text:
\subsection{The $4\times4$ pixel detector}
The detector, consisting of 16 stilbene scintillator cuboids of size $5 \times 5 \times 25\,\si{mm^3}$ arranged in a $4 \times 4$ array, allows the detection of neutrons and gammas with spatial resolution. The scintillators are coupled to a Hamamatsu MPPC\textsuperscript{\textregistered} S13361-6050AE-04 SiPM array \cite{sipmarray} and are separated by a grid made from black PVC\footnote{Polyvinyl chloride}. This assembly is surrounded by a black PVC housing to shield it from ambient light. All PVC surfaces facing the scintillators are covered by Vikuiti{\texttrademark} ESR (Enhanced Specular Reflecting) foil to enhance the light collection efficiency. An Elastosil\textsuperscript{\textregistered} RT~604 silicone pad is used to efficiently couple the scintillators to the SiPM array. This optical coupling pad is separated by a white PLA\footnote{Polylactic acid} grid to reduce the amount of optical crosstalk between the pixels. In Figure \ref{fig:detector_setup}, photographs of the detector components are shown.

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.30\textwidth}
    \includegraphics[width=\textwidth]{Detector/photo_detector16px.jpg}
    \subcaption{Scintillator matrix}
    \end{subfigure}
    \begin{subfigure}{0.33\textwidth}
    \includegraphics[width=\textwidth]{Detector/sipmarray_cut.jpg}
    \subcaption{SiPM array}
    \end{subfigure}
    \begin{subfigure}{0.33\textwidth}
    \includegraphics[width=\textwidth]{Detector/20200709_101846.jpg}
    \subcaption{Optical coupling pad}
    \end{subfigure}
    \caption{Photographs of the $4\times4$ pixel detector components.}
    \label{fig:detector_setup}
\end{figure}

\subsubsection{Stilbene}
The organic scintillator crystal stilbene (chemical formula \ce{C14H12}) can be used to discriminate neutron- and gamma-induced signals. For gamma interactions, the scintillation light is created by electrons. For neutron interactions, scintillation light mainly comes from proton recoil events. Stilbene shows longer decay times of scintillation light emission for protons than for electrons \cite{stilbene_decay}. Therefore, neutron-induced signals have a longer falling edge, allowing their identification by pulse shape discrimination methods. \\
Stilbene shows a significant quenching effect. The same amount of deposited energy leads to much less scintillation light in the case of heavy charged particles (e.g. protons) compared to electrons. Also, unlike electrons, heavy charged particles exhibit a non-linear relation between deposited energy and scintillation light output \cite{stilbene_quenching_1, stilbene_quenching_2}. Anisotropy of stilbene's light response for proton recoils is reported, depending on the direction of the recoil relative to the crystal axes \cite{anisotropy}.

\subsubsection{Electronics}
The detector readout system is shown as a schematic sketch in Figure \ref{subfig:blockdiagram}. It consists of the SiPM array, the front end electronics board developed in-house, and the digitization system. \\
The front end electronics board includes the amplifier circuits for all 16 SiPM channels as well as the SiPM bias power supply. For each channel, a positive and a negative unipolar output signal is produced to allow the use of different digitizer types. For the SiPM bias power supply, two Hamamatsu MPPC\textsuperscript{\textregistered} C11204-02 slow control chips \cite{HamamatsuPS} are used. This chip allows for a temperature correction of the SiPM's bias voltage in order to keep the SiPM gain constant. Figure \ref{subfig:camerasetup} shows a photograph of the $4 \times 4 $ detector mounted on the front end electronics board. The detector and the board are housed in an aluminium box. \\
For signal digitization, two CAEN N6730B FADCs \cite{CAENFADC} are used. They have a sampling rate of up to \SI{500}{MS \per \second}, a resolution of 14 bits and a dynamic range of \SI{2}{Vpp}.

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.51\textwidth}
    \includegraphics[width=1.\textwidth]{Detector/blockschaltbild_gross.png}
    \subcaption{}
    \label{subfig:blockdiagram}
    \end{subfigure}
    ~
    \begin{subfigure}{0.46\textwidth}{
    \includegraphics[width=1.\textwidth]{Detector/camera_setup.png}
    \subcaption{}
    \label{subfig:camerasetup}
    }
    \end{subfigure}
    \caption{(a): Schematic sketch of the detector readout. (b): Photograph of the $4 \times 4$ detector with its front end electronics.}
    \label{fig:electronics_setup}
\end{figure}

\subsection{Pulse Shape Discrimination}
\label{sec:psd}
The classification of signals as neutron- or gamma-induced is based on the Tail-to-Total pulse shape discrimination (PSD) method. It is a commonly used method and was recently applied to measurements with stilbene in \cite{stilbene_quenching_2, psd_additional_1}. All analyses described in the following are done individually for each detector pixel. \\
The recorded signals are baseline-corrected and filtered to avoid pile-up events and parasitic signals from the microwave-driven ion source used in the neutron generator. For each remaining event, a PSD variable is calculated, defined as the ratio of the tail integral $Q_\mathrm{Tail}$ and the total integral $Q_\mathrm{L}$ of the pulse:
\begin{equation}
    PSD = \frac{Q_\mathrm{Tail}}{Q_\mathrm{L}} = \frac{Q_\mathrm{L}-Q_\mathrm{S}}{Q_\mathrm{L}}
\end{equation}
$Q_\mathrm{Tail}$ can also be expressed using $Q_\mathrm{L}$ and the short integral $Q_\mathrm{S}$ over the beginning of the pulse. The integrals are defined relative to the \textit{trigger position}, $t_\mathrm{Trg}$, where $50\%$ of the pulse height is reached, and are calculated according to:
\begin{equation}
    Q_\mathrm{L,S} = \int_{t_\mathrm{Trg} + \Delta_\mathrm{off}}^{t_\mathrm{Trg} + \Delta_\mathrm{L,S}}{S(t)\mathrm{d}t}
\end{equation}
with the signal $S(t)$. The integration limits were optimized with regard to the neutron-gamma separation to $\Delta_\mathrm{off} = -40\,\si{\nano\second}$, $\Delta_\mathrm{S} = 24\,\si{\nano\second}$ and $\Delta_\mathrm{L} = 270\,\si{\nano\second}$.

\subsubsection{Energy calibration}
Energy calibration was performed to translate the pulse integrals of unit $\mathrm{mV \cdot ns}$ into the energy deposited in terms of $\mathrm{keV}$ electron equivalent ($\mathrm{keVee}$). For the calibration, the compton edges from a \isotope[22]{Na} and a \isotope[207]{Bi} radioactive source were used, as no photopeak is visible in the recorded gamma spectra due to the low atomic number of the elements present in stilbene. The edge positions are determined following the procedure described in \cite{calibration}. A linear relation between the pulse integral and deposited energy is assumed, based on a fit to the four edge energies and their corresponding pulse integrals.

\subsubsection{Neutron-gamma classification and particle detection rate}
In a 2D histogram with the energy in $\mathrm{keVee}$ on the x-axis and the PSD variable on the y-axis, two distinct bands are present. An example is shown in Figure \ref{fig:psd_3sigma}, including a ``neutron band'' (upper) and a ``gamma band'' (lower). \\
To quantify the amount of neutron and gamma events, 1D histograms of the PSD variable can be produced over the range of energies using a given bin width, with the value in each bin corresponding to vertical slices from the 2D histogram. If neutron and gamma events are separated within such a 1D histogram, two peaks form which can be described by a double-Gaussian fit, corresponding to gamma events (lower peak) and neutron events (higher peak). For higher energies, almost no events occur in the neutron band region. Therefore, only the gamma band is fitted in this region. From the fit results, the neutron and gamma band limits are calculated as the $3\sigma$ boundaries of the Gaussians at each energy, later portrayed on the 2D histogram and shown in Figure \ref{fig:psd_3sigma} as green and red lines. There the neutron and gamma band limits are extrapolated horizontally into the energy regions where almost no neutron and gamma events occur.
A criterion for the separation is the \textit{Figure of Merit (FOM)}:
\begin{equation}
    FOM = \frac{\mu_n - \mu_g}{FWHM_n + FWHM_g} = \frac{\mu_n - \mu_g}{2\sqrt{2 \ln(2)}(\sigma_n + \sigma_g)}
    \label{eq:FOM}
\end{equation}
with the means $\mu_n$ and $\mu_\gamma$ and the standard deviations $\sigma_n$ and $\sigma_\gamma$ extracted from the respective neutron and gamma band Gaussian peaks. If separation is exactly $3(\sigma_n + \sigma_g)$, the formula simplifies to $FOM = \frac{3}{2\sqrt{2 \ln(2)}}  \approx 1.27$. When calculating the FOM for all slices, one can see that it increases towards higher energies, eventually exceeding the $3\sigma$ separation value of $FOM=1.27$. In Figure \ref{fig:psd_3sigma}, the energy where $FOM=1.27$ is exceeded is marked as a red dashed line. For the region to the right of the $FOM=1.27$ position, an event is classified as neutron (gamma) if it lies inside the $3\sigma$ region of the neutron (gamma) band. The region to the left of the $FOM=1.27$ position is not taken into account due to unreliability (sensitivity to fit parameters). \\
Neutron and gamma rates are calculated from the particle counts in the acceptance regions divided by the measurement time. The rates, which differ from pixel to pixel, are typically around $10\,\mathrm{Hz}$ for neutrons. For the example shown in Figure \ref{fig:psd_3sigma}, the accepted neutron rate is $(11.10 \pm 0.07)\,\si{\Hz}$, corresponding to $2.2\%$ of the recorded events. The accepted gamma rate is $(3.60 \pm 0.04)\,\si{\Hz}$, corresponding to $0.7\%$ of the events. Most of the other recorded events lie at very low pulse integrals where there is no reliable separation between gammas and neutrons. \\
The $3\sigma$ limits described above were in practice determined using measurements without any object in front of the detector. In case additional measurements with objects are done with the same detector settings, the limits are re-used, as the absorption measurements are always considered in relation to the measurement without object (the so-called calibration image), see also section \ref{subsec:Absorption_meas}.

\begin{figure}[htbp!]
\centering
\begin{subfigure}{.99\textwidth}
\includegraphics[width=\textwidth]{PSD/fitbands_cal_pixelA4_forward_noAbs_151220.png}
\end{subfigure}
\caption{Example PSD plot, detector pixel A4 (pixel labeling described in figure \ref{fig:efficiency_forward}). The $3\sigma$ limits of the neutron and gamma band are shown in green and red. Extrapolations are performed to the regions where too few events for Gaussian fits are located. The red dashed line marks the energy where $FOM=1.27$.}
\label{fig:psd_3sigma}
\end{figure}

\subsection{The $4\times4$ pixel detector}
The detector consists of 16 stilbene scintillator cuboids that are arranged in a $4 \times 4$ array allowing the detection of neutrons and gammas with spatial resolution. The scintillators are cuboids of size $5 \times 5 \times 25\,\mathrm{mm^3}$ and are coupled to a Hamamatsu MPPC\textsuperscript{\textregistered} S13361-6050AE-04 SiPM array \cite{sipmarray}. The cuboids are separated by a grid made from black PVC\footnote{Polyvinyl chloride}. Everything is surrounded by a black PVC housing to shield it from ambient light. All PVC surfaces facing the scintillators are covered by Vikuiti{\texttrademark} ESR (Enhanced Specular Reflecting) foil to enhance the light collection efficiency. For the same reason, an Elastosil\textsuperscript{\textregistered} RT 604 silicone pad is used to couple the scintillators to the SiPM array. This optical coupling pad is separated by a white PLA\footnote{Polylactic acid} grid reducing the amount of optical crosstalk between the pixels. In Figure \ref{fig:detector_setup}, photographs of the detector components are shown.

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.30\textwidth}
    \includegraphics[width=\textwidth]{Detector/photo_detector16px.jpg}
    \subcaption{Scintillator matrix}
    \end{subfigure}
    \begin{subfigure}{0.33\textwidth}
    \includegraphics[width=\textwidth]{Detector/sipmarray_cut.jpg}
    \subcaption{SiPM array}
    \end{subfigure}
    \begin{subfigure}{0.33\textwidth}
    \includegraphics[width=\textwidth]{Detector/20200709_101846.jpg}
    \subcaption{Optical coupling pad}
    \end{subfigure}
    \caption{Photographs of the $4\times4$ pixel detector components.}
    \label{fig:detector_setup}
\end{figure}

\subsubsection{Stilbene}
The usage of the organic scintillator crystal stilbene (chemical formula \ce{C14H12}) enables the discrimination of neutron- and gamma-induced signals. For gamma interactions, the scintillation light is created by electrons while for neutron interactions, the scintillation light mainly comes from proton recoil events. Stilbene shows longer decay times of scintillation light emission for neutron-induced signals, than for gamma-induced signals \cite{stilbene_decay}. Therefore, neutron-induced signals have a longer falling edge, allowing neutron-gamma discrimination by pulse shape discrimination methods. \\
Stilbene shows a significant quenching effect. The same amount of deposited energy leads to much fewer scintillation light when caused by heavy charged particles (e.g. protons) instead of electrons. For electrons, a linear relation between the deposited energy and the scintillation light output can be assumed, while the relation is non-linear for heavy charged particles \cite{stilbene_quenching_1, stilbene_quenching_2}. Also, an anisotropy of Stilbene's light response for proton recoils is reported, depending on the direction of the recoil relative to the crystal axes \cite{anisotropy}.

\subsubsection{Electronics}
The detector readout system is shown as a schematic sketch in Figure \ref{subfig:blockdiagram}. It consists of the SiPM array plus the front end custom electronics board developed in-house, and the digitization system. \\
The front end electronics board includes the amplifier circuits for all 16 SiPM channels as well as the SiPM power supplies. For each channel, a positive and a negative unipolar output signal is provided to enable the use of different digitizer types. For the SiPM power supply, two Hamamatsu MPPC\textsuperscript{\textregistered} C11204-02 slow control chips \cite{HamamatsuPS} are used. This chip allows for a temperature correction of the SiPM's bias voltage in order to keep the SiPM gain constant. Figure \ref{subfig:camerasetup} shows a photograph of the $4 \times 4 $ detector mounted on the front end electronics board. The detector and the board are placed inside an aluminium box. \\
For signal digitization, two CAEN N6730B FADCs \cite{CAENFADC} are used. They have a sampling rate of up to \SI{500}{MS \per \second}, a resolution of 14 bits and a dynamic range of \SI{2}{Vpp}.

\begin{figure}[h!]
    \centering
    \begin{subfigure}{0.47\textwidth}
    \includegraphics[width=1.\textwidth]{Detector/blockschaltbild.png}
    \subcaption{}
    \label{subfig:blockdiagram}
    \end{subfigure}
    \begin{subfigure}{0.47\textwidth}{
    \includegraphics[width=1.\textwidth]{Detector/camera_setup.png}
    \subcaption{}
    \label{subfig:camerasetup}
    }
    \end{subfigure}
    \caption{(a): Schematic sketch of the detector readout. (b): Photograph of the $4 \times 4$ detector with its front end electronics.}
    \label{fig:electronics_setup}
\end{figure}

\subsection{Pulse Shape Discrimination}
\label{sec:psd}
The classification of signals as neutron- or gamma-induced is based on the Tail-to-Total pulse shape discrimination (PSD) method. All analyses described in the following are done individually for each detector pixel. \\
In a first instance, the recorded signals are baseline-corrected and pile-up events and microwave-induced portions of the signal (caused by the neutron generator ion source) are filtered. For each remaining event, a PSD variable is calculated that is defined as the ratio of the tail integral $Q_\mathrm{Tail}$ and the total integral of the pulse $Q_\mathrm{L}$:
\begin{equation}
    PSD = \frac{Q_\mathrm{Tail}}{Q_\mathrm{L}} = \frac{Q_\mathrm{L}-Q_\mathrm{S}}{Q_\mathrm{L}}
\end{equation}
$Q_\mathrm{Tail}$ can also be expressed using $Q_\mathrm{L}$ and the short integral $Q_\mathrm{S}$ over the beginning of the pulse. The integrals are defined relative to the \textit{trigger position}, $t_\mathrm{Trg}$, where $50\%$ of the pulse height is reached, and are given by
\begin{equation}
    Q_\mathrm{L,S} = \int_{t_\mathrm{Trg} + \Delta_\mathrm{off}}^{t_\mathrm{Trg} + \Delta_\mathrm{L,S}}{S(t)\mathrm{d}t}
\end{equation}
with the signal $S(t)$. The integration limits were optimized with regard to the neutron-gamma separation to $\Delta_\mathrm{off} = -40\,\si{\nano\second}$, $\Delta_\mathrm{S} = 24\,\si{\nano\second}$ and $\Delta_\mathrm{L} = 270\,\si{\nano\second}$.

\subsubsection{Energy calibration}
An energy calibration was performed to translate the pulse integral in $\mathrm{mV \cdot ns}$ into the energy deposited in $\mathrm{keV}$ electron equivalent ($\mathrm{keVee}$). For the calibration, a \isotope[22]{Na} and a \isotope[207]{Bi} radioactive source were used. The calibration was done using the compton edge position, as no photopeak is visible in the recorded gamma spectra due to the low atomic number of the elements present. The position is determined following the procedure described in \cite{calibration}. A linear relation between the pulse integral and deposited energy is assumed, based on a fit to the four measured calibration compton edge energies and their corresponding pulse integrals.

\subsubsection{Neutron-gamma classification and particle detection rate}
When creating a 2D histogram with the energy in $\mathrm{keVee}$ on the x-axis and the PSD variable on the y-axis, a plot with two distinct bands is created. An example plot is shown in Figure \ref{fig:psd_3sigma}. The upper band can be assigned to neutron events (``neutron band''), the lower band to gamma events (``gamma band''). \\
To quantify the amount of neutron and gamma events, 1D histograms of the PSD variable can be produced over the range of energies over a given bin width, corresponding to vertical slices from the 2D histogram. If neutron and gamma events are separated, within such a 1D histogram, two peaks form which can be described by a double-Gaussian fit. The peak region at lower PSD corresponds to gamma events and the other one to neutron events. For higher energies, almost no events occur in the neutron band region. Therefore, only the gamma band is fitted in this region. From the fit results, the neutron and gamma band limits are calculated as the $3\sigma$ boundaries of the Gaussians at each energy. These boundaries can then be portrayed as lines on the 2D histogram. In Figure \ref{fig:psd_3sigma}, the $3\sigma$ boundaries of both bands are shown as green and red lines. Here, the neutron band limits are extrapolated horizontally into the energy region where almost no neutron events occur.
A criterion for the separation is the \textit{Figure of Merit (FOM)}:
\begin{equation}
    FOM = \frac{\mu_n - \mu_g}{FWHM_n + FWHM_g} = \frac{\mu_n - \mu_g}{2\sqrt{2 \ln(2)}(\sigma_n + \sigma_g)}
    \label{eq:FOM}
\end{equation}
In case the separation is exactly $3(\sigma_n + \sigma_g)$, the formula simplifies to $FOM = \frac{3}{2\sqrt{2 \ln(2)}}  \approx 1.27$. When calculating the FOM for all slices, one can see that it increases towards higher energies, exceeding the $3\sigma$ separation value of $FOM=1.27$. In Figure \ref{fig:psd_3sigma}, the energy where $FOM=1.27$ is exceeded is marked as red dashed line. For the region to the right of the $FOM=1.27$ position, an event is classified as neutron (gamma) if it lies inside the $3\sigma$ region of the neutron (gamma) band. The region to the left of the $FOM=1.27$ position is not taken into account as sometimes fit problems occur and the determined event type separation would be highly dependent on the chosen fitting parameters. \\
The accepted neutron and gamma rates are calculated from the particle counts in the acceptance regions divided by the measurement time. The rates differ from pixel to pixel, typical values for neutrons lie around $10\,\mathrm{Hz}$ for the measurements described in this paper. For the example shown in Figure \ref{fig:psd_3sigma}, the accepted neutron rate is $(11.06 \pm 0.06)\,\si{\Hz}$, corresponding to $2.2\%$ of the recorded events. The accepted gamma rate is $(3.57 \pm 0.03)\,\si{\Hz}$, corresponding to $0.7\%$ of the events. Most of the other recorded events lie at very low pulse integrals where no reliable separation between gammas and neutrons can be determined. \\
The $3\sigma$ limits described above are always determined for measurements without any object in front of the detector. In case additional measurements with objects are done with the same detector settings, the limits are re-used and applied to these measurements. The reason is that the absorption measurements are always put in relation to the measurement without object (the so-called calibration image), see also section \ref{subsec:Absorption_meas}.

\begin{figure}[htbp!]
\centering
\begin{subfigure}{.67\textwidth}
\includegraphics[width=\textwidth]{PSD/fitbands_cal_pixelA4_forward_noAbs.png}
\end{subfigure}
~
\begin{subfigure}{.31\textwidth}
\includegraphics[width=\textwidth]{Detector/pixel_labeling.pdf}
\end{subfigure}
\caption{Left: Example PSD plot, detector pixel A4. The $3\sigma$ limits of the neutron and gamma band are shown in green and red. Extrapolations are performed to the regions where too few events for Gaussian fits are located. The red dashed line marks the energy where $FOM=1.27$. Right: Detector pixel labeling, as seen from the incoming particle's perspective.}
\label{fig:psd_3sigma}
\end{figure}

\subsection{Comparison with Geant4 simulations}
\label{sec:Geant4}
Geant4 simulations of the setup were done to better understand the neutron interactions in the attenuator objects and in the detector.

\subsubsection{Geant4 setup}
The Geant4 simulation setup consists of a detailed detector model along with attenuator objects and optionally a PE block, as shown in Figure \ref{fig:geant4model}. It is assumed that incoming neutrons are emitted from a point source at \SI{80}{cm} distance from the detector with a spectrum defined according to an emission in either the forward or \SI{90}{\degree} direction. \\
The simulation stores the neutron interactions in the step wedge and the interactions, energy losses by particle type and amount of created scintillation light in the detector pixels.
Geant4 version 10.05.p01 \cite{Geant4} is used and the physics list essentially corresponds to the QGSP\textunderscore BIC\textunderscore HP list, but using G4EmStandardPhysics\textunderscore option4 and G4OpticalPhysics \cite{Geant4Physics}. The JEFF3.3 library is used for the neutron interaction data. The particle-dependent scintillation light output is modeled based on Birk's law \cite{Birk}.

\begin{figure}[htbp!]
    \centering
    \includegraphics[width=0.7\textwidth]{Geant4/Example_stepwedge_rotated_3_labels.png}
    \caption{Geant4 detector model with attenuator step wedge (Fe-Al-PMMA) placed in front of the detector. In the simulation, steel is approximated as pure iron because the exact steel composition is unknown, but the difference in attenuation should be very small.}
    \label{fig:geant4model}
\end{figure}

\subsubsection{Spectra and Efficiency}
One aspect of the simulation is the amount of scintillation light, which can be transferred to an energy spectrum in keVee by dividing the number of photons produced by stilbene's light yield. When excluding scintillation light caused by electrons and gammas, one gets a spectrum that can be compared to the measured one. In Figure \ref{fig:sim_spec}, very good agreement between simulation and experiment can be seen for two different pixels. In order to achieve this agreement, the simulation parameters \textit{Birk's constant, kB,} and the \textit{intrinsic resolution} were optimized. A larger value of $kB$ means that proton recoils lead to less light compared to electron interactions. The intrinsic resolution describes the fluctuation of the amount of created scintillation light. To get a good agreement for all pixels, it turned out that at least two different classes of stilbene need to be defined, one with a Birk's constant of $kB=0.135~\si{mm/MeV}$ and one with $kB=0.185~\si{mm/MeV}$ (red or blue stilbene crystals in Figure \ref{fig:geant4model}). These values of $kB$ cannot be seen as a physical Birk's constant but are simply parameters used to increase the simulation accuracy. The same is true for the intrinsic resolution. Reasons for the pixel to pixel differences may include the anisotropy of stilbene \cite{anisotropy}, differences in the light propagation within the scintillators, and variation of light detection at the SiPMs. Light propagation is not included explicitly in the simulation, so its effect is instead represented by the tuning of the aforementioned parameters.

\begin{figure}[htbp!]
    \centering
    \includegraphics[width=.49\textwidth]{Geant4/comparespec_sim_A1_180820_fontsize.png}
    ~
    \includegraphics[width=.49\textwidth]{Geant4/comparespec_sim_B1_180820_fontsize.png}
    \caption{Example simulated (black) and measured (green) spectra, representing the two different stilbene classes. The red and blue dashed lines mark the experimental FOM=1.27 position and the artificial energy cut at \SI{450}{keVee}.  Left: Pixel A1. Right: Pixel B1. The energies are significantly smaller than for pixel A1.}
    \label{fig:sim_spec}
\end{figure}

\noindent To calculate the simulated detection efficiency, the experimentally determined $FOM=1.27$ values are applied to the spectra on a pixel by pixel basis and the integral of the remaining spectra is calculated. Also, a simulation with a PE block was performed and its resulting spectrum subtracted. By dividing the integrals by the expected incoming amount of neutrons at the detector, calculated from the amount of created neutrons, their angular distribution and the distance to the detector, the efficiency is obtained. For the optimized simulation setup, a mean detection efficiency of $(9.87 \pm 0.01)\%$ in the forward direction was determined. This is approximately $0.3$ percentage points higher than the experimentally determined value but within the overall experimental uncertainty. When applying a \SI{450}{keVee} threshold instead of the $FOM=1.27$ thresholds to the simulated data, the mean efficiency is at $(6.25\pm0.01)\%$ approximately 0.9 percentage points larger than the experimental value.\\
In the \SI{90}{\degree} direction, however, the simulated efficiency is only $(9.36 \pm 0.01)\% $, which is approximately 2.5 percentage points smaller than the experimental one, and particularly smaller than in the forward direction. One reason for the higher experimental efficiency is the behavior of pixels A2 and A3, where the experimental efficiencies have quite large uncertainties compared to the other pixels, while the simulation uncertainties are similar for all pixels. This influences the weighted mean efficiency. However, also for the other pixels, the simulated efficiencies are around 1.5-2 percentage points smaller. When applying the \SI{450}{keVee} threshold instead, the mean efficiency is $(4.70\pm0.01)\%$, which is very close to the experimental result. It is therefore still an open question where the discrepancy for the FOM criterion comes from. Also, to get a good agreement between the simulated and measured spectra, the values of the $kB$ parameters need to be set to \SI{0.125}{mm/MeV} and \SI{0.175}{mm/MeV}, indicating a tendency to larger pulse heights at the same amount of deposited energy than for the forward direction measurement. It is an open question what causes these differences. It could be a temperature effect in the measurements, e.g. a higher SiPM overvoltage, even though a temperature correction is applied to the SiPM bias voltage. The SiPM temperature during the \SI{90}{\degree} measurements was approximately \SI{2}{\celsius} lower than during the forward direction measurements.

\subsubsection{Simulated macroscopic cross sections}
Figure \ref{fig:sim_mac} shows the simulated macroscopic cross section $\Sigma$ determined from a simulation with the Fe-Al-PMMA step wedge which assumes a perfect alignment of the step wedge in front of the pixels and the detectors with respect to the source. $\Sigma$ is determined as in the experiment. \\%The determination method of $\Sigma$ is similar to the experiment. \\
As in the experiment, the calculated cross sections are significantly smaller than the literature values for all three materials. Two possible reasons were identified in the simulation. The first contribution is from neutrons interacting in both the object and the detector, which cause up to approximately 8\% of the detected neutrons in the simulation. However, this effect alone cannot fully describe the discrepancy between simulated and literature cross sections. Another contribution comes from multiple interactions in the detector, either in two or more different pixels or in the detector housing and then in a pixel, leading to a background rate of neutrons. The background generated in this way reduces the determined cross section and is of relatively greater importance for pixels covered with a higher-attenuating material and/or a greater material thickness. This effect is not corrected by subtracting the PE measurement, as the PE block is much larger than the detector volume. Multiple interaction events in detector pixels with at least one interaction above the required FOM threshold occur in about 20\% - 25\% of the simulated events when assuming the mean FOM threshold of \SI{318}{keVee} in the forward direction. However, this value also includes very small energy losses of a few keV and does not consider if the neutron was scattered into the pixel where it was counted or vice versa. Using e.g. an arbitrarily chosen \SI{100}{keV} threshold, which corresponds to approximately 3.5\% of the initial neutron energy, the multi-pixel interaction fraction is already reduced to approximately 13\%.  Additionally, neutrons that interact in the detector box and then in the detector need to be considered. It would be interesting for the future to extend the simulation so that the order of neutron interactions in the detector can be reconstructed to quantify the influence of multiple interactions on the determined macroscopic cross section.

\begin{figure}[htbp!]
    \centering
    \includegraphics[width=.9\textwidth]{Geant4/simulated_Sigma_forward115kV.pdf}
    \caption{Simulated macroscopic cross section determined from the Fe-Al-PMMA step wedge's neutron attenuation. The literature cross sections are added for comparison as dotted lines.}
    \label{fig:sim_mac}
\end{figure}

\noindent Both the cross sections for small material thicknesses and the slope of the decrease of the cross sections towards higher material thicknesses are smaller in the simulation than in the experiment. A possible explanation could be a slight misalignment of the step wedge in the experiment. This could either be a shift or a rotation of the step wedge compared to the direct neutron direction of flight, influencing the attenuation in front of the detector pixels. To investigate effects of shifts, the step wedge in the simulation was misaligned in the vertical and horizontal direction by $\pm 1~\si{mm}$ and $\pm~2~\si{mm}$. It should be mentioned that a \SI{2}{mm} shift in the experiment is quite unlikely as great effort was made to correctly position the step wedge in front of the detector. \\
A misalignment in the horizontal direction to the right, shifting the PMMA part slightly into the empty detector row, can be limited to (much) less than \SI{1}{\milli\meter} as this misalignment would cause a much larger shadowing of up to approximately $-12\%$ in the empty row than observed in the measurement. Also, a shift of \SI{2}{mm} to the left can be excluded, as this would cause a smaller experimental cross section for PMMA than for Al, which is not observed.
The decrease of the cross section towards higher material thicknesses could be explained, among other possibilities, by a shift upwards. For example, a pixel that was assumed to be covered by \SI{1}{cm} of material would now be partially covered by \SI{2}{cm} of the same material. Such a shift leads to a higher experimental cross section. This effect is in percentage terms larger for the small material thicknesses. A simulation with such a shift of \SI{1}{mm} fits better to the data than the unshifted simulation. To illustrate this, correction factors for the cross section can be calculated from the simulated data by dividing the literature macroscopic cross sections by the simulated ones. When multiplying the experimental values by the correction factor, the resulting values should ideally correspond to the literature cross sections. Figure \ref{fig:corrected_xs} shows the results for the original and the vertically shifted case. The shifted simulation leads to better agreement between corrected values and literature values, even though there are still some deviations (e.g. \SI{6}{cm} of PMMA). However, it can be concluded that lower experimental macroscopic cross sections are expected, and the exact dependency of the thickness is probably explained by alignment difficulties.

\begin{figure}[htbp!]
    \centering
    \begin{subfigure}{.49\textwidth}
    \includegraphics[width=\textwidth]{Geant4/fGraph_mac_corr_noshift_fontsize.pdf}
    \subcaption{No shift.}
    \end{subfigure}
    ~
    \begin{subfigure}{.49\textwidth}
    \includegraphics[width=\textwidth]{Geant4/fGraph_mac_corr_shiftx-1mm_fontsize.pdf}
    \subcaption{Vertical shift by \SI{1}{mm}.}
    \end{subfigure}
    \caption{Corrected experimental macroscopic cross sections by the simulated cross sections. (a): Using data from the unshifted simulation. (b): Using data from the vertically shifted simulation by \SI{1}{mm} upwards. }
    \label{fig:corrected_xs}
\end{figure}
\subsection{Comparison with Geant4 simulations}
\label{sec:Geant4}
Geant4 simulations of the setup were done to better understand the neutron interactions in the attenuator objects and in the detector.

\subsubsection{Geant4 setup}
The Geant4 simulation setup consists of a detailed detector model along with attenuator objects and optionally a PE block, as shown in Figure \ref{fig:geant4model}.
It is assumed that incoming neutrons are emitted from a point source at \SI{80}{cm} distance from the detector with spectrum defined according to an emission in either the forward or \SI{90}{\degree} direction. \\
The simulation stores the neutron interactions in the step wedge and the interactions, energy losses by particle type and amount of created scintillation light in the detector pixels.
Geant4 version 10.05.p01 \cite{Geant4} is used, the physics list essentially corresponds to the QGSP\textunderscore BIC\textunderscore HP list, but using G4EmStandardPhysics\textunderscore option4 and G4OpticalPhysics \cite{Geant4Physics}. The JEFF3.3 library is used for the neutron interaction data. The particle-dependent scintillation light output is modeled based on Birk's law \cite{Birk}.

\begin{figure}[htbp!]
    \centering
    \includegraphics[width=0.7\textwidth]{Geant4/Example_stepwedge_rotated_3_labels.png}
    \caption{Geant4 detector model with attenuator step wedge (Fe-Al-PMMA) placed in front of the detector. In the simulation, steel is approximated as pure iron because the exact steel composition is unknown, but the difference in attenuation should be very small.}
    \label{fig:geant4model}
\end{figure}

\subsubsection{Spectra and Efficiency}
One aspect of the simulation is the amount of scintillation light, which can be transferred to an energy spectrum in keVee by dividing the number of photons by stilbene's light yield. When excluding scintillation light caused by electrons and gammas, one gets a spectrum that can be compared to the measured one. In Figure \ref{fig:sim_spec}, very good agreement between simulation and experiment can be seen for two different pixels. In order to achieve this agreement, the simulation parameters \textit{Birk's constant, kB,} and the \textit{intrinsic resolution} were optimized. A larger value of $kB$ means that proton recoils lead to less light compared to electron interactions. The intrinsic resolution describes the fluctuation of the amount of created scintillation light. It turned out that to get a good agreement for most pixels at least two different classes of stilbene need to be defined, one with a Birk's constant of $kB=0.135~\si{mm/MeV}$ and one with $kB=0.185~\si{mm/MeV}$ (red or blue stilbene crystals in Figure \ref{fig:geant4model}). These values of $kB$ cannot be seen as a physical Birk's constant but are simply parameters used to increase the simulation accuracy. The same is true for the intrinsic resolution. A reason for the pixel to pixel differences may be the anisotropy of stilbene \cite{anisotropy}, but also differences in the light propagation within the scintillators and the light detection at the SiPMs could play a role. This light propagation is not included explicitly in the simulation, so its effect is instead represented by the tuning of these parameters.

\begin{figure}[htbp!]
    \centering
    \includegraphics[width=.45\textwidth]{Geant4/comparespec_sim_A1_180820.png}
    \quad
    \includegraphics[width=.45\textwidth]{Geant4/comparespec_sim_B1_180820.png}
    \caption{Example simulated (black) and measured (green) spectra, representing the two different stilbene classes. The red and blue dashed lines mark the experimental FOM=1.27 position and the artificial energy cut at \SI{450}{keVee}.  Left: Pixel A1. Right: Pixel B1. The energies are significantly smaller than for pixel A1.}
    \label{fig:sim_spec}
\end{figure}

\noindent To calculate the simulated detection efficiency, the experimentally determined $FOM=1.27$ values are applied to the spectra pixel per pixel and the integral of the remaining spectra is calculated. Also, a simulation with a PE block was performed and its resulting spectrum subtracted. By dividing by the expected incoming neutron rate at the detector, the efficiency is obtained. For the optimized simulation setup, a mean detection efficiency of $(9.87 \pm 0.01)\%$ in the forward direction was determined. This is approximately $0.3$ percentage points higher than the experimentally determined value and compatible with this result within the overall experimental uncertainty. When applying a \SI{450}{keVee} threshold instead of the $FOM=1.27$ thresholds to the simulated data, the mean efficiency is with $(6.25\pm0.01)\%$ approximately 0.9 percentage points larger than the experimental value.\\
In the \SI{90}{\degree} direction, however, the simulated efficiency is only $(9.36 \pm 0.01)\% $, so approximately 2.5 percentage points smaller than the experimental one, and particularly smaller than in the forward direction. One reason for the higher experimental efficiency is the behavior of pixels A2 and A3, where the experimental efficiencies have quite large uncertainties compared to the other pixels, while the simulation uncertainties are similar for all pixels. This influences the weighted mean efficiency. However, also for the other pixels, the simulated efficiencies are around 1.5-2 percentage points smaller. When applying the \SI{450}{keVee} threshold instead, the mean efficiency is $(4.70\pm0.01)\%$, which is very close to the experimental result. It is therefore still an open question where the discrepancy for the FOM criterion comes from. Also, to get a good agreement between the simulated and measured spectra, the values of the $kB$ parameters need to be set to \SI{0.125}{mm/MeV} and \SI{0.175}{mm/MeV}, indicating a tendency to larger pulse heights at the same amount of deposited energy than for the forward direction measurement. It is an open question what causes these differences. It could be a temperature effect in the measurements, e.g. a higher SiPM overvoltage, even though a temperature correction is applied to the SiPM bias voltage. The SiPM temperature during the \SI{90}{\degree} measurements was approximately \SI{2}{\celsius} lower than during the forward direction measurements.

\subsubsection{Simulated images and macroscopic cross section}
Figure \ref{fig:sim_mac} shows the simulated macroscopic cross section $\Sigma$ determined from a simulation with the Fe-Al-PMMA step wedge which assumes a perfect alignment of the step wedge in front of the pixels and the detectors with respect to the source. The determination method of $\Sigma$ is similar to the experiment. \\
As in the experiment, the calculated cross sections are significantly smaller than the literature values for all three materials. Two possible reasons were identified in the simulation. The first contribution is from neutrons interacting in both the object and the detector, which cause up to approximately 8\% of the detected neutrons in the simulation. It is seen in the simulation that this effect alone cannot fully describe the discrepancy between simulated and literature cross sections. Another contribution could come from multiple interactions in the detector, either in two or more different pixels or in the detector housing and then in a pixel, leading to a background rate of neutrons. The background generated in this way reduces the determined cross section and is of relatively greater importance for pixels covered with a higher-attenuating material and/or a greater material thickness. This effect is not corrected by subtracting the PE measurement, as the PE block is much larger than the detector volume. Multiple interaction events in detector pixels with at least one interaction above the required FOM threshold occur in about 20\% - 25\% of the simulated events when assuming the mean FOM threshold of \SI{318}{keVee} in the forward direction. However, this value also includes very small energy losses of a few keV and does not consider if the neutron was scattered into the pixel where it was detected or vice versa. Using e.g. an arbitrarily chosen \SI{100}{keV} threshold, which corresponds to approximately 3.5\% of the initial neutron energy, the multi-pixel interaction fraction already reduces to approximately 13\%.  Additionally, neutrons that interact in the detector box and then in the detector need to be considered. It would be interesting for the future to extend the simulation so that neutrons that interact first somewhere in the detector box or e.g. in an uncovered pixel and then in a certain covered pixel are counted to quantify the influence on the determined macroscopic cross section.

\begin{figure}[htbp!]
    \centering
    \includegraphics[width=.7\textwidth]{Geant4/simulated_Sigma_forward115kV.pdf}
    \caption{Simulated macroscopic cross section determined from the Fe-Al-PMMA step wedge's neutron attenuation. The literature cross sections are added for comparison as dotted lines.}
    \label{fig:sim_mac}
\end{figure}

\noindent The decrease of the cross section towards higher material thicknesses is smaller in the simulation than in the experiment. Also, the simulated cross sections for small material thicknesses seem to be smaller than in the experiment. A possible explanation could be a slight misalignment of the step wedge in the experiment. This could either be a shift or a rotation of the step wedge compared to the direct neutron direction of flight. To investigate effects of shifts, the step wedge in the simulation was misaligned in the vertical and horizontal direction by $\pm 1~\si{mm}$ and $\pm~2 \si{mm}$. It should be mentioned that a \SI{2}{mm} shift in the experiment is quite unlikely as great effort was made to correctly position the step wedge in front of the detector. \\
A misalignment in horizontal direction to the right, shifting the PMMA part slightly into the empty detector row can be limited to (much) less than \SI{1}{\milli\meter} as this misalignment would cause a much larger shadowing of up to approximately $-12\%$ in the empty row than observed in the measurement. Also, a shift of \SI{2}{mm} to the left can be excluded, as this would cause a smaller experimental cross section for PMMA than for Al, which is also not observed.
The decrease of the cross section towards higher material thicknesses could be i.a.~explained by a shift upwards. In this case, a pixel e.g. covered with \SI{1}{cm} of material would also be partially covered by \SI{2}{cm} of material, leading to a higher cross section. This effect is as a percent larger for the small material thicknesses. A simulation with such a shift of \SI{1}{mm} fits better to the data than the unshifted simulation. To illustrate this, correction factors for the cross section can be calculated from the simulated data by dividing the literature macroscopic cross sections by the simulated ones. When multiplying the experimental values by the correction factor, the resulting values should ideally correspond to the literature cross sections. Figure \ref{fig:corrected_xs} shows the results for the original and the vertically shifted case. The shifted simulation leads to better agreement between corrected values and literature values, even though there are still some deviations (e.g. \SI{6}{cm} of PMMA). However, it can be concluded that lower experimental macroscopic cross sections are expected, and the exact dependency of the thickness is probably explained by alignment difficulties.

\begin{figure}[htbp!]
    \centering
    \begin{subfigure}{.47\textwidth}
    \includegraphics[width=\textwidth]{Geant4/fGraph_mac_corr_noshift.png}
    \subcaption{No shift.}
    \end{subfigure}
    \begin{subfigure}{.47\textwidth}
    \includegraphics[width=\textwidth]{Geant4/fGraph_mac_corr.png}
    \subcaption{Vertical shift by \SI{1}{mm}.}
    \end{subfigure}
    \caption{Corrected experimental macroscopic cross sections by the simulated cross sections. (a): Using data from the unshifted simulation. (b): Using data from the vertically shifted simulation by \SI{1}{mm} upwards. }
    \label{fig:corrected_xs}
\end{figure}

\section{Introduction}
\label{sec:intro}
\input{introduction.tex}
\section{Detector and set-up}
\label{sec:detector}
\input{detector_revised.tex}
\section{Experimental setup}
\label{sec:generator}
\subsection{D-D neutron source}
\label{subsec:source}
\input{source_info.tex}
\subsection{Detector arrangement}
\label{subsec:setup}
\input{measurement_setup_revised.tex}
\section{D-D generator measurement results}
\label{sec:results}
\input{results_revised.tex}
\input{geant4_revised.tex}
\section{Conclusion}
\input{conclusion_revised.tex}

\acknowledgments
We would like to thank the Paul Scherrer Institute Laboratory for Reactor Physics and Thermal-Hydraulics, in particular Heiko Kromer and Alexander Wolfertz, for the opportunity to test our detector system at their facility as well as their support during the organisation, execution and analysis of the measurements.

\subsection{Detection efficiency for D-D neutrons}
The detection efficiency $\epsilon$ is defined by
\begin{equation}
    \epsilon = \frac{R_\mathrm{det}}{R_\mathrm{inc}}
\end{equation}
with the detected neutron rate $R_\mathrm{det}$ and the incoming neutron rate at the scintillator position $R_\mathrm{inc}$, which can be expressed by
\begin{equation}
    R_\mathrm{inc} = R_0 \cdot \frac{F_\mathrm{det} \cdot f_\mathrm{geom} \cdot f_\mathrm{abs} }{4 \pi d^2}
\end{equation}
Here, $R_0$ is the emitted neutron rate, $d$ is the distance to the detector and $F_\mathrm{det}$ is the scintillators' front surface area. The factor $f_\mathrm{geom}$ describes the non-isotropic neutron emission of the generator, see also section \ref{sec:generator}. The factor $f_\mathrm{abs}$ describes the attenuation of neutrons in the generator itself (e.g.. vacuum chamber and target rod) for a given measurement direction, as well as in the lead plate used to shield X-rays. For the estimation of $f_\mathrm{abs}$, microscopic cross section data from the JEFF 3.3 \cite{JEFF} and ENDF/B-VII.1 \cite{ENDF} database evaluated for the neutron generator output spectrum is used. \\
The detected rate $R_\mathrm{det}$ only refers to neutrons directly coming from the generator. Therefore, the background rate, which are neutrons scattered from other directions into the detector, needs to be subtracted from the total rate measured without any object in between the generator and the detector. The background rate is determined by a measurement with PE block, as described in section \ref{subsec:setup}. To consider the fluctuating neutron generator emission, the emitted neutron rate $R_0$ is determined as the average emitted neutron rate during the measurement without object and the rate with PE block needs to be weighted by this rate so that the scattered contribution is proportionally subtracted. The weighting factor can be expressed as $R_0/R_\mathrm{0,PE}$, with $R_\mathrm{0,PE}$ being the average emitted neutron rate during the measurement with PE block.

\subsubsection{Uncertainty estimation}
The uncertainty of the efficiency consists of two parts: a statistical uncertainty from the particle counts that varies from detector pixel to pixel, and a correlated systematic uncertainty for all pixels due to a potential fixed offset between estimated and actual incoming neutron rate. This systematic uncertainty would shift the efficiencies for all pixels in the same direction.\\
The statistical uncertainty can be subdivided into a Poisson error based on the number of counts as well as an uncertainty from the $FOM=1.27$ position. The main contributions to the systematic uncertainty are the errors on the emitted neutron rate $R_0$, on the distance $d$ and on the factor $f_\mathrm{abs}$. The uncertainty on $f_\mathrm{abs}$ arises from the  uncertainties on the thickness of the lead plate, the neutron paths through the generator and, to a small extent, on the microscopic cross sections of the materials. It was roughly estimated to be a 2\% from the amount of material crossed by the neutrons in the generator structures and varying the lead plate thickness in between 1 and 2 \si{\milli\metre}. \\
The weighted mean over all pixels is calculated taking only the statistical uncertainties into account. To illustrate the effect of the correlated uncertainty, the weighted mean is also calculated after shifting the data by $1\sigma_\mathrm{sys}$ up or down.

\subsubsection{Results}
In Figure \ref{fig:efficiency_forward}, the detection efficiencies for each pixel determined from a measurement in the forward direction are shown. In Figure \ref{fig:efficiency_90and115deg}, the same is shown for measurements along the \SI{90}{\degree} and the \SI{115}{\degree} directions. \\
The efficiency is overall on the order of $10\%$, but fluctuates from pixel to pixel, especially for A3 which has a much smaller efficiency than the others. A closer look at this pixel shows that its pulses are smaller and the separation between neutrons and gammas is worse than for most other pixels. In contrast, the pixels B2, C4, and D4 show an above average efficiency. In these pixels the neutron band ends at a relatively high energy, which results in better particle separation. The difference in performance from one pixel to another might be explained by variations in SiPM to crystal coupling or in characteristics of the stilbene crystal itself. Differences can occur in light propagation (e.g., different surface structures), but also in scintillation light creation, e.g., due to Stilbene's anisotropy \cite{anisotropy}.  \\
Comparing the measured efficiency in the \SI{90}{\degree} and \SI{115}{\degree} direction, the former is approximately 2.4 percentage points larger, the latter approximately 0.5 percentage points smaller than in forward direction. The variation from pixel to pixel, however, looks similar in all measurements. A larger efficiency in the \SI{90}{\degree} direction is a priori unexpected, as the neutron energy is smaller and therefore the number of events above the energy threshold should be smaller. This effect should only be partly compensated by the increase of stilbene's proton recoil interaction cross section towards lower neutron energies. The difference is probably not explained by the uncertainty in the total neutron generator output rate, as this error is expected to be a shift of the output that is in the same direction for all measurements. Also, the uncertainty on the distance and the self-absorption cannot explain the large difference. We therefore think that the difference is due to the process of neutron event identification in the two measurements. As described in section \ref{sec:psd}, only the $FOM>1.27$ energy region in the PSD plot is considered for neutron counting, and this is determined separately for each angle. For the \SI{90}{\degree} measurement, $FOM=1.27$ is reached at $E=303.2\,\si{keVee}$ when averaging over all pixels, for the forward direction, it is reached at $E=318.7\,\si{keVee}$, indicating a better separation of neutron and gamma band in \SI{90}{\degree} direction. The lower threshold needed to achieve the defined $FOM$ leads to a larger energy range considered for neutron counting, and effectively a higher detection efficiency. When applying an arbitrarily chosen constant higher energy threshold of \SI{450}{keVee} across all measured data, which is slightly above the largest $FOM=1.27$ position, the mean efficiency in the \SI{90}{\degree} direction is $4.7\,\%$, which is smaller than the forward direction value of $5.4\,\%$, which fits qualitatively much better to the expected trend. One possible explanation for the variation in neutron-gamma separation is a varying amount of gamma and X-ray flux around the source, for example if one direction was better shielded with lead than another. The lead shielding was not applied in a precisely uniform way, so it could be that the \SI{90}{\degree} direction was better lead shielded, leading to less gamma and X-ray contamination at low energies and therefore a ``cleaner'' PSD plot and a neutron-gamma separability at lower energy. However, to be certain, this should be studied more carefully in the future.

\begin{figure}[htbp!]
    \centering
    \begin{subfigure}{.68\textwidth}
    \includegraphics[width=\textwidth]{Efficiency/PSI_DD_AbsStair_fw_7_02032020_plot_efficiency_PE_corr_avshift_pb1_5mm.pdf}
    \end{subfigure}
    ~
    \begin{subfigure}{.3\textwidth}
    \includegraphics[width=\textwidth]{Detector/pixel_layout_fontsize.pdf}
    \end{subfigure}
    \caption{Left: Detection efficiency in \SI{0}{\degree} direction for each detector pixel. Three uncertainties are shown. The statistical (Poisson) uncertainty due to the particle counts (in black), an uncertainty due to the error on the $FOM = 1.27$ position (in blue) and a combined uncertainty including the systematic error arising from the error on $R_\mathrm{inc}$ (in green). Also, the weighted mean (green line) with its statistical and systematic error (green dotted lines) is shown. Right: Detector pixel labeling, as seen from the incoming particle's perspective.}
    \label{fig:efficiency_forward}
\end{figure}

\begin{figure}[htbp!]
\centering
\begin{subfigure}{.49\textwidth}
\includegraphics[width=\textwidth]{Efficiency/PSI_DD_NoAbs90Deg_AbsStair_fw_2_03032020_plot_efficiency_PE_corr_avshift_pb1_5mm.pdf}
\subcaption{\SI{90}{\degree} direction}
\end{subfigure}
~
\begin{subfigure}{.49\textwidth}
\includegraphics[width=\textwidth]{Efficiency/PSI_DD_AbsStair115Deg_fw_5_03032020_plot_efficiency_PE_corr_avshift_pb1_5mm.pdf}
\subcaption{\SI{115}{\degree} direction \textit{(*)}}
\end{subfigure}
\caption{Detection efficiency in \SI{90}{\degree} and \SI{115}{\degree} direction for each detector pixel. For an uncertainty description, see Figure \ref{fig:efficiency_forward}. \textit{(*): No data for pixel C4 available as it wasn't connected to the readout electronics in this measurement. }}
\label{fig:efficiency_90and115deg}
\end{figure}

\subsection{Attenuation measurements}
\label{subsec:Absorption_meas}
The goal of the attenuation measurements is the experimental calculation of macroscopic cross sections which can be compared to literature values. Gamma signals are separated by the PSD algorithm and gamma attenuation is not considered, as the neutron generator does not produce a localized source of gammas but they are rather created from activation processes in all surrounding materials, so that their direction of origin is not well defined. \\
Three different attenuation objects (see Figure \ref{fig:absorbers}) are investigated by placing them on a sample holder directly in front of the detector, with the detector in the forward emission direction.
\begin{figure}[htbp!]
    \centering
    \includegraphics[width=.7\textwidth]{Absorber/absorbertreppen.jpg}
    \caption{Photograph of the absorber objects. Left and mid: Small step wedges, step sizes $\{0.5,1.0,1.5,2.0\}\,\si{cm}$. The material combinations are Al-PMMA and PVC-Steel. Right: Large step wedge with step sizes $\{1,2,4,6\}\,\si{cm}$. The materials are steel, Al, PMMA.}
    \label{fig:absorbers}
\end{figure}

\noindent Three measurements (images) were used to determine the attenuation: a so-called calibration image without any material placed in front of the camera, the so-called absorption image with the object and a background image with the PE block. In each case, a neutron rate $R_i$ with $i \in \{cal, obj, PE\}$ relative to the incoming neutron rate during each measurement is calculated. The neutron attenuation can then be expressed by the \textit{differential rate} ($\Delta Rate$) which can be defined as

\begin{equation}
    \label{eq:DeltaRate}
    \Delta Rate = \frac{(R_\mathrm{obj} - R_\mathrm{PE}) - (R_\mathrm{cal} - R_\mathrm{PE})}{R_\mathrm{cal} - R_\mathrm{PE}} = \frac{R_\mathrm{obj} - R_\mathrm{PE}}{R_\mathrm{cal} - R_\mathrm{PE}} -1
\end{equation}

\noindent From the differential rate, the macroscopic cross section $\Sigma$ can be calculated by

\begin{equation}
   \label{eq:attenation_exp}
   R_\mathrm{obj} - R_\mathrm{PE} = (R_\mathrm{cal} - R_\mathrm{PE})\cdot e^{-\Sigma \cdot x}
\end{equation}

\begin{equation}
    \label{eq:Sigma_exp}
     \Sigma = \frac{-1}{x} \ln{\left( \frac{R_\mathrm{obj} - R_\mathrm{PE}}{R_\mathrm{cal} - R_\mathrm{PE}}\right)} = \frac{-1}{x} \ln{\left(\Delta Rate +1\right)}
\end{equation}
The uncertainties of $\Delta Rate$ and $\Sigma$ are calculated via Gaussian error propagation from the uncertainties of $R_i$. Since the detector is not moved during a given measurement series, the uncertainties related to the detector position do not need to be considered.

\subsubsection{Results}
Figure \ref{fig:diffrate} shows the differential rates for the large step wedge and the small Al-PMMA\footnote{Polymethyl methacrylate} and PVC-Steel step wedges (photo in Figure \ref{fig:absorbers}).
The large step wedge covers the detector pixel columns 1, 2 and 3 with steel, aluminium and PMMA. The pixel column 4 is left uncovered. The pixel rows A, B, C and D are covered by \SI{6}{cm}, \SI{4}{cm}, \SI{2}{cm} and \SI{1}{cm} of material, respectively (detector pixel arrangement in Figure \ref{fig:efficiency_forward}). Looking at the differential rates, one can clearly identify the step wedge's structure. Also, differences between the materials can be seen. The smallest attenuation is seen for \SI{1}{\centi\metre} aluminium, the largest attenuation for \SI{6}{\centi \metre} steel. Overall, aluminium is the weakest attenuator and steel is the strongest. For the uncovered row, no significant rate reduction is seen, indicating in particular no shadowing effect. \\
The small step wedges cover all detector pixels. Always two neighbouring pixels in the vertical direction are covered by the same material thickness. The pixel columns 1 and 2 are covered with Al (PVC), the columns 3 and 4 with PMMA (steel). Pixel rows C and D are covered by \SI{0.5}{\centi \meter} or  \SI{1.5}{\centi \meter}, A and B by  \SI{1}{\centi \metre} or  \SI{2}{\centi \metre} of material. In the differential rates, these small thickness differences are still visible, despite some fluctuations. As for the large step wedge, aluminium is the weakest attenuator, it attenuates much less than PMMA and slightly less than PVC. The strongest attenuator is steel. However, the differential rates also show a characteristic problem of the radiographic imaging method. For example, $\Delta Rate$ for \SI{1.5}{\centi \meter} Al and \SI{1}{\centi \meter} PMMA are comparable, so, for an unknown sample, it would be impossible to discriminate between two such objects in case both material and thickness are unknown. Only if one of the quantities is known a priori, the other can be potentially determied from a radiographic image, as long as the materials to be identified have sufficiently different attenuation coefficients. With a tomographic image, this problem is not present, and a spatial distribution of the attenuation coefficient could be determined.

\begin{figure}[htbp!]
    \centering
    \begin{subfigure}{.49\textwidth}
    \includegraphics[width=\textwidth]{Absorber/diffrate_stepwedge.png}
    \subcaption{}
    \end{subfigure}
    ~
    \begin{subfigure}{.49\textwidth}
    \includegraphics[width=\textwidth]{Absorber/diffrate_stepwedge_AlPMMA_PVCFe.png}
    \subcaption{}
    \end{subfigure}
    \caption{Measured neutron differential rates for the step wedges. (a): Steel-Al-PMMA step wedge. Materials from left to right: Steel $\{6,4,2,1\}\,\si{\centi\meter}$, Al $\{6,4,2,1\}\,\si{\centi\meter}$, PMMA $\{6,4,2,1\}\,\si{\centi\meter}$, not-covered. (b): Al-PMMA and PVC-Steel step wedge. Materials from left to right: Al (PVC) $\{1,1,0.5,0.5\}\,\si{\centi\meter}$, Al (PVC) $\{2,2,1.5,1.5\}\,\si{\centi\meter}$, PMMA (steel) $\{2,2,1.5,1.5\}\,\si{\centi\meter}$, PMMA (steel) $\{1,1,0.5,0.5\}\,\si{\centi\meter}$.}
    \label{fig:diffrate}
\end{figure}

\noindent From the $\Delta Rate$, the macroscopic cross sections are calculated according to equation \eqref{eq:Sigma_exp} and are shown in Figure \ref{fig:mac_crosssection} both for the large step wedge and the small step wedges Al-PMMA and PVC-Steel. The figures also show the expected values according to microscopic cross section data (JEFF3.3 and ENDF/B-VII.1 database) combined with the previously given fast neutron spectra. The results from the large and the small step wedges for steel, Al and PMMA are within the uncertainties. While the material sequence is correctly reproduced within the uncertainties, it can be seen that the experimentally determined cross sections are generally significantly smaller that the literature values. For the large step wedge, the difference gets larger as the material thickness increases, especially for steel. This discrepancy was further studied using simulations, as described in section \ref{sec:Geant4}

\begin{figure}[htbp!]
    \centering
    \begin{subfigure}{.49\textwidth}
    \includegraphics[width=\textwidth]{Absorber/PSI_DD_AbsStair_fw_7_02032020_Sigma_PE_fontsize.pdf}
    \subcaption{Step wedge Steel-Al-PMMA}
    \end{subfigure}
    ~
    \begin{subfigure}{.49\textwidth}
    \includegraphics[width=\textwidth]{Absorber/PSI_DD_AbsSmallStep_fw_10_02032020_Sigma_PE_fontsize.pdf}
    \subcaption{Step wedges Al-PMMA and PVC-Steel}
    \end{subfigure}
    \caption{Macroscopic cross section for steel, aluminium, PMMA, and PVC, determined from measurements with the Fe-Al-PMMA step wedge (in (a)) and the small step wedges (in (b)). The literature values calculated from JEFF 3.3 and ENDF/B-VII.1 microscopic cross section data are marked in the plots as dotted lines. }
    \label{fig:mac_crosssection}
\end{figure}

\subsection{Detection efficiency for D-D neutrons}
The detection efficiency $\epsilon$ is defined by
\begin{equation}
    \epsilon = \frac{R_\mathrm{det}}{R_\mathrm{inc}}
\end{equation}
with the detected neutron rate $R_\mathrm{det}$ and the incoming neutron rate at the scintillator position $R_\mathrm{inc}$, which can be expressed by
\begin{equation}
    R_\mathrm{inc} = R_0 \cdot \frac{F_\mathrm{det} \cdot f_\mathrm{geom} \cdot f_\mathrm{abs} }{4 \pi d^2}
\end{equation}
Here, $R_0$ is the emitted neutron rate, $d$ is the distance to the detector and $F_\mathrm{det}$ is the scintillators' front surface area. The factor $f_\mathrm{geom}$ describes the non-isotropic neutron emission of the generator, see also section \ref{sec:generator}. The factor $f_\mathrm{abs}$ describes the attenuation of neutrons in the generator itself or in the lead plate used to shield X-rays. For the estimation of $f_\mathrm{abs}$, microscopic cross section data from the JEFF 3.3 \cite{JEFF} and ENDF/B-VII.1 \cite{ENDF} database evaluated for the neutron generator output spectrum is used. An uncertainty of 2\% is assumed, due to uncertainties on the lead plate thickness, the cross sections and the neutron paths through the generator.
For the detected rate $R_\mathrm{det}$, two measurements are necessary. First, a measurement without any object between the generator and the detector, which includes detected neutrons both directly from the generator and scattered from other directions (background neutrons). For the efficiency calculation, only the direct neutrons are needed. Therefore, the background rate $R_\mathrm{BG}$ needs to be subtracted. The background is determined from a measurement with PE block, as described in section \ref{subsec:setup}. The neutron rate from this measurement must be weighted by the neutron generator output during the efficiency measurement, as the output varies with time.

\subsubsection{Uncertainty estimation}
The uncertainty on the efficiency consists of two parts: a statistical uncertainty from the particle counts that varies from detector pixel to pixel, and a correlated systematic uncertainty for all pixels due to the incoming neutron rate. This systematic uncertainty would shift all efficiencies in the same direction.\\
The statistical uncertainty can be subdivided into a Poisson error based on the number of counts as well as an uncertainty from the $FOM=1.27$ position. The main contributions to the systematic uncertainty are the errors on the initial neutron rate $R_0$, on the distance $d$ and on the factor $f_\mathrm{abs}$. The errors are propagated to $\epsilon$ via Gaussian error propagation. \\
The weighted mean over all pixels is calculated taking only the statistical uncertainties into account. To illustrate the effect of the correlated uncertainty, the weighted mean is also calculated after shifting the data by $1\sigma_\mathrm{sys}$ up or down.

\subsubsection{Results}
In Figure \ref{fig:efficiency_forward}, the detection efficiencies for each pixel determined from a measurement in the forward direction are shown. In Figure \ref{fig:efficiency_90and115deg}, the same is shown for measurements along the \SI{90}{\degree} and the \SI{115}{\degree} directions. \\
The efficiency lies overall in the order of $10\%$, but fluctuates from pixel to pixel. Especially pixel A3 has a much smaller efficiency than the other pixels in all measurements. A closer look at this pixel shows that its pulses are smaller and the separation between neutrons and gammas is worse than for most other pixels. In contrast, the pixels B2, C4, and D4 show an above average efficiency. In these pixels the neutron band ends at relatively high energy combined with good particle separation. The fluctuations from pixel to pixel may be explained by setup differences such as the coupling qualities between the scintillators and the SiPMs, or by differences of the crystals themselves. Differences can occur in light propagation (e.g., different surface structures), but also in scintillation light creation, e.g., due to Stilbene's anisotropy \cite{anisotropy}.  \\
When comparing the forward direction with the \SI{90}{\degree} and \SI{115}{\degree} direction, it is seen that the efficiency in \SI{90}{\degree} direction seems to be approximately 2.4 percentage points larger, while in \SI{115}{\degree} direction, the efficiency is slightly smaller. The variation from pixel to pixel however looks similar in all measurements. A larger efficiency in \SI{90}{\degree} direction is a priori unexpected, as the neutron energy is smaller and therefore the number of events above the energy threshold should be smaller. This effect should only be slightly compensated by the higher proton recoil interaction cross section in stilbene at around \SI{2.45}{MeV}. The difference is probably not explained by the uncertainty in the total neutron generator output, as this error corresponds to a shift of the output that should be in the same direction for all measurements. Also, the uncertainty on the distance and the self-absorption cannot explain the large difference. We therefore think that the reason lies within the way the signal data was processed, in terms of what signals are considered neutron events and which not. As described in section \ref{sec:psd}, only the $FOM>1.27$ energy region in the PSD plot is considered for neutron counting, and this is determined separately for each angle. For the \SI{90}{\degree} measurement, $FOM=1.27$ is reached at $E=303.2\,\si{keVee}$ when averaging over all pixels, for the forward direction, it is reached at $E=318.7\,\si{keVee}$, indicating a better separation of neutron and gamma band in \SI{90}{\degree} direction. The lower threshold needed to achieve the defined $FOM$ leads to a larger energy range that is considered for the neutron counting, and effectively a higher detection efficiency. When applying an arbitrarily chosen constant higher energy threshold of \SI{450}{keVee} across all measured data, which is slightly above the largest $FOM=1.27$ position, the mean efficiency in the \SI{90}{\degree} direction is $4.7\,\%$, which is smaller than the forward direction value of $5.4\,\%$, which fits qualitatively much better to the expected trend. One possible explanation for the variation in neutron to gamma separation is a varying amount of gamma flux around the source, for example if one direction was better shielded with lead than another. The lead shielding was not applied in a precisely uniform way, and that might contribute to this effect and the variation in efficiency from one direction to another. This effect might be even stronger if X-rays (not gammas) are contributing to the ``gamma'' contribution, as they are more sensitive to variations in the lead shielding. Even though they are nominally of too-low energy to be registered as gamma events, it might be that a very small percentage of them interact within the stilbene very close to the surface of the SiPM, and therefore produce an abnormally large signal which appears as a relatively high energy.  However, to be certain this should be studied more carefully in the future.

\begin{figure}[htbp!]
    \centering
    \includegraphics[width=\textwidth]{Efficiency/PSI_DD_AbsStair_fw_7_02032020_plot_efficiency_PE_corr_avshift_pb1_5mm.pdf}
    \caption{Detection efficiency in \SI{0}{\degree} direction for each detector pixel. Three uncertainties are shown. The statistical (Poisson) uncertainty due to the particle counts (in black), an uncertainty due to the error on the $FOM = 1.27$ position (in blue) and a combined uncertainty including the systematic error arising from the error on $R_\mathrm{inc}$ (in green). Also, the weighted mean (green line) with its statistical and systematic error (green dotted lines) is shown. }
    \label{fig:efficiency_forward}
\end{figure}

\begin{figure}[htbp!]
\centering
\begin{subfigure}{.47\textwidth}
\includegraphics[width=\textwidth]{Efficiency/PSI_DD_NoAbs90Deg_AbsStair_fw_2_03032020_plot_efficiency_PE_corr_avshift_pb1_5mm.pdf}
\subcaption{\SI{90}{\degree} direction}
\end{subfigure}
\begin{subfigure}{.47\textwidth}
\includegraphics[width=\textwidth]{Efficiency/PSI_DD_AbsStair115Deg_fw_5_03032020_plot_efficiency_PE_corr_avshift_pb1_5mm.pdf}
\subcaption{\SI{115}{\degree} direction \textit{(*)}}
\end{subfigure}
\caption{Detection efficiency in \SI{90}{\degree} and \SI{115}{\degree} direction for each detector pixel. For an uncertainty description, see Figure \ref{fig:efficiency_forward}. \textit{(*): No data for pixel C4 available as it wasn't connected to the readout electronics in this measurement. }}
\label{fig:efficiency_90and115deg}
\end{figure}

\subsection{Attenuation measurements}
\label{subsec:Absorption_meas}
The goal of the attenuation measurements is the experimental measurement of fast neutron attenuation in different materials, leading to the calculation of the macroscopic cross section and its comparison to literature values. The attenuation of gammas is not considered, as the neutron generator does not produce initial gammas but they are rather created from activation processes in all surrounding materials, so that their direction of origin is unknown. The recorded gamma interactions are rejected by pulse shape discrimination. \\
Three different attenuation objects (see Figure \ref{fig:absorbers}) are investigated by placing them on a sample holder directly in front of the detector. The detector is placed in the forward direction relative to the generator.
\begin{figure}[htbp!]
    \centering
    \includegraphics[width=.7\textwidth]{Absorber/absorbertreppen.jpg}
    \caption{Photograph of the absorber objects. Left and mid: Small step wedges, step sizes $\{0.5,1.0,1.5,2.0\}\,\si{cm}$. The material combinations are Al-PMMA and PVC-Steel. Right: Large step wedge with step sizes $\{1,2,4,6\}\,\si{cm}$. The materials are steel, Al, PMMA.}
    \label{fig:absorbers}
\end{figure}

\noindent To determine the attenuation of an object, three measurements (images) must be taken: a so-called calibration image without any material placed in front of the camera, the so-called absorption image with the object and a background image with the PE block. In each case, a neutron rate $R_i$ with $i \in \{cal, obj, BG\}$ relative to the incoming neutron rate is calculated. The neutron attenuation can then be expressed by the \textit{differential rate} ($\Delta Rate$) that can be defined as

\begin{equation}
    \label{eq:DeltaRate}
    \Delta Rate = \frac{(R_\mathrm{obj} - R_\mathrm{PE}) - (R_\mathrm{cal} - R_\mathrm{PE})}{R_\mathrm{cal} - R_\mathrm{PE}} = \frac{R_\mathrm{obj} - R_\mathrm{PE}}{R_\mathrm{cal} - R_\mathrm{PE}} -1
\end{equation}

\noindent From the differential rate, the macroscopic cross section $\Sigma$ can be calculated by

\begin{equation}
   \label{eq:attenation_exp}
   R_\mathrm{obj} - R_\mathrm{PE} = (R_\mathrm{cal} - R_\mathrm{PE})\cdot e^{-\Sigma \cdot x}
\end{equation}

\begin{equation}
    \label{eq:Sigma_exp}
     \Sigma = \frac{-1}{x} \ln{\left( \frac{R_\mathrm{obj} - R_\mathrm{PE}}{R_\mathrm{cal} - R_\mathrm{PE}}\right)} = \frac{-1}{x} \ln{\left(\Delta Rate +1\right)}
\end{equation}
The uncertainties of $\Delta Rate$ and $\Sigma$ are calculated via Gaussian error propagation from the uncertainties of $R_i$. Since the detector is not moved during a given measurement series, the uncertainties related to the detector position do not need to be considered.

\subsubsection{Results}
Figure \ref{fig:diffrate} shows the differential rates for the large step wedge and the small Al-PMMA\footnote{Polymethyl methacrylate} and PVC-Steel step wedges (photo in Figure \ref{fig:absorbers}).
The large step wedge covers the detector pixel columns 1, 2 and 3 with steel, aluminium and PMMA. The pixel column 4 is left uncovered. The pixel row A is covered with \SI{6}{\centi \metre} of material, B with \SI{4}{\centi \metre}, C with \SI{2}{\centi \metre} and D with \SI{1}{\centi \metre} (for detector pixel arrangement, see Figure \ref{fig:psd_3sigma}). Looking at the differential rates, one can clearly identify the steps of the step wedge. Also, differences between the materials can be seen. The smallest attenuation is seen for \SI{1}{\centi\metre} aluminium, the largest attenuation for  \SI{6}{\centi \metre} steel. Overall, aluminium is the weakest attenuator, steel the strongest. For the uncovered row, no significant rate reduction is seen, indicating especially no shadowing effect. \\
The small step wedges cover all detector pixels. Always two neighbouring pixels are covered by the same material thickness. The pixel columns 1 and 2 are covered with Al (PVC), the columns 3 and 4 with PMMA (steel). Pixel rows C and D are covered by \SI{0.5}{\centi \meter} or  \SI{1.5}{\centi \meter}, A and B by  \SI{1}{\centi \metre} or  \SI{2}{\centi \metre} of material. In the differential rates, these small thickness differences are still visible, despite some fluctuations. As for the large step wedge, aluminium is the weakest attenuator, it absorbs less than PMMA and slightly less than PVC. The strongest attenuator is Steel. However, the differential rates also show a characteristic problem of the radiographic imaging method. For example, $\Delta Rate$ for \SI{1.5}{\centi \meter} Al and \SI{1}{\centi \meter} PMMA are comparable, so, for an unknown sample, it would be impossible to discriminate between two such objects in case both material and thickness are unknown. If one or the other is known a priori, then the other can potentially be determined from a radiographic image, as long as the materials to be identified have sufficiently different attenuation coefficients. With a tomographic image, this problem is not present, and a spatial distribution of the attenuation coefficient could be determined.

\begin{figure}[htbp!]
    \centering
    \begin{subfigure}{.47\textwidth}
    \includegraphics[width=\textwidth]{Absorber/diffrate_stepwedge.png}
    \subcaption{}
    \end{subfigure}
    \begin{subfigure}{.47\textwidth}
    \includegraphics[width=\textwidth]{Absorber/diffrate_stepwedge_AlPMMA_PVCFe.png}
    \subcaption{}
    \end{subfigure}
    \caption{Measured neutron differential rates for the step wedges. (a): Steel-Al-PMMA step wedge. Materials from left to right: Steel $\{6,4,2,1\}\,\si{\centi\meter}$, Al $\{6,4,2,1\}\,\si{\centi\meter}$, PMMA $\{6,4,2,1\}\,\si{\centi\meter}$, not-covered. (b): Al-PMMA and PVC-Steel step wedge. Materials from left to right: Al (PVC) $\{1,1,0.5,0.5\}\,\si{\centi\meter}$, Al (PVC) $\{2,2,1.5,1.5\}\,\si{\centi\meter}$, PMMA (Steel) $\{2,2,1.5,1.5\}\,\si{\centi\meter}$, PMMA (Steel) $\{1,1,0.5,0.5\}\,\si{\centi\meter}$.}
    \label{fig:diffrate}
\end{figure}

\noindent From the $\Delta Rates$, the macroscopic cross sections are calculated according to equation \eqref{eq:Sigma_exp}. The resulting values are shown in Figure \ref{fig:mac_crosssection} both for the large step wedge  and the small step wedges Al-PMMA and PVC-Steel. The figures also show the theoretically expected values according to literature microscopic cross section data (JEFF3.3 and ENDF/B-VII.1 database) combined with the previously given fast neutron spectra. It can be seen that the experimentally determined cross sections are generally significantly smaller than the literature values. For the large step wedge, the difference gets larger as the material thickness increases, especially for steel. However, the relative attenuation from one material to another qualitatively follows the expected trend. This discrepancy was further studied using simulations, as described in section \ref{sec:Geant4}. The results from the large and the small step wedges for steel, Al and PMMA are within the uncertainties. The material sequence is correctly reproduced within the uncertainties.

\begin{figure}[htbp!]
    \centering
    \begin{subfigure}{.47\textwidth}
    \includegraphics[width=\textwidth]{Absorber/PSI_DD_AbsStair_fw_7_02032020_Sigma_PE.pdf}
    \subcaption{Step wedge Steel-Al-PMMA}
    \end{subfigure}
    \begin{subfigure}{.47\textwidth}
    \includegraphics[width=\textwidth]{Absorber/PSI_DD_AbsSmallStep_fw_10_02032020_Sigma_PE.pdf}
    \subcaption{Step wedges Al-PMMA and PVC-Steel}
    \end{subfigure}
    \caption{Macroscopic cross section for steel, aluminium, PMMA, and PVC, determined from measurements with the Fe-Al-PMMA step wedge (in (a)) and the small step wedges (in (b)). The literature values calculated from JEFF 3.3 and ENDF/B-VII.1 microscopic cross section data are marked in the plots as dotted lines.  }
    \label{fig:mac_crosssection}
\end{figure}

redpajama_set_name: RedPajamaArXiv


Welcome to Limited Motors Auto Group. Be sure to visit our virtual showroom of inventory available for purchase. There you will see detailed information about each vehicle, a picture gallery, as well as convenient ways to contact us for more information about that vehicle. We are located at 2136 East California Ave and are available by phone at 661-404-4599 . You can also get driving directions and hours of service from our user friendly website.


text:
Maxine Waters encourages supporters to harass Trump administration officials
Posted 12:46 PM, June 25, 2018, by CNN Wire
https://ht.cdn.turner.com/cnn/big/politics/2018/06/25/maxine-waters-confront-white-house-officials-espaillat-reax-sot-newday.cnn_2153567_ios_440.mp4
(CNN) — Rep. Maxine Waters called on her supporters to publicly confront and harass members of the Trump administration in response to the "zero tolerance" policy that led to the separation of families at the border.
The California Democrat and vehement critic of President Donald Trump made the comments on Saturday, first at a rally in Los Angeles and later in a television interview. The comments, which come after several Trump administration officials have been recently protested at restaurants, have raised fresh questions about the state of American political discourse and were seized on by Trump for political gain.
"Let's make sure we show up wherever we have to show up. And if you see anybody from that Cabinet in a restaurant, in a department store, at a gasoline station, you get out and you create a crowd. And you push back on them. And you tell them they're not welcome anymore, anywhere. We've got to get the children connected to their parents," Waters said at the Wilshire Federal Building, according to video of the event.
"We don't know what damage has been done to these children. All that we know is they're in cages. They're in prisons. They're in jails. I don't care what they call it, that's where they are and Mr. President, we will see you every day, every hour of the day, everywhere that we are to let you know you cannot get away with this," she added.
Waters appeared on MSNBC later in the day to double down on her remarks, saying she has "no sympathy" for members of the Trump administration.
"The people are going to turn on them. They're going to protest. They're going to absolutely harass them until they decide that they're going to tell the President, 'No, I can't hang with you.'"
CNN reached out to Waters' office on Monday morning and did not immediately receive a response.
Trump misconstrued Waters' comments when he weighed in Monday afternoon.
"Congresswoman Maxine Waters, an extraordinarily low IQ person, has become, together with Nancy Pelosi, the Face of the Democrat Party. She has just called for harm to supporters, of which there are many, of the Make America Great Again movement. Be careful what you wish for Max!"
Waters, however, did not call for physical harm to the officials or harassment against Trump's supporters.
Her comments were criticized by Republicans, though some Democrats were reluctant to take on Waters, a popular figure among progressives and a longtime member of Congress.
House Majority Leader Kevin McCarthy told Fox News Monday the remarks were "very dangerous" and called upon Waters to issue a public apology. Sen. Jeff Flake, a retiring Arizona Republican who has repeatedly criticized Trump, tweeted, "Left or right, nobody deserves this kind of treatment."
Meghan McCain, the daughter of Arizona Republican Sen. John McCain, called Waters' comments "absolutely insane" and "extremely dangerous." McCain, who is also the daughter-in-law of Douglas Domenech, the current Assistant United States Secretary of the Interior for Insular Areas, asked on Twitter, "does this mean when we go out to dinner we should be ambushed?!?"
House Minority Leader Nancy Pelosi referred to Waters' comments as "unacceptable" but blamed Trump's "daily lack of civility" for provoking responses such as that of Waters.
"In the crucial months ahead, we must strive to make America beautiful again. Trump's daily lack of civility has provoked responses that are predictable but unacceptable. As we go forward, we must conduct elections in a way that achieves unity from sea to shining sea," Pelosi tweeted, linking out to a story about the remarks.
Asked about Waters' comments on CNN's "New Day" Monday, Rep. Adriano Espaillat of New York would not criticize his fellow Democrat.
"To get sidetracked into these debates about whether or not somebody was welcome at a restaurant takes our eyes off of what's going on in America today," Espaillat said, later adding, "Maxine Waters is entitled to her opinion and I respect that."
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text:
The new intergenerational workplace: What needs to change?
Last week's ThinkIn, hosted by Tortoise in collaboration with Fora, covered a topic that is on all of our minds. It's one that has been touched on and critiqued from all corners. Can an intergenerational workplace thrive? Can you appeal to Gen Z and your older employees at the same time? These are all questions that were looming over the evening, but we sure got into the granular.
Back in our day…
Now, we tend to live 10 years longer than our parents. An entire decade to fill. This alone brings with it a lot of anxiety and pressure. From a practical level, this has implications on our preparation for retirement, our family plans and fundamentally our careers. It's easy to latch on to stereotypes and point the finger at the younger employees, but we're all very much living it. Equally, as much as Gen Z are firmly rooted in (or just entering) the workplace, this doesn't mean that they should become the be-all and end-all. By next year, a third of the work force will be over 50. That's massive, and it's a great launch point for this topic. The research that came to light on the night suggested that 50s to 60s are half as likely to be offered training opportunities as the 20-30 age bracket, proving employers still have some way to got to catch up with… well… ageing.
Being attuned to our needs
We all have needs in the workplace, but having an awareness of what those needs are and how companies can support them, is key for success. It's something that so many organisations struggle with, brought to light by the audience and their experiences. Beth, who is on a graduate scheme at a London IT company, talked about the struggles she observes with retention at her clients' businesses. It almost seems impossible to get young talent to stay. This opened a broader conversation around modern and current ways of working, and as a result, can we just part with the idea that everyone's goal is to progress at the company they work for? A lot of people use roles as a stepping stone or 'project' to leap into something else. There's nothing wrong with this, and there's an inevitably to this behaviour, especially when you consider the current economic climate. Young people are looking to carve out the best career (and life) for themselves, and that sometimes means taking risks. Due to the fast-moving nature of our time, young people have a lot of anxieties around their future, which sometimes causes them to jump ship and pursue new opportunities if in doubt about their existing role (and its longevity). It's not an attitude that older generations have grown up with, but that doesn't make it wrong.
Bin the blueprint
There's a way to go before we successfully bridge the gap between the generations, and between education and entering work. Take the way Executives treat their teenage children versus how they treat the grads that work for them. There's a stark difference. This dichotomy illuminates the work that needs to be done to create a thriving intergenerational workplace. We need to find a formula for lifelong learning, starting at apprentice level and spanning right through to retirement. This should play into other elements of careers, with opportunities to move sideways and upskill, all while having the support to meet individual potential. This stands for every age group. Pleasingly, there are examples of businesses becoming attuned to the requirements of an intergenerational workplace. The Economist have done away with CVs for their intern programme, and as a result hired a 48-year old mother. This woman doesn't conform to the standard 'intern' image, but she was the best person they interviewed and has gone on to achieve wonderful things in her career. If the format hadn't changed, there's a good chance she wouldn't have been the chosen candidate. Another example is EY dropping degrees form their grad scheme application process, instead favouring interdisciplinary skills.
We're certainly not there yet, but with commitment and an open-mind, we can ensure intergenerational workplaces get the most from everyone. Companies' actions need to reflect the standards that they claim to live by. This currently isn't the case, and leads to a lack of trust and belief in employers. To do this, we need to step away from the idea that the two spectrums of generations are radically different to each other, they're not. Times are changing and jobs no longer have the permanence that they once held. That's fact, and although Gen Z have been born into this reality, it is still well within everyone's rights to adopt and demonstrate this point of view.
Equally we need to tackle age discrimination at both ends, making sure that everyone is judged only on skill and commitment. A report by LinkedIn found that Gen Z are four times more likely to change jobs than Baby Boomers, who average just two jobs in 10 years. But, the desire to leave and move on is measured at a fairly similar level across the two generations. So the difference for Gen Z is the action itself, rather than the feeling.
Heads up: We'll be releasing the full discussion as a podcast episode very soon so keep an eye on our social channels to listen. Looking for more to get stuck into? To see what other ThinkIns are on the horizon and to sign up to join an upcoming conversation, click here. Upcoming Future of Work topics include 'Is it OK to have an office romance?' and 'Do you have to be a psychopath to be a CEO?' – Come and join the discussion.
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text:
The Government Could Be Booting Over 250,000 Legal Salvadoran Immigrants from the US
Kat Armstrong
After nearly 20 years legally working and living in the US, a new rule by the Department of Homeland Security will rescind protections allowing upwards of 250,000 Salvadorans to stay in the country, potentially forcing those protected to be deported to their native El Salvador.
In 2001, an earthquake rocked El Salvador, devastating the country. The earthquake measured between 7.7 and 7.9 on the Richter scale, with at least 944 people killed, and another 5,565 injured. The quake destroyed hundreds of thousands of homes, public buildings, and infrastructure. Within a month, the nation had over 2,500 aftershocks, doing more damage before anything could be repaired in the first place.
Hundreds of thousands of people fled the devastation, with over 250,000 settling in the US. Then-US Attorney General John Ashcroft issued an offer of temporary protected status (TPS) for those in the country. In the intervening years, the TPS has been rolled over, in part due to the fact that El Salvador has never recovered from the quake and its aftershocks, and it remains, according to our own government, "unable…to handle adequately the return of its nationals."
This is the fourth time since his inauguration that the president's administration has announced they would rescind TPS protections. In the summer, thousands of Haitians fled on foot to Montreal, Canada, after the president threatened to rescind TPS protection (which eventually happened in November 2017) for those who fled to the US after the 2010 earthquake that left the nation without electricity and clean water. Haitians cannot return since 2016 saw the country further devastated by Hurricane Matthew.
TPS protections are a form of humanitarian aid that the government provides. This form of immigration allows people already in the country (often without papers) to stay while building a life. Both the GOP and the Democratic party have continued to support the TPS program for decades. Those here under TPS must pay a $495 processing fee every 18 months when they reapply, must keep a clean criminal record, and pass a background check, and in return, they can work legally, while staving off deportation.
Between slowly pulling TPS from the nations enrolled in the program (currently 10: El Salvador, Haiti, Honduras, Nepal, Nicaragua, Somalia, Sudan, South Sudan, Syria, and Yemen, with El Salvador, Haiti, Nicaragua, and Honduras being pulled from the program), and the plans to rescind DACA, millions of legally documented people could be deported in the next 18 months.
The administration, in place of these protections, wants to enact what they describe as a "merit-based" immigration scheme, a points-based system that would only allow "highly skilled" workers into the country. While the plan has been mentioned numerous times, as of yet, there has been no official plan or action on how to roll out such an idea.
Do you know someone whose family may be affected by TPS deportations? Let us know @BritandCo!
(Photo by Alex Wong/Getty Images)
Kat has been a writer, social media maven and mom for longer than she's willing to admit. She's also spent time in front of and behind the camera, interviewing celebs, politicians and acting as a producer for fashion and artistic photography shoots. When she isn't writing for various orgs and publications, she's hanging with her kids, husband and French Bulldog, Peter, in Toronto, Canada.
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text:
Les Garçons est une nouvelle d'Anton Tchekhov parue en 1887
  (Jungens), un film allemand de Robert A. Stemmle sorti en 1941.
 Les Garçons (La Notte brava), un film franco-italien de Mauro Bolognini sorti en 1959.
 Les Garçons, un roman de Henry de Montherlant paru en 1969.

redpajama_set_name: RedPajamaWikipedia