Total Power Calibration

EOVSA Total Power Calibration Method, Observations, and Analysis

The current EOVSA system should now be amenable to total power calibration based on RSTN/Penticton total solar flux density measurements. The outline of the method is to read the daily flux density measurements available from NOAA (e.g. [1]), calculate a suitable mean value for the multiple measurements made during the day, apply a second-order fit for interpolation/extrapolation to the EOVSA frequencies ($f$), and then adjust the flux density to account for the finite size of the EOVSA (2.1-m diameter) antennas. Once this as-observed flux density spectrum $S(f)$ is known, the results of daily SOLPNTCAL observations are used to determine the on-Sun spectrum for antenna $i$, polarization $p$, $S_{on}(p,f,i)$, and off-Sun spectrum for antenna $i$, polarization $p$, $S_{off}(p,f,i)$. The resulting calibration factors for antenna $i$ are determined as

$c(p,f,i)=s(f)/[S_{on}(p,f,i)-S_{off}(p,f,i)]$.

To apply to some observed measurements on a particular antenna $o_{i}(p,f,i)$, to obtain the calibrated total power values $T(p,f,i)$, the calculation is:

$T(p,f,i)=[o(p,f,i)-S_{off}(p,f,i)]\times c(p,f,i)$.

This analysis ignores any change in gain (or attenuation) between the SOLPNTCAL measurement of the solar increment and the observed measurements to which it is applied. Gain calibration is a separate issue that will be described in another document.

1. SOLPNTCAL Pointing Calibration

This is based primarily on the scheme developed for KSRBL (Dou et al. 2009, PASP, 121, 512). The pointing offsets for all antennas can be determined simultaneously, and as a function of frequency, by offsetting each antenna in a cross pattern and measuring the total power spectrum. This provides multiple useful parameters: (i) frequency-dependent pointing offsets, which can be surprisingly large, and are necessary for primary beam corrections to all interferometer amplitudes, (ii) direct measurement of the primary beam size and shape, and (iii) a check on overall total power gain calibration relative to that determined interferometrically on cosmic sources.

This type of pointing can be done quickly (the observation takes 5 minutes for EOVSA) and is done twice daily (in case one of the observations is not successful). A special antenna control sequence (trajectory) has been implemented, which points a maximum of 5 degrees off Sun in a cross pattern. The current offset sequence in degrees is

• RAO = -5.0,-2.0,-1.0,-0.5,-0.2,-0.1, 0.0, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
• DECO= 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,-5.0,-2.0,-1.0,-0.5,-0.2,-0.1, 0.0, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0

where RAO must be divided by cos(Dec) to convert to a plane-of-the-sky offset.

2. RSTN Flux Density Database

The daily RSTN/Penticton flux density measurements reported by NOAA are taken at 9 frequencies, with four measurements per day at 8 frequencies from RSTN stations and three per day (generally) from Penticton at 2800 MHz (F10.7).

Below is a typical example (missing data is flagged with -1):

2014 Nov 26
  245       24        27        24         -1         -1        20        -1
  410       44        55        50         -1         -1        51        -1
  610       70        -1        73         -1         -1        79        -1
 1415      130       131       117         -1         -1       131        -1
 2695      160       163       162         -1         -1       157        -1
 2800       -1        -1        -1        169        171        -1       171
 4995      190       191       188         -1         -1       202        -1
 8800      246       299       284         -1         -1       315        -1
15400      551       605       475         -1         -1       594        -1

Obviously, this table cannot be completed until after a particular day’s observations are done (typically around 0300 UT on the following day), although Learmonth and San Vito data are available at the start of EOVSA’s observing day. Therefore, a real-time calibration of data must be a preliminary one based only on those two stations. The calibration should be redone overnight after more complete information has become available. Although these multiple flux density measurements could differ due to actual changes in solar flux density over the day, differences are generally small and this effect is ignored. The set of points is reduced to a single spectrum by taking the median of multiple values (where they occur). These measurements at a few discrete frequencies must then be both interpolated and extrapolated onto EOVSA’s frequencies. When such discrete frequency points are plotted, it is easy to see that points below 1.4 GHz do not follow a frequency-squared law (see blue points in Fig. 1).

Fig. 1: Flux density points from 2014 Nov. 26 (the above table), together with 2nd-degree polynomial fit and adjustment for 2.1-m dish primary beam.

Therefore, only the points above 1.4 GHz are used to define a 2nd-degree polynomial (fit shown by the green line in Fig. 1). This curve does not fit the low frequencies well in this case, being 10% too low between 2-3 GHz, and 8% too high below 2 GHz. To the extent these flux density measurements are accurate, the resulting total power calibration can be 10% off in some frequency ranges. EOVSA’s 2.1-m antennas have a finite beam size that becomes increasingly important at higher frequencies and must be corrected. This is done in an approximate sense by multiplying a uniform disk by a unit-amplitude primary beam of the theoretical, frequency-dependent size to determine the extent of dimunition of the flux density seen by the dishes. The red points (appears as a dashed line) indicate the corrected flux density. This assumes three things that are not precisely correct:

1. That the solar flux density is evenly distributed over the disk (good assumption at high frequencies, but not at low frequencies where active regions can dominate);
2. That the frequency-dependent primary beam is centered on the Sun;
3. That the beam size is the theoretical one.

These assumptions can in principle be relaxed by using EOVSA radio images in some way (when available), and using the measured beam size and pointing offsets, but these are things to be checked to see if they make the total power spectrum substantially smoother with frequency.

Python routines for reading the flux density tables, doing the interpolation, and making the primary beam correction are available in module rstn.py.

3. Example Results from SOLPNTCAL

A given SOLPNTCAL scan is analyzed using routines in module solpnt.py. The pointing information is obtained from the stateframe data in the SQL database. The routine solpnt.get_solpnt() retrieves the stateframe information, while solpnt.process_solpnt() compares the stateframe tracking information with the original trajectory file and creates a tracking mask for isolating only data with good tracking at each pointing position. The actual Miriad data are found and extracted via routines in the dump_tsys.py module, and further processed by routines in the solpnt.py module. Once the appropriate data with good tracking has been isolated, a Gaussian fit is done for each antenna, polarization, frequency, and axis (RA or Dec) to determine the parameters $(A,x_{0},w,b)$, where $A$ is the solar increment above background (arbitrary units), $x_{0}$ is the offset of the peak of the Gaussian in the antenna “user units” (1/10000th of a degree), $w$ is the $1/e$ half-width of the Gaussian in “user units,” and $b$ is the background (off-Sun value), also in arbitrary units. Each parameter is a function of $p,f,i$ and axis (RA or Dec).

Figure 2 shows the values of RA (actually cross-Dec) and Dec offsets for the X-feed (or H-feed) for antennas 1-4 as a function of frequency, at a time when Ant 2 is not working well (damaged feed?). Figure 3 shows the same offsets for the Y-feed. The horizontal lines show the median offset for each axis and feed, also given as annotation RA and Dec. These offsets are converted to equivalent cross-elevation/elevation offsets, also annotated on each plot. The XEL/EL values can be used to update the antenna pointing parameters P1 and P7, respectively. Note that the X- and Y-feeds cannot be adjusted separately, so any pointing update must minimize the combined off-pointing of the two feeds.