From 660f86919ece2da910208f9f4a109c49e8c70a20 Mon Sep 17 00:00:00 2001 From: "lorenzo.zolfanelli93" Date: Wed, 26 Aug 2020 19:00:44 +0000 Subject: [PATCH] Update on Overleaf. --- chapters/3-methods.tex | 57 ++++++++++++++++++++++++++++++++++++----- images/PSD.pdf | Bin 0 -> 59339 bytes 2 files changed, 50 insertions(+), 7 deletions(-) create mode 100644 images/PSD.pdf diff --git a/chapters/3-methods.tex b/chapters/3-methods.tex index 7672027..3e17c1b 100644 --- a/chapters/3-methods.tex +++ b/chapters/3-methods.tex @@ -275,19 +275,62 @@ di posizioni delle trappole. Il codice si occupo di memorizzare le tracce temporali per ogni posizione spostare la trappola modificando la frequenza inviata agli AOM. -Dalle tracce temporali viene calcolata per ogni posizione di ciascuna -trappola la distribuzione spettrale di rumore, utilizzando i seguenti parametri +Le tracce temporali vengono acquisite per una durata di \SI{10}{\second} per ogni +posizione e una frequenza di campionamento di \SI{200}{kS/s}. +In seguito viene calcolata per ogni posizione di ciascuna +trappola la distribuzione spettrale di rumore, utilizzando un algoritmo +per la trasformata di Fourier veloce (\textit{Fast Fourier Transform}, FFT), +con i seguenti parametri riportati in tabella \ref{tab:fft_par}. -\begin{table}[] +\begin{table}[h] \centering - \begin{tabular}{c c} + \begin{tabular}{>{\bf}l l} + \toprule Accumulo medie & Metodo di Welch\cite{Welch1967} \\ - Finestra & + {\it Segmenti accumulati} & 32 \\ + {\it Lunghezza segmenti} & N/32 \\ + \midrule + Finestra & Hann \\ + \midrule + \bottomrule + \end{tabular} - \caption{Caption} - \label{tab:my_label} + \caption{Parametri FFT} + \label{tab:fft_par} \end{table} +Su ciascuno spettro viene eseguito un \textit{fit} per determinare +i valori di $\beta$ e $k$ imponendo i valori noti riportati in tabella \ref{tab:fit}. + +\begin{table}[h] + \centering + \begin{tabular}{l l l} + \toprule + Parametro & Simbolo & Valore \\ + \midrule + Raggio della sfera & $R$ & \SI{450}{\nm} \\ + Temperatura & $T$ & \SI{295}{\K} \\ + Distanza sfera da superificie & $d$ & \SI{1}{\um} \\ + Viscosità & $\eta$ & \SI{1e-3}{Pl} \\ + Coefficiente attrido idrodinamico & $\gamma$ & $6 \pi \eta R \left(1+\frac{9R}{16d}\right)$\\ + Frequenza minima & $\nu_\text{min}$ & \SI{15}{\Hz} \\ + Frequenza massima & $\nu_\text{max}$ & \SI{50}{\kHz} \\ + \bottomrule + \end{tabular} + \caption{Parametri $fit$ distribuzione spettrale} + \label{tab:tab:fit} +\end{table} + +In figura \ref{fig:psd} si riporta una distribuzione spettrale tipica +confrontata con la funzione teorica. + +\begin{figure} + \centering + \includegraphics{images/PSD.pdf} + \caption[scale=0.8]{Densità spettrale di rumore per la posizione di una trappola + ottica.} + \label{fig:psd} +\end{figure} \section{Retroazione AOM e \textit{force-clamp}} diff --git a/images/PSD.pdf b/images/PSD.pdf new file mode 100644 index 0000000000000000000000000000000000000000..51df2e5e57dc5feb8973caa23fa6f401c8782a57 GIT binary patch literal 59339 zcmY(qWmp_d)Ge9-2@)h&aJOKCdw?Xk4DL>V;KSe!!6Cuj3GVLh3=#$lI)ht~!Cf!! z`Odlb++Ve;o?2_|THQ}~mo$Tlq%=DhfER2IJEwY7P}sOABXe z?w1xdY7Pxgumv@TgsF?Eor5K{m>7ly$o#*Kg8vsl%ELuQ-Nn?!f|~b#K++B%7iymW ziB(KpTr8YG)O`O{F*sD59L&@$T&VS5bR?x;_$@qKs5#{9Uo^k|?^5D_mvYpG)Ew$o zrsmclOKSfAf$J!Lv#~I9p%(aGx%?m3)GVAGT%F8bZ2Zrs|JTOP!p zlXzF+@rh`4|N8l+)93l!{cgA4^USgT_vicL?)hW?Z_f`9hry?V>aHlwuINXY@lf|A zS9kKGw&xS#`RNKF?sI=BUf+G@&VQubHEs_UH!cJ``B50RZ~H%QpRZc@%(`KotWWsc zG$!x;jW^tXBgFD(eu26zu9xQ&$DJNiLJG9h^i}sudDeG$K4Z^DyLx3{RV 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