where A is the aperture or collecting area, O the solid angle of the field of view, Av the spectral resolution (or, more generally, the spectral bandwidth) in cm-1, e the efficiency or throughput of the optical components, and to the measurement time in seconds. A modulation factor of 1/2a/2 appears (in the denominator) because the chopper, usually a rotating toothed wheel with equally spaced teeth and gaps, passes this fraction of the total energy if the beam has a circular cross-section. The signal-to-noise ratio for a one-second measurement is then equal to the power Ps at the detector due to the source radiance Is divided by the noise equivalent power of the detector, or min Ps Is AO Ave , .
If the signal is integrated for a dwell time t0 then the output is increased in proportion while the noise, assumed random, accumulates with a i/to dependency, so we can write
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