# Observing APOD with the AuScope VLBI Array
## 4 Correlation and Post-Processing
### Fringe Fitting  
All fringe fittings of the APOD data used the zoom-bands as an input. Across the 32 kHz zoom-band channels the APOD signal is coherent. Using the fringe fitting program fourfit (as part of HOPS), a multi-band delay was fitted for each of the two frequency bands. Due to the residual delay rate, the minimum integration time of 1 s was used to generate a time series of data.  
On the initial inspection of the data, large offsets (on the order of tens to hundreds of ns) in the estimated residual delays between the S- and X-band were noted. For the frequency sequence defined by the DOR tones, we expect a multi-band delay ambiguity spacing of 972.8 ns at the S-band and 261.2 ns at the X-band. Manually applying integer multiples of these ambiguities revealed that a constant additional clock offset of \(-2.9\) us at Hobart and 7.8 us at Katherine removes the large offsets between the two bands. These offsets stayed approximately the same for all experiments and  
Figure 8: Cross-spectrum magnitudes (left column) and phases (right column) of the S-band (\(\mathrm{Carr}_{S}\), upper panels) and X-band (\(\mathrm{Carr}_{X}\), lower panels) carrier tones of Scan 168 of Experiment a332. The time axes (horizontal) indicate seconds since the start of Scan 168 (10:41:04 UTC).  
Figure 7: Cross-spectrum magnitudes (left column) and phases (right column) of the X-band zoom-bands of Scans 168 (upper panels) and 169 (lower panels) of Experiment a332. The frequency axes (horizontal axes) depict the five 32 kHz wide DiFX zoom-band described in Table 3 next to one another. The time axes indicate seconds since the start of Scan 168 (10:41:04 UTC).  
are assumed to be related to the orbit modeling or the absolute timing of the observations. Another indication of this apparent ambiguity issue is found in the phase calibration, when applying a manual phase calibration in fourfit. After introducing the additional offsets, a flat residual phase against frequency is obtained. This is expected when using zoom-bands, which are taken from a common baseband converter, as is the case for all S-band channels.  
Examining the results of our scans shows clear differences between the S- and X-band data in amplitude, while the residual delay and delay rate are in good agreement. Examples are shown in Figures 9 and 10. Signal-to-noise ratios are typically 500-800 and stable across the track for the S-band, while the X-band data show a time-variable SNR between 200 and 700. The dominant effect here is expected to be mis-pointing of the antennas. The formal error for the S- and X-bands is typically less than 100 ps.  
The observations in two frequency bands, S and X, enabled us to correct for dispersive propagation effects of the ionosphere on the observed microwave signals. First-order effects are accounted for by calculating the ionosphere free linear combination according to Equation (1) [38]. The ionosphere free delays \(\tau_{if}\) were determined as linear combination of the observed group delays in the S- and X-bands, \(\tau_{gs}\) and \(\tau_{gx}\), respectively. The factors \(c1\) and \(c2\) are functions of the effective frequencies of the observed S- and X-band channels, \(f_{gs}=2256.85\) MHz and \(f_{gx}=8404.87\) MHz.  
Figure 10: Fourfit results of Scan 169 in Experiment a332. Residual multi-band delays, residual delay rates, formal delay errors, and SNRs are plotted versus time indicated as seconds since scan start.  
Figure 9: Fourfit results of Scan 168 in Experiment a332. Residual multi-band delays, residual delay rates, formal delay errors, and SNRs are plotted versus time, indicated as seconds since scan start.  
\[\tau_{if} =c1\cdot\tau_{gx}-c2\cdot\tau_{gs}\qquad\text{with} \tag{1}\] \[c1 =\frac{f_{gx}^{2}}{f_{gx}^{2}-f_{gs}^{2}}=1.0777\] \[c2 =\frac{f_{gs}^{2}}{f_{gx}^{2}-f_{gs}^{2}}=0.0777\]