From 78c36509144339974960e0d70a5a96313ad7dbe7 Mon Sep 17 00:00:00 2001 From: Lorenzo Zolfanelli Date: Sun, 11 Oct 2020 19:35:33 +0200 Subject: [PATCH] incluse correzioni Capitans CAP 3 --- chapters/1-introduction.tex | 6 +- chapters/2-setup.tex | 4 +- chapters/3-methods.tex | 97 +++++-- images/aom.pdf | Bin 39242 -> 39077 bytes images/bfp.pdf | Bin 11530 -> 22496 bytes images/radial_intensity.pdf | Bin 49329 -> 43708 bytes images/z-est.pdf | Bin 21110 -> 17248 bytes images_src/aom.svg | 14 +- images_src/bfp.svg | 529 +++++++++++++++++++++++++++++++++++- 9 files changed, 602 insertions(+), 48 deletions(-) diff --git a/chapters/1-introduction.tex b/chapters/1-introduction.tex index 7897104..a7e24aa 100644 --- a/chapters/1-introduction.tex +++ b/chapters/1-introduction.tex @@ -136,7 +136,7 @@ rispetto alla zona illuminata nelle vicinanze del vetrino coprioggetti. Scopo dell'apparato sperimentale sarà anche studiare la possibilità di superare questo limite usando la sfera dielettrica come risuonatore -o foceggiatore ottico, e quindi come strumento in grado di trasferire la radiazione +o focheggiatore ottico, e quindi come strumento in grado di trasferire la radiazione di eccitazione dall'immediata prossimità del vetrino coprioggetti ai fluorofori presenti in prossimità del sito di interazione. In questo modo il segnale proveniente da molecole fuori fuoco, @@ -228,7 +228,7 @@ di actina del citoscheletro. Oltre a questa connessione diretta esistono altre proteine che mantengono una connessione indiretta, legando ad esempio le catenine -con il citoscheletro. É stato scoperto +con il citoscheletro. È stato scoperto \cite{Goldmann2016,Dumbauld2014} che le proteine \emph{vinculina} e \emph{$\alpha$-actinina} svolgono questa attività. @@ -481,7 +481,7 @@ scattering e una energia cinetica delle particelle intrappolate sufficientemente bassa (quindi un fluido sufficientemente viscoso). Per le nostre applicazioni è sufficiente considerare, su un piano -perpendicolare alla dirazione di propagazione del fascio, una forza di +perpendicolare alla direzione di propagazione del fascio, una forza di richiamo del tipo: \begin{equation} diff --git a/chapters/2-setup.tex b/chapters/2-setup.tex index 3d41005..c5c1a45 100644 --- a/chapters/2-setup.tex +++ b/chapters/2-setup.tex @@ -65,7 +65,7 @@ a stato solido Nd:YAG con emissione a \SI{1064}{\nm}. Per la microscopia di fluorescenza si usano per l'eccitazione sorgenti laser a diodo alle lunghezze d'onda di \SIlist{488;532;635}{\nm} e l'emissione dei fluorofori fino a \SI{700}{\nm} può essere raccolta -e disaccopiata dall'illuminazione a luce trasmessa. +e disaccoppiata dall'illuminazione a luce trasmessa. Tuttavia, la necessità di ottenere una sensibilità di singola molecola rende particolarmente critica la scelta delle caratteristiche @@ -168,7 +168,7 @@ i protocolli di comunicazione GCS per i moduli Physik Instrumente e GC \cite{gclib} per il modulo Galil Motion Control. Per semplificare l'utilizzo dei tre gli attuatori durante -la manipolazione di un campione è stato propgramma +la manipolazione di un campione è stato programma in ambiente LabVIEW che implementa i protocolli di comunicazione richiesti (\texttt{Joystick Control}). In particolare il codice sviluppato consente di utilizzare diff --git a/chapters/3-methods.tex b/chapters/3-methods.tex index aa88ba4..e067f7e 100644 --- a/chapters/3-methods.tex +++ b/chapters/3-methods.tex @@ -12,11 +12,14 @@ del nanometro, precludendo la possibilità di poter eseguire misurazioni di forza con la sensibilità del \si{pN}. Gli effetti più evidenti e rilevabili sono rapide oscillazioni della -posizione del campione dovute a vibrazioni acustiche residue e, quando -queste non vengono corrette, una -progressiva deriva rispetto alla posizione fissata che diventa -significativa ($> \SI{100}{\nm}$) per tempi di osservazione di -diversi minuti. +posizione del campione dovute a vibrazioni acustiche residue e, +in aggiunta a queste, una più lenta deriva della posizione dovuta +alla dilatazione o alla compressione delle strutture del microscopio +in conseguenza delle fluttuazioni termiche. +Senza alcuna correzione, sono sufficienti fluttuazioni termiche +dell'ordine dei decimi di grado per causare, su tempi di osservazione +di qualche minuto, una significativa e progressiva deriva rispetto +alla posizione iniziale ($> \SI{100}{\nm}$). Per quantificare quest'effetto viene usato un apposito campione in cui diverse microsfere in silice, di diametro \SI{0.5}{\um}, vengono @@ -29,8 +32,10 @@ in dettaglio nell'appendice \ref{app:protocols}, protocollo Le microsfere immobilizzate nel campione possono essere messe a fuoco e visualizzate attraverso il sistema di microscopia a luce trasmessa. Una volta selezionata e messa a fuoco una microsfera, analizzando -l'immagine prodotta da uno dei due sensori CMOS è possibile calcolare -le coordinate (in pixel) del suo centroide: +l'immagine prodotta da uno dei due sensori CMOS è possibile, dopo aver +filtrato i pixel con una soglia d'intensità ($I_S$) determinate empiricamente, +in modo da non considerare il segnale residuo nello sfondo, calcolare +le coordinatedel suo centroide: \begin{equation} (x_{cen}, y_{cen}) = @@ -40,7 +45,11 @@ le coordinate (in pixel) del suo centroide: \sum_{(x, y)} I(x, y) } \end{equation} - + +La sommatoria si intende estesa a tutti i pixel con coordinate $(x, y)$ +dell'immagine che verificano la condizione di soglia $I(x, y) > I_s$. +$I(x, y)$ è l'intensità del pixel misurata in unità del CMOS. + Per evitare di considerare altre microsfere o imperfezioni sul campione si sceglie di effettuare il calcolo del centroide limitando la regione dell'immagine utilizzata a un rettangolo nel quale una microsfera è @@ -48,9 +57,9 @@ sufficientemente isolata. Ricalcolando il centroide a intervalli temporali fissati è possibile osservare la deriva della posizione (x, y) della microsfera. -Inoltre si ha la possibilità sfruttare questo stesso campione per effettuare -una calibrazione del fattore di conversione pixel/nm lungo due assi -ortogonali. +Inoltre si ha la possibilità di sfruttare questo stesso campione per effettuare +una calibrazione del fattore di conversione pixel/nm della telecamera +lungo due assi ortogonali. Per effettuare la calibrazione, dopo aver calcolato il centroide della microsfera, si sposta la posizione dal campione lungo uno dei @@ -72,18 +81,22 @@ radiale della luce diffusa dalla microsfera. In figura \ref{fig:radial_itensity} è rappresentato l'andamento del profilo radiale che si ottiene variando la quota del piano focale (z). +Il profilo radiale è stato calcolato, dopo aver determinato il centroide +della microsfera, per ogni valore intero di $r$, come la media delle +intensità dei pixel la cui distanza dal centro (approssimata all'intero +più vicino) sia uguale a $r$. \begin{figure}[ht] \centering \includegraphics{images/radial_intensity.pdf} \caption{Profilo di intensità radiale rispetto al centroide - per una microsfera, in diversi piani } + per una microsfera, in diversi piani.} \label{fig:radial_itensity} \end{figure} Da questi dati è stato possibile osservare che il rapporto tra l'intensità integrata in un anello centrato sulla microsfera e quella -integrata nella regione interna al medesimo anello (regioni gialle -e arancioni in figura), mostra un andamento proporzionale alla quota +integrata nella regione interna al medesimo anello (regioni arancioni +e gialle in figura), mostra un andamento proporzionale alla quota del piano focale in un certo intorno del centro della sfera. In figura \ref{fig:z_est} viene mostrato l'andamento del rapporto @@ -107,6 +120,25 @@ una calibrazione spostando il campione di una quota controllata attraverso il traslatore piezoelettrico dell'obiettivo, e costruire una curva di calibrazione come quella in figura \ref{fig:z_est}. +La curva in figura \ref{fig:z_est} è stata realizzata acquisendo dieci +immagini per ciascuna quota e campionando la quota a passi di 300 +nm. Per la regione in cui l’andamento è lineare (delimitata tra le +barre rosse in figura, tra \SI{2.8}{\um} e \SI{5.6}{\um}) è stato +eseguito un fit lineare ottenendo i seguenti parametri: + +\begin{table}[ht] + \centering + \begin{tabular}{ l l l } + \toprule + {\it Nome parametro} & {\it Valore} & {\it Err. percentuale}\\ + \midrule + Costante & $(0.9520\pm0.0025)$ & 0.26\% \\ + Pendenza & $(0.0206\pm0.0006)\si{\um^{-1}}$ & 2.9\% \\ + \bottomrule + \end{tabular} + \caption{Parametri del fit per la determinazione di z a partire dalle immagini.} +\end{table} + Conoscendo quindi tre fattori di calibrazione è possibile, partendo da un'immagine della microsfera, ottenere una stima della sua posizione nello spazio tridimensionale. Questo ci permette @@ -117,7 +149,7 @@ eseguono le misurazioni di forza è possibile rilevare gli spostamenti del campione e compensarli inviando appositi comandi ai traslatori piezoelettrici. -In ambiente LabVIEW è stato sviluppato un codice di controllo +In ambiente LabVIEW ho sviluppato un codice di controllo che implementa un meccanismo di retroazione tra le letture sulla posizione della sfera e i traslatori piezoelettrici. Il codice consente all'operatore di selezionare la regione @@ -132,10 +164,6 @@ arrivare fino a \SI{100}{\Hz}), viene comandato ai traslatori uno spostamento proporzionale alla differenza tra la posizione della sfera rilevata e quella iniziale. -Quando il sistema di stabilizzazione meccanica viene attivato -è stato possibile mostrare che la posizione media del campione resta -stabile indipendentemente dal tempo di osservazione, con fluttuazioni -che hanno una deviazione standard di circa \SI{1}{\nm}. Il fattore di proporzionalità del ciclo di retroazione (guadagno, $g$) influenza le caratteristiche della risposta del sistema: un fattore troppo @@ -144,7 +172,8 @@ oscillazioni smorzate, mentre un fattore troppo piccolo aumenterà inutilmente il tempo di risposta. Per trovare il valore ottimale si osserva la risposta del sistema per diversi valori di $g$, in seguito ad una perturbazione fittizia ottenuta modificando di -\SI{50}{\nm} il \textit{set point} lungo una direzione. +\SI{50}{\nm} il \textit{set point} del sistema di retroazione +lungo una direzione. In figura \ref{fig:step_response} si riporta la risposta del sistema di stabilizzazione per gli assi $x$ e $z$ a diversi valori del fattore di proporzionalità $g$. @@ -157,6 +186,10 @@ del fattore di proporzionalità $g$. \label{fig:step_response} \end{figure} +Quando il sistema di stabilizzazione meccanica viene attivato +è stato possibile mostrare che la posizione media del campione resta +stabile indipendentemente dal tempo di osservazione, con fluttuazioni +che hanno una deviazione standard di circa \SI{1}{\nm}. L'acquisizione di diverse tracce della durata di 5-10 minuti ha sempre mostrato deviazioni standard delle fluttuazioni comprese tra \SIlist{1;2}{\nm}. @@ -179,7 +212,7 @@ fluttuazioni della posizione del campione, con (nero) e senza Per poter eseguire misurazioni di forza su sistemi biologici è fondamentale riuscire a conoscere il valore della tensione applicata alle microsfere intrappolate nelle pinzette ottiche. Questo si può - effettuare poriché l'azione di una pinzetta ottica su una + effettuare poiché l'azione di una pinzetta ottica su una microsfera può essere modellizzata come una forza di richiamo elastica (vedi sezione \ref{sec:ot}). @@ -262,30 +295,30 @@ per i valori di $k$ ottenibili con il nostro sistema di pinzette ottiche è possibile ridurre $\tau_{\textrm{diff}}$ fino a circa \SI{100}{\us}. -Il tempo di risposta del sistema nel regime balistico è quindi +Il tempo di risposta del sistema nel regime balistico è quindi completamente trascurabile, e il transiente tra una perturbazione e la stabilizzazione nella nuova posizione di equilibrio può essere descritto trascurando il termine inerziale dell'equazione di moto. - + Il protocollo di calibrazione sviluppato consente, partendo dal campionamento della posizione relativa della microsfera lungo un'asse spaziale, di determinare con precisione i valori di $\tau$, e quindi di $k$ per ogni posizione della trappola. - + Per fare questo si tiene conto che la densità spettrale delle fluttuazioni della posizione è data da \cite{Gittes1998}: - + \begin{equation} S_x(\nu) = \frac{k_B T}{\pi^2 \gamma (\nu^2 + \nu_c^2)} \end{equation} - + Dove $\nu_c = 1 / (2\pi\tau) = k / 2\pi\gamma$ é la frequenza di taglio, inversamente proporzionale al tempo di rilassamento. Da un semplice $fit$ della distribuzione spettrale del rumore della posizione è possibile quindi estrarre il valore di k. - + Il segnale misurabile in uscita dagli amplificatori differenziali dei QPD è un segnale in tensione, compreso tra \SIlist{-10;+10}{\V}, proporzionale alla posizione relativa della microsfera. @@ -314,6 +347,15 @@ trappola la distribuzione spettrale di rumore, utilizzando un algoritmo per la trasformata di Fourier veloce (\textit{Fast Fourier Transform}, FFT), con i parametri riportati in tabella \ref{tab:fft_par}. +Il limite teorico imposto dal teorema di Shannon fissa a \SI{100}{\kHz} la +massima frequenza rilevabile, tuttavia si sceglie di tagliare la coda +finale dello spettro selezionando solo le frequenze compresa tra \SI{15}{\Hz} +e \SI{50}{\kHz}. Mentre in questo intervallo la sensibilità del rilevatore al +silicio usato nei QPD è relativamente costante, inizia a decrescere +per frequenze maggiori, e la coda finale dello spettro delle +fluttuazioni viene nascosta dal rumore elettronico e altri disturbi, +come quelli generati ad esempio dagli alimentatori AC/DC. + \begin{table}[ht] \centering \begin{tabular}{>{\bf}l l} @@ -323,7 +365,6 @@ con i parametri riportati in tabella \ref{tab:fft_par}. 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+1261,129 @@ id="radialGradient9226" xlink:href="#linearGradient9224" inkscape:collect="always" /> + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -1436,7 +1571,7 @@ y="13.115568" x="37.147316" id="tspan9128" - sodipodi:role="line">Sx [mV] + sodipodi:role="line">Vx [mV] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + A BC D + A BC D