Effect of 1/f noise in integrating sensors and detectors

The authors calculate the variance in the output of an integrating sensor or detector when in the presence of 1/f a noise in the input of the sensor. The calculations are based on mapping the detector onto a linear, time-invariant filter; the approach is general and can be used for any detector that can be so mapped. Formulae for the output variance and signal-to-noise ratio are given for a simple integrating detector and a detector with three different methods of background subtraction, including double sampling, that has two integrations, and triple sampling where the average of two integrations before and after the signal is subtracted from the integration during the signal. The authors consider cases in which a is unity, less than unity and more than unity, given that quite often a is not ideally unity. Also, for the case of an integrating detector that is used to sample a signal, a formula is derived for the expected variance of N samples when the input contains 1/f noise. The authors apply the treatise herein to the input stage of an a-Se based flat panel X-ray image detector and demonstrate that the 1/f noise fluctuations in the dark current of the photoconductor exceeds those because of shot noise.