[Shiraz (Ray)]

Hi

Just finished developing a model of the way in which flats introduce noise into broadband images. Also did a validation using some real data, to be reasonably sure that the model describes reality. This analysis has nothing at all to do with removal of vignetting or dust donuts - just noise reduction. If flats are good enough to fix noise they will take care of other stuff.

Real world results in the first figure show the way in which image noise varies with total flat signal - these four images were obtained using the same sequence of real images (totaling just under 4 hours with dark sky), but with different flats exposure. The data has been processed using flat data where the total flat signal was 0.05, 0.5, 2.7 and 11x the total sky signal. The images show the effects of noise reduction as the total flat exposure goes up. Note that the noise shows up as lines since the imaging system had some drift - this makes any fixed pattern noise stand out well and shows how this form of noise affects bright parts of the image as well as the background (it really is a nasty form of noise). Clearly there is some advantage in having a reasonably long total flat exposure - the fourth image has flat exposure as recommended by the model and would need more light exposure to reduce noise further (and of course longer flat exposure).

The real world SNR results from the 4 images are compared with model results in the second figure. Model data is shown as a dashed line and the four measured results as diamonds. The model results are "worst case", so the agreement between model and real world seems convincing enough (at least to me) for the model to be used to derive some general guidance on how to expose flats. It shows that, if you are doing broadband imaging, flat induced noise will be negligible if you get at least 10x as many flat electrons as you get total sky electrons. This very simple rule will apply under all circumstances and can be used to replace ad-hoc guessing, rumor or one-off observations. Since the model is "worst case", you will probably be able to get by with fewer flats most of the time, but flats are easy to obtain, so it makes sense to use enough to ensure that you will not be troubled by flat noise in any circumstances.

If you want an even easier rule of thumb that will get you close enough, expose your light subs properly (eg about 2-3000 ADU in the sky background) and then make sure that you take at least one flat of 20-30,000 ADU for each light sub. If you take sky flats with widely varying exposures, adjust the number of flats to maintain the total ADU over the set.

The graph also shows the measured SNR for no flats (a single dot on the y axis) - with ~4 hours of lights and a very low noise CCD (in this case an icx-694), there is not much point in using flats at all. This is definitely not the case for much longer total exposures, or for CCDs with a little more fixed pattern variabilty (eg some of the Kodak ones) - then flats are necessary.

Thanks for looking. Regards ray

Added: for anyone looking for the last skerrick of SNR, the 10x rule gets you within 5% of the SNR you would get with infinite flats - but you can always squeeze a little more SNR by using more flat data.