Measurements from long-baseline interferometry are commonly analysed in terms of the power spectrum and the bispectrum
(or triple-product) of the fringe patterns, as these estimators are invariant in the presence of phase instabilities. At low
light levels, photon and detector noise give rise to systematic "bias" in the power spectrum and bispectrum. This paper extends previous work on computing the expected biases and variances for these quantities by introducing a general method
which can be applied to any fringe-encoding scheme where the measurement equation is linear and to measurements affected
by a combination of photon noise and detector noise. We apply our method to a number of interesting practical
cases, including systems with unevenly-sampled fringe patterns and in the presence of read noise.