Changeset 248 in ETALON for reconstruction


Ignore:
Timestamp:
Jun 24, 2015, 10:51:37 PM (9 years ago)
Author:
hodnevuc
Message:
 
Location:
reconstruction/long_paper3
Files:
6 edited

Legend:

Unmodified
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Removed

  • reconstruction/long_paper3/jacow.cls

    r130 r248  
    192192  \RequirePackage{lmodern}
    193193  \RequirePackage{tgtermes}
    194   \RequirePackage{newtxmath}
     194 % \RequirePackage{newtxmath}
    195195 }
    196196

  • reconstruction/long_paper3/phase_reconstruction_paper.aux

    r215 r248  
    1717\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Effect of scaling the constraints on the parameters $\sigma _i$ (top) and $\mu _i$ (bottom) on the $\chi ^2$.\relax }}{2}}
    1818\newlabel{sigma_chi2}{{2}{2}}
    19 \newlabel{eq:lamb}{{7}{2}}
     19\newlabel{eq:lamb}{{7}{3}}
    2020\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Comparison of different samplings with $\chi ^2$ criterium (top) and $\Delta _{FWHM}$ (bottom)\relax }}{3}}
    2121\newlabel{samp}{{3}{3}}
    2222\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Detector position for linear sampling with $10^o$ (top) and $5^o$ (bottom) MDD.\relax }}{3}}
    2323\newlabel{lin12}{{4}{3}}
    24 \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Comparison of different sampling with number of MDD with $\chi ^2$ criterium (top) and $\Delta _{FWHM}$ (bottom). Ls is linear sampling with $1^o,5^o,10^0$ MDD and Ts is Triple sine sampling; mx mean the reconstruction use th maximum number of detectors (blue and red dots on figure \ref  {lin12})\relax }}{3}}
    25 \newlabel{biglin}{{5}{3}}
    2624\citation{pchip}
    2725\citation{VBthesis}
    2826\citation{VBthesis,DESYthesis}
    29 \citation{LaiS}
     27\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Comparison of different sampling with number of MDD with $\chi ^2$ criterium (top) and $\Delta _{FWHM}$ (bottom). Ls is linear sampling with $1^o,5^o,10^0$ MDD and Ts is Triple sine sampling; mx mean the reconstruction use th maximum number of detectors (blue and red dots on figure \ref  {lin12})\relax }}{4}}
     28\newlabel{biglin}{{5}{4}}
    3029\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Effect of the sampling frequencies on the $\chi ^2$ (top) and $\Delta _{FWHM}$ (bottom). \relax }}{4}}
    3130\newlabel{sampling_chi2}{{6}{4}}
     31\citation{LaiS}
    3232\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Comparison of different LF extrapolation: example of spectrum (top) and profile (bottom) and histogram with mean $\chi ^2$ for each method (bottom). Gaussian and Taylorian methods are described in the text. "Real LF spectrum" means that the real LF spectrum is used. For this simulation was used the Hilbert method of phase recovery and $A\omega ^B$ high frequency extrapolation.\relax }}{5}}
    3333\newlabel{lf}{{7}{5}}
    34 \@writefile{toc}{\contentsline {section}{Study of the reconstruction performance}{5}}
    3534\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Comparison of different LF extrapolation: histogram with mean $\chi ^2$ for each method (top) and $\Delta _{FWHM}$ (bottom). \relax }}{5}}
    3635\newlabel{lf2}{{8}{5}}
    37 \@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Comparison of different HF extrapolation~: example of spectrum (top) and profile (bottom). For these simulation was used the Hilbert reconstruction method of phase recovery and Gaussian LF extrapolations.\relax }}{5}}
    38 \newlabel{hf}{{9}{5}}
     36\@writefile{toc}{\contentsline {section}{Study of the reconstruction performance}{5}}
    3937\citation{Pelliccia:2014vba}
     38\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Comparison of different HF extrapolation~: example of spectrum (top) and profile (bottom). For these simulation was used the Hilbert reconstruction method of phase recovery and Gaussian LF extrapolations.\relax }}{6}}
     39\newlabel{hf}{{9}{6}}
    4040\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Comparison of different HF extrapolation for Gaussian~:histogram with mean $\chi ^2$ (top) and $\Delta _{FWHM}$ (bottom).\relax }}{6}}
    4141\newlabel{hf2}{{10}{6}}
    4242\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Comparison of different HF extrapolation for Lorenzians~:histogram with mean $\chi ^2$ (top) and $\Delta _{FWHM}$ (bottom).\relax }}{6}}
    4343\newlabel{hf3}{{11}{6}}
    44 \@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Examples of well reconstructed profile. The original profile is in blue and the profiles reconstructed with the Hilbert transform and the full Kramers-Kronig procedures are in red and black respectively.\relax }}{6}}
    45 \newlabel{good_profiles}{{12}{6}}
     44\bibcite{OTR_LURE}{1}
     45\bibcite{ODR_Cianchi}{2}
     46\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Examples of well reconstructed profile. The original profile is in blue and the profiles reconstructed with the Hilbert transform and the full Kramers-Kronig procedures are in red and black respectively.\relax }}{7}}
     47\newlabel{good_profiles}{{12}{7}}
     48\@writefile{toc}{\contentsline {section}{Discussion}{7}}
    4649\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Example of poorly reconstructed profile. The original profile is in blue and the profiles reconstructed with the Hilbert transform and the full Kramers-Kronig procedures are in red and black respectively.\relax }}{7}}
    4750\newlabel{bad_profiles}{{13}{7}}
    48 \@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces {$\Delta _{FWHM}$ (top) and $\chi ^2$ (bottom) distribution of 1000 simulations reconstructed using the Hilbert transform method (black line) and Kramers-Kronig reconstruction method (red line). XXX If the top figure is delta FWHM, then the title should say so XXX }\relax }}{7}}
    49 \newlabel{profiles_stats_hilbert}{{14}{7}}
    50 \@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Example of reconstructed profile with zooms on the peak and tails. One can see that the profile reconstructed using the Kramers-Kronig method has a negative component. This will dominate the final $\chi ^2$ and explains why the $\chi ^2$ obtained by this method is higher as shown on figure~\ref  {profiles_stats_hilbert}.\relax }}{7}}
    51 \newlabel{expKK}{{15}{7}}
    52 \@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces $\Delta _{FWXM}$ for 1000 profiles with both methods.\relax }}{7}}
    53 \newlabel{fwxm}{{16}{7}}
    54 \bibcite{OTR_LURE}{1}
    55 \bibcite{ODR_Cianchi}{2}
    5651\bibcite{Doucas_ESB}{3}
    5752\bibcite{KK}{4}
    … …  
    6156\bibcite{pchip}{8}
    6257\bibcite{LaiS}{9}
     58\bibcite{DESYthesis}{10}
     59\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces {$\Delta _{FWHM}$ (top) and $\chi ^2$ (bottom) distribution of 1000 simulations reconstructed using the Hilbert transform method (black line) and Kramers-Kronig reconstruction method (red line). XXX If the top figure is delta FWHM, then the title should say so XXX }\relax }}{8}}
     60\newlabel{profiles_stats_hilbert}{{14}{8}}
     61\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Example of reconstructed profile with zooms on the peak and tails. One can see that the profile reconstructed using the Kramers-Kronig method has a negative component. This will dominate the final $\chi ^2$ and explains why the $\chi ^2$ obtained by this method is higher as shown on figure~\ref  {profiles_stats_hilbert}.\relax }}{8}}
     62\newlabel{expKK}{{15}{8}}
     63\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces $\Delta _{FWXM}$ for 1000 profiles with both methods.\relax }}{8}}
     64\newlabel{fwxm}{{16}{8}}
    6365\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Original and reconstructed profile and their difference for bad profile (top) and good profile (bottom).\relax }}{8}}
    6466\newlabel{mod}{{17}{8}}
    65 \@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Distribution of the $\chi ^2$ in the case of a lorenzian distribution. XXX Can you add delta FWHM? XXX\relax }}{8}}
    66 \newlabel{lorenz}{{18}{8}}
    67 \@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Mean $\chi ^2$ as function of noise amplitude. XXX Can you add delta FWHM? XXX\relax }}{8}}
    68 \newlabel{noise}{{19}{8}}
    69 \@writefile{toc}{\contentsline {section}{Discussion}{8}}
    70 \bibcite{DESYthesis}{10}
     67\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Distribution of the $\chi ^2$ in the case of a lorenzian distribution. \relax }}{9}}
     68\newlabel{lorenz}{{18}{9}}
     69\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Mean $\chi ^2$ and $\Delta _{FWXM}$ as function of noise amplitude.\relax }}{9}}
     70\newlabel{noise}{{19}{9}}

  • reconstruction/long_paper3/phase_reconstruction_paper.log

    r215 r248  
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     2240ype1/public/tex-gyre/qtmri.pfb>
     2241Output written on phase_reconstruction_paper.pdf (9 pages, 544328 bytes).
    21322242PDF statistics:
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     2243 539 PDF objects out of 1000 (max. 8388607)
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    2137 
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     2247

  • reconstruction/long_paper3/phase_reconstruction_paper.tex

    r215 r248  
    55              ]{jacow}
    66%\usepackage{lineno}
    7 
     7\usepackage{mathtools}
    88\makeatletter%                           % test for XeTeX where the sequence is by default eps-> pdf, jpg, png, pdf, ...
    99\ifboolexpr{bool{xetex}}                 % and the JACoW template provides JACpic2v3.eps and JACpic2v3.jpg which might generates errors
    … …  
    136136   \label{Offsine}
    137137\end{figure}
    138 To ensure that the choice of the parameters $\sigma_i$ and $\mu_i$ for the simulations does not biais significantly the results, their value has been varied and this is shown on figure~\ref{sigma_chi2} XXX can you add FWHM ? XXX.
    139 
    140 \begin{figure}[htbp]
    141  \centering
    142   \includegraphics*[width=70mm]{newfigures/chi_sigma.eps}\\
    143   \includegraphics*[width=70mm]{newfigures/chi_mu.eps}%add new figure
     138To ensure that the choice of the parameters $\sigma_i$ and $\mu_i$ for the simulations does not biais significantly the results, their value has been varied and this is shown on figure~\ref{sigma_chi2}.
     139
     140\begin{figure}[htbp]
     141 \centering
     142  \includegraphics*[width=70mm]{del24/muCHI.eps}\\
     143  \includegraphics*[width=70mm]{del24/muFW.eps}\\
     144  \includegraphics*[width=70mm]{del24/sigCHI.eps}\\
     145  \includegraphics*[width=70mm]{del24/sigFW.eps}\\
    144146  \caption{Effect of scaling the constraints on the parameters $\sigma_i$ (top) and $\mu_i$ (bottom) on the $\chi^2$.}
    145147   \label{sigma_chi2}
    … …  
    242244
    243245The other extrapolation method is based on Taylor expansion with the following definition:
    244 \begin{multline}
     246\begin{equation}
     247\begin{split}
    245248F(\omega)=\int_0^\infty dtS(t)e^{-i(\omega t)}
    246249=\int_0^\infty dtS(t) \sum_{k=0}^{\infty}\frac{(-i\omega t)^k}{k!}=\\
    247250= \sum_{k=0}^{\infty} \left(\frac{(-i\omega)^k}{k!} \int_0^\infty dtS(t)t^k\right)
    248251=\sum_{k=0}^{\infty} \left(\frac{(-i\omega)^k}{k!} <t^k>\right)
    249 \end{multline}
     252\end{split}
     253\end{equation}
     254
     255 
    250256
    251257Approximation to the 4th order gives the following LF extrapolation:
    … …  
    419425\begin{figure}[htbp]
    420426 \centering
    421   \includegraphics*[width=70mm]{THPME088f9.eps} \\
     427  \includegraphics*[width=70mm]{del24/chiL} \\
     428  \includegraphics*[width=70mm]{del24/FWL} \\
    422429%  \includegraphics*[width=75mm]{THPME088f10.eps}
    423   \caption{Distribution of the $\chi^2$ in the case of a lorenzian distribution. XXX Can you add delta FWHM?  XXX}
     430  \caption{Distribution of the $\chi^2$ in the case of a lorenzian distribution. }
    424431   \label{lorenz}
    425432\end{figure}
    … …  
    436443\begin{figure}[htbp]
    437444 \centering
    438   \includegraphics*[width=70mm]{newfigures/new2/noise.eps}\\
    439   \caption{Mean $\chi^2$ as function of noise amplitude. XXX Can you add delta FWHM?  XXX}
     445  \includegraphics*[width=70mm]{del24/noiseCHI.eps}\\
     446  \includegraphics*[width=70mm]{del24/noiseFW.eps}\\
     447  \caption{Mean $\chi^2$ and $\Delta_{FWXM}$  as function of noise amplitude.}
    440448   \label{noise}
    441449\end{figure}
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