Spectral Analysis of the Signal from the Laser Doppler Flowmeter: Time-Independent Systems

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Abstract
A method for prediction of the spectrum observed with the laser Doppler flowmeter (LDF) is developed. A detailed analysis of the spectrum observed with steady flows is presented. The effects of diffusive motion of the scattering centers, spatially varying velocities, finite transit time of the centers through the sample volume, and uncertainty in scattering vector are computed. The latter two effects are shown to be identical. A computation of the sample volume size and shape is made using the optical parameters of the system. The calculated linewidths and shapes are in good agreement with data taken on two independent LDF systems. The general formalism is also applicable to measurements made on turbulent fluids and diffusely reflecting solid objects. The special case of a static fluid (zero velocity) is considered in detail and the low angle correction to the conventional expressions used in laser ``beat‐frequency'' spectroscopy is developed.