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 spectrometerbased
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), 38333848 (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).
