CERN Accelerating science

Geometry of a ray emitted by the source point $S$ at $(\vec r, z)$ and absorbed by the detector at $\vec r\ ''$ after passing through the coded mask in $\vec r\ '$.

A typical MURA $17\times 17$ matrix. The orange pads correspond to entry 1 and the white ones correspond to 0.

A mosaic of four MURA $17\times 17$ matrices, after global permutations both of raws and columms. Black dashed lines delimit a basic central mask, the other three are spread in the remaining sectors. The orange pads correspond to entry 1 and the white ones correspond to 0.

Possible setup with couples of parallel devices (mask-mosaics and detectors). The distances $a$ and $b$ are for mask-focal plane and mask - detector, respectively. In this work the setup with $s=0$ (coincident focal planes) is used for the simulation. Also a setup with $s<0$ could be designed.

\emph{Left} - A source S seen by a pair of single-pinhole cameras sharing the focal plane ($f_A = f_B$). $P_A$ and $P_B$ are the apparent positions observed by $O_A$ and $O_B$, respectively. \emph{Right} - A source S seen by a pair of single-pinhole cameras with distinct focal planes ($f_A \neq f_B$), separated by a supplementary distance $s$. Again, $P_A$ and $P_B$ are the apparent positions observed by $O_A$ and $O_B$, respectively.

\emph{Left} - A source S seen by a pair of single-pinhole cameras sharing the focal plane ($f_A = f_B$). $P_A$ and $P_B$ are the apparent positions observed by $O_A$ and $O_B$, respectively. \emph{Right} - A source S seen by a pair of single-pinhole cameras with distinct focal planes ($f_A \neq f_B$), separated by a supplementary distance $s$. Again, $P_A$ and $P_B$ are the apparent positions observed by $O_A$ and $O_B$, respectively.

Stereographic projections of a given segment (in red) from three different poles $O_1, \; O_2, \; O_6$. $O_1$ and $O_2$ are on the same $x$-axis, symmetrically placed at the distance $\pm a$ from the origin. The third pole $O_6$ is at $-a$ on the $z$-axis. The red segment $\overline{P_0 P_1}$ indicates a light track, whose projections are indicated in green and orange on the plane $z-y$ and in pink on the plane $x-y$. The other visual poles have been indicated for future reference.

\emph{Left column} The light track crossing is shown in real dimensions in three different views. \emph{Central and right columns} Reconstruction of the light track on 3 couples of parallel detectors. The experimental setup is that in Fig.~\ref{fiducial}.

Simulation of the 4 light-points. The left frame represents the actual sources in the $x-z$ view. The other two frames represent the reconstructed signal by means of two different detectors. Detector A (central frame) is closer to the sources, detector B (right frame) is farther. For detail on the image reconstruction see Sec.~\ref{sec:4punti}.

\emph{Left} frame - simulation of a neutrino interaction. The three tracks do not lay on the same plane. \emph{Central} and \emph{Right} frames show the reconstructed image in the $x-z$ view. The superimposed green dots characterize the pixels selected as signal. The position of the points $\alpha$, $\beta$ and $\gamma$ is estimated by means of the harmonic mean. To compare "truth" and reconstruction look at Table~\ref{tab:vertex}.

Reconstruction of a linear track on three different detectors ($O_1$, $O_2$ and $O_6$). The linear fit is applied to the pixels (black dots) selected according to the preliminary algorithm of signal recognition. The fit parameters shown in the frames have been used to reconstruct the original track in 3-D. See Sec.~\ref{Imanalysis} for details.