2024

These authors contributed equally to this work.

[1,3,4]F. Guatieri These authors contributed equally to this work.

1]Research Neutron Source Heinz Maier-Leibnitz (FRM II), Technical University
of Munich, Lichtenbergstr. 1, Garching bei München, 85748, Bayern, Germany
2]Institute of Communications and Navigation, German Aerospace Centre (DLR),
Münchener Str. 20, 82234 Weßling, Germany 3]Department of Physics, University
of Trento, via Sommarive 14, 38123 Povo, Trento, Italy 4]TIFPA/INFN Trento,
via Sommarive 14, 38123 Povo, Trento, Italy 5]University of Siegen, Department
of Physics, Walter-Flex-Straße 3, 57072 Siegen, Germany 6]University of
Latvia, Department of Physics Raina boulevard 19, LV-1586, Riga, Latvia
7]Institute of Experimental and Applied Physics, Czech Technical University in
Prague, Husova 240/5, 110 00, Prague 1, Czech Republic 8]Department of
Physics, University of Oslo, Sem Sælandsvei 24, 0371 Oslo, Norway 9]INFN
Milano, via Celoria 16, 20133 Milano, Italy 10]Department of Physics “Aldo
Pontremoli”, University of Milano, via Celoria 16, 20133 Milano, Italy
11]Institut für Experimentalphysik, University of Innsbruck, Technikerstrasse
25, 6020 Innsbruck, Austria 12]Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus University in Toruń,
Grudziadzka 5, 87-100 Toruń, Poland 13]Department of Aerospace Science and
Technology, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
14]Physics Department, CERN, 1211 Geneva 23, Switzerland 15]Warsaw University
of Technology, Faculty of Physics, ul. Koszykowa 75, 00-662, Warsaw, Poland
16]Department of Physics, NTNU, Norwegian University of Science and
Technology, Trondheim, Norway 17]Institute for Experimental Physics,
Universität Hamburg, 22607, Hamburg, Germany 18]Warsaw University of
Technology, Faculty of Electronics and Information Technology, ul. Nowowiejska
15/19, 00-665 Warsaw, Poland 19]Systems Department, CERN, 1211 Geneva 23,
Switzerland 20]Marian Smoluchowski Institute of Physics, Jagiellonian
University, Kraków, Poland 21]Centre for Theranostics, Jagiellonian
University, Kraków, Poland 22]Institute of Physics, Polish Academy of
Sciences, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland 23]Czech Technical
University, Prague, Brehová 7, 11519 Prague 1, Czech Republic 24]Raman
Research Institute, C. V. Raman Avenue, Sadashivanagar, Bangalore 560080,
India 25]Felix Bloch Institute for Solid State Physics, Universität Leipzig,
04103 Leipzig, Germany 26]Department of Physics, University of Liverpool,
Liverpool L69 3BX, UK 27]The Cockcroft Institute, Daresbury, Warrington WA4
4AD, UK 28]INFN Pavia, via Bassi 6, 27100 Pavia, Italy 29]Department of Civil,
Environmental, Architectural Engineering and Mathematics, University of
Brescia, via Branze 43, 25123 Brescia, Italy

# Real-time antiproton annihilation vertexing with sub-micron resolution

M. Berghold<EMAIL_ADDRESS>D. Orsucci<EMAIL_ADDRESS><EMAIL_ADDRESS>S. Alfaro  M. Auzins  B. Bergmann  P. Burian
R. S. Brusa  A. Camper  R. Caravita  F. Castelli  G. Cerchiari  R. Ciuryło  A.
Chehaimi  G. Consolati  M. Doser  K. Eliaszuk  R. Ferguson  M. Germann  A.
Giszczak  L. T. Glöggler  Ł. Graczykowski  M. Grosbart  N. Gusakova  F.
Gustafsson  S. Haider  S. Huck  C. Hugenschmidt  M. A. Janik  T. Januszek  G.
Kasprowicz  K. Kempny  G. Khatri  Ł. Kłosowski  G. Kornakov  V. Krumins  L.
Lappo  A. Linek  S. Mariazzi  P. Moskal  D. Nowicka  P. Pandey  D. Pęcak  L.
Penasa  V. Petracek  M. Piwiński  S. Pospisil  L. Povolo  F. Prelz  S. A.
Rangwala  T. Rauschendorfer  B. S. Rawat  B. Rienäcker  V. Rodin  O. M. Røhne
H. Sandaker  S. Sharma  P. Smolyanskiy  T. Sowiński  D. Tefelski  T. Vafeiadis
M. Volponi  C. P. Welsch  M. Zawada  J. Zielinski  N. Zurlo  [  [  [  [  [  [
[  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [

###### Abstract

The primary goal of the AE$\bar{\text{g}}$IS experiment is to precisely
measure the free fall of antihydrogen within Earth’s gravitational field. To
this end, a cold ($\approx$50\text{\,}\mathrm{K}$$) antihydrogen beam has to
pass through two grids forming a moiré deflectometer before annihilating onto
a position-sensitive detector, which shall determine the vertical position of
the annihilation vertex relative to the grids with micrometric accuracy. Here
we introduce a vertexing detector based on a modified mobile camera sensor and
experimentally demonstrate that it can measure the position of antiproton
annihilations with an accuracy of
$0.62^{+0.40}_{-0.22}\,$$\text{\,}\mathrm{\SIUnitSymbolMicro m}$, which
represents a 35-fold improvement over the previous state-of-the-art for real-
time antiproton vertexing. Importantly, these antiproton detection methods are
directly applicable to antihydrogen. Moreover, the sensitivity to light of the
sensor enables the in-situ calibration of the moiré deflectometer,
significantly reducing systematic errors. This sensor emerges as a
breakthrough technology for achieving the AE$\bar{\text{g}}$IS scientific
goals and has been selected as the basis for the development of a large-area
detector for conducting antihydrogen gravity measurements.

###### keywords:

Antiproton, Annihilation, Gravity, Detectors, Semiconductors

##  1 Introduction

General relativity currently stands as the prevailing paradigm for
understanding gravity and any departure from it would require a fundamental
reevaluation of our understanding of physics. At its core lies the Weak
Equivalence Principle (WEP), postulating the equality of gravitational and
inertial mass and thus the universality of free fall. The WEP has been tested
across various materials to very high precision through Eötvös-type
experiments wagner2012torsion ; MICROSCOPE . Testing the WEP with antimatter
presents a formidable challenge due to the difficulty of producing abundant
low-energy antiparticles and the susceptibility to stray electromangnetic
fields witteborn1968experiments ; HOLZSCHEITER1993 . The idea that antimatter
should adhere to the WEP is supported both by theoretical considerations, such
as conservation of energy combined with the observed blue-shift of light in
gravitational fields morrison1958approximate ; and by indirect experimental
evidence, such as the lack of anomalous regeneration of $K$-short kaons
Good1961 , the precise measurement of the antiproton cyclotron frequency
borchert2022 , and the times of arrival of neutrinos and antineutrinos from
the supernova SN1987a LoSecco . However, such arguments are not conclusive
nieto1991arguments  and a direct experimental confirmation was lacking until
recently.

Over the past decade, several experimental collaborations have been
established with the goal of measuring the acceleration of antimatter in
Earth’s gravitational field, with most of these efforts taking place at the
antimatter factory at CERN. These have culminated in an experiment by the
ALPHA-g collaboration Alpha_g , which has measured the gravitational
acceleration of antihydrogen ($\overline{H}$) to be $g_{\overline{H}}=(0.75\pm
0.13_{\text{stat}+\text{sys}}\pm 0.16_{\text{sim}})\,g$ where $g$ is the local
gravitational acceleration on ordinary matter. Zero gravitational pull
($g_{\overline{H}}=0$) is disfavored compared to ordinary gravity
($g_{\overline{H}}=g$) with a Bayes factor of $2.9\cdot 10^{-4}$, while anti-
gravity ($g_{\overline{H}}=-g$) is conclusively ruled out.

The next steps in advancing the field involve replicating the measurement and
then increasing the accuracy to subject the WEP to more stringent tests.
Theoretical models that presuppose that antimatter and energy respond
differently to gravitational fields bondi1957negative ;
schiff1959gravitational  result in potential deviations from the WEP at the
percent level for hadronic matter, including antiprotons and antihydrogen. In
fact, according to the Standard Model most of the mass of an antiproton,
around $938\text{\,}\mathrm{M}\mathrm{eV}\mathrm{/}\mathrm{c}\mathrm{{}^{2}}$,
stems from its internal binding energy wilczek2012origins , whereas the masses
of the three constituent antiquarks add up to around
$9\text{\,}\mathrm{M}\mathrm{eV}\mathrm{/}\mathrm{c}\mathrm{{}^{2}}$ pdg .
Since it is established that binding energy responds positively to gravity
wagner2012torsion ; MICROSCOPE , the deviation $\Delta g=g_{\overline{H}}-g$
would not be expected to exceed 1% fischler2008direct ; alves2009experimental
.

Achieving a 1% precision on $g_{\overline{H}}$ is a challenging but realistic
goal pursued by the competing experiments ALPHA-g alphag1 , GBAR gbar1  and
AE$\bar{\text{g}}$IS aegis1  at CERN. These employ substantially different
methods to measure the effect of gravity on antihydrogen, each one requiring
the development of bespoke technologies and the solution of distinctive
technological challenges. The gravitational measurement at
AE$\bar{\text{g}}$IS is based on a moiré deflectometer (already tested with
antiprotons aghion2014moire ) in which the particles pass through two material
grids before annihilating onto a position-sensitive detector. The vertical
deflection of the moiré pattern, given by $\delta y=-t^{2}g_{\overline{H}}$
for a time of flight $t$ between the grids, is expected to be tens of
micrometers for the cold antihydrogen beam of AE$\bar{\text{g}}$IS. Therefore,
a crucial requirement for high-precision gravity measurements at
AE$\bar{\text{g}}$IS is the real-time detection of the position of
$\overline{H}$ annihilations with micrometric accuracy. Previously considered
detection technologies included nuclear photographic emulsions
kimura2013development ; aghion2013prospects ; pistillo2015emulsion  and
bespoke silicon detectors aghion2014detection , such as Timepix3
pacifico2016direct ; holmestad2018data . Nuclear emulsions feature a high
resolution, approaching $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$
kimura2013development , but, due to the lack of real-time detection, it is
challenging to perform on-line monitoring of the position of the photographic
plate relative to the grids. On the other hand, real-time detection is
possible with silicon detectors, but the ones so far available had a
significantly lower resolution. For instance, the pixels of Timepix3 and of
Timepix4 are $\qtyproduct{55x55}{\micro}$ in size poikela2014timepix3 ;
llopart2022timepix4 .

In this work we introduce a groundbreaking $\overline{H}$ detection technology
which, for the first time, meets all the requirements to reach a 1% precision
measurement of $g_{\overline{H}}$ at AE$\bar{\text{g}}$IS. This is based on
the Sony IMX219, a commercial CMOS optical image sensor with 8 megapixels and
a $\qtyproduct{3.67x2.76}{\milli}$ sensitive area Datasheet ;
ReverseEngineering , originally developed for mobile applications and which
has already been shown to be capable of imaging low-energy positrons with
exceptional efficiency and resolution Berghold2023 . Its
$\qtyproduct{1.12x1.12}{\micro}$ pixels111In this paper, we use the convention
$$1\text{\,}\mathrm{p}\mathrm{x}$=$1.12\text{\,}\mathrm{\SIUnitSymbolMicro
m}$.$ are fifty times smaller than that of Timepix3 and of size similar to
that of nuclear emulsions grains. We have now experimentally observed that the
annihilation of antiprotons ($\overline{p}$) on the surface of the CMOS sensor
results in the secondary charged particles leaving detectable signals in the
exposed images. By reconstructing the vertex lying at the intersection of the
tracks, the position of the antiproton annihilation can be determined with
sub-micron accuracy. Since antihydrogen is an antiproton having only an extra
positron bound to it, our detector is expected to be an antihydrogen
annihilation vertexer as well and thus enable $\overline{H}$ gravity
measurements.

##  2 Results

###  2.1 Detection

Figure 1: Curated selection of antiproton annihilation events as imaged by the
CMOS sensor. The observed shapes are similar to those recorded by the Timepix3
detector pacifico2016direct ; holmestad2018data , albeit at a scale
approximately fifty times smaller. Pixels marked in magenta have been deemed
non-functional by taking background images.

Low-energy antiprotons impinging on matter are trapped, through the Day-Snow-
Sucher mechanism DaySnowSucher , by atomic nuclei and then quickly annihilate
with either a proton or a neutron, releasing almost $1.9\text{\,}\mathrm{GeV}$
of energy. Through the interaction of the constituents quarks $p\overline{p}$
and $n\overline{p}$ annihilations result in the emission of 2 to 8 pions
($\pi^{-},\pi^{0},\pi^{+}$) and other particles von1987interaction ;
richard2020antiproton . The annihilation in heavy nuclei can result in the
recoil of some of the adjacent protons and neutrons and each of these, if the
trajectory crosses the nucleus, can also pick-up other nucleons and result in
the emission of deuterons, tritium, helium and other heavier nuclear fragments
clover1982low ; von1987interaction . The secondary particle branching ratios
and spectra had been experimentally characterised at the Low Energy Anti-
Proton Ring facility between 1982 and 1996 walcher1988experiments ;
hofmann1990charged ; amsler1991low ; polster1995light ; amsler1998proton ;
amsler2019nucleon .

We have detected $\overline{p}$ annihilation events by repeatedly exposing the
CMOS sensor to a low-intensity beam of antiprotons. Over the course of 8 days
a total of 1576 images were exposed to collect antiproton events. Each shot
was preceded by an exposure without antiprotons for background subtraction.
Within the recorded images a total of 2601 $\overline{p}$ annihilation events
were manually identified. Annihilations appear as star-shaped events with
multiple prongs emanating from one single primary vertex (see Figure 1).

The sensor was prepared by removal of the microlenses and Bayer filter using
the procedure described in Berghold2023 , but leaving the passivation and wire
grid layers in place. At the employed implantation energy of
$8\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$ most of the antiprotons annihilate
within $0.25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ from the surface, directly
above the sensor’s sensitive volume, which is thus intersected by half of the
emitted secondary particles. Some of these are energetic charged particles
that generate electron-hole pairs in the silicon, a process that results in a
signal similar to the one produced by visible light which the detector
integrated electronics is designed to pick up Datasheet ; Berghold2023 ;
ReverseEngineering . Neutrons, neutral pions, photons and Auger electrons are
also featured prominently among the annihilation products, but are not
expected to produce a significant signal. Tertiary particles, e.g. due to in-
flight decay of a secondary, are rarely observed.

###  2.2 Prong identification and detection efficiency

$\boldsymbol{\alpha}$ |  $\boldsymbol{p}$ $\boldsymbol{\pi}$ | 0 | 1 | 2 | 3 | 4 | 5 | 6
---|---|---|---|---|---|---|---|---
0 | 0 | — | — | 71 | 34 | 9 | 1 | 0
1 | — | 116 | 149 | 61 | 24 | 5 | 2
2 | 81 | 107 | 108 | 64 | 17 | 5 | 0
3 | 33 | 51 | 59 | 31 | 11 | 5 | 1
4 | 4 | 16 | 12 | 9 | 2 | 3 | 0
5 | 0 | 0 | 1 | 1 | 1 | 1 | 0
6 | 0 | 0 | 0 | 0 | 1 | 0 | 0
1 | 0 | — | 101 | 44 | 17 | 5 | 0 | 0
1 | 289 | 247 | 88 | 23 | 5 | 0 | 0
2 | 156 | 153 | 67 | 13 | 6 | 0 | 0
3 | 29 | 43 | 30 | 11 | 5 | 1 | 0
4 | 6 | 4 | 3 | 1 | 3 | 0 | 0
5 | 0 | 0 | 1 | 0 | 0 | 0 | 0
2 | 0 | 21 | 14 | 5 | 1 | 0 | 0 | 0
1 | 23 | 30 | 6 | 6 | 2 | 0 | 0
2 | 17 | 10 | 5 | 1 | 0 | 0 | 1
3 | 1 | 2 | 2 | 0 | 0 | 0 | 0
3 | 0 | 5 | 0 | 0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0 | 0 | 0 | 0
2 | 0 | 0 | 1 | 0 | 0 | 0 | 0
Table 1: Number of recorded events sorted by prong composition. Prongs
appearing as ellipses are identified as alpha particles or other multi-nucleon
fragments ($\boldsymbol{\alpha}$), thick tracks are identified as protons
($\boldsymbol{p}$) and thin tracks are identified as charged pions
($\boldsymbol{\pi}$). Annihilation events featuring zero or one prongs cannot
be traced and are excluded from the analysis (—).

The vast majority of the recorded prongs are either straight lines whose
thickness remains roughly constant along their entire length (tracks) and
elliptical-shaped prongs (ellipses). We have manually flagged the number and
location of every track and ellipse within the dataset. We have run a least-
square fit algorithm to precisely determine the average thickness in pixels of
all tracks in the dataset (see Section 4.2). The distribution in thickness of
tracks is bimodal (see Figure 2, top). By applying a threshold at
$1.0\text{\,}\mathrm{p}\mathrm{x}$ of thickness, we can classify all prongs as
either thick tracks (2382 instances, 29.9% of recorded prongs), thin tracks
(3929 instances, 49.2% of recorded prongs) or ellipses (1666 instances, 20.9%
of recorded prongs). Table 1 details the composition of recorded events.

We have experimentally characterized the response of the CMOS sensor to
specific charged particles to assess the most likely associations between
secondaries and the observed prongs. We have exposed the sensor to the decay
products of an 241Am source positioned at a
$20\text{\,}\mathrm{\SIUnitSymbolDegree}$ angle with respect to the surface
and observed that the tracks left by the
$5.4\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$ alpha particles appear as
elliptical-shaped prongs with a consistent size of $\qtyproduct{4x12}{px}$. We
have also exposed the sensor to a proton beam of
$4\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$ of energy impinging at
$10\text{\,}\mathrm{\SIUnitSymbolDegree}$ angle with respect to the surface
and observed them to produce linear tracks of consistent thickness in the
images. We applied the same algorithm as described in Section 4.2 to determine
the thickness of the proton tracks and found them to have thickness comprised
between 1.0 and $1.5\text{\,}\mathrm{p}\mathrm{x}$ (see Figure 2, bottom).

Based on these observation we attribute thick tracks to protons, thin tracks
to charged pions and the ellipses to deuterons, tritium, alpha particles or
heavier fragments. This assignment is supported by the fact that similar
features can be observed in both experimental and simulated $\overline{p}$
annihiliation events on the Timepix3 holmestad2018data . Furthermore, these
three species are known to produce similar formations within cloud chambers
balestra1985experimental , albeit three orders of magnitude larger in size as
the density inside of a cloud chamber is about a thousand times lower than
that of crystalline silicon.

We have further validated this prong identification by comparing experimental
and simulated data. We have tallied the observed multiplicities per vertexed
annihilation event, as reported in the last row of Table 2. We have then
employed FLUKA FLUKA , which includes a state-of-the-art model of antiproton
annihilation, to simulate $\overline{p}$-Si annihiliations and count the
multiplicities of secondary particles that are emitted towards the half-space
containing the sensor active volume. This results in the “FLUKA base
prediction” in Table 2 which, however, significantly deviates from the
experimental data. This is due to selection bias, since not all annihilation
events can be vertexed, and to missed prong identifications, e.g. when a track
is too short or due to occlusion from other prongs. To account for these
effects, we have generated a synthetic dataset employing 1000 FLUKA-generated
events. For each event a collection of tracks and ellipses is printed,
according to the species of the secondary particles and their emission
direction. We have manually flagged the events as traceable or untraceable
and, for the latter, counted the number of tracks and ellipses that could be
recognised. This results in the “FLUKA occlusion corrected” prediction, which
shows a reasonable agreement with the observed data. Furthermore, by counting
the traceable events we estimate the vertex reconstruction efficiency to be
around 70%.

Figure 2: In blue the distribution in thickness of the tracks in recorded antiprotons events. We attribute the higher-thickness peak of the distribution to tracks left in the sensor by protons and the lower peak to tracks left by pions. In red the distribution in thickness of tracks left by $4\text{\,}\mathrm{M}\mathrm{e}\mathrm{V}$ protons within the detector, matching the topmost part of the distribution in thickness of proton tracks. We attribute the difference between the distributions mainly to the difference in energy spectrum of the protons.  Prong type |  Ellipse ($\boldsymbol{\alpha}$) |  Thick track ($\boldsymbol{p}$) |  Thin track ($\boldsymbol{\pi}$)
---|---|---|---
Particle identification | alpha/fragment | proton | charged pion
FLUKA base prediction | 1.91 | 0.85 | 1.37
FLUKA occlusion corrected | 0.75 | 0.90 | 1.46
Selection criteria | hand tagging | width $\geq 1.0$ px | width $<1.0$ px
Experimental data | 0.64 | 0.91 | 1.50
Table 2: Prongs multiplicities as observed in the experimental dataset and in
FLUKA-based predictions. For simulated data it is assumed that charged pions
result in thin tracks, protons in thick tracks, all fragments containing two
or more nucleons result in ellipses, while all other particles are ignored.
The base FLUKA predictions have to be corrected for selection bias in the
vertexing procedure and for occlusions among prongs, see main text for
details.

###  2.3 Annihilation vertex reconstruction

Figure 3: a) Optical image of the silicon nitride grid acquired using a point
light source before installing the setup in vacuum. b) A similar image
obtained by exploiting the light emitted by a vacuum gauge in the apparatus.
Arrows indicate the two grid teeth that were bent by the adhesive deforming
under vacuum. c) The reconstructed position of antiproton annihilations
recorded with the grid installed onto the sensor. Towards the left side two
distinct areas nearly devoid of annihilations events can be seen. These are
the regions where the thermoplastic adhesive keeping the grid in place was
applied. d) A histogram of the distance of the annihilations events from the
nearest edge. Overlayed in orange is the best fitting error function found via
maximum likelihood.

We have attempted algorithmic fitting of the annihilation events, as
previously done for Timepix3-based detections holmestad2018data . We have
developed a model that predicts the intensity recorded by each pixel in the
event based on a parameterization of the event (position of the vertex, number
and positions of the prongs); the fitting algorithm then finds the
parameterization that minimizes the $\ell^{2}$-distance between the recorded
data and the prediction. Despite promising initial results from this approach
(reaching approximately $2.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$
resolution), we found out that humans actually achieve higher accuracy.

We have then assigned the task of determining the position of the annihilation
vertex in each of the 2601 recorded events to 8 researchers within our team.
The reconstructed positions are shown in Figure 3c. The volunteers were
provided with a graphical interface that prompted them with a
$\qtyproduct{128x128}{px}$ portion of the image containing an annihilation
event. The interface allows marking the vertex position with a precision of
$1/4$ of a pixel and a tool to trace straight lines from the vertex outwards,
easing the evaluation of the alignment of the vertex position with the tracks
in the event. Reconstructions of a vertex position made by different
volunteers for the same event differ typically by less than one pixel, with a
standard deviation of $0.9\text{\,}\mathrm{p}\mathrm{x}$ in both the $x$ and
$y$ direction. We have averaged the output of the volunteers to determine a
best estimation of the vertex position. As long as no significant systematic
bias is present, the accuracy of the average position should scale as
$0.9/\sqrt{n}\,$\text{\,}\mathrm{p}\mathrm{x}$$, where $n$ is the number of
independent vertex reconstructions. For $n=8$ this would theoretically result
in a resolution of $0.32\text{\,}\mathrm{p}\mathrm{x}$
($0.36\text{\,}\mathrm{\SIUnitSymbolMicro m}$).

###  2.4 Grid positioning and vertexing accuracy

Figure 4: Left: Relative drift of the endpoints of the 50 grid teeth as
determined by the fitting algorithm described in appendix 4.3 over the course
of one hour. One of the edges has been highlighted in red to better show the
typical progression of the algorithm output over time. The fluctuations in the
so reconstructed coordinates are below
$0.12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ RMS for all the grid vertices -
with median being $0.031\text{\,}\mathrm{\SIUnitSymbolMicro m}$ RMS. Right:
relative position of one grid vertex tracked over the course of the 8 day
measurement campaign. The linear fit used to compensate for the grid movement
in the data analysis is shown in orange.

We have performed a bias-free assessment of the crowd-based vertexing accuracy
via a procedure akin to a optical transfer function measurement, a method used
to determine the resolution of digital camera sensors Reichenbach_Resolution .
Namely, we have occluded part of the sensor so that it cannot be reached by
the impinging antiprotons and observed the sharpness of the transition in the
density of annihilation events between occluded and non-occluded portions of
the sensor. We have placed a silicon nitride grid of thickness
$125\text{\,}\mathrm{\SIUnitSymbolMicro m}$ consisting of teeth with a pitch
of $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and openings of
$40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ directly onto the sensor surface.
In order to cover most of the active surface of the sensor while not
interfering with the bonding wires, the grid was cut to size using a hardened
steel scribe and then glued in place with thermoplastic adhesive. The grid was
brought as close as possible to the sensor by observing the grid shadow as
imaged by the device in real-time using visible light and employing the
sharpness of its shadow to assess its proximity to the surface. An image of
the grid, obtained from the sensor itself after it was installed in vacuum is
shown in Figure 3b). In the image, two of the grid teeth are bent upwards,
which was not the case before air was pumped out of the chamber. Most likely,
this is due to mechanical stress caused by air pockets deforming the adhesive
when vacuum was applied and had to be factored in during the data analysis.

The position of the grid relative to the sensor was measured between each run
by using the residual light given off by a Pirani gauge, which was then
switched off to allow the sensor to operate in darkness. We determined the
position of each tooth of the grid with sub-pixel accuracy by using the
algorithm described in Section 4.3. By fitting multiple images acquired in
quick succession over the course of one hour (see Figure 4, left) we found the
algorithm to be stable, with a standard deviation of the results below
$0.12\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Tracking of the grid position
over the course of the measurement campaign reveals a linear drift in the
order of
$0.1\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}\,\mathrm{p}\mathrm{e}\mathrm{r}\,\mathrm{d}\mathrm{a}\mathrm{y}$
(see Figure 4, right). This effect is most likely due to the combination of
the mechanical tension introduced in the adhesive during evacuation and the
adhesive softening under the heat load of the detector during operation, which
reaches temperatures in excess of $60\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
To account for this drift, the position of the grid at any given time was
interpolated using a linear regression model. This technique allowed in-situ
calibration of the grid position, ensuring consistency throughout the
measurement campaign.

Antiprotons annihilating onto the grid also sometimes produce tracks, but
these have a different appearance from the events shown in Figure 1, allowing
their exclusion of these events from the analysis. In these cases the
annihilations are offset by $125\text{\,}\mathrm{\SIUnitSymbolMicro m}$ from
the surface of the sensor, resulting in disjoint tracks that do not touch at a
vertex. For each crowd-reconstructed vertex the signed distance $d$ to the
closest tooth edge was computed and the vertices having
$|d|\leq$25\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ were collected. The
resulting distribution (in Figure 3d) resembles, as expected, an error-
function distribution Reichenbach_Resolution  and is modelled as
$f(d)=b+n\,\text{erf}[d/(\sqrt{2}r)]$ with fit parameters $b,n,r$, where $r$
represents a upper bound of the resolution that is acheivable with the sensor.
Via a maximum likelihood fit we obtain
$r=0.62^{+0.40}_{-0.22}\,$$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for crowd-
based vertexing, while
$r=0.79^{+0.35}_{-0.24}\,$$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ is
consistently obtained when the vertexing from a single volunteer is employed.

###  2.5 Sensor resilience

As the measurement was carried out, the emergence of dead pixels has been
observed. Malfunctioning pixels in the detector manifest characteristically as
pixels whose measurement baseline is uncharacteristically high, typically
exceeding one fourth of the total dynamic range and often saturating it
completely. These pixels can be easily identified in the background images
taken before each antiproton implantation.

The pristine sensor contained about 2500 dead pixels (one in 3200), defined as
pixels whose baseline exceeded $400\text{\,}\mathrm{l}\mathrm{s}\mathrm{b}$
(least significant bits), when acquiring in complete darkness with the same
settings employed to detect antiprotons, with the maximum possible readout
being $1023\text{\,}\mathrm{l}\mathrm{s}\mathrm{b}$. As we implant antiprotons
in the device we observe pixels which get permanently damaged by the radiation
impinging on the detector. Due to the limitations of the beam optics during
this run, most of the energy deposited in the sensor during our measurements
did not come from antiprotons annihilating on the detector, but instead from
antiprotons annihilating elsewhere in the chamber whose annihilation products
traversed the active volume of the sensor. We evaluated their contribution to
the total irradiation of the sensor by integrating the signal that they
produced in the sensor and then dividing it by the average signal induced by
an antiproton ($38\text{\,}\mathrm{k}\mathrm{l}\mathrm{s}\mathrm{b}$). Using
this conversion we observed the appearance of one additional permanently
damaged pixel every four equivalent antiprotons implanted into the sensor.
This rate of degradation is completely negligible for its use in
AE$\bar{\text{g}}$IS where an integrated flux of a few thousand antihydrogen
atoms is expected during the course of the entire experiment. In fact the
detector can be foreseen to be suitable to support experiments requiring an
antiproton/antihydrogen flux between two and three order of magnitude larger.

##  3 Discussion

We have demonstrated the possibility of detecting antiproton annihilations
using a commercial mobile camera sensor. We have shown that, employing crowd-
sourced vertex reconstruction, a position accuracy of
$0.62^{+0.40}_{-0.22}\,$$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ can be
achieved, a 35-fold improvement over the previous state-of-the-art of
$22\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for real-time detection
holmestad2018data . Making use of FLUKA simulations, we can estimate that
around 70% of the annihilating antiprotons result in traceable events.
Differently from previous use of the same detector for positrons Berghold2023
, most of the energy deposited in the sensor by antiprotons comes from the
rest mass of the annihilating particles. As such we expect no lower limit in
the antiparticle kinetic energy in order to vertex the annihilation event and,
thus, this sensor could be directly employed to detect cold antihydrogen in
AE$\bar{\text{g}}$IS gravity measurement.

Importantly, the sensor is by design sensitive to visible light, which enables
the accurate determination of its position relative to the moiré deflectometer
grids by means of optical alignment. In essence, photons can serve as test
particles in a gravitational experiment: being their deflection by Earth’s
gravitational field negligible, they can be used to ascertain the expected
arrival point of particles in the absence of gravitational
acceleration222Electrons with keV-scale energy might also be employed in
alternative to photons.. Thus, by alternating between optical calibrations and
antihydrogen shots a direct differential measurement of particle arrival
positions at the detector can be performed. The use of a single device both
for optical imaging and for antimatter detection ensures that all measurements
occur within the same physical frame of reference, minimizing systematic
errors. Furthermore, any drift in the position of the deflectometer grids can
be detected and accounted for, as demonstrated in this work.

Following the measurements results presented here, this sensor technology has
been selected as the basis for the development of a bespoke detector to be
employed within the AE$\bar{\text{g}}$IS deflectometer. The detector will
feature a large sensitive area (around $\qtyproduct{5.8x5.7}{\centi}$),
consisting of 48 individual CMOS sensors arranged in a compact rectangular
tessellation, which is expected to collect 56% of the antihydrogen atoms that
pass through the deflectometer grids. The sub-micrometric accuracy and the in-
situ calibration capabilities of this detector technology should allow
measuring the gravitational acceleration to $1\%$ precision, which is the
AE$\bar{\text{g}}$IS scientific goal, under relaxed experimental constraints.
Ultimately, we expect that this detector technology could enable in future
upgrades to significantly exceed the $1\%$ precision goal in the measurement
of $g_{\overline{H}}$.

As a final outlook, this sensor technology shows great promise for a broad
range of applications, beyond the detection of antiprotons, due to its
sensitivity to both energetic charged particles and light. We have already
demonstrated that it can detect positrons Berghold2023  and extreme-
ultraviolet (XUV) light XUVPeparation  and we expect that it may be employed
in biomedical imaging Medipix , in visible and XUV light spectrometry, as well
as in high-resolution particle tracking.

##  4 Methods

###  4.1 Hardware setup

The apparatus used in Berghold2023 , seen there in Figure 1, was repurposed
for this experiment. The flange there depicted was installed horizontally onto
a $45\degree$ offshoot of the injection line of AE$\bar{\text{g}}$IS, facing
in the direction of the $5\text{\,}\mathrm{T}$ magnet of the experiment.
Between the detector and the injection line a
$10.4\text{\,}\mathrm{c}\mathrm{m}$ long, $4\text{\,}\mathrm{c}\mathrm{m}$
wide restriction terminating in a $2\text{\,}\mathrm{c}\mathrm{m}$ wide
aperture on the side of the detector was installed, while on the side of the
injection line a pneumatically actuated gate valve was placed. The portion of
tube containing the detector and the restriction were both evacuated using
separate turbo pumps, reaching a vacuum of $2\cdot
10^{-7}$\text{\,}\mathrm{m}\mathrm{b}\mathrm{a}\mathrm{r}$$. The gate valve
was opened only briefly during the injection of the antiprotons, to limit the
contamination of the AE$\bar{\text{g}}$IS vacuum from the sensor readout
system, which was not designed to reach higher levels of vacuum.

Antiprotons were captured from the Extra Low Energy Antiproton ring (ELENA) by
the main AE$\bar{\text{g}}$IS apparatus and then dumped back into the
injection line using a purposely implemented procedure in the experiment
control system Circus . The injection line has been instrumented with two
pairs of einzel lenses and a pair of deflecting electrodes, to allow the
formation of a beam of antiprotons in two offshoot lines onto one of which the
detector apparatus was installed. Unfortunately many of the electrodes were
not available during the course of this experiment, so only minimal focusing
of the re-emitted antiprotons was possible. This was not an issue, as the high
number of antiprotons available from AE$\bar{\text{g}}$IS (estimated $4\cdot
10^{6}$) allowed to record on average $1.9$ events on the detector in each
run, thus allowing for the execution of the experiment.

As in Berghold2023 , images from the sensor were transmitted outside the
vacuum chamber through a WiFi bridge. Syncronization of the valve actuation
and minimization of its opening time was achieved acoustically by installing a
microphone onto the valve and matching the recorded audio to the master clock
of the experiment.

###  4.2 Track fitting algorithms

The algorithm processes a $128\times 128$ pixel section of the image that
includes a preselected annihilation event and outputs the widths of all
present tracks. Since tracks and ellipses in each annihilation event often
overlap, it is essential to estimate their widths jointly to minimize biases.
As auxiliary input, the number of tracks and ellipses that are present in the
image has to be provided, as well as a preliminary estimation of positions of
these tracks and ellipses. Each track position is identified by its two
endpoints, $\vec{p}_{0}=(x_{0},y_{0})$ and $\vec{p}_{1}=(x_{1},y_{1})$, while
each ellipse is identified by its center $\vec{p_{c}}=(x_{c},y_{c})$ and by
two distinct points on its boundary, $\vec{p}_{a}=(x_{a},y_{a})$ and
$\vec{p}_{b}=(x_{b},y_{b})$, so that the boundary can be parameterized as
$\vec{p}(\phi)=(\vec{p}_{a}-\vec{p}_{c})\sin(\phi)+(\vec{p}_{b}-\vec{p}_{c})\cos(\phi)$,
for $\phi\in[0,2\pi)$. The initial positions are a human inputs and must be
accurate within 2 pixels.

The widths of the tracks are estimated by modeling the expected appearance of
the annihilation event based on a few underlying parameters and then
identifying the parameters that best fit the observed data. Specifically, an
annihilation event containing $n_{\text{ell}}$ ellipses and $n_{\text{tr}}$
tracks is described via the parameter set
$\mathcal{T}=\\{(\vec{p}_{a,i},\vec{p}_{b,i},\vec{p}_{c,i})\\}_{i=1}^{n_{\text{ell}}}\bigcup\\{(\vec{p}_{0,i},\vec{p}_{1,i},w_{i})\\}_{i=1}^{n_{\text{tr}}}$,
where $w_{i}>0$ is the width of the $i$-track.

Given the parameterization $\mathcal{T}$ of an event, a model of the
intensities of the pixels is obtained as follows. The intensity $I(\vec{r})$
of the pixel with coordinates $\vec{r}=(x,y)$, assumed to be at the center of
the pixel, ranges from 0 (black) to 1 (white). The distance $d$ of each pixel
to the boundary of each ellipse is numerically computed, with $d>0$ ($d<0$)
indicating points inside (outside) an ellipse. The pixel intensities due the
$i$-th ellipse are

$\displaystyle I_{i}^{\text{ell}}(\vec{r})=\begin{cases}1&\text{if}~{}d<0\\\
1-d&\text{if}~{}0\leq d<1\\\ 0&\text{if}~{}d\geq 1.\end{cases}$ (1)

Similarly, the distance $d$ of each pixel to each track is also numerically
computed (being a track identified by a segment, this distance cannot be
negative). The pixel intensities due the $i$-th track are

$\displaystyle
I_{i}^{\text{tr}}(\vec{r})=\begin{cases}1&\text{if}~{}d<w_{i}\\\
1-d&\text{if}~{}w_{i}\leq d<w_{i}+1\\\ 0&\text{if}~{}d\geq
w_{i}+1.\end{cases}$ (2)

This differs from anti-aliasing algorithms for drawing lines in computer
graphics, but it more closely resembles the detector physics and provides a
better fit to the tracks. Finally, the intensity of each pixel in the model is
obtained by summing the individual contributions and clipping the result to
one, i.e.
$I_{\mathcal{T}}(\vec{r})=\min\left(1,\sum_{i=1}^{n_{\text{ell}}}I_{i}^{\text{ell}}(\vec{r})+\sum_{i=1}^{n_{\text{tr}}}I_{i}^{\text{tr}}(\vec{r})\right)$.

The $\ell^{2}$ distance between the modelled intensities $I_{\mathcal{T}}$ and
the observed intensities $I_{\text{data}}$ is computed as

$\displaystyle\ell^{2}(\mathcal{T})=\sum_{\vec{r}\in\mathcal{R}}\big{|}I_{\mathcal{T}}(\vec{r})-I_{\text{data}}(\vec{r})\big{|}^{2},$
(3)

where the dead pixels are excluded from the summation domain $\mathcal{R}$.
The parameters in $\mathcal{T}$ are then varied within $2$ pixels from their
preset values and a local minimum of $\ell^{2}(\mathcal{T})$ is obtained via a
Nelder-Mead optimiser. From our analyses, we expect these local minima to be
also global ones. The values of the track thicknesses are extracted from the
value of $\mathcal{T}$ found by the optimiser.

###  4.3 Grid fitting algorithms

Given as input an image taken by the sensor and set of segments providing a
preliminary estimation of the positions of the edges of the teeth, the
algorithm outputs a refined estimation of the position of these edges. The
preliminary position estimation is a human input.

Let $k$ be the number of tooth edges (typically, twice the number of teeth)
and for each $i\in\\{1,\ldots,k\\}$ let the points
$(x_{0,i},y_{0,i}),(x_{1,i},y_{1,i})$ be the endpoints of a segment indicating
approximately the position of the $i$-th edge. It is assumed that the segment
is almost horizontal (i.e., $|x_{1,i}-x_{0,i}|\gg|y_{1,i}-y_{0,i}|$) and,
without loss of generality, that $x_{1,i}>x_{0,i}$. The equation of the $i$-th
segment is

$\displaystyle
y_{i}(x)=\frac{y_{1,i}-y_{0,i}}{x_{1,i}-x_{0,i}}x+\frac{x_{1,i}y_{0,i}-x_{0,i}y_{1,i}}{x_{1,i}-x_{0,i}}\qquad\text{for}~{}x_{0,i}\leq
x\leq x_{1,i}.$ (4)

A band of pixels having width $2w$ around each segment is considered, given by
the pixels having coordinates $(x,y)$ within vertical distance $w$ from the
$i$-th segment. Let their intensities in the image be $I_{i}(x,y)$. We define
$\bar{I}_{i}(x,y)$ as a Gaussian smoothing of these intensities along the
vertical direction within a band, i.e.

$\displaystyle\bar{I}_{i}(x,y)=\frac{\sum_{y^{\prime}\in{B_{i}}(x)}I(x,y^{\prime})\,e^{\frac{(y-y^{\prime})^{2}}{s^{2}}}}{\sum_{y^{\prime}\in{B_{i}}(x)}e^{\frac{(y-y^{\prime})^{2}}{s^{2}}}}\qquad
B_{i}(x)=\\{y:~{}|y-y_{i}(x)|\leq w\\}.$ (5)

Let $p$ be a real indicating the portion of image covered by the grid and
$N(I)$ the number of pixels having intensity smaller or equal than $I$, with
$N(\infty)$ denoting the total number of pixels in the image. First, a
threshold value $I_{p}$ is determined as the largest intensity such that
$N(I_{p})<p\cdot N(\infty)$. Then the equation

$\displaystyle\bar{I}_{i}(x_{i},y)=I_{p}$ (6)

is solved numerically in $y$ for all $i\in\\{1,\ldots,k\\}$ and for all
$x_{i}\in\\{x_{0,i},\ldots,x_{1,i}\\}$. If the solution to Eq.(6) is not
unique, the point is discarded and a warning is raised. For each edge $i$, a
collection of points
$\mathcal{C}_{i}=\\{(x_{i},y_{i}):\bar{I}_{i}(x_{i},y_{i})=I_{p}\text{~{}and~{}}y_{i}\text{~{}is~{}unique}\\}$
is created. Finally, for each edge $i$, the output is a straight line obtained
via linear regression of $y$ as a function of $x$ over the collection
$\mathcal{C}_{i}$.

In our case, the tunable parameters of the algorithm were set to $p=0.6$,
$w=10$ and $s^{2}=3$.

##  5 Acknowledgements

We would like to thank Michael Fußeder and Thomas Schwarz-Selinger from the
tandem accelerator lab of the Max Planck Institute for Plasma Physics (IPP)
for granting us the beam time necessary to characterize proton interactions
with the sensor. Also funding from Istituto Nazionale di Fisica Nucleare; the
CERN Fellowship programme and the CERN Doctoral student programme; the EPSRC
of UK under grant number EP/X014851/1; Research Council of Norway under Grant
Agreement No. 303337 and NorCC; CERN-NTNU doctoral program; the Research
University – Excellence Initiative of Warsaw University of Technology via the
strategic funds of the Priority Research Centre of High Energy Physics and
Experimental Techniques; the IDUB POSTDOC programme; the Polish National
Science Centre under agreements no. 2022/45/B/ST2/02029, and no.
2022/46/E/ST2/00255, and by the Polish Ministry of Education and Science under
agreement no. 2022/WK/06; Marie Sklodowska-Curie Innovative Training Network
Fellowship of the European Commission’s Horizon 2020 Programme (No. 721559
AVA); European Union’s Horizon 2020 research and innovation programme under
the Marie Sklodowska-Curie grant agreement ANGRAM No. 748826; Wolfgang Gentner
Programme of the German Federal Ministry of Education and Research (grant no.
13E18CHA); European Research Council under the European Unions Seventh
Framework Program FP7/2007-2013 (Grants Nos. 291242 and 277762); the European
Social Fund within the framework of realizing the project, in support of
intersectoral mobility and quality enhancement of research teams at Czech
Technical University in Prague (Grant No. CZ.1.07/2.3.00/30.0034);

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