Narrower band observations have tried observing with
no off position. The bandpass can be removed by using a smoothed or fitted
version of the on data. An alternative is to use the cal deflection to
remove the bandpass created downstream from the cal injection. Let Txxx
be the temperature from the xxx location and Fxxx be the frequency dependence
of this temperature then:

calOn =(((Tsrc*Fsrc + Tsky*Fsky2 + Tgrnd*Fgrnd2)*Fant2 + Trcv + Tcal)*Fiflo

Where 1,2 are taken at the calOff and calOn times. If these times are close together then 1=2 and:

caldif=calon-caloff = Tcal*Filfo

You could then use the calDif to divide out the bandpass from the IFLO. Any frequency dependence in front of the cal injection would remain. The example below use a 5 minute on, 5 minute off position switch on a galaxy with the lbn receiver. At the end of the off position, the cal is turned on for 10 seconds and then turned off for 10 seconds. The correlator setup was 9 level sampling with 2048 channels over 25 Mhz. The different page/figures show:

Fig 1: 5 minute on/off -1 bandpass

5minute on/ 10secOff

calOn-calOff spectra

5 minuteOn/(calon-caloff)

Fig 2: smoothing (calOn-caloff) to increase signal to noise Fig 3: Fittin polynomials to Calon-calOff Fig 4: Fitting polynomials to CalOff

The resulting band passes are:

- Fig 1 top: 5 minute On/Off - 1. The galaxy is at 1383 Mhz. The rms is computed within the dashed lines. The expected value is .0007 and the measured value is .00081 Tsys.
- Fig 1 2nd: This is the 5 minute On divided by the 10 second calOff to show how the rms degrades with the smaller integration time in the Off. You barely see the galaxy. The expected rms is .0028 and the measured value is .0031. Since the calOff was not taken at the same spot on the dish as the On position, the rms was recomputed for 10 second sections taken at the beginning, center, and end of the 300 second Off scan. The rms's were: .0029, .0029, and .0031 so not tracking the same part of the dish does not degrade the baseline too much.
- Fig 1 3rd: This is the cal difference spectra. The lbn cal is only 5% of the system temperature.
- Fig 1 bottom: The 5 minute Onposition is divided by the calDifference to remove the bandpass. The rms is now .0865 Tsys. This is 18 time larger than the calDif rms and 30 times larger than the 5 minOn/10secCalOff in the 2nd frame. The problem is that the rms error for caldif is the same order of magnitude of the calOff or calOn but the average value is 20 times smaller (.05 Tsys). When we normalize with this bandpass, everything gets scaled by 20 times before division.. the mean and the rms.

The larger smoothing values are biased because the filter is extending into the region where the bandpass is overshooting. In spite of this the smoothing is not bringing the rms anywhere near the theoretical value. As soon as the smoothing width reaches the systematic errors caused by the ripples in the bandpass, the rms improvement will start to degrade.Fig 2 top: The calDif spectra was smoothed by 31 (.38 Mhz). This should compensate for the 300sec/10sec integration difference between the cal and the posOn. The red lines show a sine wave at the period of the smoothing. The rms has decreased from .0865 to .0202. This is an improvement of 4.3. The expected improvement of sqrt(31)=5.6 Fig 2 2nd: This has a smoothing of 101 channels (1.23 Mhz). The measured rms is .0157 compared to an expected value of .0086 ( .0865/sqrt(101)). Fig 2 3rd: A smoothing of 201 channels (2.45 Mhz) with an rms of .0152 vs an expected rms of .006. Fig 2 bottom: Has a smoothing of 301 (3.67 Mhz) with an rms of .0154 vs an expected rms of .005

Fitting polynomials to Calon-CalOff

Fig 3. This shows fitting polynomials (5,9,12,15 order) to the calon-caloff. The best rms of .0138 used a 5th order polynomial. This gave comparable results to smoothing by 2.45 Mhz. Fig 4. The polynomial fitting was done on the calOff rather than the calOn-calOff. The best rms was .0028 which was 3.6 times larger than the full 5minOn/5minOff.

If the cal deflection is less than the system temperature, then any errors in the cal spectra and any standing waves from in front of the cal injection will be multiplied by this factor when the calDeflection is normalized prior to the divide. With the present cal size, using the calDeflection does not appear to be practical. If we had a cal value that was many times the system temperature, and if the correlator linearity extended over this range, then any ripples in the calDifference spectra would be diminished rather than amplified when the calDifference spectra was normalized to unity prior to the division.

Fitting polynomials to the calOff does a better job than using calOn-calOff. It would interesting to know if the extra structure from the calOn-calOff is just from the small cal, or there is frequency structure in the cal from say reflection of the cal signal going out the horn, reflecting off something and then coming back in.

All of calDifference spectra will not do anything
to the standing waves that are coming in from in front of the cal Injection
point.

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