Changeset 264 in ETALON for reconstruction

Timestamp:

Sep 1, 2015, 5:19:42 PM (9 years ago)

Author:

hodnevuc

Message:

 

Location:

reconstruction/long_paper3

Files:

• phase_reconstruction_paper.aux (modified) (2 diffs)
• phase_reconstruction_paper.log (modified) (106 diffs)
• phase_reconstruction_paper.pdf (modified) (previous)
• phase_reconstruction_paper.synctex.gz (modified) (previous)
• phase_reconstruction_paper.tex (modified) (3 diffs)
• sep (added)
• sep/Np.eps (added)
• sep/f4.eps (added)
• sep/ss1-eps-converted-to.pdf (added)
• sep/ss1.eps (added)
• sep/ss2-eps-converted-to.pdf (added)
• sep/ss2.eps (added)

reconstruction/long_paper3/phase_reconstruction_paper.aux

@@ -24 +24 @@
 \citation{pchip}
 \citation{VBthesis}
-\citation{VBthesis,DESYthesis}
 \@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 the maximum number of detectors (blue and red dots on figure \ref  {lin12}).\relax }}{4}}
 \newlabel{biglin}{{5}{4}}
 \@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Effect of the sampling frequencies on the $\chi ^2$ (top) and $\Delta _{FWHM}$ (bottom). \relax }}{4}}
 \newlabel{sampling_chi2}{{6}{4}}
+\citation{VBthesis,DESYthesis}
 \citation{LaiS}
 \@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}}
@@ -34 +34 @@
 \@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}}
 \newlabel{lf2}{{8}{5}}
-\@writefile{toc}{\contentsline {section}{Study of the reconstruction performance}{5}}
-\citation{Pelliccia:2014vba}
 \@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}}
 \newlabel{hf}{{9}{6}}
 \@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}}
 \newlabel{hf2}{{10}{6}}
-\@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}}
-\newlabel{hf3}{{11}{6}}
-\@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}}
-\newlabel{good_profiles}{{12}{7}}
-\@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}}
-\newlabel{bad_profiles}{{13}{7}}
-\@writefile{toc}{\contentsline {section}{Discussion}{7}}
-\@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). }\relax }}{8}}
-\newlabel{profiles_stats_hilbert}{{14}{8}}
-\@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}}
-\newlabel{expKK}{{15}{8}}
-\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces $\Delta _{FWXM}$ for 1000 profiles with both methods.\relax }}{8}}
-\newlabel{fwxm}{{16}{8}}
-\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Original and reconstructed profile and their difference for bad profile (top) and good profile (bottom).\relax }}{8}}
-\newlabel{mod}{{17}{8}}
-\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Distribution of the $\chi ^2$ in the case of a lorenzian distribution. \relax }}{9}}
-\newlabel{lorenz}{{18}{9}}
-\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Mean $\chi ^2$ and $\Delta _{FWXM}$ as function of noise amplitude.\relax }}{9}}
-\newlabel{noise}{{19}{9}}
+\@writefile{toc}{\contentsline {section}{Study of the reconstruction performance}{6}}
+\@writefile{lof}{\contentsline {figure}{\numberline {11}{\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}}
+\newlabel{good_profiles}{{11}{6}}
+\citation{Pelliccia:2014vba}
+\@writefile{lof}{\contentsline {figure}{\numberline {12}{\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}}
+\newlabel{bad_profiles}{{12}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {13}{\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). }\relax }}{7}}
+\newlabel{profiles_stats_hilbert}{{13}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14}{\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}}
+\newlabel{expKK}{{14}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces $\Delta _{FWXM}$ for 1000 profiles with both methods.\relax }}{8}}
+\newlabel{fwxm}{{15}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Original and reconstructed profile and their difference for bad profile (top) and good profile (bottom).\relax }}{8}}
+\newlabel{mod}{{16}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Distribution of the $\chi ^2$ in the case of a lorenzian distribution. \relax }}{8}}
+\newlabel{lorenz}{{17}{8}}
+\@writefile{toc}{\contentsline {section}{Discussion}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Mean $\chi ^2$ and $\Delta _{FWXM}$ as function of noise amplitude.\relax }}{9}}
+\newlabel{noise}{{18}{9}}
 \bibcite{OTR_LURE}{1}
 \bibcite{ODR_Cianchi}{2}

reconstruction/long_paper3/phase_reconstruction_paper.log

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reconstruction/long_paper3/phase_reconstruction_paper.tex

@@ -214 +214 @@
 \begin{figure}[htbp]
  \centering
-  \includegraphics*[width=90mm]{rev1/hist1.eps} \\
-  \includegraphics*[width=90mm]{rev1/hist1fw.eps} 
+  \includegraphics*[width=90mm]{sep/ss1.eps} \\
+  \includegraphics*[width=90mm]{sep/ss2.eps} 
   \caption{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 the maximum number of detectors (blue and red dots on figure \ref{lin12}).}%VH add  picture 
    \label{biglin}
@@ -334 +334 @@
 \end{itemize}
 
-These HF extrapolation methods are compared on figure~\ref{hf} and~\ref{hf2}.
-
+These HF extrapolation methods are compared on figure~\ref{hf} and~\ref{hf2}.\par
+Thus, by virtue of the above arguments and simulations, It's naturally to choose the high-frequency extrapolation by power function. Constants of extrapolation functions are selected from crosslinking conditions above.
  
  
@@ -357 +357 @@
 
 
-\begin{figure}[htbp]
- \centering
-        \includegraphics*[width=65mm]{new203/HFLorenz.eps}\\
-          \includegraphics*[width=65mm]{rev4/hflor.eps}
-        \caption{Comparison of different HF extrapolation for Lorenzians~:histogram with mean $\chi^2$ (top) and $\Delta_{FWHM}$ (bottom).}
-   \label{hf3}
-\end{figure}
-
-
-
-\textbf{XXX If you show Lorenzian profiles for HF extrapolation why don't you also show it for LF extrapolation? XXX}
+%\begin{figure}[htbp]
+% \centering
+%        \includegraphics*[width=65mm]{new203/HFLorenz.eps}\\
+%          \includegraphics*[width=65mm]{rev4/hflor.eps}
+%        \caption{Comparison of different HF extrapolation for Lorenzians~:histogram with mean $\chi^2$ (top) and $\Delta_{FWHM}$ (bottom).}
+%   \label{hf3}
+%\end{figure}
+
+
+
+%\textbf{XXX If you show Lorenzian profiles for HF extrapolation why don't you also show it for LF extrapolation? XXX}