7.3 Sensitivity, Count Rate, and Signal-to-Noise

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

Both COS detectors are photon counters, which means that they have no read noise and their gain is unity. COS is optimized for point sources, and in this case the signal-to-noise ratio is given by

\frac{S}{N}=\frac{C\times t} {\sqrt{C\times t +N_{\rm pix} \left(B_{\rm sky} + B_{\rm det} \right)\times t}} ,

C = the signal from the astronomical source, in count s1,
t = the integration time, in seconds,
Npix = the total number of detector pixels integrated to achieve C,
Bsky = the sky background, in count s1 pixel1, and
Bdet = the detector dark count rate, in count s1 pixel1.

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 count.

Note that the detector dead-time effects discussed in Section 4.1.5 and Section 4.2.5 are not included in the ETC, which will over-predict the count rates and resulting S/N ratios for bright targets.