Noise Behavior of a Heterodyne Interferometer with Optical Phase Locked Loop in Dependence from Phase-Delay and Working Distance

Heterodyne interferometers with a Bragg cell (an acousto-optical modulator) as a frequency shifter are widely used, for example as the sensor in a Laser Doppler Vibrometer (LDV). An optical phase-locked loop (OPLL) can replace the Bragg cell and allows the carrier frequency to be set flexibly. We derived an electric network model for the OPLL based on the small-signal approximation and used it to explore the influence of phase delays generated by optical pathlengths in the interferometer. This small-signal model of the OPLL-LDV, which includes power feedback, is derived from network theory for an OPLL matched to an LDV. Our model allows the investigation of noise performance in dependence of OPLL-LDV phase delays, OPLL bandwidth, laser noise and working distance of the LDV. The comparison with measurements performed with our experimental setup confirms the validity of our model. Finally, we explore the degradation of coherence (related to the noise behavior of the photodetector) at different delays introduced by varying the working distance. The insights of this investigation allow to set the phase delay in the OPLL optimally in respect to the working distance of the interferometer.