diff options
Diffstat (limited to 'quantitative_ta')
| -rw-r--r-- | quantitative_ta/chapter.tex | 33 |
1 files changed, 18 insertions, 15 deletions
diff --git a/quantitative_ta/chapter.tex b/quantitative_ta/chapter.tex index c8b594d..099b606 100644 --- a/quantitative_ta/chapter.tex +++ b/quantitative_ta/chapter.tex @@ -1,32 +1,35 @@ -\chapter{Quantitative transient absorbance} \label{cha:qta} +\chapter{Quantitative differential absorbance} \label{cha:qta} -\subsubsection{Quantitative TA} +\clearpage Transient absorbance (TA) spectroscopy is a self-heterodyned technique. % Through chopping you can measure nonlinearities quantitatively much easier than with homodyne -detected (or explicitly heterodyned) experiments. +detected (or explicitly heterodyned) experiments. % -\begin{figure} - \includegraphics[width=\textwidth]{"spectroscopy/TA setup"} - \label{fig:ta_and_tr_setup} - \caption{CAPTION TODO} -\end{figure} +%\begin{figure} +% \includegraphics[width=\textwidth]{"spectroscopy/TA setup"} +% \label{fig:ta_and_tr_setup} +% \caption{CAPTION TODO} +%\end{figure} -\autoref{fig:ta_and_tr_setup} diagrams the TA measurement for a generic sample. % -Here I show measurement of both the reflected and transmitted probe beam \dots not important in -opaque (pyrite) or non-reflective (quantum dot) samples \dots % +%\autoref{fig:ta_and_tr_setup} diagrams the TA measurement for a generic sample. % +%Here I show measurement of both the reflected and transmitted probe beam \dots not important in +%opaque (pyrite) or non-reflective (quantum dot) samples \dots % Typically one attempts to calculate the change in absorbance $\Delta A$ \dots % \begin{eqnarray} \Delta A &=& A_{\mathrm{on}} - A_{\mathrm{off}} \\ -&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}} + I_{\Delta\mathrm{R}}}{I_0}\right) + \log\left(\frac{I_\mathrm{T}+I_\mathrm{R}}{I_0}\right) \\ -&=& -\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}})-\log_{10}(I_0)\right)+\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R})-\log_{10}(I_0)\right) \\ +&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}} + + I_{\Delta\mathrm{R}}}{I_0}\right) + \log\left(\frac{I_\mathrm{T}+I_\mathrm{R}}{I_0}\right) \\ +&=& -\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ + I_{\Delta\mathrm{R}})-\log_{10}(I_0)\right)+\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R})-\log_{10}(I_0)\right) + \\ &=& -\left(\log_{10}(I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}})-\log_{10}(I_\mathrm{T}+I_\mathrm{R})\right) \\ -&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}}}{I_\mathrm{T}+I_\mathrm{R}}\right) \label{eq:ta_complete} +&=& -\log_{10}\left(\frac{I_\mathrm{T}+I_\mathrm{R}+I_{\Delta\mathrm{T}}+ I_{\Delta\mathrm{R}}}{I_\mathrm{T}+I_\mathrm{R}}\right) \label{qta:eqn:ta_complete} \end{eqnarray} -\autoref{eq:ta_complete} simplifies beautifully if reflectivity is negligible \dots +\autoref{qta:eqn:ta_complete} simplifies beautifully if reflectivity is negligible \dots Now I define a variable for each experimental measurable: \begin{center} |