Gaussian fluctuations (or Gaussian noise) appear in almost all measurements in physics. Here, a concise and self-contained introduction to thermal Gaussian noise is presented. Our analysis in the frequency domain centers on thermal fluctuations of the position of a particle bound in a one-dimensional harmonic potential, which in this case is a microcantilever immersed in a bath of room-temperature gas. Position fluctuations of the microcantilever, detected by the optical beam deflection technique, are then fed into a lock-in amplifier to measure the probability distribution and spectral properties of the fluctuations. The lock-in amplifier measurement is designed to emphasize the frequency-domain properties of Gaussian noise. The discussion here can be complementary to a discussion of Gaussian fluctuations in the time domain.

Topics
Acoustic noise measurement, Structural vibrations, Amplifiers, Cantilever, Signal processing, Thermal fluctuations, Optical beam deflection, Probability theory, Spectral phenomena and properties, Random walks
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2014
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