Noise in mdi instrument

Measuring shot noise in full-disk dopplergrams (13nov97)

The idea is to compute a spatial power spectrum of a single image, measure the flat component at high spatial frequencies, get the rms value of it. This will be done separately for 30 and 60 sec data. Exported an hour's worth of data from 7/15/96 (hour 31000). Found the dpcs 0x42020FC0 for the first image and 0x42420FC0 for the second image. From the header param DPC_SMPL, we find that 0x42020FC0 corresponds to 60 second data and 0x42420FC0 to 30 second data.

As the 60-second data has twice as many exposures, we would expect the shot-noise power to be twice as high in the 30-second data. The power level is still falling in the far corners of the power spectrum, probably indicating that we have not reached the shot noise floor. At the lowest level, found 21.0 m/s for the 60-second data and 23.5 for the 30-second data. Then, assuming that 21.0**2 = a + b**2 and 23.5**2 = a + 2b**2, we get b=10.5 for the shot-noise component.

To check that this was similar in 1997, exported an hour from 5/11/97 (hour 38184) and did a similar thing. Got 22.1 m/s for the 60-second data and 24.3 m/s for 30-sec data. This implies b=10.1 m/s.

The overall power level of the images is larger for 30-second data. If this were due to shot noise, it would imply b=45.3 m/s for the hour 38184 and b=39.3 m/s for the hour 31000. This is not a good way to measure the shot noise, as the 60-second boxcar reduces the rms of a 5-min. wave by 5% more than a 30-second boxcar.

So it looks like it will be necessary to do a short 3-d power spectrum to get a better estimate of the shot noise. Certainly we have a good upper limit given by the power level near the spatial nyquist frequency of ~20 m/s. Whether it is as low as the above estimates of 10 m/s could be determined by a 3-d analysis. We should be able to get by with a 16-point temporal transform, giving a 1mhz resolution.

Using the hour 38184, got 10.2 m/s for the power level near the spatio-temporal nyquist frequency. To get 16 minutes of 30-second data, exported hour 39476 (Jul.3,1997). Found the noise level to be 14.3 m/s (10.2*sqrt(2)=14.4). So it seems pretty secure that 60-second data has 10m/s shot noise and 30-second data has 14m/s shot noise. Computed the rms of the 5-minute oscillation power at 103 m/s. The rms of the 512x512 area for a given image is 187 m/s.

Noticed a large spike at (kx,ky) = (202,149-150) in the transform of a 512x512 area. It is presumably the herringbone pattern seen in the dark. By notching it out, found it to have rms 0.7 m/s. In principle, this could be removed in general by a notch filter. This is at .975 of the spatial nyquist frequency, or l=1462. So, some signal would be sacrificed near this l, although it is probably obliterated by this artifact.

Measuring shot noise in hi-res dopplergrams (14nov97)

For the hi-res case, exported an hour (one image) of 1024x500 data from hour 42118 (10/21/97). Took a 512x500 area and made a 2-d power spectrum. It is pretty flat near the nyquist frequencies. The rms of the pic is 253.9 m/s. Get 12.5 m/s for the estimate of shot noise from this flat part.