From 9d89c09dfe49aba4c68b6911600715add419babd Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Tue, 27 Feb 2018 23:58:32 -0600 Subject: 2018-02-27 23:58 --- instrument/chapter.tex | 250 ------------------------------------------------- 1 file changed, 250 deletions(-) delete mode 100644 instrument/chapter.tex (limited to 'instrument/chapter.tex') diff --git a/instrument/chapter.tex b/instrument/chapter.tex deleted file mode 100644 index be8ed71..0000000 --- a/instrument/chapter.tex +++ /dev/null @@ -1,250 +0,0 @@ -% TODO: BerkTobyS1975.000 people trust computers too much - -\chapter{Instrumental Development} - -\section{Hardware} % ----------------------------------------------------------------------------- - -\subsection{Delay Stages} - -% TODO: discuss _all 3_ delay configurations.... implications for sign conventions etc - -\section{Signal Acquisition} - -Old boxcar: 300 ns window, ~10 micosecond delay. Onset of saturation ~2 V. - -\subsection{Digital Signal Processing} - -% TODO: - -\section{Artifacts and Noise} % ------------------------------------------------------------------ - -\subsection{Scatter} - -Scatter is a complex microscopic process whereby light traveling through a material elastically -changes its propagation direction. % -In CMDS we use propagation direction to isolate signal. % -Scattering samples defeat this isolation step and allow some amount of excitation light to reach -the detector. % -In homodyne-detected 4WM experiments, -\begin{equation} -I_{\mathrm{detected}} = |E_{\mathrm{4WM}} + E_1 + E_2 + E_{2^\prime}|^2 -\end{equation} -Where $E$ is the entire time-dependent complex electromagnetic field. % -When expanded, the intensity will be composed of diagonal and cross terms: -\begin{equation} -\begin{split} -I_{\mathrm{detected}} = \overline{(E_1+E_2)}E_{2^\prime} + (E_1+E_2)\overline{E_{2^\prime}} + |E_1+E_2|^2 + (E_1+E_2)\overline{E_{\mathrm{4WM}}} \\ + (E_1+E_2)\overline{E_{\mathrm{4WM}}} + \overline{E_{2^\prime}}E_{\mathrm{4WM}} + E_{2^\prime}\overline{E_{\mathrm{4WM}}} + |E_{\mathrm{4WM}}|^2 -\end{split} -\end{equation} -A similar expression in the case of heterodyne-detected 4WM is derived by -\textcite{BrixnerTobias2004a}. % -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. % -Scatter from excitation fields will interfere on the amplitude level with TrEE signal, causing -interference patterns that beat in delay and frequency space. % -The pattern of beating will depend on which excitation field(s) reach(es) the detector, and the -parameterization of delay space chosen. % - -First I focus on the interference patterns in 2D delay space where all excitation fields and the -detection field are at the same frequency. % - -\begin{figure}[p!] \label{fig:scatterinterferenceinTrEEold} - \centering - \includegraphics[scale=0.5]{"instrument/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.} -\end{figure} -Here I derive the slopes of constant phase for the old delay space, where -$\mathrm{d1}=\tau_{2^\prime1}$ and $\mathrm{d2}=\tau_{21}$. % -For simplicity, I take $\tau_1$ to be $0$, so that $\tau_{21}\rightarrow\tau_2$ and -$\tau_{2^\prime1}\rightarrow\tau_{2^\prime}$. % -The phase of signal is then -\begin{equation} -\Phi_{\mathrm{sig}} = \mathrm{e}^{-\left((\tau_{2^\prime}-\tau_2)\omega\right)} -\end{equation} -The phase of each excitation field can also be written: -\begin{eqnarray} -\Phi_{1} &=& \mathrm{e}^0 \\ -\Phi_{2} &=& \mathrm{e}^{-\tau_2\gls{omega}} \\ -\Phi_{2^\prime} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} -\end{eqnarray} -The cross term between scatter and signal is the product of $\Phi_\mathrm{sig}$ and $\Phi_\mathrm{scatter}$. The cross terms are: -\begin{eqnarray} -\Delta_{1} = \Phi_{\mathrm{sig}} &=& \mathrm{e}^{-\left((\tau_{2^\prime}-\tau_2)\omega\right)} \\ -\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}. -% TODO: Yurs 2011 Data - -\begin{figure}[p!] \label{fig:scatterinterferenceinTrEEcurrent} - \centering - \includegraphics[width=7in]{"instrument/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.} -\end{figure} - -Here I derive the slopes of constant phase for the current delay space, where $\mathrm{d1}=\tau_{22^\prime}$ and $\mathrm{d2}=\tau_{21}$. I take $\tau_2$ to be $0$, so that $\tau_{22^\prime}\rightarrow\tau_{2^\prime}$ and $\tau_{21}\rightarrow\tau_1$. The phase of the signal is then -\begin{equation} -\Phi_{\mathrm{sig}} = \mathrm{e}^{-\left((\tau_{2^\prime}+\tau_1)\omega\right)} -\end{equation} -The phase of each excitation field can also be written: -\begin{eqnarray} -\Phi_{1} &=& \mathrm{e}^{-\tau_1\omega} \\ -\Phi_{2} &=& \mathrm{e}^{0} \\ -\Phi_{2^\prime} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} -\end{eqnarray} -The cross term between scatter and signal is the product of $\Phi_\mathrm{sig}$ and $\Phi_\mathrm{scatter}$. The cross terms are: -\begin{eqnarray} -\Delta_{1} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_1\omega} &=& \mathrm{e}^{-\tau_{2^\prime}\omega} \\ -\Delta_{2} = \Phi_{\mathrm{sig}} &=& \mathrm{e}^{-\left((\tau_2+\tau_1)\omega\right)} \\ -\Delta_{2^\prime} = \Phi_{\mathrm{sig}}\mathrm{e}^{-\tau_{2^\prime}\omega} &=& \mathrm{e}^{-\tau_1\omega} -\end{eqnarray} -Figure \ref{fig:scatterinterferenceinTrEEcurrent} presents numerical simulations of scatter interference for the current delay parameterization. - -\subsubsection{Instrumental Removal of Scatter} - -The effects of scatter can be entirely removed from CMDS signal by combining two relatively -straight-forward instrumental techniques: \textit{chopping} and \textit{fibrillation}. % -Conceptually, chopping removes intensity-level offset terms and fibrillation removes -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{center} - \begin{tabular}{ r | c | c | c | c } - & A & B & C & D \\ - signal & & & \checkmark & \\ - scatter 1 & & \checkmark & \checkmark & \\ - scatter 2 & & & \checkmark & \checkmark \\ - 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.} -\end{table} - -We use the dual chopping scheme developed by \textcite{FurutaKoichi2012a} called `phase shifted -parallel modulation'. % -In this scheme, two excitation sources are chopped at 1/4 of the laser repetition rate (two pulses -on, two pulses off). % -Very similar schemes are discussed by \textcite{AugulisRamunas2011a} and -\textcite{HeislerIsmael2014a} for two-dimensional electronic spectroscopy. % -The two chop patterns are phase-shifted to make the four-pulse pattern represented in Table -\ref{tab:phase_shifted_parallel_modulation}. % -In principle this chopping scheme can be achieved with a single judiciously placed mechanical -chopper - this is one of the advantages of Furuta's scheme. % -Due to practical considerations we have generally used two choppers, one on each OPA. % -The key to phase shifted parallel modulation is that signal only appears when both of your chopped -beams are passed. % -It is simple to show how signal can be separated through simple addition and subtraction of the A, -B, C, and D phases shown in Table \ref{tab:phase_shifted_parallel_modulation}. % -First, the components of each phase: -\begin{eqnarray} -A &=& I_\mathrm{other} \\ -B &=& I_\mathrm{1} + I_\mathrm{other} \\ -C &=& I_\mathrm{signal} + I_\mathrm{1} + I_\mathrm{2} + I_\mathrm{other} \\ -D &=& I_\mathrm{2} + I_\mathrm{other} -\end{eqnarray} -Grouping into difference pairs, -\begin{eqnarray} -A-B &=& -I_\mathrm{1} \\ -C-D &=& I_\mathrm{signal} + I_\mathrm{1} -\end{eqnarray} -So: -\begin{equation} \label{eq:dual_chopping} -A-B+C-D = I_\mathrm{signal} -\end{equation} -I have ignored amplitude-level interference terms in this treatment because they cannot be removed -via any chopping strategy. % -Interference between signal and an excitation beam will only appear in `C'-type shots, so it will -not be removed in Equation \ref{eq:dual_chopping}. % -To remove such interference terms, you must \textit{fibrillate} your excitation fields. - -An alternative to dual chopping is single-chopping and `leveling'... % -this technique was used prior to May 2016 in the Wright Group... % -`leveling' and single-chopping is also used in some early 2DES work... -\cite{BrixnerTobias2004a}. % - -\begin{figure}[p!] \label{fig:ta-chopping-comparison} - \centering - \includegraphics[scale=0.5]{"instrument/scatter/TA chopping comparison"} - \caption[Comparison of single, dual chopping.]{Comparison of single and dual chopping in a MoS\textsubscript{2} transient absorption experiment. Note that this data has not been processed in any way - the colorbar represents changes in intensity seen by the detector. The grey line near 2 eV represents the pump energy. The inset labels are the number of laser shots taken and the chopping strategy used.} -\end{figure} - -Figure \ref{fig:ta-chopping-comparison} shows the effects of dual chopping for some representative -MoS\textsubscript{2} TA data. % -Each subplot is a probe wigner, with the vertical grey line representing the pump energy. % -Note that the single chopper passes pump scatter, visible as a time-invariant increase in intensity -when the probe and monochromator are near the pump energy. % -Dual chopping efficiently removes pump scatter, but at the cost of signal to noise for the same -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. % - -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, -averaging over many shots with random phase will cause the interference term to approach zero. % -This is a well known strategy for removing unwanted interference terms \cite{SpectorIvanC2015a, - McClainBrianL2004a}. % - -\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{ - - \frac{B}{B_{PU}} + - \frac{D}{D_{PR}}}{} -\end{equation} - -\section{Light Generation} % --------------------------------------------------------------------- - -\subsection{Automated OPA Tuning} - -\section{Optomechanics} % ------------------------------------------------------------------------ - -\subsection{Automated Neutral Density Wheels} -- cgit v1.2.3