\relax \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}The HESSI Imager}{1}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Expected Imaging Capabilities}{2}} \newlabel{imager_schematic}{{1.1}{3}} \@writefile{toc}{\contentsline {section}{\numberline {2}Modulation Principles}{4}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}One-dimensional Modulation}{4}} \newlabel{slit_pitch_effect}{{2.1}{6}} \newlabel{count_1}{{2}{7}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Rotational Modulation}{8}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}The HESSI Event List}{9}} \newlabel{S_ijk}{{7}{9}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Visibilities}{9}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Count Rates and Visibilities}{10}} \newlabel{c_series}{{10}{10}} \newlabel{vis_1}{{13}{11}} \newlabel{vis_2}{{15}{11}} \newlabel{count_2}{{16}{11}} \newlabel{V_count}{{17}{12}} \newlabel{vis_3}{{18}{12}} \newlabel{count_3}{{19}{12}} \newlabel{v_count_n}{{20}{12}} \@writefile{toc}{\contentsline {section}{\numberline {3}Image Reconstruction}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Linear Methods: Backprojection and Fourier Transforms}{13}} \newlabel{D_m}{{21}{13}} \newlabel{W_im}{{22}{13}} \newlabel{O_pred}{{23}{13}} \newlabel{D_m_pred}{{24}{13}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Nonlinear Reconstruction Methods}{14}} \newlabel{bproj_fig}{{3.1}{15}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.1}CLEAN (Cartesian, Polar)}{16}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2}Maximum Entropy Methods (MEM Sato, Polar MEM)}{17}} \newlabel{clean_fig}{{3.2.1}{18}} \newlabel{mem_fig}{{3.2.2}{19}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.3}Forward Fitting (pixelized, non-pixelized)}{19}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.4}The PIXON Method}{20}} \newlabel{pixon_fig}{{3.2.4}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Undeveloped Techniques}{22}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}Wavelets}{22}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2}Non-Negative Least Squares}{22}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.3}Two-Dimensional Autocorrelation}{22}} \@writefile{toc}{\contentsline {section}{\numberline {4}Statistical Limits}{22}} \newlabel{ansatz}{{31}{23}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Fourier Coefficient Distribution}{23}} \newlabel{cos}{{34}{23}} \newlabel{sin}{{34}{23}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Regularization}{24}} \newlabel{regularization}{{4.2}{25}} \@writefile{toc}{\contentsline {section}{\numberline {5}Figure Captions}{26}} \@writefile{toc}{\contentsline {section}{\numberline {6}Appendix}{29}}