Cosmic Origins Spectrograph Instrument Handbook for Cycle 17

10.2 Count Rate, Sensitivity, and S/N

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10.2.1 Centering accuracy and photometric precision

A complete theoretical discussion of the exposure time as a function of instrument sensitivity and signal-to-noise ratio is given in the Chapter 6 of the STIS Instrument Handbook and will not be repeated here. However, COS has several characteristics which simplify the signal-to-noise calculations.

Both COS detectors are photon counters, which means that they have zero read noise. COS is optimized for point sources, and in this case the signal-to-noise ratio is given by:

where:

C = the signal from the astronomical source, in counts sec^-1

t = the integration time, in sec

N_pix = the total number of detector pixels integrated to achieve C

B_sky = the sky background, in counts sec^-1 pixel^-1

B_det = the detector dark count rate, in counts sec^-1 pixel^-1

With no detector read noise, the signal-to-noise ratio is proportional to the square root of the exposure time whether the target is bright or faint compared to the backgrounds and dark.