In the ANITA (Antarctic Impulse Transient Array) experiment, accurate
timing measurement is important for the precise angle reconstruction of
the radio Chrenchov signal. The better angular resolution
provides
the better background rejection power. Consequently it will
provide wider effective area by distinguishing the signal from the
atmosphere backgrounds. There was the first flight of ANITA with two
antennas (ANITA-Lite) in the last Austral summer season (2003-2004).
During the initial flight we took the calibration runs using the radio
signals transmitted from the ground calibration system located at the
Williams field near McMurdo station. It is a main goal of
calibration run to measure the time resolution of the ANITA-Lite
system. In this report, we describe the analysis procedure of the
calibration data and show the results on the time resolution, its
amplitude dependency, the correlation between time and azimuthal
angle, the angular resolution of the ANITA-Lite and expectation of the
angular resolution for the ANITA-Heavy detector.
Calibration System and Data sample
A detailed description about the ground calibration system and data
sample can be found else where.
In this report we analyze only 98 good events skimmed by Andrea
Silvestri. The signals frequency for those events is 375 MHz. Figure 1.
shows the altitude and orientation of the payload as a function of time
(UTC) during the calibration period. The orientations are measured by Predrag
Miocinovic using the sun sensors data. The orientation is less
reliable in the early period of calibration because the payload was
unstable and rapidly rotated until it reached the stable
altitude. The waveforms for the 98 events are found here.
Figure
1. Altitude and orientation of the payload during the calibration
period.
Modulation Free Method
The only useful measurement for
angle reconstruction can be the time difference (dt) between two antennas. Figure 1
shows how to determine the dt
between two waveforms in this analysis. We are measuring a
phase difference between two waveforms by comparing the time of the
zero-crossing points. This is a good method to evaluate the time
resolution under the current tone burst of the ground calibration
system. Because the amplifier creates the slow growing shape on the
beginning of the waveform, the typical threshold-crossing time makes
large errors due to the long rising time of the growing waveform.
We can avoid it by measuring only the zero-crossing time for the given
cycle of waveforms. This method can work if the time resolution is
better then one cycle of the signal. In order to obtain the
realistic S/N ratio, we take the first cycle of waveform over the
threshold of 150mV which is about 4 sigma of the noise level in
voltage. It is a modulation-free method simulating realistic time
determination for the short radio signals.
Figure
2 How to measure the time difference between two waveforms.
Results
Figure 3. shows the dtdistributions for T1-T2
(top), T1-T4 (middle) and T2-T4 (bottom). The 0.17 ns of time
resolution on the cross-polarization on the antenna 1 should be near
the optimal value for the 4 sigmas threshold. The distributions of the
cross antennas are more widely spread than the same
antenna's. This broadening is mainly due to azimuthal variation in the
antenna orientation.
Figure
3. dt distribution (stable period)
Figure 4. plots dt (T4-T2) distribution as a function of ø which
is azimuthal angle between the center line of two antennas and the
transmitter. The ø is obtained by the recorded GPS
position and orientation information. A detailed description for the
ø determination can be found here.
Several corrections for the period of the signal, the zenith angle
dependency and time offset are applied. This description also written here. The solid curve shows that the
dependence of the time difference of the events on orientation agrees
with expectation.
Figure 6 shows the angle difference distribution (dø) which is angle between
reconstructed azimuthal angle and its expectation. Obtained
azimuthal angular resolution is 2.7±0.3 degrees.
Figure 7 shows the time resolution (of
T2-T4) as a function of the applied threshold. There is a good
aggreement between data and simulation. A explanation of the simulation
can be found here.
Figure. 8 plots the intrinsic time resolution, delta_t, as a
function of the ratio of the signal amplitude to Vrms. The intrinsic
timing was obtained by measuring the time interval between consecutive
cycles in a given antenna. At large ratios, signal is much larger
than noise, so timing is limited by the digitization interval of
0.5ns. At small ratios the noise degrades the intrinsic timing
response of the system.
The measured in-flight timing response of ANITA-lite is consistent with
expectation based on the 1.2m separation between the center axis of the
two antenna and time resolution limited by the signal to noise ratio
and the waveform digitization interval of 0.5ns. Further, these
studies show that the systematic dependence on zenith are weak owing to
the excellent phase properties of the dual ridge design. The resolution
is only weakly dependent on amplitude for thresholds anticipated in
ANITA.
These encouraging results can be used to anticipate the timing
resolution of the ANITA payload. In fact, several factors are
expected to improve the resolution. First, the ANITA trigger
requires 4 or more antennas to observe a signal, which implies that the
measured time resolution should improve (decrease) by a factor of
sqrt(2). Second, the time digitization interval will decrease
from 0.5ns to 0.28ns, or roughly a factor of 2. Thus, the
limitation of the intrinsic time resolution due to waveform
digitization will improve (decrease) also. Thus, we estimate that
the timing resolution should be ~0.1ns in ANITA, a value that is
consistent with
that achieved by previous balloon-borne instruments [1,2]. The analysis
would first use the timing response and antenna geometry to estimate
the azimuth and zenith angle, theta, of the event, then correct the
arrival time information based on the angular direction, and then
iterate the procedure. Of course, it is vitally important to
differentiate events initiated in the ice from those produced in the
atmosphere, a task that increases in difficultly toward the horizon.
Fortunately, events near the horizon generate signals that arrive
nearly parallel to the antenna axis, a condition that is relatively
easy to model and measure. Taking into account the expected
improvements in time resolution for ANITA and 3.3m vertical separation
between the upper and lower antenna arrays, we expect
