Bruce McNamara
= Bruce McNamara
{c}
<Bruce McNamara> coauthored the 1988 paper <Observation of Stochastic Resonance in a Ring Laser by Bruce McNamara and others> with <Kurt Wiesenfeld> and <Rajarshi Roy>. The publisher lists the School of Physics at Georgia Tech and gives McNamara a permanent-address footnote at the Physics Department of the University of California, Santa Cruz.<Observation of Stochastic Resonance in a Ring Laser by Bruce McNamara and others>[Publisher byline, affiliations and author footnote]{ref} These publication details identify the contributor to this optical experiment.
The experiment's abstract reports improved <signal-to-noise ratio> in a bidirectional <ring laser> after externally injected noise was added to periodic asymmetry modulation.<Observation of Stochastic Resonance in a Ring Laser by Bruce McNamara and others>[Abstract]{ref} Interpreting that result requires a defined output statistic: a larger optical fluctuation alone need not be a clearer periodic signal.
An original finite-trial model makes the distinction precise. Suppose a phase-referenced statistic from each independent trial is
$$
Z_j=A+\epsilon_j,\qquad \mathbb E[\epsilon_j]=0,\qquad
\operatorname{var}(\epsilon_j)=\sigma^2.
$$
For $n$ trials, the average has <variance> $\sigma^2/n$. Its squared-mean-to-variance detection ratio is
$$
R=\frac{nA^2}{\sigma^2}.
$$
The statistic could be a consistently measured in-phase <Fourier coefficient>; its construction and phase reference must remain the same across the comparison.
For stipulated $n=100$, let three injected-noise settings produce modeled pairs $(A,\sigma^2)=(0.02,0.01)$, $(0.10,0.05)$ and $(0.11,0.50)$. The corresponding ratios are 4, 20 and 2.42. The middle case is best even though its output variance exceeds the first case's and its mean signal is smaller than the last case's. The response-to-background ratio determines this comparison. These invented values illustrate the statistic; they are not recovered laser data or the paper's exact spectral convention.
Independence is part of the toy model. With correlated trials,
$$
\operatorname{var}(\overline Z)=\frac1{n^2}\sum_{j,k}\operatorname{cov}(Z_j,Z_k),
$$
so merely collecting more adjacent records does not guarantee the same averaging gain. A proposed experimental comparison fixes observation duration, trial handling, input forcing and output statistic while changing injected noise. It measures both coherent response and background before concluding that detection improved.
The experiment connects <stochastic resonance> to a concrete comparison between a periodic optical response and its noise background.