A generalized noise variance analysis model and its application to the characterization of 1/f noise

We present a novel generalized model for the analysis of noise with a known spectral density. This model is particularly appropriate for the analysis of noise with a 1/f(a) distribution in a homodyne interferometer. The noise model reveals that, for alpha>1, 1/f(a) noise significantly impacts the homodyne signal-to-noise ratio (SNR) for integration times that near a characteristic time, beyond which the SNR will no longer significantly improve with increasing integration time. We experimentally verify our theoretical findings with a set of experiments employing a quadrature homodyne optical coherence tomography (OCT) system, finding good agreement. The characteristic integration time is measured to be approximately 2 ms for our system. Additionally, we find that the 1/f noise characteristics, including the exponent, alpha, as well as the characteristic integration time, are system and photodetector dependent.