From 00fb8d01e53be66fe4dfde3beee3c98acc18f3b7 Mon Sep 17 00:00:00 2001
From: Blaise Thompson <blaise@untzag.com>
Date: Sat, 14 Apr 2018 12:59:30 -0500
Subject: 2018-04-14 12:59

---
 active_correction/chapter.tex | 70 ++++++++++++++++++++++++++++++-------------
 1 file changed, 50 insertions(+), 20 deletions(-)

(limited to 'active_correction/chapter.tex')

diff --git a/active_correction/chapter.tex b/active_correction/chapter.tex
index 4f7003d..7ecbe2f 100644
--- a/active_correction/chapter.tex
+++ b/active_correction/chapter.tex
@@ -19,13 +19,13 @@ MR-CMDS is subject to a number of possible artifacts, many of them stemming from
 nature of the frequency-tunable light sources we currently have.  %
 It is self-evidently desirable to correct these artifacts, when possible.  %
 Indeed many of these artifacts, such as OPA power, phase mismatch and absorption effects have
-regularly been corrected for.  % TODO: link to examples in applications section
+regularly been corrected for.  % TODO: link to examples in applications section, cite
 These corrections are applied after measurement, typically including information from other sources
 (such as absorption spectra, in the case of absorption effect corrections).
 
 A more interesting class of corrections are ``active'' corrections---that is, corrections that must
 be actively applied during acquisition and cannot be applied in post processing.  %
-These corrections are more insidious, and they are often neglected because the hardware and/or
+These corrections are more insidious, as they are often neglected because the hardware and/or
 software does not allow for them.  %
 
 In this chapter I explore some of these active correction strategies that are useful in the context
@@ -34,17 +34,19 @@ 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.  %
 
-[SPECTRAL DELAY PARAGRAPH]
+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.  %
 
-[POYNTING CORRECTION PARAGRAPH]
+Section ... addresses poynting correction, where mirrors with motorized pitch and yaw control are
+used to actively correct for small changes in OPA output poynting.  %
 
-[EXCITATION POWER CORRECTION PARAGRAPH]
+Section ... 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.  %
 
-[CHOPPING PARAGRAPH]
-
-[FIBRILLATION]
-
-\clearpage
 \section{Spectral delay correction}  % ============================================================
 
 As a frequency domain technique, MR-CMDS requires automated tuning of multiple OPAs.  %
@@ -53,13 +55,14 @@ Crucially, the relative arrival time of each pulse must be carefully controlled
 the MR-CMDS experiment.  %
 Unfortunately, changing the output frequency also changes the optical path length, meaning that
 there is some unavoidable coupling between delay and frequency axes.  %
-Because we have full control over delay through delay stages, we can correct for this phenomenon by
-choosing a different zero delay \emph{offset} for each OPA output color.  %
+Because we have full control over delay with our automated stages, we can correct for this
+phenomenon by choosing a different zero delay \emph{offset} for each OPA output color.  %
 This strategy has been dubbed ``spectral delay correction''.  %
 
-Spectral delay correction (SDC) is certainly the longest running active correction strategy employed
+Spectral delay correction (SDC) is certainly the oldest active correction strategy employed
 within the Wright Group.  %
-SDC was first implemented by Schuyler Kain within his COLORS acquisition software. [CITE]  %
+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 ...).  %
 Erin Boyle ``backported'' similar functionality into to ps\_control, although her implementation
@@ -74,7 +77,13 @@ A special method of \python{Data}, \python{Data.offset} is designed to do the ne
 interpolation for \emph{post hoc} SDC.  %
 
 In many experiments spectral delay must be actively corrected for.  %
-Fully coherent experiments do 
+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
+offset in post processing.  %
+Indeed it can easily become time-prohibitive to collect the full response.  %
+For a three-beam experiment, an entire two dimensional delay-delay collection would be required at
+each pixel to allow for post-correction.  %
 
 It has been found that SDC is necessary for each individual scanned OPA, and for each separate path
 when pulses from a single OPA are split.  %
@@ -82,7 +91,7 @@ The difference between different paths is typically small, but enough to move pu
 amount relative to each-other.  %
 For this reason, SDC for split OPAs is a multidimensional problem, which in principle requires a
 multi-dimensional acquisition to fully record.  %
-In practice, however, these corrections are recorded iteravely.  %
+In practice, however, these corrections are typically recorded iteratively.  %
 
 White light sources are also interesting to consider in the context of spectral delay
 correction.  %
@@ -101,7 +110,28 @@ using a delay stage.  %
 COLORS' has taken this idea to it's logical conclusion, with support for ``OPAs'' that are actually
 controlled by delay stages, although the idea has not yet been realized in practice.  %
 
-[DESCRIPTION OF FIGURE]
+\autoref{act:fig:sdc} contains two plots that were automatically generated by PyCMDS in the context
+of an experiment.  %
+In this case, the user used a sapphire plate as a nonresonant medium to record the spectral delay
+dependence.  %
+It was a three beam $\omega_1$, $\omega_2$, $\omega_{2^\prime}$ experiment, so three corrections
+were necessary: D2 vs OPA1, D1 vs OPA2, and D2 vs OPA2.  %
+Here we focus only on D2 ($\tau_{21}$) vs OPA1, the simplest of the corrections.  %
+
+In the left-hand subplot of \autoref{act:fig:sdc} we see the original experiment.  %
+Without corrections applied, the user scanned OPA1 vs D2.  %
+The curvature in the plot is due entirely to SDC, as sapphire is entirely nonresonant (driven).  %
+Using WrightTools, PyCMDS fits each slice to find the delay that gives maximum signal.  %
+It then passes those separate fits through a spline to guess the ultimate SDC dependence.  %
+PyCMDS makes a best guess in regions where there is not enough signal to determine the appropriate
+delay, like in at 800 nm in the left hand plot.  %
+The magnitude of the corrections are roughly 30 fs in this particular experiment: not large, but
+enough to change signal levels by roughly a factor of 2.  %
+In other cases SDC is as much as 200 fs.  %
+
+In the right-hand subplot the user has taken the same scan again, this time after corrections were
+applied.  %
+The delay traces (horizontal) peaks at the same value for every OPA1 position (vertical).  %
 
 \begin{figure}
 	\includegraphics[width=0.45\textwidth]{"active_correction/sdc_before"}
@@ -109,6 +139,7 @@ controlled by delay stages, although the idea has not yet been realized in pract
   \caption[CAPTION TODO]{
     CAPTION TODO: SPECTRAL DELAY CORRECTION FIGURE
   }
+  \label{act:fig:sdc}
 \end{figure}
 
 \section{Poynting correction}  % ==================================================================
@@ -130,9 +161,6 @@ controlled by delay stages, although the idea has not yet been realized in pract
   }
 \end{figure}
 
-\section{Excitation power correction}  % ==========================================================
-
-\clearpage
 \section{Chopping}  % =============================================================================
 
 \subsection{Scatter}  % ---------------------------------------------------------------------------
@@ -374,3 +402,5 @@ This is a well known strategy for removing unwanted interference terms \cite{Spe
   McClainBrianL2004a}.  %
 
 \section{Conclusions}  % ==========================================================================
+
+In the future I'd like to do excitation power correction.  %
\ No newline at end of file
-- 
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