Earthshine blog

On the July 26 2011 occasion of observing the star tau Tauri being occulted by the Moon we followed the Moon from just after Moonrise until Sun rose some hours later. During that time we tracked the star at sidereal rate so the Moon drifted through the frame.

Determining the radius and image-plane coordinates of the lunar disc we plot these:
We note that the radius increases slightly as the Moon rises – probably an effect of differential refraction decreasing as airmass approached 1. At most the radius estimate increased by about 1.5 pixels during the sequence. The standard deviation about the line is 1 pixel, telling us what the precision is of the method used to estimate lunar disc properties (it works by fitting a circle to points on the edge of the lunar disc).

We also see that the Moon did not follow a straight line across the image plane. The deviation is up to 5 or 6 pixels – about half an arc minute. This may be a refraction effect or a tracking effect or indeed an orbital effect – the mount we have does not track the Moon in declination.

In summary we see that the effect of differential refraction across the field is not more than half an arc minute at large air masses, consistent with physical estimates.

I have measured the pixel noise in the Canon EOS 35 mm camera. This is the same one as used to measure the halo of the moon at large distances (up to 15 degrees) from my Sydney backyard.

60 exposures were taken of a flat white surface, in groups of 10, with 5 exposures times from 1 second down to 1/200th of a second. (A 6th exposure time was discarded due to saturation).

Frames converted from CR2 format to fits format using cdraw and convert:

ls *.CR2 | awk ‘{print “dcraw -T -4 ” $1}’ | bash
ls *.tiff | awk ‘{print “convert ” $1, $1″.fits”}’ | sed -e s/.tiff.fits/.fits/ | bash

the tiff files this produces still have colour information, which I wasn’t expecting. The fits files are of course grey scale, but I suspect they are averaged over the three colours (RGB), so that the apparent photon counts are three times smaller than the actual photon counts.

The standard deviation and mean flux in 9 randomly chosen individual pixels was computed across the of 10 images obtained for each of 5 exposure times. The square root of the mean (times 3) is then plotted versus the standard deviation of the values, yielding 45 noise measurements (i.e. 9 pixels x 5 exposure levels of the pixel = 45). If the noise is anything like Poisson noise, these should lie on the 1:1 line.

This proves to be approximately the case as seen below.

It’s pretty noisy though! (i.e. the noise measurement is noisy).

Inspection of the fits files ds9 shows that there are clear correlations on various scales in both the X and y directions in the images — so the camera is surely introducing smoothing of some sort, so there is only so far one can push this analysis!

Conclusion : Poisson noise is a fair first order approximation for the behaviour of a commercial camera CCD chip.