From 37989608b63fdbc4d555a51b6135dea5a3555975 Mon Sep 17 00:00:00 2001
From: Blaise Thompson <blaise@untzag.com>
Date: Sun, 15 Apr 2018 19:43:48 -0500
Subject: 2018-04-15 19:43

---
 active_correction/chapter.tex | 201 ++++++++++++++++++++++++------------------
 1 file changed, 113 insertions(+), 88 deletions(-)

(limited to 'active_correction/chapter.tex')

diff --git a/active_correction/chapter.tex b/active_correction/chapter.tex
index 7ecbe2f..d3028fe 100644
--- a/active_correction/chapter.tex
+++ b/active_correction/chapter.tex
@@ -1,4 +1,4 @@
-\chapter{Active Correction in MR-CMDS} \label{cha:act}
+\chapter{Active correction} \label{cha:act}
 
 \begin{dquote}
   Calibrate, \\
@@ -9,7 +9,7 @@
   run.
 
   \dsignature{Long-hanging poster in Wright Group laser lab.}
-\end{dquote}  % TODO: verify this quote
+\end{dquote}
 
 \clearpage
 
@@ -34,20 +34,20 @@ Some of these strategies have already been implemented, others are partially imp
 others are still just ideas.  %
 I hope to show that active correction is a particularly useful strategy in MR-CMDS.  %
 
-Section ... addresses spectral delay correction, where automated delay stages are used to
-explicitly correct for small changes in optical path length at different pulse frequencies.  %
+Section \ref{act:sec:sdc} addresses spectral delay correction, where automated delay stages are
+used to explicitly correct for small changes in optical path length at different pulse frequencies.  %
 
-Section ... addresses poynting correction, where mirrors with motorized pitch and yaw control are
-used to actively correct for small changes in OPA output poynting.  %
+Section \ref{act:sec:poynting} addresses poynting correction, where mirrors with motorized pitch
+and yaw control are used to actively correct for small changes in OPA output poynting.  %
 
-Section ... addresses (dual) chopping, used to actively subtract artifacts such as scatter and
-unwanted nonlinear outputs.  %
+Section \ref{act:sec:chop} addresses (dual) chopping, used to actively subtract artifacts such as
+scatter and unwanted nonlinear outputs.  %
 Chopping can only account for intensity level (additive) artifacts.  %
 Fibrillation is the opposite of chopping, as it can only account for amplitude level
 \emph{iterference} effects.  %
-Section ... addresses fibrillation.  %
+Section \ref{act:sec:chop} also addresses fibrillation.  %
 
-\section{Spectral delay correction}  % ============================================================
+\section{Spectral delay correction} \label{act:sec:sdc} % =========================================
 
 As a frequency domain technique, MR-CMDS requires automated tuning of multiple OPAs.  %
 These OPAs generate pulses, which are then manipulated and directed into a sample of interest.  %
@@ -64,7 +64,8 @@ within the Wright Group.  %
 SDC was first implemented by Schuyler Kain within his COLORS acquisition software.
 \cite{KainSchuyler2017a}  %
 COLORS' implementation was hardcoded for one particular OPA / delay configuration---it wasn't until
-PyCMDS that fully arbitrary SDC became possible through the autonomic system (see section ...).  %
+PyCMDS that fully arbitrary SDC became possible through the autonomic system (see
+\autoref{acq:sec:autonomic}).  %
 Erin Boyle ``backported'' similar functionality into to ps\_control, although her implementation
 allowed only for a simple, first order linear correction.  %
 
@@ -76,7 +77,7 @@ color coordinate.  %
 A special method of \python{Data}, \python{Data.offset} is designed to do the necessary
 interpolation for \emph{post hoc} SDC.  %
 
-In many experiments spectral delay must be actively corrected for.  %
+In many experiments spectral delay \emph{must} be actively corrected for.  %
 Fully coherent experiments are typically performed by scanning OPA frequencies while attempting to
 keep delays constant.  %
 In such experiments, the dataset does not in-and-of-itself contain the information needed to
@@ -104,7 +105,7 @@ If a fully coherent experiment is performed with chirped white light as one of t
 pulses, the other pulses will provide a gating effect in time that isolates interaction from one
 frequency in the white pulse.  %
 This is similar to the gating that is accomplished using ``delay 1'' in the TOPAS-C OPAs (see
-section  ...).  %
+\autoref{cha:opa}).  %
 By gating in this way, a \emph{frequency} axis along the white light dimension could be scanned
 using a delay stage.  %
 COLORS' has taken this idea to it's logical conclusion, with support for ``OPAs'' that are actually
@@ -136,19 +137,36 @@ The delay traces (horizontal) peaks at the same value for every OPA1 position (v
 \begin{figure}
 	\includegraphics[width=0.45\textwidth]{"active_correction/sdc_before"}
  	\includegraphics[width=0.45\textwidth]{"active_correction/sdc_after"}
-  \caption[CAPTION TODO]{
-    CAPTION TODO: SPECTRAL DELAY CORRECTION FIGURE
+  \caption[Spectral delay correction.]{
+    Spectral delay correction.
   }
   \label{act:fig:sdc}
 \end{figure}
 
-\section{Poynting correction}  % ==================================================================
+\section{Poynting correction} \label{act:sec:poynting}  % =========================================
 
-[CONTENT FROM KYLE SUNDEN]
+With scanning OPAs, output Poynting can change along with optical path length.  %
+We now correct for such changes actively using mirrors with motorized pitch and yaw controls.  %
+These Poynting corrections are implemented as part of the recursive OPA tuning curve system (see
+\autoref{cha:opa}), and not through the autonomic system.  %
+
+To determine the appropriate positions for a Poynting correction, a pitch vs setpoint and yaw vs
+setpoint scan is performed.  %
+A pinhole is placed at the sample location, and a detector is place \emph{immediately} after the
+pinhole.  %
+
+\autoref{act:fig:poynting} is an autogenerated figure from PyCMDS.  %
+It is a typical Poynting correction scan.  %
+Like in spectral delay correction, each slice is fit and then a spline is fit to all slices
+simultaneously.  %
+The top plot of \autoref{act:fig:poynting} show the initial Poynting correction in comparison with
+the new one.  %
+In this case the change in the correction is mostly an offset, although there is a fairly dramatic
+shape change at the lowest energy setpoints.  %
 
 \begin{figure}
 	\includegraphics[width=0.45\textwidth]{"active_correction/poynting_correction/intensity"}
-  \caption[Poynting Correction curve generation.]{
+  \caption[Poynting correction.]{
     A typical example of the output of the Poynting Tune module.
     The top figure shows the curve for the axis designated Theta.
     The thin, solid line is the previous curve, the thick transparent line is the new tuning curve.
@@ -159,9 +177,10 @@ The delay traces (horizontal) peaks at the same value for every OPA1 position (v
     This figure was automatically generated by PyCMDS on March 28, 2018 using an OPA-800 generating
     1 ps infrared light.
   }
+  \label{act:fig:poynting}
 \end{figure}
 
-\section{Chopping}  % =============================================================================
+\section{Chopping} \label{act:sec:chop}  % ========================================================
 
 \subsection{Scatter}  % ---------------------------------------------------------------------------
 
@@ -186,10 +205,6 @@ A similar expression in the case of heterodyne-detected 4WM is derived by
 The goal of any `scatter rejection' processing procedure is to isolate $|E_{\mathrm{4WM}}|^2$ from
 the other terms.  %
 
-% TODO: verify derivation
-
-\subsubsection{Abandon the Random Phase Approximation}
-
 \subsubsection{Interference Patterns in TrEE}
 
 TrEE is implicitly homodyne-detected.  %
@@ -203,12 +218,14 @@ detection field are at the same frequency.  %
 
 \begin{figure}
 	\includegraphics[scale=0.5]{"active_correction/scatter/scatter interference in TrEE old"}
-	\caption[Simulated interference paterns in old delay parameterization.]{Numerically simulated
-    interference patterns between scatter and TrEE for the old delay parametrization. Each column
-    has scatter from a single excitation field. The top row shows the measured intensities, the
-    bottom row shows the 2D Fourier transform, with the colorbar's dynamic range chosen to show the
-    cross peaks.}
-  label{fig:scatterinterferenceinTrEEold}
+	\caption[Simulated interference paterns in old delay parameterization.]{
+    Numerically simulated interference patterns between scatter and TrEE for the old delay
+    parametrization.
+    Each column has scatter from a single excitation field.
+    The top row shows the measured intensities, the bottom row shows the 2D Fourier transform, with
+    the colorbar's dynamic range chosen to show the cross peaks.
+  }
+  \label{fig:scatterinterferenceinTrEEold}
 \end{figure}
 
 Here I derive the slopes of constant phase for the old delay space, where
@@ -231,16 +248,20 @@ The cross term between scatter and signal is the product of $\Phi_\mathrm{sig}$
 \Delta_{2} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_2\omega} &=&  \mathrm{e}^{-\left((\tau_{2^\prime}-2\tau_2)\omega\right)}\\
 \Delta_{2^\prime} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_{2^\prime}\omega} &=& \mathrm{e}^{-\tau_{2}\omega}
 \end{eqnarray}
-Figure \ref{fig:scatterinterferenceinTrEEold} presents numerical simulations of scatter interference as a visual aid. See Yurs 2011 \cite{YursLenaA2011a}.
+Figure \ref{fig:scatterinterferenceinTrEEold} presents numerical simulations of scatter
+interference as a visual aid.  %
+See Yurs 2011 \cite{YursLenaA2011a}.  %
 % TODO: Yurs 2011 Data
 
 \begin{figure}
 	\includegraphics[width=7in]{"active_correction/scatter/scatter interference in TrEE current"}
-	\caption[Simulated interference paterns in current delay parameterization.]{Numerically simulated
-    interference patterns between scatter and TrEE for the current delay parametrization. Each
-    column has scatter from a single excitation field. The top row shows the measured intensities,
-    the bottom row shows the 2D Fourier transform, with the colorbar's dynamic range chosen to show
-    the cross peaks.}
+	\caption[Simulated interference paterns in current delay parameterization.]{
+    Numerically simulated interference patterns between scatter and TrEE for the current delay
+    parametrization.
+    Each column has scatter from a single excitation field.
+    The top row shows the measured intensities, the bottom row shows the 2D Fourier transform, with
+    the colorbar's dynamic range chosen to show the cross peaks.
+  }
   \label{fig:scatterinterferenceinTrEEcurrent}
 \end{figure}
 
@@ -271,7 +292,7 @@ amplitude-level interference terms.  %
 Both techniques work by modulating signal and scatter terms differently so that they may be
 separated after light collection.  %
 
-\begin{table}[h] \label{tab:phase_shifted_parallel_modulation}
+\begin{table} \label{tab:phase_shifted_parallel_modulation}
 	\begin{center}
 		\begin{tabular}{ r | c | c | c | c }
 			& A       & B          & C          & D                       \\
@@ -281,7 +302,11 @@ separated after light collection.  %
 			other     & \checkmark & \checkmark & \checkmark & \checkmark
 		\end{tabular}
 	\end{center}
-	\caption[Shot-types in phase shifted parallel modulation.]{Four shot-types in a general phase shifted parallel modulation scheme. The `other' category represents anything that doesn't depend on either chopper, including scatter from other excitation sources, background light, detector voltage offsets, etc.}
+	\caption[Shot-types in phase shifted parallel modulation.]{
+    Four shot-types in a general phase shifted parallel modulation scheme.
+    The `other' category represents anything that doesn't depend on either chopper, including
+    scatter from other excitation sources, background light, detector voltage offsets, etc.
+  }
 \end{table}
 
 We use the dual chopping scheme developed by \textcite{FurutaKoichi2012a} called `phase shifted
@@ -346,54 +371,7 @@ number of laser shots.  %
 Taking twice as many laser shots when dual chopping brings the signal to noise to at least as good
 as the original single chopping.  %
 
-\subsection{Normalization of dual-chopped self-heterodyned signal}
-
-%\begin{table}[!htb]
-%  \centering
-%  \renewcommand{\arraystretch}{1.5}
-%\begin{array}{r | c | c | c | c }
-%  & A           & B & C & D \\ \hline
-%  \text{signal}   & S_A=V_A^S   & S_B=R^SC^1I_B^S & S_C=R^S(C^1) & S_D=R^SC^2I_D^S \\ \hline
-%  \text{source 1} & M_A^1=V_A^1 & M_B=R^1I_B^1    & M_C^1=R^1I_C^1 & M_D^1=V_D^1 \\ \hline
-%  \text{source 2} & M_A^2=V_A^2 & M_B^2=V_B^2     & M_C^2=R^2I_C^2 & M_D^2=R^2I_D^2
-%\end{array}
-%  \caption{CAPTION}
-%\end{table}
-
-Shot-by-shot normalization is not trivial for these experiments.  %
-As in table above, with 1 as pump and 2 as probe.  %
-
-Starting with $\Delta I$ from \ref{eq:dual_chopping}, we can normalize by probe intensity to get
-the popular $\Delta I / I$ representation.  %
-Using the names defined above:
-\begin{equation}
-  \frac{\Delta I}{I} = \frac{A-B+C-D}{D-A}
-\end{equation}
-Now consider the presence of excitation intensity monitors, indicated by subscripts PR for probe
-and PU for pump.
-
-We can further normalize by the pump intensity by dividing the entire expression by $C_{PU}$:
-\begin{equation}
-  \frac{\Delta I}{I} = \frac{A-B+C-D}{(D-A)*C_{PU}}
-\end{equation}
-
-Now, substituting in BRAZARD formalism:
-
-\begin{eqnarray}
-  A &=& constant \\
-  B &=& S I_{PU}^B (1+\delta_{PU}^B) \\
-  C &=& I_{PR}^C(1+\delta_{PR}^C) + S I_{PU}^C(1+\delta_{PR}^C) \\
-  D &=& I_{PR}^D(1+\delta_{PR}^D)
-\end{eqnarray}
-
-\begin{equation}
-  \frac{\Delta I}{I} = \frac{<A> -
-    \frac{<B_{PU}>B}{B_{PU}} +
-    \frac{<C_{PU}><C_{PR}C}{C_{PU}C_{PR}} -
-    \frac{<D_{PR}>D}{D_{PR}}}{<PR><PU>}
-\end{equation}
-
-\section{Fibrillation}  % =========================================================================
+\subsection{Fibrillation}  % ----------------------------------------------------------------------
 
 Fibrillation is the intentional randomization of excitation phase during an experiment.  %
 Because the interference term depends on the phase of the excitation field relative to the signal,
@@ -401,6 +379,53 @@ averaging over many shots with random phase will cause the interference term to
 This is a well known strategy for removing unwanted interference terms \cite{SpectorIvanC2015a,
   McClainBrianL2004a}.  %
 
-\section{Conclusions}  % ==========================================================================
-
-In the future I'd like to do excitation power correction.  %
\ No newline at end of file
+% \subsection{Normalization of dual-chopped self-heterodyned signal}
+
+% %\begin{table}[!htb]
+% %  \centering
+% %  \renewcommand{\arraystretch}{1.5}
+% %\begin{array}{r | c | c | c | c }
+% %  & A           & B & C & D \\ \hline
+% %  \text{signal}   & S_A=V_A^S   & S_B=R^SC^1I_B^S & S_C=R^S(C^1) & S_D=R^SC^2I_D^S \\ \hline
+% %  \text{source 1} & M_A^1=V_A^1 & M_B=R^1I_B^1    & M_C^1=R^1I_C^1 & M_D^1=V_D^1 \\ \hline
+% %  \text{source 2} & M_A^2=V_A^2 & M_B^2=V_B^2     & M_C^2=R^2I_C^2 & M_D^2=R^2I_D^2
+% %\end{array}
+% %  \caption{CAPTION}
+% %\end{table}
+
+% Shot-by-shot normalization is not trivial for these experiments.  %
+% As in table above, with 1 as pump and 2 as probe.  %
+
+% Starting with $\Delta I$ from \ref{eq:dual_chopping}, we can normalize by probe intensity to get
+% the popular $\Delta I / I$ representation.  %
+% Using the names defined above:
+% \begin{equation}
+%   \frac{\Delta I}{I} = \frac{A-B+C-D}{D-A}
+% \end{equation}
+% Now consider the presence of excitation intensity monitors, indicated by subscripts PR for probe
+% and PU for pump.
+
+% We can further normalize by the pump intensity by dividing the entire expression by $C_{PU}$:
+% \begin{equation}
+%   \frac{\Delta I}{I} = \frac{A-B+C-D}{(D-A)*C_{PU}}
+% \end{equation}
+
+% Now, substituting in BRAZARD formalism:
+
+% \begin{eqnarray}
+%   A &=& constant \\
+%   B &=& S I_{PU}^B (1+\delta_{PU}^B) \\
+%   C &=& I_{PR}^C(1+\delta_{PR}^C) + S I_{PU}^C(1+\delta_{PR}^C) \\
+%   D &=& I_{PR}^D(1+\delta_{PR}^D)
+% \end{eqnarray}
+
+% \begin{equation}
+%   \frac{\Delta I}{I} = \frac{<A> -
+%     \frac{<B_{PU}>B}{B_{PU}} +
+%     \frac{<C_{PU}><C_{PR}C}{C_{PU}C_{PR}} -
+%     \frac{<D_{PR}>D}{D_{PR}}}{<PR><PU>}
+% \end{equation}
+
+% \section{Conclusions}  % ==========================================================================
+
+% In the future I'd like to do excitation power correction.  %
\ No newline at end of file
-- 
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