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Optically driven recirculating delay lines, often used in fiber-optic signal processors, convert the source phase noise to spectrally structured intensity noise at the loop output. This spectrum is characterized by deep notches at zero frequency as well as at other multiples of 1/(loop delay). An expression is derived for the power spectral density of the output noise. The formulae obtained, are then used to investigate the dependence of the magnitude and shape of this noise on the source coherence time, the coupling ratio, the coupler and loop losses, and the fiber birefringence.