142c142 < %The module dimensions are {79 x 192}{ mm}, and the maximum drift distance is {40}{ mm}. --- > %The module dimensions are {79 x 192}{mm}, and the maximum drift distance is {40}{mm}. 148c148 < The result for the transverse diffusion coefficient $D_{T}$ is {(287.2 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 0 T} and $D_{T}$ {(120.3 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 1 T}. --- > The result for the transverse diffusion coefficient $D_{T}$ is {(287 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 0 T} and $D_{T}$ {(121 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 1 T}. 185c185 < The TPX3 chip can be operated with a low threshold of 515 $e^-$, and has a low equivalent noise charge of about 70 $e^-$. The GridPix single chip and quad detectors have a very fine granularity of {55$\times$55}{ $\rm \mu m^2$} with 256$\times$256 pixels per chip. The device has a high efficiency of about 85\% - discussed in this paper - to detect single ionisation electrons. --- > The TPX3 chip can be operated with a low threshold of 515 $e^-$, and has a low equivalent noise charge of about 70 $e^-$. The GridPix single chip and quad detectors have a very fine granularity of {55$\times$55}{ $\rm \mu m^2$} and a high efficiency of about 85\% - demonstrated in this paper - to detect single ionisation electrons. 187c187 < Based on the experience gained with these detectors a 32 GridPix detector module - consisting of 8 quad detectors - was built. A drift box defining the electric field and gas envelop was constructed. A read out system for up to 128 chips with 4 multiplexers read out by one Speedy Pixel Detector Readout (SPIDR) board \cite{Visser:2015bsa} \cite{Heijden:2017iqd} was designed. After a series of tests using the laser setup \cite{Hartjes:1990} and cosmics in the laboratory at Nikhef, the detector was taken to DESY for a two week testbeam campaign. --- > Based on the experience gained with these detectors a 32 GridPix detector module - consisting of 8 quad detectors - was built. A drift box defining the electric field and gas envelop was constructed. A readout system for up to 128 chips with 4 multiplexers readout by one Speedy Pixel Detector Readout (SPIDR) board \cite{Visser:2015bsa} \cite{Heijden:2017iqd} was designed. After a series of tests using the laser setup \cite{Hartjes:1990} and cosmics in the laboratory at Nikhef, the detector was taken to DESY for a two week testbeam campaign. 198c198 < The four chips which are mounted on a cooled base plate (COCA), are connected with wire bonds to a common central {6}{ mm} wide PCB. A 10 mm wide guard electrode is placed over the wire bonds {1.1}{ mm} above the aluminium grids, in order to prevent field distortions of the electric drift field. The guard electrode is the main inactive area, and its dimensions are set by the space required for the wire bonds. On the back side of the quad module, the PCB is connected to a low voltage regulator. The aluminium grids of the GridPix detectors are connected by {80}{ $\rm \mu$m} insulated copper wires to a high voltage (HV) filtering board. The quad module consumes about {8}{ W} of power of which {2}{ W} is used in the LV regulator. --- > The four chips which are mounted on a cooled base plate (COCA), are connected with wire bonds to a common central {6}{ mm} wide PCB. A 10 mm wide guard electrode is placed over the wire bonds {1.1}{ mm} above the aluminium grids, in order to prevent field distortions of the electric drift field. The guard electrode is the main inactive area, and its dimensions are set by the space required for the wire bonds. On the back side of the quad module, the PCB is connected to a low voltage regulator. The aluminium grids of the GridPix detectors are connected by {80}{ $\rm \mu$m} insulated copper wires to a high voltage (HV) filtering board. The quad module consumes about {8}{W} of power of which {2}{W} is used in the LV regulator. 204c204 < The internal dimensions of the box are {79}{ mm} along the $x$-axis, {192}{ mm} along the $y$-axis, and {53}{ mm} along the $z$-axis (drift direction), and it has a maximum drift length (distance between cathode and read out anode) of {40}{ mm}. --- > The internal dimensions of the box are {79}{ mm} along the $x$-axis, {192}{ mm} along the $y$-axis, and {53}{ mm} along the $z$-axis (drift direction), and it has a maximum drift length (distance between cathode and readout anode) of {40}{ mm}. 225c225 < The data acquisition system of the quad module was adopted to allow for reading out multiple quad detectors. A multiplexer card was developed that handles four quad detectors or 16 chips and combines the TPX3 data into one data stream. For the 32 GridPix module two multiplexers are connected to a SPIDR board that controls the chips and read out process. The read out speed per chip is {160}{ Mbps} and for the multiplexer {2.56}{ Gbps} this corresponds to a maximum rate of {21}{ MHits/s}. For each pixel the precise Time of Arrival (ToA) using a 640 MHz TDC and the time over threshold (ToT) are measured. --- > The data acquisition system of the quad module was adopted to allow for reading out multiple quad detectors. A multiplexer card was developed that handles four quad detectors or 16 chips and combines the TPX3 data into one data stream. For the 32 GridPix module two multiplexers are connected to a SPIDR board that controls the chips and readout process. The readout speed per chip is {160}{ Mbps} and for the multiplexer {2.56}{ Gbps} this corresponds to a maximum rate of {21}{MHits/s}. For each pixel the precise Time of Arrival (ToA) using a 640 MHz TDC and the time over threshold (ToT) are measured. 230c230 < In preparation of the two weeks DESY testbeam campaign, a support frame was designed to move the 32-chip GridPix detector module in the plane perpendicular to the beam by a remotely controlled stage such that the whole detector volume could be probed. The module was mounted upside down with respect to Figure \ref{fig:boxrender} to allow access to the electronics from above. The support frame also held three Mimosa26 silicon detector planes \cite{Diener:2019} - with an active area of (21.2 mm $\times$ 10.6 mm) - placed in front of the detector and three Mimosa26 planes behind the detector. --- > In preparation of the two weeks DESY testbeam campaign, a support frame was designed to move the 32-chip GridPix detector module in the plane perpendicular to the beam by a remotely controlled stage such that the whole detector volume could be probed. The module was mounted upside down with respect to figure \ref{fig:boxrender} to allow access to the electronics from above. The support frame also held three Mimosa26 silicon detector planes \cite{Diener:2019} - with an active area of (21.2 mm $\times$ 10.6 mm) - placed in front of the detector and three Mimosa26 planes behind the detector. 267c267 < The double scintillator coincidence provided a trigger signal to the Trigger Logic Unit (TLU) \cite{TLU} that sends a signal to the telescope read out and the trigger SPIDR. --- > The double scintillator coincidence provided a trigger signal to the Trigger Logic Unit (TLU) \cite{TLU} that sends a signal to the telescope readout and the trigger SPIDR. 269c269 < Unfortunately, the SPIDR trigger had - due to a cabling mistake at the output of the TLU - a common {25}{ ns} flat time jitter. --- > Unfortunately, the SPIDR trigger had - due to a cabling mistake at the output of the TLU - a common {25}{ns} flat time jitter. 302c302 < The $z$ drift coordinate was calculated as the product of the drift time and the drift velocity. This implies that $z_{\rm drift} = - z$ as defined in Figure~\ref{fig:boxrender}. --- > The $z$ drift coordinate was calculated as the product of the drift time and the drift velocity. This implies that $z_{\rm drift} = - z$ as defined in figure~\ref{fig:boxrender}. 304c304 < Based on a Hough transform an estimate of the TPC track position and angles in the middle of the module (at $y$ = 1436 pixels) were obtained. This estimate was used to collect the hits around the TPC track and fit the track parameters. For this fit a linear (for {$B$ = 0 T data}) or a quadratic track (for {$B$ = 1 T} data) model was used. In the fit, the expected uncertainties per hit $\sigma_{xy}$ and $\sigma_z$ were used. The expected uncertainties were derived using the parametrisations discussed in section \ref{sec:hitResolution}. The fit was iterated three times to reject outlier hits at respectively 10, 5 and 2.5 sigma. --- > Based on a Hough transform an estimate of the TPC track position and angles in the middle of the module (at $y$ = 1436 pixels) were obtained. This estimate was used to collect the hits around the TPC track and fit the track parameters. For this fit a linear (for {$B$ = 0 T data}) or a quadratic track (for {$B$ = 1 T} data) model was used. In the fit, the expected uncertainties per hit $\sigma_xy$ and $\sigma_z$ were used. The expected uncertainties were derived using the parametrisations discussed in section \ref{sec:hitResolution}. The fit was iterated three times to reject outlier hits at respectively 10, 5 and 2.5 sigma. 331c331 < An example event from run 6916 without $B$ field with a TPC and a telescope track is shown in Figure \ref{fig:eventDisplay}. --- > An example event from run 6916 without $B$ field with a TPC and a telescope track is shown in figure \ref{fig:eventDisplay}. 350,351c350 < The track residual in $xy$ is the closest point of the the hit at the center of the pixel to track in the $xy$ plane. The residual in $z$ is calculated at this point of closest approach. < The single electron hit resolutions in $xy$ and $z$ will be extracted from the track residuals. --- > The single electron hit resolutions in $xy$ and $z$ will be extracted from the residuals with respect to the fitted track. The track residual in $xy$ is the closest point of the track in the $xy$ plane to the hit at the center of the pixel. The residual in $z$ is calculated at this point of closest approach. 353,354c352,353 < For the resolution studies, runs at three different $z$ stage positions of the TPC were selected where the beam gave hits in the central chips. < The data of 14 central chips (9, 12, 21, 20, 17, 16, 2, 3, 6, 7, 30, 31, 26 and 27) were used. Two chips (8 and 13) were left out because of the E field deformations caused by the short circuit in chip 11. --- > For the resolution studies runs at three different $z$ stage positions of the TPC were selected where the beam gave hits in the central chips. > The data of 14 central chips (9, 12, 21, 20, 17, 16, 2, 3, 6, 7, 30, 31, 26 and 27) was used. Two chips (8 and 13) were left out because of the E field deformations caused by the short circuit in chip 11. 365c364 < Tracks were selected that crossed the fiducial region defined by the central core of the beam. Hits were removed in a region of 20 pixels near the chip edges in $x$. --- > Only hits are used crossing the fiducial region defined by the central core of the beam and staying 20 pixels away in $x$ from the chip edges. 376c375 < to the {$B$ = 0 T} data shown in Figure \ref{fig:resolutionx}. The fit gives a transverse diffusion coefficient $D_T$ of {(287.2$ \pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$. The measured value is in agreement with the value of {287}{ $\rm \mu$m/$\sqrt{\rm cm}$} $\pm$ 4\% predicted by the gas simulation software Magboltz 11.9 \cite{Biagi:1999nwa}. The values of the diffusion coefficients depend on the humidity that was not precisely measured during the testbeam. The humidity strongly affects the drift velocity. Therefore the drift velocity prediction from Magboltz was used to determine the water content per run and predictions for the diffusion coefficients could be obtained. --- > to the {$B$ = 0 T} data shown in Figure \ref{fig:resolutionx}. The fit gives a transverse diffusion coefficient $D_T$ of {(287$ \pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$. The measured value is in agreement with the value of {287}{ $\rm \mu$m/$\sqrt{\rm cm}$} $\pm$ 4\% predicted by the gas simulation software Magboltz 11.9 \cite{Biagi:1999nwa}. The values of the diffusion coefficients depend on the humidity that was not precisely measured during the testbeam. The humidity strongly affects the drift velocity. Therefore the drift velocity prediction from Magboltz was used to determine the water content per run and predictions for the diffusion coefficients could be obtained. 378c377 < A fit to the {$B$ = 1 T} data, also shown in Figure \ref{fig:resolutionx}, gives a transverse diffusion coefficient $D_T$ of {(120.3 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$}. The measured value is in agreement with the value of {119}{ $\rm \mu$m/$\sqrt{\rm cm}$} $\pm$ 2\% predicted by Magboltz. --- > A fit to the {$B$ = 1 T} data, also shown in Figure \ref{fig:resolutionx}, gives a transverse diffusion coefficient $D_T$ of {(121 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$}. The measured value is in agreement with the value of {119}{ $\rm \mu$m/$\sqrt{\rm cm}$} $\pm$ 2\% predicted by Magboltz. 453,454c452,453 < %To compare the precision of the GridPix read out with the precision of conventional pad based TPC read outs, the resolution can be calculated over the length of one pad row. < %For example, at a drift distance of {4}{ mm} the resolution of a single ionisation electron is approximately {250}{ $\rm \mu$m}, so the resolution of a {6}{mm} track segment which has on average 32 electrons is therefore about {44}{ $\rm \mu$m}. --- > %To compare the precision of the GridPix readout with the precision of conventional pad based TPC readouts, the resolution can be calculated over the length of one pad row. > %For example, at a drift distance of {4}{mm} the resolution of a single ionisation electron is approximately {250}{ $\rm \mu$m}, so the resolution of a {6}{mm} track segment which has on average 32 electrons is therefore about {44}{ $\rm \mu$m}. 476c475 < Only tracks crossing the fiducial region - defined by the central core of the beam - were accepted and hits with a ToT value above {0.6}{ $\rm \mu$s} were selected. --- > Only tracks crossing the fiducial region were accepted and hits with a ToT value above {0.6}{ $\rm \mu$s} were selected. 489c488 < A fit to the {$B$ = 1 T} data shown in Figure \ref{fig:resolutionz} gives a longitudinal diffusion coefficient $D_L$ of ($224 \pm 2$ (stat) $\pm 14$ (sys)) { $\rm \mu$m/$\sqrt{\rm cm}$}. The measured value is lower than the value of ($245 \pm 4$) { $\rm \mu$m/$\sqrt{\rm cm}$} predicted by Magboltz. --- > A fit to the {$B$ = 1 T} data shown in Figure \ref{fig:resolutionz} gives a longitudinal diffusion coefficient $D_L$ of ($224 \pm 2 (stat) \pm 14$ (sys)) { $\rm \mu$m/$\sqrt{\rm cm}$}. The measured value is lower than the value of ($245 \pm 4$) { $\rm \mu$m/$\sqrt{\rm cm}$} predicted by Magboltz. 514c513 < A few critical areas can be observed in Figure \ref{fig:deformationsB0}: the region around chip 11 is affected (chips 14, 8 and 13), because the grid of chip 11 was disconnected. --- > A few critical areas can be observed in figure \ref{fig:deformationsB0}: the region around chip 11 is affected (chips 14, 8 and 13), because the grid of chip 11 was disconnected. 519c518 < In order to reduce the statistical fluctuations and quantify the tracking precision, the module was regrouped in (4$\times$256)$\times$256 pixel planes put side by side on the horizontal axis, as shown in Figure \ref{fig:deformationsGroupedB0}. E.g. the selected chips from the upper left and bottom left quad detectors are superimposed into the 0-256 ($x$) and 0-256 ($y$) plane. --- > In order to reduce the statistical fluctuations and quantify the tracking precision, the module was regrouped in (4$\times$256)$\times$256 pixel planes put side by side on the horizontal axis, as shown in figure \ref{fig:deformationsGroupedB0}. E.g. the selected chips from the upper left and bottom left quad detectors are combined into the 0-256 ($x$) and 0-256 ($y$) plane. 534c533 < In the {$B$ = 1 T} data set, the electrons will drift mainly along the magnetic field lines. Deformations are in that case due to e.g. the non-alignment of the electric and magnetic field, giving $E \times B$ effects. --- > In the {$B$ = 1 T} data set, the electrons will drift mainly along the magnetic field lines. Deformations are in that case due to e.g. the non-alignment of the electric and magnetic field, giving $ExB$ effects. 538c537 < The mean residuals in the pixel and drift planes are shown in Figure \ref{fig:deformationsB1} for the {$B$ = 1 T} data set using a large set of runs to cover the whole module. The (biased) residuals were calculated with respect to the TPC track prediction. Because of limited statistics, bins were grouped into {16$\times$16}{} pixels. --- > The mean residuals in the pixel and drift planes are shown in figure \ref{fig:deformationsB1} for the {$B$ = 1 T} data set using a large set of runs to cover the whole module. The (biased) residuals were calculated with respect to the TPC track prediction. Because of limited statistics bins were grouped into {16$\times$16}{} pixels. 548,549c547,548 < In Figure \ref{fig:deformationsB1} the critical areas discussed above - around chip 11, the four corner chips and chip 16 in the upper corner edge - can be clearly observed. < For the deformation studies, the hits of these nine chips were removed. The TPC track fit was redone leaving these hits out of the fit, thus that they could not bias and affect the results. --- > In figure \ref{fig:deformationsB1} the critical areas discussed above - around chip 11, the four corner chips and chip 16 in the upper corner edge - can be clearly observed. > For the deformation studies the hits of these nine chips have to be removed. The TPC track fit was redone leaving these hits out of the fit, thus that they could not bias and affect the results. 552c551 < In order to reduce the statistical fluctuations and quantify the tracking precision, the module was again regrouped in (4$\times$256)$\times$256 pixels as described above, as shown in Figure \ref{fig:deformationsGroupedB1}. --- > In order to reduce the statistical fluctuations and quantify the tracking precision, the module was regrouped in (4$\times$256)$\times$256 pixels as described above, as shown in figure \ref{fig:deformationsGroupedB1}. 580c579 < The distribution of the number of TPC track hits per chip - without requiring a matched telescope track - are shown in Figure \ref{fig:nHits} for the data without magnetic field and for the {$B$ = 1 T} data. --- > The distribution of the number of TPC track hits per chip - without requiring a matched telescope track - are shown in figure \ref{fig:nHits} for the data without magnetic field and for the {$B$ = 1 T} data. 582c581 < For the {$B$ = 0 T} data, the central chips 2,6,7,9,16,17,26 and 27 were selected. For the {$B$ = 1 T} data, the same chips plus chips 12,13,20 and 21 were selected. --- > For the {$B$ = 0 T} data the central chips 2,6,7,9,16,17,26 and 27 were selected. For the {$B$ = 1 T} data the same chips plus chips 12,13,20 and 21 were selected. 607c606 < %The module dimensions are {79 $\times$ 192}{ mm}, and the maximum drift distance is {40}{ mm}. --- > %The module dimensions are {79 $\times$ 192}{mm}, and the maximum drift distance is {40}{mm}. 613,614c612,613 < The result for the transverse diffusion coefficient $D_{T}$ is {(287.2 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 0 T} and $D_{T}$ is {(120.3 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 1 T}. < The longitudinal diffusion coefficient $D_L$ is measured to be {(251 $\pm$ 14)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 0 T} and {(224 $\pm$ 14)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 1 T}. --- > The result for the transverse diffusion coefficient $D_{T}$ is {287 $\pm$ 0.5)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 0 T} and $D_{T}$ is {121 $\pm$ 0.5}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 1 T}. > The longitudinal diffusion coefficient $D_L$ is measured to be {251 $\pm$ 14)}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 0 T} and {224 $\pm$ 14}{ $\rm \mu$m/$\sqrt{\rm cm}$} at {$B$ = 1 T}. 671c670 < {A GridPix TPC read out for the ILD experiment at the future International Linear --- > {A GridPix TPC readout for the ILD experiment at the future International Linear 688,689c687,688 < channel hybrid pixel read out chip with simultaneous ToA/ToT and sparse < read out}}, JINST 9~(05) (2014) C05013. --- > channel hybrid pixel readout chip with simultaneous ToA/ToT and sparse > readout}}, JINST 9~(05) (2014) C05013. 702c701 < B.~Munneke, F.~Schreuder, {SPIDR, a general-purpose read out system for pixel --- > B.~Munneke, F.~Schreuder, {SPIDR, a general-purpose readout system for pixel