EXACT PROBABILITY-DENSITY FUNCTION FOR PHASE-MEASUREMENT INTERFEROMETRY

Conventional analyses of the accuracy of phase-measurement interferome try derive a figure of merit that is either a variance or a signal-to- noise ratio. We derive the probability-density function of the phase-m easurement output, so that the measurement confidence interval can be determined. We include both laser phase noise and additive Gaussian no ise, and we consider both unmodulated interferometers and those employ ing phase or frequency modulation. For both unmodulated and modulated interferometers the confidence interval can be obtained by numerical i ntegration of the probability-density function. For the modulated inte rferometer we derive a series summation for the confidence interval. F or both unmodulated and modulated interferometers we derive approximat e analytical expressions for the confidence interval, which we show to be extremely accurate at high signal-to-noise ratios.