Prime Focus Imaging with CCDs

The most often used set-up is imaging through UBVRI filters at the f/3.3 prime focus with the TEK CCD, where the image scale is 0.391"/pixel and the available field of view 6.67' x 6.67'.  Imaging can also be carried out at the auxiliary Cassegrain focus, normally in conjunction with spectroscopic observations at the main Cassegrain focus - in which case you have to use one of the CCD's other than the TEK, which is usually the Thomson - 0.128"  per pixel and the field size 1.31' x 1.31'.

Calculation of Signal-to-Noise Ratios

The signal to noise ratio for a given exposure can be calculated from

where
is the total number of counts in the object,
is the number of pixels covered by the object (i.e. the size of the photometrickaperture adopted if the object is a star),

is the number of counts per pixel from the sky background, and
is the CCD readout noise in electrons.

For broadband imaging, where even the shortest exposures through a broad band filter are sky limited, this simplifies to:

For an exposure of time t seconds, let

N_obj = O  x  t

N_sky = S x  t

Then the above expression simplifies to

S/N = O/sqrt(O+N_pix x S) x sqrt(t)

Example: for the f/1 + Thomson,  a star with R=23 has an expected total count rate of about 8.8 photons/second, ie. O = 6.4 and, for a dark sky, S = 46 photons/second/pixel in R (see 3.1 below). Assuming the seeing is 1.5 arcsec FWHM and the star image is spread over 9 pixels (Npix=9), we have S/N = 5.7 after 300 seconds. From this, we can estimate that a five minute exposure with the Thomson  CCD in 1.5 arcsec seeing will reach a limiting magnitude (5 sigma detection) slightly fainter than 23.2 in R.

TEK CCD at f/3.3

Table B.5 shows typical object and sky countrates for the TEK chip for observations at the zenith with the chip at 200K ("warm").  These have been used to calaculate the ratio of the noise to the signal (ie 1/SNR) purely due to photon counting for a 300s exposure in 1.5" seeing in a 3" aperture.

Thomson CCD at f/1

Table B.5 object and sky countrates for the Red Thomson chip at f/1, based on the standard star observations of 01 January 1992.

From these rates, it is estimated that in dark time a 5 minute exposure in 1.5" seeing will reach a limiting magnitude ( 5 sigma detection) of R = 23.2. With the f/1 system, even the shortest exposures through the broadband filters are sky limited, due to the low readout noise of the Thomson CCD and the large pixels. Stars brighter than 13th magnitude saturate in less than 3s, which is the minimum exposure time set by the shutter speed.