Monitoring the 12meter total power has shown
that it varies. As the temperature increases the total power
goes down.

On 8nov21 a peltier cooler was installed to temperature
stabilize the cal diode. If the cal diode output is constant,
then it can be used to correct for gain variations in the
system.

The analysis used the 25Hz hardware winking cal data taken on 17jan22 when the cal temperature was measured (more info)

- 7 172 Mhz bands were recorded with 2048 freq channels/band
- the band frequencies were:
- 8219.00 8363.00 8505.00 8647.00 8789.00 8931.00 9073.00
MHz.

- the 25Hz hardware winking cal cycled with 20 milliseconds cal on followed by 20 milliseconds cal off
- the spectra were dumped at 2 milliseconds (giving 10 samples per calOn and cal Off.
- the spectra around the transition were excluded giving 8*2ms = 16 ms for cal on and 16 ms caloff for each cal cycle
- Data was taken for 120 seconds tracking blank sky giving
120/.04=3000 cal cycles in the 120 secs of data.

For each 120 seconds of data:

- The calOn and caloff spectra were input
- they were averaged to 16 milliseconds giving 1 cal on, off spectra per cal cycle
- The rms/mean by freq channel was computed for the 3000 calon, cal off spectra
- a robust linear fit to the rms vs freq was done to help exclude rfi from the total power computation.
- 6% of the spectra on each edge was ignored for the
first iteration of the fit.

- freq chans with 3 sigma outliers were ignored.
- this was done to the calOn and caloff spectra separately and then the masks were anded to give a single mask for the on,off.
- This was repeated for each pol,band
- The mask was then used to compute the total power.

- We usually ended up with 165 Mhz out of the original
172 Mhz band (excluding about 3% of the bandpass).

- The gain correction is done by dividing the tpCalOff/CalDeflection.
- If the cal outpt is stable then this should cancel gain variations slower than 40 milliseconds.
- The cal is about 40K, Tsys is about 120K.
- The noise on the calDeflection is sqrt(2) less than the tsys noise (since we subtracted calon,off)
- The fractional noise on the calDeflection is 120/40/sqrt(2) times the tpOff noise or about 2.12.
- This will blow up the noise on the tpCalOffCorrected signal (probably by less than sqrt(1+2.12^2) since the caldeflecttion noise will be correlated with the calOff).

The first plots shows the total
power vs time for the 120 seconds of data (.ps) (.pdf)

- Page 1: Normalize total power vs time.

- Black in the calOn total power, red is the caloff total power
- each of these has been normalized to their median value (to show variations).
- The left column is polA the right column is polB
- The 7 rows are the 7 frequency bands.
- All of polA has a negative going slope of about .6% in 120 seconds
- PolB has and increasing level with 1% in 120 seconds.
- The calOn and calOff power track one another.
- Page 2 over plot caloff total power
- top: polA
- bottom: polB
- The frequencies track one another.
- must be a variation prior to our mixing the separate bands.

- The tpCalDif=tpCalOn - TpCalOff was computed for each cal cycle.
- The tpOffCorrected=tpOff /tpCalDif was computed for each cal cycle.
- dividing by the calDif blows up the noise.
- each of the total power time series have been normalized to their median value
- Black is the tpCalOff with no correction.
- You can see the larger curvature of the polB signal.

- red has been corrected by dividing by the cal deflection
- green is the red signal smoothed to .4 seconds.
- There are 4 frames per page.
- the top 2 frames are polA,B of a freq band,
- the bottom 2 frames are polA,B of the next freq band.

- the rms for each set of data is printed at the top of each frame.
- The expected rms would be 1./sqrt(165e6*.016secs). =.00055

The final plot reduces the corrected
TotPwr noise by smoothing and fitting to the calDeflection
(.ps) (.pdf)

- Page 1 rms of Corrected totalPower using different polynomial fits to the cal deflection
- The 120 secs of CalOff total power was corrected by
fitting polynomials of order 1 thru 5 to the cal
deflection.

- horizontal axis: order of polynomial fit
- Vertical axis rms [tsys units] of calOfftotalpwr after cal correction.
- Colors: the 7 frequency bands.. Purples is the expected
rms for 165Mhz, 16milliseconds.

- Top: polA
- there is little difference between a 1st and 5th order
fit for polAl

- Bottom: polB
- The rms decreases up to a 3rd order fit.
- this is fitting the curvature seen in the polB gain variation.
- Page 2: Compare the totPwrCalOff rms noise for the different methods:
- + solid lines are polA
- *---- are polB
- Each point is separate 172 Mhz band.

- Top plot: 120 seconds of 16 ms total power data.

- Black is the original data with no cal correction
- red: correct with calDeflection (no smoothing or fitting).
- The rms is larger than the raw data since the calDeflection division blows up the noise.
- Green: smooth the CalDeflection by 25 calcycles (1 second of wall time)
- the rms is better than the uncorrected data by factors of 2 to 3.
- Blue: fit a 3rd order polynomial to the calDeflection before correction.
- The rms smaller than the green 1 second averaging.
- Bottom: Look at data averaged to 25 calcycles (1 sec wall time, .4 sec integration)
- The vertical scale is blown up from the top frame
- Black no correction.
- the tp rms for 1 sec is the same as 16 milliseconds because of the large gain variation across 120 seconds.
- red, green correct with 16ms calDeflection then average to 1 second of wall time.
- the red,green are the same since they both end up
averaging the same time.

- blue,: correct with 3rd order caldeflection fit then average to 1 second of wall time
- the rms is better than the other methods
- purple: expected rms for 165Mhz, .4 sec integration. (.00012 Tsys)

- Blank sky was tracked for 120 seconds with the 25Hz hardware winking cal running.
- The measured total power varied by about 1%
- polA was linear
- polB was curved.
- Dividing by the 25Hz caldeflection

- can correct for this gain variation.
- It will also blowup the noise (since cal deflection is much smaller than Tsys)
- The increase in total power noise can be compensated by:
- average the caldeflection (in this case to 1 second wall
time)

- fit a polynomial to the cal deflection (using the 120 secs of data).
- For this example a 3rd order polynomial gave the best results.
- The order of the fit will probably be a function of :
- how long the dataset to process
- polA,B
- the current gain variations.
- For 165MHz, .4 sec integration, 1 sec all time
- we got within a factor of 2-3 of the expected rms.
- Part of the rms will be determined by how well we removed any rfi from the total power samples.
- Drawbacks for this technique:
- we are ignoring 50% of the integration time by only looking at the calOff data
- if the caldeflection was smaller (currently 40K) we might avg the calon,off and take a hit of 1/2 the cal value in tsys.
- But a smaller Caldeflection will blow up the noise more (hopefully the fitting will do good enough job)
- We are ignoring samples adjacent to the cal deflection.

- This reduces the integration time by 2*spectralTm/20ms
- we could sample faster (say 1ms) but this would increase the disk usage.
- The data rate for 1freqbandx2048chanx2pol*16bit/sample

- 2ms sampling:

- 1 band: 4 MBytes/sec
- 7 bands: 28MBytes/sec
- 1ms sampling:
- 1 band: 8MBytes/sec
- 7 bands: 56MBytes/sec
- You could increase the sampling rate while decreasing the freq channels (depending on how narrow the rfi is).

*processing:x101/220218/wcal_stability.pro*

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