Changeset 306 in ETALON for reconstruction

Timestamp:

Dec 3, 2015, 11:43:55 PM (9 years ago)

Author:

delerue

Message:

Version of the phase reconstruction paper submitted to ArXiV

Location:

reconstruction/long_paper3

Files:

• phase_reconstruction_paper.log (modified) (87 diffs)
• phase_reconstruction_paper.pdf (modified) (previous)
• phase_reconstruction_paper.synctex.gz (modified) (previous)
• phase_reconstruction_paper.tex (modified) (6 diffs)

reconstruction/long_paper3/phase_reconstruction_paper.log

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reconstruction/long_paper3/phase_reconstruction_paper.tex

@@ -76 +76 @@
 
 When it is only possible to measure the amplitude of the complex signal, it is necessary to recover the phase of the available data. 
-We assume that the function of the longitudinal beam density is analytical.%VH question 4
+We assume that the function of the longitudinal beam density is analytical. 
 For an analytic function this is easier because the real and imaginary part are not completely independent.
 The Kramers-Kronig relations~\cite{KK} helps restore the imaginary part of an analytic function $\varepsilon(\omega)$ from its real part and vice versa.
@@ -103 +103 @@
 {\cal F}(\textit{H}(u))(\omega)=(-isgn(\omega)){\cal F}(u)(\omega),
 \end{equation}
-the calculation of phase can use optimised FFT code and is much faster than  calculating the Kramers-Kronig's integral.}%VH add text
+the calculation of phase can use an optimised FFT code and is therefore much faster than calculating the Kramers-Kronig's integral.}
 We implemented in Matlab these two different phase reconstruction methods. The Hilbert transform method has the advantage of being directly implemented in Matlab, allowing a much faster computing.
 
@@ -183 +183 @@
 \omega_0*exp(log(\omega_f/\omega_0)\times[0:1:32]/32).
 \end{equation}
-For this sampling also the first and last points are the same as in Triple-sine sampling. %This was done to avoid impact of extrapolations on result. 
-%Further we will see, that due to space limitations of detector size, only Triple-sine sapmling is physical, but this study will give us information which sampling and further detector position are preferable.
+For this sampling also the first and last points are the same as in Triple-sine sampling. 
 \end{itemize}
 {The study of the sampling is important, as it shows the  best position of the detectors and also  how to optimize the system. Linearly sampled spectrum gives the best result as shown in figure~\ref{samp}.
-%XXX WE need to discuss this XXX  This is not surprising, because in the process of profile recovery is present  interpolation procedure  for spectrum, which is well known works best with a uniform sampling.  
 }
 
@@ -195 +193 @@
     \includegraphics*[width=70mm]{plot1510/32.eps}
   %\includegraphics*[width=70mm]{newFig/lin27e203line203.eps} 
-  \caption{Comparison of different samplings with $\chi^2$ criterium (top) and $\Delta_{FWHM}$ (bottom).}%VH add  picture 
+  \caption{Comparison of different samplings with $\chi^2$ criterium (top) and $\Delta_{FWHM}$ (bottom).}
    \label{samp}
 \end{figure}
@@ -206 +204 @@
     \includegraphics*[width=70mm]{plots/42.eps}
   %\includegraphics*[width=70mm]{newFig/lin27e203line203.eps} 
-  \caption{Detector position for linear sampling for a minimal detector distance of $5^o$ (top) and $10^o$ (bottom) .}%VH add  picture 
+  \caption{Detector position for linear sampling for a minimal detector distance of $5^o$ (top) and $10^o$ (bottom) .} 
    \label{lin12}
 \end{figure}
@@ -218 +216 @@
   \includegraphics*[width=90mm]{plots/51.eps} \\
   \includegraphics*[width=90mm]{plots/52.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 in figure \ref{lin12}).}%VH add  picture 
+  \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 in figure \ref{lin12}).}
    \label{biglin}
 \end{figure}