diff --git a/documents/thesis/chapters/introduction.tex b/documents/thesis/chapters/introduction.tex
index b805f4a..0904dbd 100644
--- a/documents/thesis/chapters/introduction.tex
+++ b/documents/thesis/chapters/introduction.tex
@@ -13,21 +13,23 @@
 %<<<
 % Intro Cosmic Ray
 In the beginning of the $\mathrm{20^{th}}$~century, various types of radiation were discovered.
-With the balloonflight of Victor Hess \Todo{ref} in \Todo{year}, one type was determined to come from beyond the atmosphere and named ``Cosmic Rays''.
+With the balloonflight of Victor Hess \Todo{ref} in 1912, one type was determined to come from beyond the atmosphere and therefore labelled ``Cosmic Rays''.
 With many discoveries following, the field of (astro-)particle physics evolved.
 \\
 % Current state, (nudge to radio)
-Large collaborations are now detecting cosmic rays with a variety of methods over a large range of energy\Todo{ref figure}.
+Large collaborations are now detecting cosmic rays with a variety of methods over a large range of energy (see Figure~\ref{fig:cr_flux}).
 Still, questions on their origin remain.\Todo{list questions or remove}
 \\
+
 % Radio
 In the last decade, the detection using radio antennas has received significant attention \Todo{ref}, such that collaborations such as \gls{GRAND} are building observatoria that fully rely on radio measurements.
 %
 For such radio arrays, the analyses require an accurate timing of signals within the array.
-Generally, \gls{GNSS} is used to synchronise the detectors.
-However, advanced analyses require an even higher accuracy.
+Generally, \glspl{GNSS} are used to synchronise the detectors.
+However, advanced analyses require an even higher accuracy than currently achieved with these systems.
+\\
+This thesis investigates a relatively straightforward method (and its limits) to obtain this required timing accuracy for radio arrays.
 \\
-In this thesis, methods (and their limits) to obtain this accuracy for radio arrays are investigated.
 
 % >>>
 \section{Cosmic Particles}%<<<<<<
@@ -41,12 +43,12 @@ In this thesis, methods (and their limits) to obtain this accuracy for radio arr
 %\hrule
 
 % Cosmic Particles = CR + Photon + Neutrino
-There is a variety of extra terrestrial particles with which the Earth is bombarded.\Todo{rephrase}
+There is a variety of extra terrestrial particles with which the Earth is bombarded.
 These can be classified into three main types: charged nuclei (typically protons $Z=1$ up to iron $Z=26$), photons and neutrinos, each with different propagation effects.
 \\
 The charged nuclei are the bulk of the measured particles.
-The various magnetic fields that they travel through deflect\Todo{word} them due to their charge.
-They do not point back to their sources because of this.
+The various magnetic fields that they travel through deflect them due to their charge.
+Because of this, they do not point back to their sources.
 \\
 Photons do not suffer from being charged, and thus have the potential to identify their sources.
 However, they can be absorbed and created by multiple mechanisms.\Todo{rephrase/expand}
@@ -79,6 +81,7 @@ Being charged, the nuclei will gyrate in magnetic fields.
 With an approximate size of $ $\Todo{size} and an average magnetic field of $5\mathrm{\;\mu G}$\Todo{}, the Milky Way can only contain particles up to an energy of about $10^{17}\eV$\Todo{fill}.
 Still, particles with higher energies have been observed (see Figure~\ref{fig:}).
 These higher energy particles must thus come from beyond our galaxy.
+\Todo{rewrite paragraph}
 \\
 Likewise, with an rapidly increasing flux for lower energies, one component can be assorted\Todo{rephrase} as coming from within the galaxy.
 \\
@@ -120,6 +123,7 @@ This muonic component is a reliable part to measure.\Todo{rephrase}
 These different components have a different width.\Todo{rephrase}
 The hadronic component is greatly collimated, while the electromagnetic component.
 \\
+\Todo{rewrite paragraph}
 
 \begin{figure}%<<< airshower:depth
 	\centering
@@ -135,7 +139,7 @@ The hadronic component is greatly collimated, while the electromagnetic componen
 Processes in an air showers also generate radiation that can be picked up as coherent radio signals.
 %% Geo Synchro
 Due to the magnetic field of the Earth, the electrons in the air shower generate radiation.
-Termed geomagnetic emission in Figure~\ref{fig:airshower:polarisation}, this has a polarisation that is dependent on the magnetic field vector $B$ and the air shower velocity $v$.
+Termed geomagnetic emission in Figure~\ref{fig:airshower:polarisation}, this has a polarisation that is dependent on the magnetic field vector $\vec{B}$ and the air shower velocity $\vec{v}$.
 \Todo{expand?}
 \\
 %% Askaryan / Charge excess
@@ -149,6 +153,7 @@ Additionally, the shower travels faster than the speed of light in the atmospher
 This generates an
 The detection of the radio signals is limited to an
 This is limited by the so-called Cherenkov angle.
+\Todo{finish paragraph}
 
 
 \begin{figure}%<<< airshower:polarisation
@@ -169,9 +174,10 @@ This is limited by the so-called Cherenkov angle.
 		\label{fig:airshower:polarisation:askaryan}
 	\end{subfigure}
 	\caption{
-		From \protect \cite{Schoorlemmer:2012xpa} \protect\cite{Huege:2017bqv}
+		From \protect \cite{Schoorlemmer:2012xpa, Huege:2017bqv}
 		\protect \Todo{Krijn?}
-		Radio Emission mechanisms: \subref{fig:airshower:polarisation:geomagnetic} geomagnetic and \subref{fig:airshower:polarisation:askaryan} charge-excess)
+		The Radio Emission mechanisms and the resulting polarisations of the radio signal: \subref{fig:airshower:polarisation:geomagnetic} geomagnetic and \subref{fig:airshower:polarisation:askaryan} charge-excess)
+		See text for explanation.
 	}
 	\label{fig:airshower:polarisation}
 \end{figure}%>>>>>>
@@ -188,13 +194,13 @@ With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore h
 \\
 
 These standalone detectors typically receive their timing from a \gls{GNSS}.
-Previously, for timing of water-Cherenkov detectors, this timing accuracy was better than the resolved data\Todo{rephrase}.
+Previously, for timing of water-Cherenkov detectors, this timing accuracy was better than the resolved data.
 Even for the first analyses of radio data, this was sufficient.
 However, for advanced analyses such as radio interferometry, the timing accuracy must be improved.
 \\
 
 % Structure summary
-In this thesis, a solution to enhance the timing accuracy of air shower radio detectors is worked out\Todo{word}.
+In this thesis, a solution to enhance the timing accuracy of air shower radio detectors is demonstrated.
 First, an introduction to radio interferometry is given in Chapter~\ref{sec:interferometry}.
 This will be used later on and gives an insight into the timing accuracy requirements.
 \\
@@ -202,7 +208,7 @@ Chapter~\ref{sec:waveform} reviews typical techniques to analyse waveforms to ob
 \\
 Chapter~\ref{sec:disciplining} introduces the concept of a beacon transmitter to synchronise an array of radio antennas and constrains the achievable timing accuracy using the techniques described in the preceding chapter.
 \\
-Chapter~\ref{sec:single_sine_sync} shows\Todo{word} how a sine wave beacon can synchronise an array while using the radio interferometric approach to resolve\Todo{word} an airshower.
+Chapter~\ref{sec:single_sine_sync} establishes a method to synchronise an array using a single sine wave beacon while using the radio interferometric approach to resolve\Todo{word} an airshower.
 \\
 Finally, Chapter~\ref{sec:gnss_accuracy} investigates the limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
 \end{document}