\contentsline {chapter}{\hbox to\@tempdima {\hfil }Summary}{xix}
\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}{6}
\contentsline {subsection}{\numberline {1.3.1}Effective Area and Efficiency Definitions}{6}
\contentsline {subsection}{\numberline {1.3.2}Effective Area Calibration Goals}{7}
\contentsline {subsection}{\numberline {1.3.3}LRF Definition}{9}
\contentsline {subsection}{\numberline {1.3.4}LRF Calibration Goals}{9}
\contentsline {section}{\numberline {1.4}Ground Calibration Overview}{10}
\contentsline {section}{\numberline {1.5}HETG Documentation}{11}
\contentsline {part}{\uppercase {i}\hspace {1em}Physics, Models, and Laboratory Measurements}{13}
\contentsline {chapter}{\numberline {2}LRF Physics and Model}{15}
\contentsline {section}{\numberline {2.1}Rowland Geometry and Astigmatism}{15}
\contentsline {section}{\numberline {2.2}LRF Approximation: Resolving Power Error Budget}{18}
\contentsline {subsection}{\numberline {2.2.1}HRMA PSF}{21}
\contentsline {subsection}{\numberline {2.2.2}Rowland Astigmatism}{23}
\contentsline {subsection}{\numberline {2.2.3}Grating Period and Roll Variations}{23}
\contentsline {subsection}{\numberline {2.2.4}Aspect and Dither Blurs}{23}
\contentsline {subsection}{\numberline {2.2.5}Detector Blur}{24}
\contentsline {section}{\numberline {2.3}Ray-trace Software: {\bf MARX\nobreakspace {}}\nobreakspace {}}{25}
\contentsline {subsection}{\numberline {2.3.1}XRCF Simulations with {\bf MARX\nobreakspace {}}\nobreakspace {}}{25}
\contentsline {chapter}{\numberline {3}Efficiency Physics and Model}{27}
\contentsline {section}{\numberline {3.1}Diffraction Theory and Models}{27}
\contentsline {subsection}{\numberline {3.1.1}Scalar Diffraction Theory}{27}
\contentsline {subsection}{\numberline {3.1.2}Rectangular Models}{28}
\contentsline {subsection}{\numberline {3.1.3}Vertex Model}{29}
\contentsline {subsection}{\numberline {3.1.4}Tilted Grating Model}{30}
\contentsline {subsection}{\numberline {3.1.5}Trapezoidal Model}{30}
\contentsline {section}{\numberline {3.2}Synchrotron Measurements}{32}
\contentsline {subsection}{\numberline {3.2.1}Synchrotron Measurements Summary}{32}
\contentsline {subsection}{\numberline {3.2.2}Synchrotron Data Analysis Techniques}{32}
\contentsline {subsection}{\numberline {3.2.3}Gold Optical Constants and Edge Structure}{32}
\contentsline {subsection}{\numberline {3.2.4}Polyimide and Chromium Optical Constants and Edge Structure}{36}
\contentsline {subsection}{\numberline {3.2.5}Reference Grating Measurements}{40}
\contentsline {subsection}{\numberline {3.2.6}Error Estimates for X-GEF Predictions of Grating Efficiency}{44}
\contentsline {subsection}{\numberline {3.2.7}Synchrotron Analysis Status}{46}
\contentsline {section}{\numberline {3.3}Scattering Model}{47}
\contentsline {subsection}{\numberline {3.3.1}Introduction}{47}
\contentsline {subsection}{\numberline {3.3.2}General Formulation}{48}
\contentsline {subsection}{\numberline {3.3.3}Displacement Variations}{51}
\contentsline {subsection}{\numberline {3.3.4}Bar Geometry Variations}{52}
\contentsline {subsection}{\numberline {3.3.5}Correlations in the Rectangular Model}{54}
\contentsline {subsection}{\numberline {3.3.6}Discussion}{57}
\contentsline {subsection}{\numberline {3.3.7}Conclusion and Next Steps}{59}
\contentsline {section}{\numberline {3.4}Efficiency Software}{61}
\contentsline {chapter}{\numberline {4}Laboratory Measurements and Predictions}{63}
\contentsline {section}{\numberline {4.1}LR Measurements}{64}
\contentsline {subsection}{\numberline {4.1.1}LR Period and Roll Variations}{64}
\contentsline {subsection}{\numberline {4.1.2}LR Calibration using NIST Samples}{69}
\contentsline {section}{\numberline {4.2}X-GEF Measurements}{70}
\contentsline {subsection}{\numberline {4.2.1}Order Assymmetry and Tilt}{75}
\contentsline {subsection}{\numberline {4.2.2}Laboratory Efficiency Predictions}{75}
\contentsline {section}{\numberline {4.3}Alignment Measurements}{78}
\contentsline {section}{\numberline {4.4}Long-term: Vacuum Storage Gratings}{80}
\contentsline {section}{\numberline {4.5}Optical Transmission of the Gratings}{80}
\contentsline {part}{\uppercase {ii}\hspace {1em}X-Ray Calibration Facility Measurements and Analysis}{81}
\contentsline {chapter}{\numberline {5}XRCF and the HETG}{83}
\contentsline {section}{\numberline {5.1}XRCF Harware Introduction}{83}
\contentsline {subsection}{\numberline {5.1.1}XSS}{84}
\contentsline {subsection}{\numberline {5.1.2}Double Crystal Monochromator (DCM)}{84}
\contentsline {subsection}{\numberline {5.1.3}BNDs}{84}
\contentsline {subsection}{\numberline {5.1.4}HRMA, Gratings, and Shutters}{86}
\contentsline {subsection}{\numberline {5.1.5}HXDS Focal Plane System}{86}
\contentsline {subsubsection}{\numberline {5.1.5.1}HXDS Axes}{86}
\contentsline {subsubsection}{\numberline {5.1.5.2}HSI in the Focal Plane}{86}
\contentsline {subsubsection}{\numberline {5.1.5.3}FPC and SSD in the Focal Plane}{87}
\contentsline {subsection}{\numberline {5.1.6}ACIS-2C}{87}
\contentsline {subsection}{\numberline {5.1.7}ACIS}{87}
\contentsline {subsection}{\numberline {5.1.8}HRC}{87}
\contentsline {section}{\numberline {5.2}Differences between XRCF and Flight}{88}
\contentsline {subsection}{\numberline {5.2.1}HETG Location at XRCF}{88}
\contentsline {subsection}{\numberline {5.2.2}Rowland Spacing Mystery}{89}
\contentsline {subsection}{\numberline {5.2.3}HETG Orientation at XRCF}{89}
\contentsline {section}{\numberline {5.3}Overview of HETG XRCF Measurements}{91}
\contentsline {subsection}{\numberline {5.3.1}Measurements and the CMDB}{91}
\contentsline {subsection}{\numberline {5.3.2}Efficiency Measurements}{92}
\contentsline {subsection}{\numberline {5.3.3}LRF Measurements}{92}
\contentsline {section}{\numberline {5.4}HETG-ACIS-S Data at XRCF}{94}
\contentsline {section}{\numberline {5.5}Examples of XRCF Data}{96}
\contentsline {section}{\numberline {5.6}Status of the HETG XRCF Analysis}{100}
\contentsline {chapter}{\numberline {6}XRCF LRF Measurements}{101}
\contentsline {section}{\numberline {6.1}Overview}{101}
\contentsline {section}{\numberline {6.2}Periods and Angles}{102}
\contentsline {subsection}{\numberline {6.2.1}Analysis Method}{102}
\contentsline {subsection}{\numberline {6.2.2}Results}{102}
\contentsline {section}{\numberline {6.3}LRF Core: Period and Roll Variations}{108}
\contentsline {subsection}{\numberline {6.3.1}Zero-order effects}{108}
\contentsline {subsection}{\numberline {6.3.2}Focus tests}{109}
\contentsline {subsection}{\numberline {6.3.3}1D Scans of Mg-K LRF}{110}
\contentsline {subsection}{\numberline {6.3.4}LRF Measurements with the Flight Detectors}{114}
\contentsline {subsection}{\numberline {6.3.5}Results}{114}
\contentsline {section}{\numberline {6.4}MEG Mis-Aligned Gratings}{116}
\contentsline {subsection}{\numberline {6.4.1}Mis-aligned grating identification}{117}
\contentsline {subsection}{\numberline {6.4.2}Mis-aligned grating angles}{118}
\contentsline {section}{\numberline {6.5}Between Core and Scatter}{122}
\contentsline {section}{\numberline {6.6}Scatter Tests}{123}
\contentsline {subsection}{\numberline {6.6.1}Scattering Data and Results Overview}{123}
\contentsline {subsection}{\numberline {6.6.2}Phase I HSI Scattering Tests}{126}
\contentsline {subsection}{\numberline {6.6.3}ACIS-2C Scattering Tests: G-H2C-SC-88.00\{1-5\}}{128}
\contentsline {subsection}{\numberline {6.6.4}ACIS-S Scattering Tests: H-HAS-SC-7.002, 7.004, and 17.006}{137}
\contentsline {section}{\numberline {6.7}Offaxis and Defocus Tests}{138}
\contentsline {section}{\numberline {6.8}ACIS-S Rowland Conformance}{139}
\contentsline {subsection}{\numberline {6.8.1}Shutter Determination of Defocus}{139}
\contentsline {subsection}{\numberline {6.8.2}System Effects and Effective $f$-ratios}{141}
\contentsline {subsection}{\numberline {6.8.3}XRCF Data \& Coordinate Systems}{142}
\contentsline {subsubsection}{\numberline {6.8.3.1}Calculation of Centroids}{142}
\contentsline {subsubsection}{\numberline {6.8.3.2}Fitting Imaged Order Defocuses}{143}
\contentsline {subsubsection}{\numberline {6.8.3.3}Tests of Robustness}{146}
\contentsline {subsection}{\numberline {6.8.4}Discussion of Geometrical Approximations}{147}
\contentsline {subsection}{\numberline {6.8.5}{\bf MARX\nobreakspace {}}Simulations}{147}
\contentsline {subsection}{\numberline {6.8.6}Monte Carlo Simulations}{151}
\contentsline {subsection}{\numberline {6.8.7}Conclusions}{153}
\contentsline {chapter}{\numberline {7}XRCF Efficiency and Effective Area Measurements}{157}
\contentsline {section}{\numberline {7.1}Overview}{157}
\contentsline {subsection}{\numberline {7.1.1}Diffracted Order Sign Convention}{157}
\contentsline {subsection}{\numberline {7.1.2}Effective Area}{157}
\contentsline {subsection}{\numberline {7.1.3}Divide and Conquer}{160}
\contentsline {subsection}{\numberline {7.1.4}Order Ratios}{161}
\contentsline {subsection}{\numberline {7.1.5}Test Strategy and Overview}{161}
\contentsline {section}{\numberline {7.2}Alignment Tests}{163}
\contentsline {section}{\numberline {7.3}XRCF Source Characteristics}{165}
\contentsline {subsection}{\numberline {7.3.1}Source Spectra and Efficiency Measurements}{165}
\contentsline {subsection}{\numberline {7.3.2}Beam Uniformity Effects on Efficiency Measurements}{168}
\contentsline {section}{\numberline {7.4}Efficiency: Phase 1, EIPS Data}{169}
\contentsline {subsection}{\numberline {7.4.1}Introduction and Overview}{169}
\contentsline {subsection}{\numberline {7.4.2}Measurements and Example Data}{169}
\contentsline {subsection}{\numberline {7.4.3}Problems with Effective Area Analysis}{170}
\contentsline {subsection}{\numberline {7.4.4}Ray-trace Simulation of Phase 1 Measurements}{173}
\contentsline {subsection}{\numberline {7.4.5}Analysis Formalism}{175}
\contentsline {subsection}{\numberline {7.4.6}Count Rate Corrections}{175}
\contentsline {subsection}{\numberline {7.4.7}Region-of-interest (ROI) Analysis}{176}
\contentsline {subsection}{\numberline {7.4.8}JMKMOD ``counts-in-bump'' Analysis}{176}
\contentsline {subsection}{\numberline {7.4.9}JMKMOD ``counts-in-line'' Analysis}{178}
\contentsline {subsection}{\numberline {7.4.10}Discussion}{179}
\contentsline {section}{\numberline {7.5}Efficiency: Phase 1, Monochromator Data}{183}
\contentsline {section}{\numberline {7.6}Efficiency: ACIS-2C Data}{184}
\contentsline {section}{\numberline {7.7}Absolute Effective Area with ACIS-S}{185}
\contentsline {subsection}{\numberline {7.7.1}Approach and Data Sets}{185}
\contentsline {subsubsection}{\numberline {7.7.1.1}Effective Area Measurement Approach}{185}
\contentsline {subsubsection}{\numberline {7.7.1.2}DCM Measurement Set}{186}
\contentsline {subsubsection}{\numberline {7.7.1.3}Beam Normalization Data}{187}
\contentsline {subsection}{\numberline {7.7.2}ACIS-S/HETG Data Reduction}{187}
\contentsline {subsection}{\numberline {7.7.3}Pileup in the Data Sets}{188}
\contentsline {subsubsection}{\numberline {7.7.3.1}Pileup Basics}{188}
\contentsline {subsubsection}{\numberline {7.7.3.2}Demonstration: the Zero-order Data}{189}
\contentsline {subsubsection}{\numberline {7.7.3.3}Pileup in diffracted orders}{190}
\contentsline {subsection}{\numberline {7.7.4}Effective Area Results}{190}
\contentsline {subsubsection}{\numberline {7.7.4.1}Zero-order Effective Area}{190}
\contentsline {subsubsection}{\numberline {7.7.4.2}Plus-Minus Order Asymetry}{190}
\contentsline {subsubsection}{\numberline {7.7.4.3}1st and 3rd order effective areas for the MEG}{191}
\contentsline {subsubsection}{\numberline {7.7.4.4}1st and 2nd order effective areas for the HEG}{192}
\contentsline {subsection}{\numberline {7.7.5}Conclusions}{192}
\contentsline {section}{\numberline {7.8}Relative Effective Area: Molecular Contamination}{200}
\contentsline {subsection}{\numberline {7.8.1}Observations and Data Reduction}{200}
\contentsline {subsubsection}{\numberline {7.8.1.1}General}{200}
\contentsline {subsubsection}{\numberline {7.8.1.2}Event Processing}{201}
\contentsline {subsection}{\numberline {7.8.2}Formation and Interpretation of the Continuum Spectra}{203}
\contentsline {subsection}{\numberline {7.8.3}Comparison of Positive and Negative Sides}{207}
\contentsline {subsection}{\numberline {7.8.4}Conclusion and Further Investigations}{210}
\contentsline {section}{\numberline {7.9}Effective Area with HRC-I}{212}
\contentsline {subsection}{\numberline {7.9.1}HETG/HRC-I Tests at XRCF}{212}
\contentsline {subsection}{\numberline {7.9.2}Processing the HRC-I Data}{212}
\contentsline {subsubsection}{\numberline {7.9.2.1}Event selection criteria}{214}
\contentsline {subsubsection}{\numberline {7.9.2.2}Background Subtraction}{215}
\contentsline {subsubsection}{\numberline {7.9.2.3}Detector Uniformity}{215}
\contentsline {subsection}{\numberline {7.9.3}Plus/minus First Order Asymetry}{216}
\contentsline {section}{\numberline {7.10}Efficiency: High-Order Efficiency Measurements}{217}
\contentsline {subsection}{\numberline {7.10.1}Overview}{217}
\contentsline {subsection}{\numberline {7.10.2}HRC-I Data Sets}{217}
\contentsline {subsection}{\numberline {7.10.3}Discussion of HRC Order Ratios}{219}
\contentsline {subsection}{\numberline {7.10.4}ACIS-S/HETG Order Ratios}{222}
\contentsline {subsection}{\numberline {7.10.5}Discussion of ACIS-S/HETG Order Ratios}{225}
\contentsline {subsection}{\numberline {7.10.6}Conclusions}{226}
\contentsline {part}{\uppercase {iii}\hspace {1em}Calibration Data and Products}{227}
\contentsline {chapter}{\numberline {8}Calibration Data}{229}
\contentsline {section}{\numberline {8.1}Synchrotron Data}{229}
\contentsline {section}{\numberline {8.2}HETG Facet Data}{230}
\contentsline {section}{\numberline {8.3}LR Data}{230}
\contentsline {section}{\numberline {8.4}X-GEF Data}{230}
\contentsline {section}{\numberline {8.5}HESS Design and Metrology Data}{230}
\contentsline {section}{\numberline {8.6}Alignment Data}{230}
\contentsline {section}{\numberline {8.7}XRCF Data}{230}
\contentsline {chapter}{\numberline {9}Calibration Products}{231}
\contentsline {section}{\numberline {9.1}Overview of Products}{231}
\contentsline {section}{\numberline {9.2}Fundamental Calibration Products for HETG}{233}
\contentsline {section}{\numberline {9.3}HETG Calibration Interface Products}{234}
\contentsline {subsection}{\numberline {9.3.1}Basic Parameters}{234}
\contentsline {subsection}{\numberline {9.3.2}Periods, Angles, and Spacing}{236}
\contentsline {subsection}{\numberline {9.3.3}Period and Roll Variation Parameters}{237}
\contentsline {subsection}{\numberline {9.3.4}Efficiency Products}{238}
\contentsline {subsection}{\numberline {9.3.5}{\bf MARX\nobreakspace {}}Parameters}{241}
\contentsline {subsubsection}{\numberline {9.3.5.1}{\bf MARX\nobreakspace {}}HETG LRF Parameters}{241}
\contentsline {subsubsection}{\numberline {9.3.5.2}{\bf MARX\nobreakspace {}}Rectangular Efficiency Parameters}{242}
\contentsline {subsubsection}{\numberline {9.3.5.3}{\bf MARX\nobreakspace {}}Efficiency Files}{245}
\contentsline {section}{\numberline {9.4}HETGS Calibration Interface Products}{245}
\contentsline {subsection}{\numberline {9.4.1}Resolving Power}{245}
\contentsline {subsection}{\numberline {9.4.2}Effective Area}{245}
\contentsline {subsection}{\numberline {9.4.3}XSPEC Response Matrices}{246}
\contentsline {chapter}{\hbox to\@tempdima {\hfil }Acronyms}{248}
\contentsline {chapter}{\hbox to\@tempdima {\hfil }Mathematical Symbols}{251}
\contentsline {chapter}{\hbox to\@tempdima {\hfil }Bibliography}{253}