From b75d9d8f2ba798fbbadc975a789cf2615b743328 Mon Sep 17 00:00:00 2001
From: Blaise Thompson <blaise@untzag.com>
Date: Sun, 15 Apr 2018 00:16:26 -0500
Subject: 2018-04-15 00:16

---
 quantitative_ta/chapter.tex | 33 ++++++++++++++++++---------------
 1 file changed, 18 insertions(+), 15 deletions(-)

(limited to 'quantitative_ta/chapter.tex')

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}
-- 
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