Calibration of AGILE-GRID with On-ground Data and Monte Carlo Simulations

The core of the GRID is the ST with the task of converting the incoming γ-rays and measuring the trajectories of the resulting e⁺−e⁻ pair (Barbiellini et al. 2002; Prest et al. 2003). The γ-rays convert in the W (Si) layers to e⁺−e⁻ pairs, which are subsequently detected by the silicon microstrip detectors.

The ST consists of 12 trays with distances between middle-planes equal to 1.9 cm. The first 10 trays consists of pairs of single-sided Si microstrip planes with strips orthogonal to each other to provide 3D points, followed by a W converter layer that is 245 μm thick (corresponding to 0.01(Si)+0.07(W) X₀). The last two trays have no W converter layer because the ST trigger requires at least three Si planes to be activated.

The base detector unit is a tile of area 9.5 × 9.5 cm², thickness 410 μm, and strip pitch 121 μm. Four tiles are bonded together to create a "ladder" with a 38.0 cm long strip. Each plane of the ST consists of four ladders. The readout pitch is 242 μm.

The ST analog readout measures the energy deposited on every second strip; that is, "readout" and "floating" strips alternate. This configuration enables a good compromise between power consumption and position resolution, the latter being ∼45 μm for perpendicular tracks (Barbiellini et al. 2002).

Each ladder is read out by three TAA1 ASICs, each operating 128 channels with low-noise, low power configuration (<400 μW/channel), self-triggering capability, and analog readout. The total number of readout channels is 36864.

The GRID is simulated using the GEANT 3.21 package (Brun et al. 1993). This package provides for a detailed simulation of the materials and describes with high precision the passage of particles through matter, including the production of secondary particles. It provides the user with the possibility of describing the response of the active sections of the detector. The GRID detector simulation used in the test beam configuration is used also to simulate the configuration with the detector mounted on the spacecraft.

In the microstrip detector with floating strips, a critical aspect of the simulation is the sharing of the charge collected on the strips to the readout channels (Cattaneo 1990). These sharing coefficients are estimated using test beam data to reproduce the observations (Barbiellini et al. 2002).

The Cartesian coordinate system employed below originates in the center of the AC plane from the top, the x and y axes parallel to the orthogonal strips of the ST, and the z axis pointing in the direction of MCAL. In the following the corresponding spherical coordinate system defined by the polar angle Θ and azimuthal angle Φ will be extensively used.

The reconstruction filter processes the reconstructed hits in the ST layers with the goal of providing a full description of the events. The reconstruction filter has several, sometimes conflicting, goals: reconstructing tracks, estimating their directions and energies, combining them to identify γ-rays, rejecting background hits from noise and charged particles escaping the AC veto, and providing an estimation of the probability that the measured tracks originate from a pair of converted γ-rays. The filter used in this analysis, FM3.119 (Bulgarelli et al. 2010; Chen et al. 2011), is the result of an optimization between those requirements and has been used in all AGILE scientific analyses.

2.3.1. Direction Reconstruction

2.3.2. Energy Measurement

The track reconstruction algorithm is based on a special implementation of the Kalman filter that estimates the energy of the single tracks on the basis of the measurement of the multiple scattering between adjacent planes.

A quantitative estimation of the single-track energy resolution can be obtained by considering the Gaussian approximation of the standard deviation of the distribution of the 3D multiple scattering angle (p is the particle momentum, β the speed, $t/{X}_{0}$ the thickness of the material expressed in term of radiation length) and the ultrarelativistic approximation (β = c and pc = E)

$$\begin{eqnarray}&&{\sigma }_{\mathrm{MS}}(\theta )=\displaystyle \frac{19.2\,\mathrm{MeV}}{c\beta p}\sqrt{\displaystyle \frac{t}{{X}_{0}}}\sim \displaystyle \frac{19.2\,\mathrm{MeV}}{{cE}}\sqrt{\displaystyle \frac{t}{{{\rm{X}}}_{0}}}.\end{eqnarray} \tag{ 1 }$$

Therefore, to estimate the error on energy measurement we can write

$$\begin{eqnarray*}&&{\rm{\Delta }}({\sigma }_{\mathrm{MS}})=\displaystyle \frac{{\rm{\Delta }}(E)}{E}\displaystyle \frac{19.2\,\mathrm{MeV}}{{cE}}\sqrt{\displaystyle \frac{t}{{{\rm{X}}}_{0}}}\end{eqnarray*}$$

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{\Delta }}(E)}{E}=\displaystyle \frac{{\rm{\Delta }}({\sigma }_{\mathrm{MS}})}{{\sigma }_{\mathrm{MS}}}.\end{eqnarray} \tag{ 2 }$$

The trajectory of a charged particle subject to multiple scattering crossing N measurement planes is a broken line consisting of N − 1 segments that define N_MS = N − 2 scattering angles. The particle direction projected on one coordinate between the planes k and k + 1 at a distance L is given by (x_k+1 − x_k)/L; this variable has an associated measurement error due to the position error σ(x_k). If the measurement of the particle direction between measurement planes is dominated by the change of direction due to multiple scattering (and not by the position measurement error), it provides N_MS sampling of the multiple scattering distribution, assuming that the particle energy is constant throughout the tracking. The error associated to the measurement of the standard deviation of the Gaussian distribution in Equation (1) is

$$\begin{eqnarray*}&&{\rm{\Delta }}({\sigma }_{\mathrm{MS}})=\displaystyle \frac{1}{\sqrt{2{N}_{\mathrm{MS}}}}{\sigma }_{\mathrm{MS}}.\end{eqnarray*}$$

From Equation (2) we obtain

$$\begin{eqnarray}&&{\rm{\Delta }}(\mathrm{log}E)=\displaystyle \frac{{\rm{\Delta }}(E)}{E}=\displaystyle \frac{{\rm{\Delta }}({\sigma }_{\mathrm{MS}})}{{\sigma }_{\mathrm{MS}}}=\displaystyle \frac{1}{\sqrt{2{N}_{\mathrm{MS}}}},\end{eqnarray} \tag{ 3 }$$

hence the relative error is independent from the energy and from the thickness of scattering material and therefore from the angle relative to the planes, and depends only on the number of hits. On average, with 12 planes, the maximum value for N_MS is 10. The average value is half this value, ∼5. Therefore, we expect ${\rm{\Delta }}(\mathrm{log}E)\sim 1/\sqrt{2\,\times \,5}\sim 0.316$.

The high-energy limit of this approach is reached when the size of the deviation from the extrapolated trajectory due to multiple scattering is comparable to the error in position measurement in the measurement plane. From Barbiellini et al. (2002) the measurement error of the single coordinate is σ_x  ∼ 45 μm, therefore for the 2D distance in the tracking plane ${\sigma }_{{xy}}\sqrt{2}\times \sim 45\,\mu {\rm{m}}\sim 64\,\mu {\rm{m}}$, while L = 1.9 cm. Hence, the limit on the capability of measuring the direction of a track segment, which has two vertices, is ${\sigma }_{{xy}}/L\sim 0.0064\sqrt{2}/1.9\ \sim$ 4.8 × 10⁻³ rad. Recalling that the thickness of a tray is 0.08 X₀ and that the angular deviation due to multiple scattering is measured from the difference between the directions of the track segments, from Equation (1) the particle energy for which the multiple scattering angle is equal to the direction error due to the finite position resolution of the planes is ∼0.8 GeV. Therefore, in the energy range available in this test, the assumption that the multiple scattering contribution dominates over measurement errors is always true.

2.3.3. Event Classification

The goal of the calibration is to estimate the instrument response functions by means of exposure to controlled γ-ray beams. The ideal calibration beam provides a flux of γ-rays, monochromatic in energy and arriving as a planar wave uniformly distributed on the instrument surface, with properties known to an accuracy better than the resolving power of the instrument.

The figures of merit to be evaluated and compared are the energy dispersion probability (EDP), the point-spread function (PSF), and the effective area (A_eff): all of them depend on the incoming γ-ray energy ${E}_{\gamma }$ and direction (Θ, Φ).

The EDP is the energy response of the GRID detector to a monochromatic planar wave with energy ${E}_{\gamma }$ and direction (Θ, Φ). It is a function of ${E}_{\gamma }$ and of (Θ, Φ), defined as

$$\begin{eqnarray}&&\mathrm{EDP}({E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }})=\displaystyle \frac{1}{N({E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }})}\displaystyle \frac{{dN}({E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }})}{{{dE}}_{\mathrm{GRID}}},\end{eqnarray} \tag{ 4 }$$

where ${E}_{\mathrm{GRID}}$ is the energy measured by the GRID.

The PSF is the response in the angular domain of the GRID detector to a planar wave. If γ-rays impinge uniformly on the GRID with fixed direction (Θ, Φ), the detector measures for each γ-ray a direction (Θ', Φ'). Assuming this function to be azimuthally symmetric, and defining the 3D angular distance θ between the true and measured directions,²⁴ it is defined as

$$\begin{eqnarray}&&\mathrm{PSF}(\theta ,{E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }})d\theta =2\pi \sin (\theta )P(\theta ,{E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }})d\theta ,\end{eqnarray} \tag{ 5 }$$

where P(θ, ${E}_{\gamma }$, Θ, Φ) is the probability distribution per steradian of measuring an incoming γ-ray at a given angular distance θ from its true direction (Sabatini et al. 2015).

The A_eff is a function of ${E}_{\gamma }$ and of (Θ, Φ), and it is defined as

$$\begin{eqnarray}&&{A}_{\mathrm{eff}}({E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }})={\int }_{A}\epsilon ({E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }},\overline{x}){da},\end{eqnarray} \tag{ 6 }$$

where the integral over the 2D coordinate variables covers the detector area A intercepted by the incoming γ-ray direction and $\epsilon ({E}_{\gamma },{\rm{\Theta }},{\rm{\Phi }},\overline{x})$ is the detection efficiency dependent on the energy and direction of the incoming γ-rays and on the position on the detector.

The GRID was calibrated at the INFN Laboratory of Frascati (LNF) from 2005 November 2–20, thanks to a scientific collaboration between AGILE Team and INFN-LNF.

The goal of the GRID calibration is to reproduce with adequate statistics in the controlled environment of the laboratory the γ-ray interactions under space conditions. The total number of required incident γ-rays N_T, not necessarily interacting within the GRID, depends on the expected counting statistics for bright astrophysical sources acquired for typical exposures. With the goal of achieving statistical errors due to the calibration that are negligible compared to those in-flight, we require a number of events about four times larger than the brightest source.

The canonical source of in-flight calibration is the Crab Nebula, with an integrated average total γ-ray flux (nebula and pulsar) of ${I}_{{\rm{c}}}({E}_{\gamma }\gt 100\,\mathrm{MeV})$ = 220 × 10⁻⁸ ph cm⁻² s⁻¹ (Pittori et al. 2009) and the calibration statistics is estimated based on its flux and the AGILE detection capability (Tavani et al. 2009). The Crab Nebula integral γ-ray intensity flux as a function of the γ-ray energy ${E}_{\gamma }$ expressed in MeV is I_c(${E}_{\gamma }$ > 100 MeV) = ${E}_{\gamma }$^−1.015 2.36 × 10⁻⁴ ph cm⁻² s⁻¹.

For a given incident direction (Θ, Φ), the number of required incident γ-rays with ${E}_{\gamma }$ > E_th is N(E_th, Θ, Φ) = αt_exp ηA_geom I_c(${E}_{\gamma }$), where α = 4 is the factor required to reduce to negligible levels the statistical error due to calibration, η is the Earth occultation efficiency (typically η = 0.45), t_exp is the exposure time (typically t_exp = 2 weeks), and A_geom is the geometric area of the GRID (A_geom = 1600cm²).

For typical values and the GRID geometry, we obtain the integrated required number of incident γ-rays for ${E}_{\gamma }$ > 30 MeV for a given combination of (Θ, Φ):

$$\begin{eqnarray}&&N(30\,\mathrm{MeV},{\rm{\Theta }},{\rm{\Phi }})=2.6\times {10}^{4}\ \mathrm{ph}.\end{eqnarray} \tag{ 7 }$$

The tagged γ-ray beam used for the calibration is described in detail in Cattaneo et al. (2012). In the following subsections we briefly summarize the most relevant elements of this beam.

3.3.1. The Beam Test Facility (BTF)

For the GRID calibration we used the BTF in the Frascati DAΦNE collider complex, which includes a LINAC at high electron and positron currents, an accumulator of e⁺−e⁻, and two accumulation rings at 510 MeV. The e⁺/e⁻ beam from the LINAC is led into the accumulation ring to be subsequently extracted and injected in the Principal Ring. When the system injector does not transfer the beams to the accumulator, the beam from LINAC can be transported in the test beam area through a dedicated transfer line: the BTF line (Figure 2). The BTF can provide a collimated beam of electrons or positrons in the energy range 20–800 MeV, with a pulse rate of 49 Hz. The pulse duration can vary from 1 to 10 ns and the average number of particles can vary from 1 to 10¹⁰. In Figure 2(a) a schematic view of the calibration setup is shown.

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The BTF can be operated in two ways:

• 1.  
  a LINAC mode operating when DAΦNE is off, with a tunable energy in the range 50–750 MeV and an efficiency around 0.9; and
• 2.  
  a DAΦNE mode operating when DAΦNE is on, with a fixed energy of 510 MeV and an efficiency around 0.6.

3.3.2. Target

3.3.3. Photon Tagging System (PTS)

3.3.4. Trade-off on the Number of e⁻/Bunch

3.3.5. Mechanical Ground Support Equipment (MGSE)

3.3.6. Simulation

A great challenge in γ-ray astronomy is the fact that cosmic rays and the secondary particles produced by the interaction of cosmic rays in the atmosphere produce in detectors a background signal much larger than that produced by cosmic γ-rays. Therefore, the development and the optimization of trigger algorithms to reject this background have been of utmost relevance for AGILE. AGILE has a data handling system (Argan et al. 2008; Tavani et al. 2008) that cuts a large part of the background rate through a trigger system, consisting of both hardware and software levels, in order not to saturate the telemetry channel for scientific data.

The on-board GRID trigger is divided into three levels: two hardware (Level 1 and 1.5) and one software (Level 2) (Giuliani et al. 2006). The hardware levels accept only the events that produce some particular configuration of fired anticoincidence panels and ST planes. The main goal of the two hardware trigger levels is to select γ-rays and provide a rejection factor of ∼100 for background events. The software level provides an additional rejection of the background by a factor ∼5.

The residual background events are further reduced offline on-ground by more complex software processing. In the first step software algorithms are applied that analyze the event morphology, using cluster identification and topology to reduce the background. A further processing step is necessary to eliminate the remaining background events, particularly those produced by albedo γ-rays that are distinguished from cosmic γ-rays only on the basis of their incoming direction (see Vercellone et al. 2008 for a description of the AGILE on-ground data reduction).

The trigger for reading out the target and the PTS data was delivered by the accelerator and was independent of the PTS data. Therefore, the PTS events were triggered independently from the GRID and written on a separate stream. Further selection based on the PTS data was performed offline by requiring that one or more strip clusters was identified. A cluster was defined as a set of neighboring strips on the same detector above a predefined threshold. The signal-to- noise ratio was high enough that the algorithm selected essentially all electrons crossing the detector (Cattaneo et al. 2012).

The PTS events and the GRID ones, which are written on two different streams, are correlated offline by exploiting the time tags recorded for both event streams. The result is a subset of GRID events that can be associated, for each event, with the γ-ray energy estimated by the PTS ${E}_{\mathrm{PTS}}$. The fraction of events with a PTS trigger and without a GRID trigger provides an estimation of the efficiency of the GRID.

MC sets are simulated by reproducing precisely the beam parameters and the position and orientation of the GRID with respect to the beam, as well as online and offline trigger conditions. Event samples comparable in size to the data are generated. The events are selected by requiring that the trigger conditions are satisfied by PTS and GRID signals, so that direct comparison with data is possible.

The rational behind the use of ${E}_{\mathrm{PTS}}$ as energy estimator in measuring the GRID resolutions is the expectation that the resolution of ${E}_{\mathrm{PTS}}$ is much better than that of ${E}_{\mathrm{GRID}}$. That can be verified for MC events of class G by comparing the distributions of ${E}_{\mathrm{PTS}}$ versus ${E}_{\gamma }$, as well as those of ${E}_{\mathrm{GRID}}$ versus ${E}_{\gamma }$ and verifying that the former distribution is much narrower than the latter. Those distributions are shown in Figure 4(a) and Figure (b), respectively, with the red markers representing the average ${E}_{\mathrm{PTS}}$ in ${E}_{\gamma }$ bins 50 MeV wide. It is apparent that the resolution of ${E}_{\mathrm{PTS}}$ as an energy estimator of ${E}_{\gamma }$ is much better than that of ${E}_{\mathrm{GRID}}$; therefore ${E}_{\mathrm{PTS}}$ provides an effective energy estimator for calibrating the GRID with real data under the mild assumption that the energy resolution of ${E}_{\mathrm{PTS}}$ for data is not much worse than that for MC.

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The EDP defined in Equation (4) can be obtained by illuminating uniformly the GRID with a monochromatic beam of γ-rays with energy ${E}_{\gamma }$ and considering the resulting spectrum of ${E}_{\mathrm{GRID}}$. This procedure, repeated for an adequate number of energies ${E}_{\gamma }$, allows us to build a matrix (${E}_{\gamma }$, ${E}_{\mathrm{GRID}}$) that defines the EDP. This can be done with MC simulations, but lacking available monochromatic γ-ray beams of variable and known energy with sufficient size to guarantee uniform illumination, this cannot be done experimentally.

In any case, this approach is not the most appropriate for the application to which GRID is dedicated. The γ-ray spectra measured by GRID during its operation in-flight are power-law spectra like $1/{E}_{\gamma }^{\alpha }$, with α ∼ 1.7 (Chen et al. 2013), therefore a matrix is built with MC events produced according to this power-law spectrum (${E}_{\gamma }$, ${E}_{\mathrm{GRID}}$)^MC_1.7 (the subscript is the power index).

The goal of the BTF calibration is to assess quantitatively the reliability of the MC simulation used to build the EDP matrix, not to measure the EDP matrix directly. One reason is that the BTF γ-ray beam follows an approximate 1/${E}_{\gamma }$ Bremsstrahlung spectrum on the restricted energy range available, producing an EDP matrix that is different from the one estimated using a power-law spectrum whose spectral index is α = −1.7 (Chen et al. 2013); the other reason is that the true energy ${E}_{\gamma }$ of the single γ-ray is unknown. At the BTF, a straightforward comparison is possible between ${({E}_{\mathrm{PTS}},{E}_{\mathrm{GRID}})}_{1.0}^{\mathrm{data}}$ and ${({E}_{\mathrm{PTS}},{E}_{\mathrm{GRID}})}_{1.0}^{\mathrm{MC}}$. Our goal is to estimate the effect of the discrepancies measured in this comparison of the errors between ${({E}_{\gamma },{E}_{\mathrm{GRID}})}_{1.7}^{\mathrm{data}}$ and ${({E}_{\gamma },{E}_{\mathrm{GRID}})}_{1.7}^{\mathrm{MC}}$, which are the actual systematic errors in the EDP.

In Figure 5 the events are partitioned into five ${E}_{\mathrm{PTS}}$ bins and the distributions of ${E}_{\mathrm{GRID}}$ are displayed for MC (blue) and real data (red). The variable log(${E}_{\mathrm{GRID}}$) is fitted with a Gaussian separately for MC and data in each ${E}_{\mathrm{PTS}}$ bin. The fitted averages and the relative standard deviations are reported in the legend as $\langle {E}_{\mathrm{GRID}}\rangle$ and ${\rm{\Delta }}{E}_{\mathrm{GRID}}/\langle {E}_{\mathrm{GRID}}\rangle$.

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The values of $\langle {E}_{\mathrm{GRID}}\rangle$ for each energy bin are within or close to the ${E}_{\mathrm{PTS}}$ bins both for MC and real data, with the exception of Figure 5(a), where, as visible in Figure 4(a), in the low-energy ${E}_{\mathrm{PTS}}$ bin there is a significant tail due to high ${E}_{\mathrm{GRID}}$ events. The widths of the distributions for MC and data are compatible with each other within 5%, which can be assumed as an upper limit estimation of the systematic error, with some discrepancy in Figure 5(e) for ${E}_{\mathrm{PTS}}$ ≈400 MeV, and consistent with the value estimated in Section 2.3.2. The discrepancy in Figure 5(e) may be due to the poor reliability of ${E}_{\mathrm{PTS}}$ as an estimator of ${E}_{\gamma }$ at this energy, as explained in Section 5.5. Similar results are obtained for different values of Θ.

The performance of the instrument with respect to the angular resolution is characterized by the PSF as defined in Section 1. The distribution of the 3D angular difference is fitted assuming that the PSF is described by the two-parameter King's function as defined in the Appendix. In addition to the function parameters, δ related to the standard deviation, and γ related to non-Gaussian tail, the value of the containment radius at 68.3% (CR₆₈) is also quoted: this value is determined by the function parameters, but it can be defined independently from the parameterization.

The angular distributions are fitted separately for different incident angles (Θ), different classes (G, L, S, P), and different intervals of energy. A subset of these fits is shown in Figure 6 for MC events and in Figure 7 for real events for two bins of ${E}_{\mathrm{GRID}}$ for Θ = $0^\circ$ and Θ = $30^\circ$. The quality of all fits is good both for MC and real data. In Figures 8–10 the results of the King's function parameters obtained with the fits for MC and real data are shown versus ${E}_{\mathrm{GRID}}$. In general, the comparison is satisfying, although the parameter γ for data is significantly lower than that for MC, especially for low ${E}_{\mathrm{GRID}}$. This implies larger containment radius boundaries for data at low energy.

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Considering the broad EDP, especially at low energy, it is worth investigating if the choice of the energy estimator significantly influences the PSF parameters. ${E}_{\mathrm{GRID}}$ and ${E}_{\mathrm{PTS}}$ are available for both data and MC, while only ${E}_{\gamma }$ is available for MC events. In Figures 11–12, the parameters of the King's function from MC and real data are displayed versus the relevant energy estimators. The agreement is good: the King's parameters for the same energy bins rarely differ more than 2σ–3σ, with the exception of the last ${E}_{\mathrm{PTS}}$ bin in real data, where the environmental background induces a large fraction of PSF events unrelated to real γ-rays of corresponding energy in the GRID, as discussed in Section 5.5.

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In Table 2 the results of the fits of the PSF distributions with the King's function are reported versus the γ-ray energy for three incident angles for MC and real data. The agreement is quite satisfactory, with the exception of the parameter γ and consequently CR₆₈ for the lowest energy channel where real data PSFs show consistently longer tails.

Table 2.  King's Function Fit Parameters of the PSF with the Containment Radius at 68.3% for Four Energy Bins and Three Angular Directions for MC and Real Data

Θ	${E}_{\mathrm{PTS}}$	MC			Real
(degree)	( MeV)	δ (degree)	γ	${\mathrm{CR}}_{68}$ (degree)	δ (degree)	γ	${\mathrm{CR}}_{68}$ (degree)
0	35–70	2.33 ± 0.05	1.97 ± 0.03	6.95 ± 0.17	2.17 ± 0.08	1.60 ± 0.04	9.18 ± 0.36
	70–140	1.41 ± 0.02	1.86 ± 0.02	4.52 ± 0.10	1.49 ± 0.04	1.84 ± 0.05	4.85 ± 0.22
	140–180	0.83 ± 0.01	1.87 ± 0.02	2.61 ± 0.06	0.90 ± 0.03	1.92 ± 0.05	2.77 ± 0.16
	280–500	0.60 ± 0.01	1.91 ± 0.02	1.87 ± 0.06	0.61 ± 0.03	1.69 ± 0.06	2.27 ± 0.23
30	35–70	2.72 ± 0.05	2.03 ± 0.04	7.77 ± 0.19	2.42 ± 0.09	1.45 ± 0.03	14.15 ± 0.57
	70–140	1.62 ± 0.02	1.85 ± 0.02	5.25 ± 0.10	1.48 ± 0.04	1.58 ± 0.03	6.54 ± 0.25
	140–180	1.00 ± 0.01	1.82 ± 0.01	3.29 ± 0.06	0.93 ± 0.03	1.70 ± 0.04	3.47 ± 0.16
	280–500	0.70 ± 0.01	1.76 ± 0.01	2.45 ± 0.05	0.69 ± 0.03	1.77 ± 0.05	2.38 ± 0.22
50	35–70	2.67 ± 0.12	1.76 ± 0.08	9.36 ± 0.17	3.09 ± 0.22	1.41 ± 0.07	19.83 ± 1.47
	70–140	1.84 ± 0.06	1.88 ± 0.04	5.86 ± 0.10	1.78 ± 0.06	1.58 ± 0.06	7.89 ± 0.44
	140–180	1.05 ± 0.02	1.76 ± 0.02	3.86 ± 0.06	1.04 ± 0.04	1.60 ± 0.04	4.40 ± 0.26
	280–500	0.82 ± 0.02	1.66 ± 0.02	3.26 ± 0.06	0.73 ± 0.06	1.48 ± 0.05	3.93 ± 0.35

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This measurement turned out to be the most critical and we are unable to provide significant results. The reason is the strong flux of low-energy photons in the experimental hall, and to a smaller extent, cosmic rays. This issue has been detected and discussed in depth in Cattaneo et al. (2012), who show that many GRID triggers are fired outside the phase of the beam and some parts of the ${E}_{\mathrm{PTS}}$ spectrum are unrelated to the γ-ray emission due to Bremsstrahlung. Furthermore, even for events in phase, there are more hits on the front faces in real data than in MC.

The GRID detection efficiency is expected to be measured by the ratio of GRID events to PTS events in data and MC. A comparison can provide an estimation of the quality of the simulation and eventually provide correction factors. This approach is sensible if the MC reproduces correctly the data and if the calibration data resemble closely the values expected in the space configuration. The presences of a significant flux of cosmic rays triggering both the GRID and the PTS at random times are extremely difficult to simulate appropriately and outside the scope of the calibration task.

An additional and even more relevant problem is the flux of low-energy photons in the experimental hall in phase with the beam. The low-energy photons down to X-ray energies are relevant because, if interacting with the silicon detectors, they release enough energy to be above the threshold for hit detection. Those photons can be due to photon production along the beam line entering the hall, photon production in the last bending magnet, and photon production in the beam dump of the electron beam followed by scattering inside the hall. This part is underestimated in the MC because it would require a simulation of the full hall and for such low-energy photons, that is unrealistic. Such low-energy photon-induced hits can overlap with γ-ray conversion events, forcing the filter to move, e.g., an event from class G (clean conversion) to class L (ambiguous).

This effect is clearly visible when comparing MC (Figure 6) and real data (Figure 7); the ratio between the numbers of G and L events is completely different: namely, it is much lower for real data. Additional efforts could bring the MC data closer to real data by adding, e.g., an additional flux of low-energy photons hitting the GRID, but it would be arbitrary and in any case significantly different from the space configuration, so little or no usable information would be gained.

Nevertheless, this discrepancy is much less relevant for the measurements of the PSF and EDP for class G events, because for those measurements we rely on events already classified as class G, that is, for events for which the influence of the low-energy photons is non-existent or negligible. Under those conditions, the comparison between MC and real data is realistic and the calibration results are expected to reproduce those in the space configuration.