.5}Between Core and Scatter}{97}
\contentsline {section}{\numberline {6.6}Scatter}{98}
\contentsline {subsection}{\numberline {6.6.1}Phase I HSI Data}{98}
\contentsline {subsection}{\numberline {6.6.2}HETG Scatter Tests with ACIS-2C}{99}
\contentsline {subsubsection}{\numberline {6.6.2.1}Setup}{99}
\contentsline {subsubsection}{\numberline {6.6.2.2}Reduction Details}{100}
\contentsline {subsubsection}{\numberline {6.6.2.3}Analysis Results}{103}
\contentsline {subsection}{\numberline {6.6.3}Interpretation of scattering profile results}{106}
\contentsline {section}{\numberline {6.7}Offaxis and Defocus Tests}{107}
\contentsline {section}{\numberline {6.8}ACIS-S Rowland Conformance}{108}
\contentsline {chapter}{\numberline {7}XRCF Efficiency and Effective Area Measurements}{109}
\contentsline {section}{\numberline {7.1}Overview}{109}
\contentsline {section}{\numberline {7.2}Alignment Tests}{110}
\contentsline {section}{\numberline {7.3}XRCF Source Characteristics}{112}
\contentsline {subsection}{\numberline {7.3.1}Source Spectra and Efficiency Measurements}{112}
\contentsline {subsection}{\numberline {7.3.2}Beam Uniformity Effects on Efficiency Measurements}{112}
\contentsline {section}{\numberline {7.4}Efficiency: Phase 1, Fixed Energies}{113}
\contentsline {subsection}{\numberline {7.4.1}System Effective Area}{113}
\contentsline {subsection}{\numberline {7.4.2}Optic Effective Area}{114}
\contentsline {subsection}{\numberline {7.4.3}Optic Effective Area Results}{114}
\contentsline {subsection}{\numberline {7.4.4}Grating Efficiency}{118}
\contentsline {subsection}{\numberline {7.4.5}Grating Efficiency Results}{118}
\contentsline {subsection}{\numberline {7.4.6}Effective Area / Efficiency Analysis Software}{118}
\contentsline {section}{\numberline {7.5}Efficiency: ACIS-2C Data}{121}
\contentsline {section}{\numberline {7.6}Efficiency: Phase 1, Monochromator Scans}{122}
\contentsline {section}{\numberline {7.7}Efficiency: Phase 2, Order Ratios}{123}
\contentsline {subsection}{\numberline {7.7.1}DCM-HETG-HRC-I Efficiency Ratio}{123}
\contentsline {section}{\numberline {7.8}Relative Effective Area: Molecular Contamination}{125}
\contentsline {subsection}{\numberline {7.8.1}HETGS Molecular Contamination Result}{125}
\contentsline {section}{\numberline {7.9}Effective Area with ACIS-S}{132}
\contentsline {section}{\numberline {7.10}Effective Area with HRC-I}{133}
\contentsline {part}{\uppercase {iii}\hspace {1em}Calibration Data and Products}{135}
\contentsline {chapter}{\numberline {8}Calibration Data}{137}
\contentsline {section}{\numberline {8.1}Synchrotron Data}{137}
\contentsline {section}{\numberline {8.2}HETG Facet Data}{137}
\contentsline {section}{\numberline {8.3}LR Data}{137}
\contentsline {section}{\numberline {8.4}X-GEF Data}{137}
\contentsline {section}{\numberline {8.5}HESS Design and Metrology Data}{137}
\contentsline {section}{\numberline {8.6}Alignment Data}{137}
\contentsline {section}{\numberline {8.7}XRCF Data}{137}
\contentsline {chapter}{\numberline {9}Calibration Products}{139}
\contentsline {section}{\numberline {9.1}Overview of Products}{139}
\contentsline {section}{\numberline {9.2}Fundamental Calibration Products for HETG}{141}
\contentsline {section}{\numberline {9.3}HETG Calibration Interface Products}{142}
\contentsline {subsection}{\numberline {9.3.1}Basic Parameters}{142}
\contentsline {subsection}{\numberline {9.3.2}Periods, Angles, and Spacing}{144}
\contentsline {subsection}{\numberline {9.3.3}Period and Roll Variation Parameters}{145}
\contentsline {subsection}{\numberline {9.3.4}Efficiency Products}{146}
\contentsline {subsection}{\numberline {9.3.5}{\bf MARX\nobreakspace {}}Parameters}{149}
\contentsline {subsubsection}{\numberline {9.3.5.1}{\bf MARX\nobreakspace {}}HETG LRF Parameters}{149}
\contentsline {subsubsection}{\numberline {9.3.5.2}{\bf MARX\nobreakspace {}}Rectangular Efficiency Parameters}{150}
\contentsline {subsubsection}{\numberline {9.3.5.3}{\bf MARX\nobreakspace {}}Efficiency Files}{153}
\contentsline {section}{\numberline {9.4}HETGS Calibration Interface Products}{154}
\contentsline {subsection}{\numberline {9.4.1}Resolving Power}{154}
\contentsline {subsection}{\numberline {9.4.2}Effective Area}{154}
\contentsline {subsection}{\numberline {9.4.3}XSPEC Response Matrices}{155}
\contentsline {chapter}{\hbox to\@tempdima {\hfil }Acronyms}{157}
\contentsline {chapter}{\hbox to\@tempdima {\hfil }Mathematical Symbols}{159}
\contentsline {chapter}{\hbox to\@tempdima {\hfil }Bibliography}{161}