When observations are autocorrelated, standard formulae for the estimators of variance, s2, and variance of the mean, s2 (x), are no longer adequate. They should be replaced by suitably defined estimators, s2a and s2a (x), which are unbiased given that the autocorrelation function is known. The formula for s2a was given by Bayley and Hammersley in 1946, this work provides its simple derivation. The quantity named effective number of observations neff is thoroughly discussed. It replaces the real number of observations n when describing the relationship between the variance and variance of the mean, and can be used to express s2a and s2a (x) in a simple manner. The dispersion of both estimators depends on another effective number called the effective degrees of freedom Veff. Most of the formulae discussed in this paper are scattered throughout the literature and not very well known, this work aims to promote their more widespread use. The presented algorithms represent a natural extension of the GUM formulation of type-A uncertainty for the case of autocorrelated observations.
The paper reports on a long-wave infrared (cut-off wavelength ~ 9 μm) HgCdTe detector operating under nbiased condition and room temperature (300 K) for both short response time and high detectivity operation. The ptimal structure in terms of the response time and detectivity versus device architecture was shown. The response time of the long-wave (active layer Cd composition, xCd = 0.19) HgCdTe detector for 300 K was calculated at a level of τs ~ 1 ns for zero bias condition, while the detectivity − at a level of D* ~ 109 cmHz1/2/W assuming immersion. It was presented that parameters of the active layer and P+ barrier layer play a critical role in order to reach τs ≤ 1 ns. An extra series resistance related to the processing (RS+ in a range 5−10 Ω) increased the response time more than two times (τs ~ 2.3 ns).