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An analysis of photon count statistics of noise in Raman fiber amplifiers and passive optical components is presented. The resuits are used for evaluating the output signal-to-noise ratio (SNR) of Raman active recirculating delay lines. It is found that the quadratic dependence of the noise on the number of recirculations causes the SNR to decay with increasing optical delays. Ultimate system performance capabilities, as determined by the SNR quantum limit, are discussed.