Detailed Description of corrections
1. Period Correction
There is the cyclic pattern in the raw dt vs ø distribution
(Figure 1.a). Because the dt is measured by the phase difference
of the signals, the one cycle (2.67 ns ) should be corrected to
the observed dt when the time
difference between two antennas is expected to be larger than one
cycle. We subtract the dt by one cycle for the points on the left line
in the Figure 1.a, and add one cycle for the right line. Figure
1.b shows the result of the correction.
Figure 1.a . Raw dt vs ø
distribution before the period correction.
Figure 1.b . dt vs ø
distribution after the period correction.
2. Zenith angle correction
More accurate air path expectation can be obtained when we consider not
only azimuth angle (phi) but
also zenith angle (theta).
The air path difference (dl)
between two antenna is dl =
1.2 sin (phi) cos (theta) here the 1.2 is
antenna spacing in meter. Because the calibration data was taken during
the early period of the flight, the theta variation is relatively
larger than other periods. We calculate the theta using the
transmitter-balloon surface distance and the altitude of the
balloon. Also antenna orientation down tilted by 10 degrees is taken
into account by adding this 10 degree to the theta. Figure 2.
shows the dt' = dt / cos (theta + 10) distribution as a function
of the phi.
Figure 2 . dt vs ø
distribution before/after the zenith angle correction.
3. Time offset correction.
After correcting phi dependency we observed 0.2 ns global time shift.
It can be caused by time offset difference between two channels. We
simply subtract 0.2 ns for all data points. Figure 3 shows this effect.
Figure 3 . dt vs ø
distribution before/after the time offset correction.
Apr 18 2004, Jiwoo Nam
