# CTA21 gain at lband, sband, and cband.

#### 04sep,2000 (16feb01 fixed focal gain error)

The source CTA21 (J0318+164) was tracked from rise to set on 22aug00 (lband), 24aug00 (sband), and 25,26aug00 cband. One minute on/offs were done followed by a ten second cal on/off. The table 1 shows the values used for the computations:

 Receiver Freq(Mhz) calVal [K] Pol A_B Flux Jy FWHM focus [in] (2*lambda) lband narrow 1405 1.85 _1.91 8.03 16.53 sband narrow 2380 6.76_6.9 5.76 9.92 cband 5000 26.93_25.6 2.98 4.70

#### Sefd, tsys, gain, and cal stability Fig 1-4:

The SEFD, system temperature, gain, and cal stability  are shown in figures 1-4. In the plots, polA is a dotted line and polB is a dashed line. Different frequencies are marked by different symbols. The average system temperature and gain for za < 15 deg is shown in the first 2 rows of table 2 below. The cal stability for cband has a linear  drift  through the night. It was caused by the temperature changing after an sband transmitter experiment (see  gain stability vs temp (aug00) ).

#### Computing the surface error from the gain at multiple frequencies Fig 5-11:

The ruze formula gives the fractional gain caused by errors in the surface:
fracgain=exp(-(4*pi*delta/lambda)^2) ... delta=rms surface error,lambda=wavelength
The fractional gain is gainMeasured/gainExpected. By taking ratios of fractional gains at different frequencies, we can eliminate the expected gain. The ruze formula only deals with errors in the surface. The gains we measured include losses from pointing errors, pitch/roll/focus (prf) errors, and errors from the surface. We need to correct the measured gains for these other losses before applying the ruze formula.  To compute the ratios of gains, the  polA gain at each frequency was fit to a function:
g(az,za)= a0+a1*za             + a2*(za-14)^2 + a3*(za-14)^3 +
a4*cos(az)   + a5*sin(az)       + a6*cos(2az)    + a7*sin(2az) +
a8*cos(3az) + a9*sin(3az)
The functions were then evaluated at the lbn az,za and the ratios computed.

• Figure 5 shows the ruze formula fractional gain versus surface error rms for lband, sband, and cband.
• Figure  6 shows the estimated pitch,roll, and focus error for the dec strip of J0318+164. The data comes from a fit to the tilt sensor and theodolite of feb-apr00. The focus is in inches and the pitch/roll units are .1 degrees.
• Figure 7 shows the fractional gain from the pitch/roll/focus errors.
• Figure 8 shows the measured gain corrected for the pitch/roll/focus errors.
• Figure 9 shows the ratio of gainSb/gainLb, gainCb/gainLb, and gainCb/gainLb. These are the measured gains with no corrections.
• Figure 10 has the gain ratios after correction for pitch/roll/focus errors.

• Figure  11. The ruse formula fractional gain for each frequency was computed for surface errors 0 to 7 mm. The ratios of sb/lb, cb/lb, and cb/lb were then plotted.  An inverse lookup was done using the average values from figure 11 (table 2 last row). The resultant rms surface error was then flagged with a vertical line.

#### Results:

Using the gain ratios, the rms surface error for the track of J0318+164 is 5.15 mm. The sb/lb and cb/lb fall within .15 mm of this average.  Table 2 shows the gains before and after. The last line assumes the surface has been corrected from 5.15 to 0 mm. The lband gain of 9 K/Jy is too low. If we assume that the lbn cal value is 5% low, then the rms error increases to 5.7 mm and the final lbn gain would be 9.6 K/Jy.  It looks like we need to find a loss mechanism that is independent of frequency (blockage??).
 avg values for za < 15 degrees lband (1405) sband (2380) cband (5000) avg Tsys  [K] 31.2_28.1 25.0_23.8 29.8_33.1 avg Gain [K/Jy] 8.0 6.6 2.2 avg Gain remove prf loss [k/Jy] 8.2 6.9 2.6 avg Gain remove prf,surfErr(5.15mm) [K/Jy] 9.0 9.0 8.4
`processing: x101/calmrcvr/cta21.pro`
`plotting  : x101/calmrcvr/cta21plt.pro`
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