Integer-locking condition for stable dual-comb interferometry in situations with fluctuating frequency-comb repetition rates

To make dual-comb interferometry usable in a wide range of applications, it is important to achieve reproducible measurement results even in non-ideal environments that affect the repetition-rate stability. Here, we consider dual-comb interferometry based on a pair of fully referenced optical frequency combs (OFCs) and investigate the impact of fluctuations in the OFC repetition frequencies on the peak position of the center burst in the interferogram. We identify a phase-locking scheme that minimizes the impact of these fluctuations through choosing a special combination of phase-locked frequencies, and the resulting type of operating condition is termed integer-locking condition. Under the integer-locking condition, the number of sampling points in each interferogram remains constant regardless of repetition-rate variations, and this enables more stable phase-resolved measurements in non-ideal environments. We demonstrate the application of this approach using absolute path-length measurements and discuss the accuracy limit imposed by the integer-locking condition. Our findings offer a strategy for robust dual-comb interferometry outside metrology laboratories.