============== Interferometry ============== Related doc. `Reco. workshop `_ Related code `py_interferometers class `_ This is done by below command:: source ../setup.sh python3 script_executor.py -k snr -s -r # calculates SNR python3 arr_time_table_maker.py # calculates arrivaltime table by ray tracing python3 script_executor.py -k reco_ele_lite -s -r # performs vertex reconstruction based on AraCorrelator method For sim:: source ../setup.sh python3 sim_script_executor.py -k rms -s -d # both signal and noise. calculates rms python3 rms_merge.py # nosie only python3 snr_maker.py # both signal and noise. calculates SNR by rms from noise event python3 sim_script_executor.py -k reco_ele -s -d # both signal and noise. finds c_max of all elevation angle User can find arrival time table from :code:`/data/ana/ARA/ARA02(or 3)/arr_time_table/arr_time_table_A2(or 3)_all.h5` Calculates the summed-cross correlation at a grid of pixels (theta, phi) for a source at fixed radius. - If signal is coming certain source, same type of antennas will have a similar WFs - By ray tracing algorithm, we can estimate arrival time differences of all air/ice positions - Cross-correlating WFs by removing arrival time differences, we can get correlation coefficient of all air/ice positions - Most highest coefficient score (Cmax) would be the reconstructed source position 5 radius (41, 170, 300, 450, 600 m), Direct / Reflect rays, D / R / D+R map, and default ice model were used for interferometry. ---------------- Detail Equations ---------------- Each cross-correlation ‘bin’ is normalized by product of sqrt of power. Hilbert envelope is applied on each cross-correlation Cross-correlation of all pairs are weighted by product of SNR. Most highest coefficient score (Cmax) was chosen as reconstructed source position .. _fig-int_eq: .. figure:: ../../figures/int_eq.png :align: center interferometry equations ----------------- Calpulser example ----------------- .. _fig-int_hist: .. figure:: ../../figures/int_hist.png :align: center calpulser example ================= Template Analysis ================= Related code `ara_matched_filter class `_ User must generate the template by AraSim. Setup file for template: `A2 `_ and `A3 `_ This is done by below command:: source ../setup.sh python3 arr_time_table_maker.py # calculates arrivaltime table by ray tracing python3 sim_script_executor.py -k temp -s -d # both signal and noise. generates template that will be used for matched filter to data and sim python3 sim_script_executor.py -k mf -s -d # both signal and noise python3 script_executor.py -k mf -s -r # perform matched filter Searching for Neutrino signal by directly comparing with Neutrino template - Aiming to find low SNR signal Simulated Neutrino templates - Preparing the expected Neutrino WFs that we can get from ARA - On/off-cone, shower, zenith gain pattern, and electronic response Matched filtering technique - Cross-correlating data and template set while suppressing noise by noise model Event-wise MF value (Mmax) - Summing up matched filter results (M(t)) after removing arrival time delay Cons. of this analysis is, it is model dependent. Currently, I’m using the AraSim model. Single model dependency will be dealt with as an systematic uncertainty ------------------ Template Parameter ------------------ Four parameters for constructing template sets (total 24 WFs per channel) - Signal chain gain: 16 - Zenith dependent antenna gain pattern: 4 (30, 50, 70, 90 deg) - On/Off-cone angle: 3 (0, 2, 4 deg) - Electromagnetic (EM) and hadronic (HAD) shower models: 2 Neutrino energy and the distance from the vertex to the detector, can be simplified using a scale factor. - Shape differences of Askaryan cut-off per energy/off-cone are not considered Receiving angle, -60, -40, -20, and 0, and On/Off-cone angle, 0, 2, and 4, are used for template set .. _fig-mf_hist: .. figure:: ../../figures/mf_hist.png :align: center template parameter test results ---------------- Detail Equations ---------------- Cross-correlation between data and template in f-domain with Hilbert envelope Suppress noise (weighting) in the f-domain by power spectral density (PSD) (averaged software triggered data) - Averaged software triggered data (Rayl. x sqrt(pi / 2)) Normalizes template and PSD amplitude (alpha_n) Sums up correlation results (Msum) after removing arrival time delay (tau_n) from AraSim ray tracing Most highest coefficient score (Mmax) was chosen for the event-wise result Cons. of template analysis is, it is model dependent. Currently, I’m using the AraSim E-field model .. _fig-mf_eq: .. figure:: ../../figures/mf_eq.png :align: center matched filter equations ------------------------- Event-wise Matched Filter ------------------------- 192 (8 chs * 24 templates) MF results are reduced to ‘single’ value (But total 2 by V/HPols) Off-cone dim. is reduced in individual channel level Channel dim. is reduced by summing up after removing arrival time delay - total 84 summed results by 2 shower, 7 zenith, and 6 azimuth - Summing is done by ~80 ns of rolling maximum Among the 84 summed results, I choose 1 result that has maximum Mmax value .. _fig-mf_chain: .. figure:: ../../figures/mf_chain.png :align: center event-wise matched filter process ------------------ Simulation example ------------------ .. _fig-mf_hist2: .. figure:: ../../figures/mf_hist2.png :align: center simulation results .. _fig-mf_hist3: .. figure:: ../../figures/mf_hist3.png :align: center simulation results with vertex reconstruction compare to interferometry