Questions

Consider two different telescopes, (A) the Kitt Peak 4 meter f/3.1 used at ``prime focus'', and (B) a 0.5 m f/6.8 Cassegrain. Assume that both telescopes have auxilliary optics to flatten and correct the images over a wide field of view, and that both are highly efficient with negligible scattered light. On both telescopes we will use a Kodak 6303E CCD which has $3072\times2048$ 9 micron ($10^{-3}$ mm) square pixels.

1. What is the image scale (seconds of arc/pixel) and field of view (minutes of arc in both directions, and the diagonal) for both telescopes?
2. Compare the angular size and the linear size of the Airy disk of both telescopes.
3. If typical ``seeing'' is at best 0.5 seconds of arc, how many pixels are there sampling the seeing disk of a star for these telescopes?
4. The standard star Vega with a visible magnitude of 0.0 delivers a flux of about $1000\;\mathrm{photons}/\mathrm{meter}^2$Å at the top of the Earth's atmosphere in the visible. We want to measure the magnitudes of other stars seen through a filter that transmits a band 1000 Å wide from 5000 to 6000 Å. How many photons/second will be delivered to a single pixel under typical seeing for both telescopes?
5. Given the quantum efficiency of this CCD, how many electrons/second will be detected for each pixel?
6. Suppose that the read noise of the CCD is 13 electrons and that we need at least $100\times$ the noise in signal in order to measure the flux from a star to 10% accuracy. For an exposure time of 1000 seconds, what would be the faintest star you could measure with both telescopes?
7. If this were done instead with photography and a quantum efficiency of 4% but roughly the same pixel size in emulsion grains, how much longer would the exposure be to achieve the same limit?
8. If you exposed the CCD to saturate a star of 10$^\mathrm{th}$ magnitude, what magnitude would correspond to the read noise? This CCD has a well depth of about $10^5$ electrons.