Figure 1
Figure 2
The random variation in exposure time from the camera shutter introduces error in measurement. The standard deviation of the exposure time of SOHO/MDI is about 12-15 microseconds at the beginning of the mission and about 40-50 microsecond now. This means that the sampled intensities F1-4 are taken in slightly different exposure durations. This shutter noise will add a certain backgroud value to observables that is called `offset' here.
This `offset' in magnetograms can be corrected under certain assumptions. We notice that MDI has a noise level 20 Gauss (Scherrer, et al., 1995) and many pixels in the magnetograms are below this level. If we assume that the noise has a Gaussian distribution, the shift of the Gaussian center whould be the `offset' introduced by the shutter noise. To determine the shift, we collect the pixels of a magnetogram within solar disk and computed the distribution of those pixels; we then use a Gaussian function to fit this distribution. The shift of this Gaussian function center is the `offset'. We also use other fitting functions, such as two Gaussian functions, three Gaussian functions, to fit the tails of the distribution that is believed to be contributed by true magnetic field ( see Figure 1). The result is similar. Moreover, test is also done by selecting different parts of the magnetogram and different maximium values above which the pixels are abandoned. The offset almost keeps constant (seeFigure 2), indicating this method is effective and reliable.
Figure 3 shows the mean field and `offset' in one month period, from August 13, 1999 to Sept. 14, 1999. The top panel is the mean field derived simply by averaging every pixel in the magnetograms. The second panel shows the `offset' computed by Gaussion function fitting. The green line in this panel represents possible residual magnetic signals in `offset' derived by using wavelet technique. The third panel shows the `offset' with correction of the residual magnetic signals. We call it `true offset'. The green line in the bottom panel is the mean field after correction of the `true offset'. The red line is the mean field after correction of `offset' and the stars show the mean field measured at Wilcox Solar Observatory (WSO). We can see the mean field is much smoother after correction of offset, showing the noise has been greatly minimized. Both mean fields with `offset' correction and `true offset' correction match well with WSO observation, but it is difficult to judge which one is better. The shutter noise introduces a 0.5 Gauss error.
MDI has 2 styles of 96 minute cadence magnetograms, 1 minute magnetograms and 5 minute magnetogram. 1 minute magnetograms are produced by one 30-second measurement, while 5 minute magnetograms are a 5-minute average of five 30-second magnetograms. This average is done on-board. The Gaussian function fitting above shows that the noise level is 16 Gauss for 1 minute magnetograms, and 9 Gauss for 5 minute magnetograms. The average and offset of 5 minute magnetograms are systematically 0.4 Gauss lower than those of 1 minute magnetograms (see Figure 4). It could be removed if the offset is corrected from observables. This difference may be caused by different observation sequences and/or solar rotation that smears the signals when the five magnetograms sum. Further investigation is needed.
