Changeset 276 in ETALON for reconstruction

Timestamp:

Sep 23, 2015, 3:58:07 PM (9 years ago)

Author:

delerue

Message:

Typos corrected in the paper

Location:

reconstruction/long_paper3

Files:

• phase_reconstruction_paper.aux (modified) (1 diff)
• phase_reconstruction_paper.log (modified) (86 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.aux

@@ -11 +11 @@
 \@writefile{toc}{\contentsline {section}{Reconstruction methods}{1}}
 \@writefile{toc}{\contentsline {section}{Description of the simulations}{1}}
+\citation{E203prstab}
 \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Example of profiles giving very different $\chi ^2$ despite being relatively similar.   $\chi ^2_{\unhbox \voidb@x \hbox {sine noise}}=3.8219e-08, \chi ^2_{\unhbox \voidb@x \hbox {offset}}=7.2661e-08$; For profile with sine noise: FW0.1M=0.0241, FW0.2M=0.044 FWHM=0.0621 FW0.8M=0.1849 FW0.9M=0.3619. For offset profile all FWXM=0. \relax }}{2}}
 \providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}

reconstruction/long_paper3/phase_reconstruction_paper.log

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 Package epstopdf Info: Source file: <plots/52.eps>
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 Package epstopdf Info: Source file: <plots/61.eps>
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reconstruction/long_paper3/phase_reconstruction_paper.tex

@@ -55 +55 @@
 %
 \begin{abstract}
-Measurements of coherent radiation at accelerators typically give the absolute value of the beam profile Fourier transform but not its phase. Phase reconstruction techniques such as Hilbert transform or Kramers Kronig reconstruction are used to recover such phase. We report a study of the performances of these methods and how to optimize the reconstructed profiles. 
+Measurements of coherent radiation at accelerators typically gives the absolute value of the beam profile Fourier transform but not its phase. Phase reconstruction techniques such as Hilbert transform or Kramers Kronig reconstruction are used to recover such phase. We report a study of the performances of these methods and how to optimize the reconstructed profiles. 
 \end{abstract}
 
@@ -67 +67 @@
 \end{equation}
 
-where $I(\lambda)$ is the emitted intensity as a function of the wavelength.  $I_1(\lambda)$ is the intensity of the signal emitted by a single particle and $F(\lambda)$ is a form factor that encodes the longitudinal and transverse shape of the particle bunch. Recovering the longitudinal profile requires to invert this equation however this is not straightforward as the information about the phase of the form factor can not be measured and therefore is not available.
+where $I(\lambda)$ is the emitted intensity as a function of the wavelength $\lambda$.  $I_1(\lambda)$ is the intensity of the signal emitted by a single particle and $F(\lambda)$ is a form factor that encodes the longitudinal and transverse shape of the particle bunch. Recovering the longitudinal profile requires to invert this equation however this is not straightforward as the information about the phase of the form factor can not be measured and therefore is not available.
 
 A phase reconstruction algorithm must therefore be used to recover this phase. Several methods exist (see for example~\cite{KK}). 
@@ -164 +164 @@
 
 Different distributions have been used for the frequencies $\omega_i$: linear, logarithmic, triple-sine. 
-In most sampling schemes 33 frequencies were used to make it comparable with Triple-sine. These sampling scheme are defined as follow:
+In most sampling schemes we used 33 frequencies  to make it comparable with the Triple-sine distribution used in~\cite{E203prstab}. These sampling scheme are defined as follow:
 \begin{itemize}
 \item \textit{Triple-sine} This sampling matches that of the E-203 experiment at FACET~\cite{E203prstab}. Eleven detectors are located every $10^o$ around the interaction point and 3 different sets of wavelengths are used, giving the following distribution:
@@ -170 +170 @@
 \frac{c}{\omega_i}=l_n (1-cos(\Theta_i )) 
 \end{equation}
-with $l_n =50, 250, 1500 \mu m$ and $\Theta$ varying between $40^o$ and $140^o$ by steps of $10^o$.
+with $l_n =50, 250, 1500 \mu m$ and $\Theta_i$ varying between $40^o$ and $140^o$ by steps of $10^o$.
 %Uniform location of detectors in space corresponds to the inhomogeneous sampling frequency and vice versa. We cho
 %So next sampling is linear in frequecy.
@@ -456 +456 @@
 \end{equation}
  where $O_i$ is the observed value,  $O_i'$ is the observed value with noise, $n_i$ is a random number between 0 and 1 (all numbers between 0 and 1 being equiprobable), and $N_{max}$ is the 
-maximum noise for that simulation (depending on the case this can be 5\%, 10\%, 20\%, 30\%, 40\% or  50\%). This study was done using linear sampling with 33 samples  and 1000 simulated profiles for each noise value. The figure~\ref{noise} shows how the $\chi^2$ is modified when this noise component is added.
+maximum noise for that simulation (depending on the case this can be 5\%, 10\%, 20\%, 30\%, 40\% or  50\%). This study was done using linear sampling with 33 samples  and 1000 simulated profiles for each noise value. Figure~\ref{noise} shows how the $\chi^2$ is modified when this noise component is added.
  
 \begin{figure}[htbp]
@@ -470 +470 @@
 \section{Discussion}
 
-We performed extensive simulation to estimate the performance of two phase recovery methods in the case of multi-gaussian and lorenzian profiles. In both cases we found that when the sampling frequencies are chosen correctly  we obtained a good agreement between the original and reconstructed profiles (in most cases $\Delta_{FWXM} < 10\%$;  $\chi^2 ~ 10^{-6}$). This confirms that such methods are suitable to reconstruct the longitudinal profiles measured at particle accelerators using radiative methods.
-
-
-
-The other are grateful for the funding received from the French ANR (contract ANR-12-JS05-0003-01), the PICS (CNRS) "Development of the instrumentation for accelerator experiments, beam monitoring and other applications" and  Research Grant \#F58/380-2013 (project F58/04) from the State Fund for Fundamental Researches of Ukraine in the frame of the State key laboratory of high energy physics.
+We performed extensive simulation to estimate the performance of two phase recovery methods in the case of multi-gaussian and lorenzian profiles. In both cases we found that when the sampling frequencies are chosen correctly  we obtained a good agreement between the original and reconstructed profiles (in most cases $\Delta_{FWXM} < 10\%$;  $\chi^2 \sim 10^{-6}$). This confirms that such methods are suitable to reconstruct the longitudinal profiles measured at particle accelerators using radiative methods.
+
+
+
+The authors are grateful for the funding received from the French ANR (contract ANR-12-JS05-0003-01), the PICS (CNRS) "Development of the instrumentation for accelerator experiments, beam monitoring and other applications" and  Research Grant \#F58/380-2013 (project F58/04) from the State Fund for Fundamental Researches of Ukraine in the frame of the State key laboratory of high energy physics.
 
 \clearpage