Commit 1116ef99 authored by Zolnierczuk, Piotr's avatar Zolnierczuk, Piotr
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clarifications in describing coordinate system

parent ae18ece4

doc/coordinate_systems.tex

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@@ -12,51 +12,51 @@ with the center (0,0,0) at the sample position, see Fig.~\ref{fig:ella_top_view} 
	the NSE Laboratory Frame. The frame center is at the sample position.

	Two NSE carriers are shown in blue. L1 - is the source to sample distance

	and L2 is the distance from the sample to the detector.

	The polar angle $\phi$ is measured with respect to the x-axis

	and the center of the of the detector is denoted by $\phi_0$}

	The polar angle $\varphi$ is measured with respect to the x-axis

	and the center of the of the detector is denoted by $\varphi_0$ (scattering angle).}

	\label{fig:ella_top_view}

\end{figure}

The x-axis is horizontal and points downstream from the source toward

sample. The z-axis is vertical pointing up, and the y-axis is

horizontal completing the right handed coordinate system.

The polar angle $\phi$ is measured with respect to the x-axis (polar

The polar angle $\varphi$ is measured with respect to the x-axis (polar

axis) and the azimuthal angle $\theta$ is measured in the y-z plane

with 0 coinciding with the y-axis and clockwise direction when looking

with $0^{\circ}$ coinciding with the y-axis and clockwise direction when looking

downstream with the neutron flux direction.





\subsection{The Detector Coordinate System}

The NSE detector can rotate in horizontal plane (x-y) around the

sample position from $\phi_0=[0,\phi_0^{max}]$, where $\phi_0^{max}$ is instrument specific.

sample position from $\varphi_0=[0,\varphi_0^{max}]$, where $\varphi_0^{max}$ is instrument specific.

\begin{figure}[h!]

	\centering

	\includegraphics[height=7cm]{detector_view}

	\caption[The detector view of the NSE Laboratory Frame]{The detector view of the NSE

	Laboratory Frame.  The spectrometer detector is at the straight configuration,  i.e.

	$\phi_0 = 0$. Neutron flux is pointing out of the page. Each detector pixel is labeled by a pair of indices $(i,j)$.

	$\varphi_0 = 0$. Neutron flux is pointing out of the page. Each detector pixel is labeled by a pair of indices $(i,j)$.

	The horizontal index $i$ is parallel to y-axis and the vertical index $j$ is anti-parallel to the z-axis.}

  \label{fig:ella_detector_view}

\end{figure}

The NSE detector pixels are labeled by a pair of integer indices $(i,j)$

that run from $(1,1)$ to $(NI, NJ)$, where in a typical configuration $NI=NJ=32$.

that run from $(1,1)$ to $(N_i, N_j)$, where in a typical configuration $N_i=N_j=32$.

The horizontal index $i$ is running parallel to the y-axis and the vertical one $j$

is running anti-parallel to the z-axis. The coordinates of

the center of a (i,j) pixel when the detector is at $\phi_0=0$ are given by

the center of a (i,j) pixel when the detector is at $\varphi_0=0$ are given by

\begin{subequations}

\label{eq:pixel_coordinates}

\begin{eqnarray}

  x_C & = & L2                       \\

  y_C & = & +(i-(NI+1)/2)\times W \\

  z_C & = & -(j-(NJ+1)/2) \times H

  y_C & = & +(i-(N_i+1)/2)\times W \\

  z_C & = & -(j-(N_j+1)/2) \times H

\end{eqnarray}

\end{subequations}

where W and H are pixel width and height.

And when the detector is rotated by the angle $\phi_0$ around the sample, the coordinates of the pixel (i,j) are now given

And when the detector is rotated by the angle $\varphi_0$ around the sample, the coordinates of the pixel (i,j) are now given

\begin{subequations}

\label{eq:pixel_coordinates_rotated}

\begin{eqnarray}

  x_R & = & x_C\cos\phi_0 - y_C\sin\phi_0 \\

  y_R & = & x_C\sin\phi_0 + y_C\cos\phi_0 \\

  x_R & = & x_C\cos\varphi_0 - y_C\sin\varphi_0 \\

  y_R & = & x_C\sin\varphi_0 + y_C\cos\varphi_0 \\

  z_R & = & z_C

\end{eqnarray}

\end{subequations}

doc/detector_view.png

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doc/detector_view.svg

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