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-\usepackage{cancel} -\usepackage{systeme} - -\title[Atmospheric Effects]{Atmospheric effects for gorund-based CMB observations} -\author[Mandelli S.]{Stefano Mandelli \\ \texttt{stefano.mandelli@unimi.it}} - -\date[STRIPConf]{24 - June - 2020} -\institute[UNIMI - INFN]{Universit\`a degli Studi di Milano - Istituto Nazionale di Fisica Nucleare} - -\titlegraphic{\includegraphics[scale=0.03]{ASI.png}\includegraphics[scale=0.03]{INFN.png}\,\,\,\,\,\includegraphics[scale=0.025]{UNIMI.png}} - -%\usetheme{AnnArbor} -\usetheme{Madrid} -%\usetheme{Warsaw} -%\usetheme{Copenhagen} -\useoutertheme[top]{sidebar} -\setbeamercovered{dynamic} -%\usecolortheme{albatross} -\usecolortheme{beetle} -%\usecolortheme{crane} -%\usecolortheme{dove} - - -\definecolor{airforceblue}{rgb}{0.36, 0.54, 0.66} -\definecolor{asparagus}{rgb}{0.53, 0.6, 0.42} -\definecolor{carmine}{rgb}{0.8, 0.0, 0.22} - -%\setbeamertemplate{blocks}[rounded][shadow=false] -%\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} - -\setbeamercolor*{block title}{fg=white, bg=airforceblue} -\setbeamercolor*{block body}{bg=lightgray, fg=black} - -\setbeamercolor*{block title example}{fg=white, bg=asparagus} -\setbeamercolor*{block body example}{bg=lightgray, fg=black} - -\setbeamercolor*{block title alerted}{fg=white, bg=carmine} -\setbeamercolor*{block body alerted}{bg=lightgray, fg=black} - -\begin{document} - -\begin{frame} - \maketitle -\end{frame} - -\begin{frame} - \frametitle{Index} - \centering - \tableofcontents -\end{frame} - -\section{Introduction} -\begin{frame} - \frametitle{The atmosphere's role in the CMB observation} - \onslide<1->\begin{block}{Atmospheric load in the microwave band} - \begin{itemize}[<+->] - \item Due to absorption / emission processes - \begin{itemize} - \item Water vapor - \item Oxygen molecules - \end{itemize} - \item The oxygen is well mixed in the atmosphere - \begin{itemize} - \item The increase of the optical load led to an increasing in the white noise level - \end{itemize} - \item The water vapor presents highly variable concentrations - \begin{itemize} - \item spurious $1/f$-like noise in the time-streams - \end{itemize} - \end{itemize} - \end{block} - - \onslide<8->\begin{alertblock}{Assessment of the scientific impact} - We have to create a model of the atmosphere and simulate its observation. We can start from the atmospheric dispersive proprieties - \end{alertblock} - - -\end{frame} - -\section{The Model} -\begin{frame} - \frametitle{The atmosphere as a dispersive medium} - \begin{columns} - \onslide<1->\begin{column}{0.6\textwidth} - \begin{itemize}[<+->] - \item Dispersive medium: $\varepsilon(\omega) = \varepsilon(\omega)_R + i \,\varepsilon(\omega)_I$ - - \item The contribute to complex permittivity are due mostly to the water vapor and the oxygen molecules that are dissolved in the atmosphere - - \item $\varepsilon(\omega)_R = \sqrt{n}$, and $\varepsilon(\omega)_I = \lambda \alpha / 4 \pi$ - \item The real and complex parts of $\varepsilon(\omega)$ are linked by the Kramers-Kr\"onig relations. - \item There is a relation also between the refractive index $n$ and the apsorption coefficient $\alpha$ - \end{itemize} - \end{column} - \onslide<1->\begin{column}{0.4\textwidth} - \onslide<5->\includegraphics[scale=0.18]{Abs_Coef.jpg} - \end{column} - \end{columns} -\end{frame} - - -\begin{frame} - \frametitle{Fluctuations in the refractive index} - \onslide<1->Refractive index fluctuations induce a change in the optical path length, and leds a two different systematic effects for interferometry or single dish, relatively - \begin{columns} - \begin{column}{0.55\textwidth} - \centering - \includegraphics[scale=0.4]{path32.png} - \textbf{Interferometer:} Phase fluctuations, degrade the interference pattern. - \end{column} - \begin{column}{0.45\textwidth} - \centering - \includegraphics[scale=0.4]{path33.png} - \textbf{Single-dish:} can cause fluctuations in the apparent pointing - \end{column} - - \end{columns} - \onslide<2->\begin{alertblock}{An interesting power-low relation} - There is a relations between the RMS phase fluctuations and the interference baseline $\langle\phi^2\rangle \sim D ^{5/3}$ [see S.E. Church paper] - \end{alertblock} -\end{frame} - -\begin{frame} - \frametitle{Fluctuations in the absorption coefficient} - \begin{columns} - \begin{column}{0.65\textwidth} - \begin{itemize}[<+->] - \item Atmospheric brightness temperature is related to $\alpha$: \only<1>{$T_B=\int_0^R\alpha(r)T_p(r)e^{-\tau'}\,dr$}\only<2-> {$T_B=\int_0^R\alpha(r)T_p(r)\cancel{e^{-\tau'}}\,dr$} - \item $e^{-\tau} \sim 1$, $\tau$ fluctuations are small compared to $\alpha$ - \item Antenna temperature: $T_A = \frac{1}{\lambda^2}\int_V A(\hat{r}_s, \vec{r})T_p(\vec{r})\frac{dV}{r^2}$ - \end{itemize} - \end{column} - \begin{column}{0.35\textwidth} - \includegraphics[scale=0.2]{Atmosphere.png} - \end{column} - \end{columns} - - \onslide<4->\begin{equation} - \langle T_A^2 \rangle = \frac{1}{\lambda^4}\int_V \frac{dV}{r^2}\int_{V'}\frac{dV'}{r'^2} A(\hat{r}_s, \vec{r})A(\hat{r'}_s, \vec{r'})T_p(\vec{r})T_p(\vec{r'})\langle\alpha(\vec{r}), \alpha(\vec{r'})\rangle\nonumber - \end{equation} - - \begin{alertblock}{Atmosphere structures} - \centering - The correlation term $\langle\alpha(r), \alpha(r')\rangle$ is unknown. - \end{alertblock} - -\end{frame} - -\begin{frame} - \frametitle{Characterizing the turbulent structure of the atmosphere} - \framesubtitle{\textcolor{gray}{Interferometric observation of the atmospheric structures}} - \begin{columns} - \begin{column}{0.75\textwidth} - \begin{itemize}[<+->] - \item Structural spatial function $D_n(r_1, r_2)=\langle[n(r_1)-n(r_2)]^2\rangle$ - \item Inner and outer correlation lengths $l_0$ and $L_0$ - \item Specific humidity $q$ - \begin{itemize} - \item Liquid (TQL) - \item Ice cristals (TQI) - \item Precipitable water vapor (TQV) - \end{itemize} - \item Ground temperature $T_0$ - \item Solar irradiation - \item Wind speed and direction - \end{itemize} - \end{column} - \begin{column}{0.25\textwidth} - \centering - \includegraphics[scale=0.4]{Energy.png} - \end{column} - \end{columns} - \onslide<10->\begin{exampleblock}{Structural spatial function for $n$} - \begin{equation} - \onslide<10->D(r_1, r_2) \propto L_0^{4/3} \left(\frac{dn}{dq}\frac{dq}{dz}\right)\lvert r_1 - r_2\rvert^{2/3} \propto C_0^2 \exp\left(-\frac{z}{z_0}\right)\nonumber - \end{equation} - \end{exampleblock} -\end{frame} - -\begin{frame} - \frametitle{Characterizing the turbulent structure of the atmosphere} - \framesubtitle{\textcolor{gray}{The structural spatial function for the atmospheric absorption coefficient}} - \begin{itemize}[<+->] - \item The refractive index and the absorption coefficient are linked by the KK relations - \item Same dependency from the atmospheric humidity $q$ - \item We can neglect second order term and consider $D_n = D_\alpha$ - \end{itemize} - \onslide<4->$D_\alpha(r_1,r_2) = \langle[\alpha(r_1)-\alpha(r_2)]^2\rangle$, using the correlation $B_\alpha(r_1, r_2) = \langle\alpha(r_1), \alpha(r_2)\rangle$ - \onslide<5->\begin{equation} - \begin{split} - D_\alpha(r_1, r_2)&=\langle[\alpha(r_1) -\alpha(r_2)]^2\rangle = B_\alpha(r_1, r_1) + B_\alpha(r_2, r_2) - 2\,B_\alpha(r_1, r_2) = \\ - &=C_\alpha^2\left(\frac{r_1+r_2}{2}\right)\lvert r_1 - r_2\rvert^{2/3} - \end{split}\nonumber - \end{equation} - - \onslide<6->\begin{equation} - B_\alpha(r_1, r_2) = \frac{1}{2} C_\alpha^2 \left(\frac{r_1+r_2}{2}\right) L_0^{2/3}\left(1-\frac{\lvert r_1 - r_2 \rvert^{2/3}}{L_0^{2/3}}\right)\nonumber - \end{equation} -\end{frame} - -\begin{frame} - \frametitle{Characterizing the turbulent structure of the atmosphere} - \framesubtitle{\textcolor{gray}{The structural spatial function for the atmospheric absorption coefficient}} - The $\langle\alpha(r_1),\alpha(r_2)\rangle$ expression - \begin{equation} - B_\alpha(r_1, r_2) = \frac{1}{2} C_\alpha^2 \left(\frac{r_1+r_2}{2}\right) L_0^{2/3}\left(1-\frac{\lvert r_1 - r_2 \rvert^{2/3}}{L_0^{2/3}}\right)\nonumber - \end{equation} - - can be written more general - - \begin{equation} - B_\alpha(r_1, r_2) = \frac{1}{2} C_\alpha^2\left(\frac{r_1+r_2}{2}\right)L_0^{2/3} b_\alpha(\lvert r_1 - r_2 \rvert) - \end{equation} - - \onslide<2->\begin{block}{Kolmogorov-Modified power spectrum} - \begin{equation} - b_\alpha(r) \propto \frac{1}{r}\int_{k_0}^{k_M} k \Phi(k) \sin(k\cdot r)\,dk - \end{equation} - \end{block} -\end{frame} - -\begin{frame} - \frametitle{Characterizing the turbulent structure of the atmosphere} - \framesubtitle{\textcolor{gray}{Different kind of $b_\alpha$ spectrum}} - \onslide<1->\begin{block}{Kolmogorov-Modified power spectrum} - \begin{equation} - b_\alpha(r) \propto \frac{1}{r}\int_{k_0}^{k_M} k \Phi(k) \sin(k\cdot r)\,dk - \end{equation} - \end{block} - - \begin{columns} - \begin{column}{0.5\textwidth} - \begin{itemize}[<+->] - \item Kolmogorov-Taylor model - \begin{itemize} - \item $\Phi(k) \propto k^{-11/3}$ - \item $k_0 = 1/L_0$ - \item $k_M=1/l_0$ - \end{itemize} - \item Gaussian-Like correlation - \begin{itemize} - \item $b_\alpha(\lvert r_1 - r_2\rvert) = \exp\left[-\frac{\lvert r_1 - r_2\rvert^2}{2(L_0/3)^2}\right]$ - \end{itemize} - \end{itemize} - \end{column} - \begin{column}{0.5\textwidth} - \centering - \includegraphics[scale=0.20]{Kol_Gauss.png}\\ - $L_0 = 100m$ - \end{column} - - \end{columns} -\end{frame} - -\begin{frame} - \frametitle{Temporal fluctuations in antenna temperature} - \framesubtitle{The rigid translation of the atmospheric structures by the wind} - \begin{equation} - T_A(t) = \frac{1}{\lambda^2}\int_{z_1}^{z_u}\iint_{-\infty}^{+\infty}\alpha(x,y,z)T_p(z)A(x-vt,y,z)\,\frac{dx\,dy\,dz}{z^2} - \end{equation} - - \begin{equation} - \begin{split} - \langle T_A(t), T_A(t+\tau) \rangle = &\frac{L_0^{2/3}}{2\pi}\int_{z_1}^{z_u}\frac{dZ}{w^2(Z)} C_\alpha^2(Z) T_p^2(Z) \iiint_{-\infty}^{+\infty}b_\alpha(\xi_x, \xi_y, \xi_z) \cdot \\ - &\cdot \exp\left[-\frac{(\xi_x+vt)^2+\xi_y^2}{w^2(Z)}\right] d\xi_x\,d\xi_y\,d\xi_z - \end{split} - \end{equation} - - \begin{equation} - S(\omega) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} \langle T_A(t), T_A(t+\tau) \rangle \exp(-i\omega\tau)\,d\tau - \end{equation} -\end{frame} - -\begin{frame} - \frametitle{Temporal fluctuations in antenna temperature} - \framesubtitle{The two-slope model} - \begin{equation} - \begin{split} - S(\omega) = &\frac{1}{2\sqrt{2\pi}}\frac{L^{2/3}_0}{v}\int_{z_1}^{z_u}\frac{dZ}{w(Z)}C_\alpha^2(Z)T^2_p(Z)\exp\left[-\frac{w^2(Z)\omega^2}{4v^2}\right]\cdot \\ - &\iiint_{-\infty}^{+\infty} \exp\left[\frac{i \xi_x \omega}{v}\right]\exp\left[-\frac{\xi_y^2}{w^2(Z)}\right]b_\alpha(\xi_x, \xi_y, \xi_z)\,d\xi_xd\xi_yd\xi_z - \end{split} - \end{equation} - - \begin{equation} - S(\omega) = \Phi(\omega/v) \cdot I(\omega/v) - \end{equation} - - \begin{columns} - \begin{column}{0.5\textwidth} - \begin{itemize} - \item If $W(Z) \gg L_0$ - \begin{itemize} - \item The exponential in $\xi_y$ vary slowly compared to $b_\alpha$ - \item Describe high altitude emission - \end{itemize} - \end{itemize} - \end{column} - \begin{column}{0.5\textwidth} - \begin{itemize} - \item If $W(Z) \ll L_0$ - \begin{itemize} - \item $b_\alpha$ vary slowly compared the exponential in $\xi_y$ - \item Describe low altitude emission - \end{itemize} - - \end{itemize} - \end{column} - - \end{columns} - -\end{frame} - - -\begin{frame} - \frametitle{Temporal fluctuations in antenna temperature} - \framesubtitle{The two-slope model} - \begin{columns} - \begin{column}{0.5\textwidth} - \begin{itemize} - \item If $W(Z) \gg L_0$ - \end{itemize} - \begin{center} - $\Phi\left(\frac{\omega}{v}\right)$ = $\left\lbrace \begin{array}{c c} \left(\frac{\omega}{v}\right)^{-11/3} & \frac{1}{L_0}\ll\left(\frac{\omega}{v}\right)\ll \frac{1}{l_0} \\ const. & \frac{\omega}{v}\ll \frac{1}{L_0} \end{array} \right.$ - \end{center} - \begin{itemize} - \item If $W(Z) \ll L_0$ - \end{itemize} - \begin{center} - $\Phi\left(\frac{\omega}{v}\right)$ = $\left\lbrace \begin{array}{c c} \left(\frac{\omega}{v}\right)^{-8/3} & \frac{1}{L_0}\ll\left(\frac{\omega}{v}\right)\ll \frac{1}{l_0} \\ const. & \frac{\omega}{v}\ll \frac{1}{L_0} \end{array} \right.$ - \end{center} - \end{column} - \begin{column}{0.5\textwidth} - \centering - \includegraphics[scale=0.35]{Figure_1.png} - \end{column} - - \end{columns} - -\end{frame} - -\section{Implementation} -\begin{frame} - \frametitle{CAL - CMB Atmospheric Library } -\end{frame} - -\section{Parameters} -\begin{frame} - \frametitle{The statistical approach based on MERRA and ERA data} -\end{frame} - - - - -% -% \section{Un esempio} -% \begin{frame} -% \frametitle{Un esempio} -% \begin{itemize}[<+->] -% \item One -% \item Two -% \item Three -% \end{itemize} -% \end{frame} -% -% \section{Diap due} -% \begin{frame} -% \frametitle{Diapositiva due} -% \framesubtitle{Sottotitolo alla diapositiva solitamente lungo} -% \end{frame} -% -% \section{Blocchi} -% \begin{frame} -% \frametitle{Esempi sull'utilizzo dei Blocchi} -% \begin{block}{Problemi Aperti} -% Simulazioni... -% \end{block} -% -% \begin{exampleblock}{Esempio} -% Questo \`e un esempio -% \end{exampleblock} -% -% \begin{alertblock}{Errore!} -% Notificare errori - punti critici -% \end{alertblock} -% -% \end{frame} -% -% \section{Immagine} -% \begin{frame} -% \begin{columns} -% \begin{column}{0.4\textwidth} -% \begin{figure} -% \centering -% Immagine dell'array di Horns -% \includegraphics[scale=0.2]{Horns.png} -% \end{figure} -% \end{column} -% \begin{column}{0.6\textwidth} -% Questa \`e la descrizione all'immagine. Le didascalie alle immagini -% vanno sempre organizzare con colonne. 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Come linea guida userò l'articolo di -Church 1995 in cui, anche se usando approssimazioni, parte da un modello di atmosfera -completo e matematicamente non banale per ottenere dei primi risultati analitici. - -Slide 2 -sono uno studente phd al secondo anno, lavoro insieme al gruppo di cosmologia osservativa -e sono principalmente collocato su due esperimenti entrambi con il principale scopo di -osservare la polarizzazione della radiazione di fondo cosmico a grandi scale angolari. -LiteBIRD è un satellite e la mia attività riguarda più che altro la calibrazione ottica e -la caratterizzazione elettromangetica del telescopio a media/alta frequenza e la -pianificazione delle strategie di calibrazione in-flight. - -LSPE/STRIP invece è un esperimento da terra sempre rivolto all'osservazione della -polarizzazione della CMB su grande scala angolare e mi occupo delle simulazioni di -sensibilità e della caratterizzazione delle sistematiche. - -Slide 3 -In questa presentazione, oltre ad una brevissima introduzione su cos'è la CMB, vedremo -il modello dispersivo dell'atmosfera presentato nel paper di church. Come il regime -turbulento dell'atmosfera crei delle strutture con diverso indice di rifrazione e -coefficiente di assorbimento e calcoleremo l'entità di queste fluttuazioni e la -loro evoluzione temporale. - -In conclusione vedremo le cose ongoing etcc... - -Slide 4 -La radiazione cosmica di fondo a microonde è una radiazione fossile, cioè rappresenta il -nostro universo quando questo aveva solo 380.000 anni. Durante questa età, l'universo era -sufficientemente freddo per permettere al plasma che vi era contenuto di formare materia -neutra, provocando una decisa diminuzione della sezione d'urto di thompson. In questo modo -i fotoni furoni liberi di propagare nello spazio libero. A causa dell'espansione -dell'universo, oggi vediamo quei fotoni con lunghezze d'onda nelle microonde e come una -radiazione di corpo nero a 2.7K, polarizzata linearmente e pressochè isotropa ed omogenea, -a meno di piccole anisotropie. - -Slide 5 - -Le anisotropie raccontano quella che è stata la storia del nostro universo prima del momento -del disaccoppiamento. Le anisotropie in intensità (temperatura) sono legate alle fluttuazioni -scalari del plasma primordiale, mentre lo studio della polarizzazione di cui una parte è legato strettamente -alle fluttuazioni tensoriali del plasma primordiale dovuta alla propagazione di onde -gravitazionali in un universo primordiale. - -Lo strumento quantitativo che viene usato per esprimere la statistica delle strutture del CMB -è lo spettro di potenza angolare. - -Slide 6 -Rappresenta lo spettro di potenza angolare in temperatura e polarizzazione. La polarizzazione -può essere decomposta in modi E e modi B e le linee in verde e blu identificano il modo in cui -andiamo a riconoscere nella volta celestre queste strutture ricorrenti. La polarizzazione -dei modi E è stata osservata con successo sin dai primi anni 90, mentre la polarizzazione -dei modi B non è stata ancora osservata, in blue viene rappresentato quello che dovebbe essere -il suo andamento teorico per un certo valore fissato del rapporto tensore-scalare. - -In un contesto in cui le informazioni cosmologiche vengono estratte dalle correlazioni angolari -che vediamo sulla mappa, è importante che tutto quello che introduce correlazione spuria -sia sotto controllo e ben caratterizzato. - -Slide 7 -Copertura in frequenza dei foregrounds // problema dell'atmosfera. - - -Slide 8 -Presentazione delle proprietà dispersive dell'atmosfera. Permittività complessa, indice di -rifrazione e coef. assorbimento, che sono legati tra loro dalle relazioni di K-K - -Il contributo maggiore alla dispersione è causato dall'ossigeno e dal vapor d'acqua che vi -sono mescolati o in sospensione. L'ossigeno fornisce un contributo smooth e non tende a -creare strutture spaziali particolarmente evidenti, il vapor acqueo si. - -Slide 9 -L'effetto delle fluttuazioni spaziali dell'indice di rifrazione è particolarmente evidente -negli esperimenti di interferometria. In questo caso con due elementi, la linea di vista -del primo intercetta zone con indice rifrazione diverso del secondo. Misure hanno mostrato -che le fluttuazioni di fase causate da questo effetto sono legate alla baseline dello -interferometro e seguono una legge di potenza. - -C'e`un effetto anche sugli esperimento a single-dish, in cui il beam subisce delle -distrosioni sempre diverse in funzione all'indice di rifrazione della bolla che intercetta, -provocando una incertezza sulla direzione massimo guadagno, e quindi sul puntamento. -Analisi sulle fluttuazioni di puntamento causate dalle fluttuazioni di indice di rifrazione -sono state fatte usando telescopi di grande diametro come l'IRAM o il JCMT. Si è mostrato che -per un beam size di circa un 1grado, e per lunghezze d'onda nell'ordine dei cm, l'incertezza -nel puntamento è di circa 10 arcsec, totalmente trascurabile. - - - -Slide 10 -Per gli espeimenti a single-dish il problema è legato soprattutto alle fluttuazioni di alpha -perchè ne dipende l'emissione dell'atmosfera. ...... Abbiamo zone quindi più brillanti e zone -meno brillanti la cui intensità non è trascurabile. - -Slide 11 - -conoscere la funzione di correlazione spaziale - -Slide 12 -costruzione della funzione di struttura per indice di rifrazione può suggerire come costruire -quella per alpha. - -Slide 13 -Funzione di struttura per alpha, che come obbiettivo quello di ricavare la funzione di correlazione - - -Slide 14 -si arriva alla funzzione di correlazione, possiamo rilassare la parte della dipendenza -dalla distanza alla 2/3 usando degli spettri più generici - - - - - - - - - - diff --git a/docs/presentation/Materiale_Esame_Bersanelli/figures_cmb_Cl.png b/docs/presentation/Materiale_Esame_Bersanelli/figures_cmb_Cl.png deleted file mode 100755 index 7f617912..00000000 Binary files a/docs/presentation/Materiale_Esame_Bersanelli/figures_cmb_Cl.png and /dev/null differ diff --git a/docs/presentation/Materiale_Esame_Bersanelli/intensity_map.png b/docs/presentation/Materiale_Esame_Bersanelli/intensity_map.png deleted file mode 100755 index 68ec28f0..00000000 Binary files a/docs/presentation/Materiale_Esame_Bersanelli/intensity_map.png and /dev/null differ diff --git a/docs/presentation/Materiale_Esame_Bersanelli/pol_map.png b/docs/presentation/Materiale_Esame_Bersanelli/pol_map.png deleted file mode 100755 index 5d61a4ab..00000000 Binary files a/docs/presentation/Materiale_Esame_Bersanelli/pol_map.png and /dev/null differ diff --git a/docs/presentation/Materiale_Esame_Bersanelli/pol_path.png b/docs/presentation/Materiale_Esame_Bersanelli/pol_path.png deleted file mode 100755 index 0432c8fc..00000000 Binary files a/docs/presentation/Materiale_Esame_Bersanelli/pol_path.png and /dev/null differ diff --git a/docs/presentation/Materiale_Esame_Bersanelli/rms.png b/docs/presentation/Materiale_Esame_Bersanelli/rms.png deleted file mode 100755 index b46209f1..00000000 Binary files a/docs/presentation/Materiale_Esame_Bersanelli/rms.png and /dev/null differ diff --git a/docs/presentation/Materiale_Esame_Bersanelli/rms_temp.png b/docs/presentation/Materiale_Esame_Bersanelli/rms_temp.png deleted file mode 100755 index 64a6dcd4..00000000 Binary files a/docs/presentation/Materiale_Esame_Bersanelli/rms_temp.png and /dev/null differ diff --git a/docs/presentation/UNIMI.png b/docs/presentation/UNIMI.png deleted file mode 100755 index aea2777b..00000000 Binary files a/docs/presentation/UNIMI.png and /dev/null differ diff --git a/docs/presentation/path32.png b/docs/presentation/path32.png deleted file mode 100755 index 4c27de50..00000000 Binary files a/docs/presentation/path32.png and /dev/null differ diff --git a/docs/presentation/path33.png b/docs/presentation/path33.png deleted file mode 100755 index dad0083e..00000000 Binary files a/docs/presentation/path33.png and /dev/null differ