Analysis of Level-B requirements regarding muons
Summary
Currently there are 13 level-B requirements related to the DPPS work on muons. I post them here, together with my analysis of them in the form of bullets. General requirements:
B-DPPS-3540 The DPPS shall provide calibration tools enabling the end‐to‐end optical throughput for each telescope as a whole (including mirror and camera) within an uncertainty of less than 5% rms
- This requirement concerns us in terms of providing precise enough value of calculated optical throughput. So we need to have enough muon tagged data and calculate not only efficiency value, but also its uncertainty.
B-DPPS-2330 The DPPS shall derive, from muon image parameters, corrections of the optical throughput to better than 5% RMS.
-
CalibPipe
will calculate optical throughput value from muon parameters and thenDataPipe
will use these values for deriving corrections.
B-DPPS-2235 The DPPS shall compute optical throughput corrections in the Category‐B analysis.
-
CalibPipe
will perform optical efficiency calculation using muons for each observational run.
B-DPPS-2320 The DPPS shall extract muon image parameters necessary for optical throughput determination from candidate muon event images in all telescopes.
-
CalibPipe
will perform processing of muon tagged events and calculate optical throughput based on the extracted muon parameters.
And requirements on precise physics of muon rings:
B-DPPS-3701 "The DPPS shall use the non‐sphericity of the reflectors in the muon analysis following the prescriptions outlined in [RD-62]."
- I think deviation in the shape of the mirror should be done in
ctapipe
in theMuonProcessor
algorithm during the step of integrating chords on the mirror for obtaining light profile of muon ring.
B-DPPS-3702 "The DPPS shall be capable to estimate and correct for biases due to the optical aberrations in the correspondence of camera coordinates to incidence angles, for the muon analysis."
- Correction for the mean aberration is already done in the
ctapipe
usingeffective_focal_length
in transformation between camera and telescope coordinate systems (from the description - OpticsDescription) - Also, in
CalibPipe
we can use cuts on reconstructed impact parameter and/or muon inclination angle to even further limit this effect (this comes from the section 5.1.5 Gaug_et_al 2019). But how to estimate the size of this bias (and if we should do this) remains an open question.
B-DPPS-3703 "The DPPS shall be capable to estimate and correct for finite camera focuses for the muon analysis."
- Finite camera focus results in a systematic error if the ring radius is directly interpreted as the mean Cherenkov angle, which is exactly the case now because it is used as the radius of the ring in the fitting procedure. There is an equation (45) to estimate the bias for the reconstructed Cherenkov angle due to the finite camera focus in Gaug_et_al 2019. But inside the
CalibPipe
we don't have any access to the fitting procedure, we only call the full pipeline of theMuonProcessor
class, which performs ring fitting and intensity fitting as a black box. For me, the most natural way to account for this problem seems to implement this bias correction inside theMuonProcessor
class ofctapipe
.
B-DPPS-3704 The DPPS shall be capable of taking into account the effect of bending of the muon trajectory due to geomagnetic field effects, and to ensure that their effects bias the estimated optical throughput from muon analysis by less than 1% rms in relative terms.
- Depending on the size of the ring and pointing of the telescope, the bending of muon trajectory in the geomagnetic field can cause bias in the reconstructed Cherenkov angle. This bias can reach up to 2% in the worst case of a full muon ring under the maximum impact distance and the azimuthal component of the magnetic field. I think possible solution can be to implement calculation of geomagnetic bias (equation 50-51, 74 of Gaug_et_al 2019) in
ctapipe
, maybe also adding corresponding "geomagnetic_bias_parameter" and then inCalibPipe
we can make cuts on the events which has too high bias value for us, i.e. >1%. Other question is the muon rate, will it still remain high enough. For this some dedicated simulations shall be needed, especially for the LST.
B-DPPS-3705 Impact distance reconstruction of the muon analysis shall include the effect of shadows from the camera and, if existing, the central hole in the main reflector and particularly its dependency on the muon inclination, and ensure that their contributions bias the estimated optical throughput from muon analysis by less than 1% (LST/SST) or 2% (MST) rms in relative terms.
- Central hole in the main reflector already is taken into account in the standard
ctapipe
muon processing algorithm. I think we can correct for the camera shadowing as some attenuation coefficient for the light of muons which undergo different camera shadowing regarding muons trajectory (i.e. with particular muon incident angles and impact positions on the mirror). But the value of this coefficient should be derived from dedicated precise simulations, and be in perfect agreement with currentSimPipe
realisation for it, because at the end we should compare data to the exact same simulations. Discussion withSimPipe
on this question is needed.
B-DPPS-3706 The muon analysis shall be calibrated during commissioning of each new telescope (or group of telescopes) against dedicated muon simulations, which shall correctly include all shadow‐casting parts of the telescope, at their respective distances to the reflector. The residual rms systematic error of the simulated muon ring image pixel‐wise sizes shall not exceed 1% of the one corresponding to the newly installed real telescope.
- Possibly we should create special field in
CalibPipe DB
and appropriate method to store the initial measurement of optical throughput as baseline for every telescope during commissioning phase.
B-DPPS-3707 The DPPS shall be capable to estimate and correct extinction of the muon Cherenkov light by molecules in the air. Its contribution to the estimated optical throughput from muon analysis shall not exceed 0.5% in relative terms.
- The uncertainty of the molecular profile on atmospheric transmission is absolutely negligible, at least for CTA-N, once the correct average atmospheric profile has been selected (from Gaug_et_al 2019). So this requirement should be satisfied by proper choice of the molecular atmospheric profile.
B-DPPS-3708 The DPPS shall be capable to estimate and correct extinction of the muon Cherenkov light by aerosols in the air. Its contribution to the estimated optical throughput from muon analysis shall not exceed 2% (LST) or 1% (MST/SST) in relative terms.
- It also depends on the profile/atmospheric data, and due to the explanatory note to this requirement - we can exclude up to 15% of "bad" muons. As been said in section 5.2.2, we should apply corrections only in the case of strong aerosol densities, very close to the ground and with an unusually high contribution of the accumulation mode particles. A possible solution for us is to monitor aerosol data and apply correction to the optical throughput only when it will be needed. One more open question is on how to flag muons as bad, in terms of atmospheric conditions (how to choose 15% of possibly excluded events).
B-DPPS-3709 The DPPS shall be capable to include awareness of dependencies of the sensitivity of the camera to light inciding from angles onto the camera and correct for these. Residual contributions to the estimated optical throughput from muon analysis shall not exceed 0.5% in relative terms.
- There is correction factor, described in Appendix E, which can be applied to the length of the chord calculation. As far the chord calculation is performing in the
MuonProcessor
, so appropriate changes should be made there.
B-DPPS-3710 The DPPS shall be capable to take into account misaligned mirrors for muon analysis and apply corrections for these. Residual contributions to the estimated optical throughput from muon analysis shall not exceed 0.5% (LST) or 1% (MST) in relative terms.
- So far we don't have access to any information about mirror alignment during standard analysis of the event. Probably some dedicated simulations for different mirror misalignments and their influence on the reconstructed optical efficiency are needed, but I am not sure its our task.
What is the expected correct behavior?
So to conclude, some of these requirements require adding new features to the processing software, i.e. ctapipe
. One of the main question for me is what should we do as CalibPipe
, in this case?