Trying to remove the 1400 Mhz resonance in software
On 21nov08 project s2425 did the following
Resonances in polA and B showed up between 1395 and 1400. Pol B is
located at the lower frequency and pol A at the higher. The resonances
made the bandpass bad enough that no statement could be made about
the existence of the galaxy.
- 14 position switch pairs on a source.
- Each position switch was 2 minutes on, 2 minutes off, and then a
10 second calon, 10 second caloff.
- The wapps were used to take data with 25 MHz bw, 2048 channels,
and 9 level sampling.
- The center frequency was 1397.93 Mhz.
After the fact an attempt was made to remove the
resonances from the recorded data. This was done for polA to see how
well it worked.
The contributions to the system temperature can be broken down into:
Tsys= (Tsky*g1 + Tomt*g2 + Tcal + Trcv)*g3
- Tsky is the power from the sky and any scattered radiation
- Tomt is the contribution from the Omt. G2 is the frequency
- Tcal is the injected cal (if present). It is injected after the
- Trcv this is the amplifier noise in the dewar.
- g1, g2, g3 are the frequency Dependant portions of the different
- g1 sky and standing wave frequency dependence
- g2 omt dependence. mainly it will be from the resonance.
- g3 everything after the dewar. Mostly filter band passes.
Steps in removing the resonances
The steps to remove the resonance are:
- make a model of the resonance from the Off source data.
- fit this model to the on source data
- subtract the resonance from each
- compute posOn/posoff .
- Do this for the avg spectra of each onoff pair.
A damped harmonic oscillator was used as the model
for the resonance:
- Y=A0/((w^2 - A1^2)^2 +
(a2*w)^2) + A3 + A4*w
- w is the frequency
- A1 is the resonance frequency
- A2 is gamma (the loss)
- A3 and A4 are a linear fit to the baseline.
- Fit to offsource/(calOn-calOff)
- CalOn-calOff = (Tcal + Trcv)*g3
- G3 is the frequency dependence of everything downstream from
- dividing by calon-caloff flattens the offSource data without
affecting the resonance.
- The integration time for the calon-caloff is only 10 seconds.
This would normally increase the noise in the spectra. But we
divide the onSource and off source by the same function so the
the noise is not part of onSrc/Offsrc at the end.
- The units are now equal to the cal value.
- Fit the model to the onsource.
- Compute ymodelOff=
A0/((w^2-A1^2)^2 + (A2*w)^2. This ignores the linear baseline fit to
- Fit to onsource: a + a*(ymodelOff) + a*w
- This fits the off model to the on data doing a separate linear
fit to the baseline.
- Remove the model fit from the on
and off data.
- The resonance should be
additive noise so subtract it out.
- We have lost the baseline so add back in the median value for
onSrcModelRemoved/offSrcModelRemoved - 1.
division puts us back to units of Tsys
- Accumulate this for each on/off pair.
Plots showing the results:
The first set
of plots shows the results for each 2min on, off pair (.pdf).
The 2nd set of plots is the on/offsource average for the 14
on/off pairs (28 minutes on) (.ps) (.pdf):
- There are 14 pages. 1 for each on/off pair.
- 1st Plot: the 2 minute average band passes for onSrc (black),
offSrc (red), and calOn - calOff (green).
- 2nd Plot: Onsrc/calDif, offSrc/calDif and the model fits to each.
- The extra noise if because the cal is only 10 seconds long (but
it is the same noise for onSrc and OffSrc).
- 3rd Plot: onSrc/calDif - modelFitOfResonance, offSrc/calDif -
- 4th Plot: onSrc/OffSrc -1 with model correction (black) and
without model correction (red).
- the rms went from about .0024 to around .0014. The expected rms
- Top: the average OnSrc (black) and offSrc (red) for the 14 pairs.
The green line is the average off source without any corrections.
- bottom: The average on/off-1 for the 14 scans. The black line is
with the correction, the green line is with no correction.
- The rms went from .00197 to .00051 when the correction was
applied. The expected rms was .00029.
- Removing the resonance decreased the rms from .00197 to .00051.
The expected rms was .00011.
- Some of the difference between .00051 and .00011 is from
structure outside the resonance region (around 1390).
- The average On, Off after correction still show a small bump
around the resonance region. This is causing a slight dip in the
on/off-1 which is probably not real.