time calibration of lofar-tbb data and cosmic ray ... · cs002 cs003 cs005 cs006 cs007 . results...
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Time calibration of LOFAR-TBB data and cosmic ray wavefront shapes
Dalfsen, March 20, 2012
Arthur Corstanje, Radboud University Nijmegen
for the LOFAR Cosmic Rays KSP
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A ‘good’ cosmic ray detection
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Characterize radio signal from air shower
• Footprint and lateral power distribution – Shower axis direction and location
• Time of arrival for each antenna – Found using Hilbert transform or cross correlations – Direction fitting – Curvature fit
– Delay calibration! • Polarization • Pulse shape
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Wavefront curvature
• Zenith angle theta = 30° • Superterp diameter d=300m • Point source at altitude h=4 km !
To lowest orders at the edges:
≈ 250 ns + 6 ns • 1 sample = 5 ns…
c!t = d2sin! + d
2
8hcos3!
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Measuring wavefront curvature • Measure time of arrival for each antenna using maximum of
Hilbert envelope or cross correlation
• Obtain direction of best-fitting plane wave, by linear regression of arrival times:
• Parameters A and B give incoming direction • Subtract plane-wave arrival times to obtain residuals, including
curvature Compare with simulations to relate to height of shower
maximum, and particle type
ti = A xi + B yi + ni +Ci
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Second-order wavefront shape example
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Second-order wavefront shape example
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Time calibration of LOFAR • Time calibration is critical for measuring wavefront
shape, especially inter-station clock offsets • Use LOFAR CalTables (June 2012) as starting point
• Test given dipole delays using plane-wave fits per station
• Test given station clock offsets using narrow-band RF transmitters (RFI)
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Plane-wave fit residuals
Event from Dec 5, 2012 CS002 LBA-Outer 3 one-sample ‘glitches’, +5 ns Measured minus fitted plane-wave arrival times
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Plane-wave fit residuals
Event from Dec 25, 2012 CS002 LBA-Outer 1 more 5 ns shift 2 at different RCUs! Measured minus fitted plane-wave arrival times
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Radio transmitter phases • Use phases of narrowband radio
signals from a known transmitter • Phases from FFT • average over ~ 50 blocks of 8000 samples • Gives time delays modulo ~ 11 ns per frequency
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Calibration method • Use phases of narrowband radio
signals from a known transmitter
• Gives time delays modulo ~ 11 ns per frequency • Compare measured phases with calculated phases
from source position • Use GPS location and distance • Calibrates delays between LOFAR stations • Smilde FM tower: 5 detectable radio stations at 88.0, 88.6, 90.8, 91.8, 94.8 MHz
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Relative measurements - Measuring at the edge of the band (filter) and a signal
coming from (essentially) the horizon - Signal propagation effects not completely known
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Relative measurements - Measuring at the edge of the band (filter) and a signal
coming from (essentially) the horizon - Signal propagation effects not completely known + Phase difference between channels takes out the
common filter characteristic at this frequency + Given a starting calibration (e.g. LOFAR or octocopter),
can take difference between observations to observe trends, drifting, glitches etc.
+ Works on datasets of ~ 2 ms + Available ‘for free’ in every dataset in our collection!
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Spectrum of LOFAR data around cosmic ray
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Close-up of FM frequency range
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Results for inter-station delays
CS002 CS003 CS005 CS006 CS007
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Results for inter-station delays
CS002 CS003 CS005 CS006 CS007
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Results for inter-station delays
CS002 CS003 CS005 CS006 CS007
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Summary • Promising results for wavefront shape, for
comparing with simulations • Cosmic ray pulse arrival times give a rough
timing diagnostic (> 1 ns) • Time calibration of LOFAR array can be done
using known radio transmitters, e.g. FM – Per antenna, sigma ~ 0.5 ns but very stable (< ~ 0.2 ns) across datasets – Inter-station delays with sigma ~ 0.15 ns
• In good agreement with LOFAR calibration tables – but some differences are significant
• Improved online radio trigger is needed to select better-quality pulses
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Clock offsets from parset Nov 5, 2012
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Second-order wavefront shape (bad)