Research

1/f noise in low signal optical detection schemes

We became interested in the effects of 1/f noise on detection sensitivity when studying the SNR characteristics of our 3x3 homodyne OCT system. Many common interferometric schemes (including time domain OCT) modulate the signal of interest, shifting the signal away from the base band and away from the effects of 1/f noise. We questioned just how much 1/f noise was degrading our signals.

In order to analyze the effects of 1/f noise we developed a generalized noise variance analysis model [1]. We can express our noisy signal, in terms of photon count rate, as

The model represents the fluctuating noise by expressing the noise power spectral density (PSD), S(f), in the time dimension via:

The actual photon count that we measure is the integral of x(t) over the integration time, τ. The variance of the measurement can be determined by evaluating the expectation of the photon count by taking the ensemble average over all possible phase shifts δi
.
For the case of the 3x3 homodyne interferometer, we measure an amplitude modulated signal, where the integration time is short compared to the total length of the experiment. Using a measurement of the noise power spectrum (of the form 1/fα), we used our model to predict the noise variance, and corresponding SNR of measurements made with this system. We find a noise variance of the form:

This expression implies that for α values greater than 1, the SNR is constant regardless of increasing integration time. Experimental results confirmed this result, showing that the SNR initially increased linearly (when dominated by white noise) then tapered to a constant value (when dominated by 1/f noise).

We have shown both theoretical and experiment results that demonstrate the deleterious effects of 1/f noise in optical detection systems. These findings are useful for researchers in order to choose appropriate detection parameters and optimize their detection sensitivity.

We are currently investigating the effects of 1/f noise on spectrometer-based Fourier domain OCT. This case is not as straightforward, since noise in the spectral domain is transformed into noise in the spatial domain nontrivially.

References

E. J. McDowell, X. Cui, Z. Yaqoob, and C. Yang, A generalized noise variance analysis model and its application to the characterization of 1/f noise, Optics Express 15(7), 3833-3848 (2007).

E. J. McDowell, J. Ren, and C. Yang, Fundamental sensitivity limit imposed by dark 1/f noise in the low optical signal detection regime, Optics Express (under review).