A Frequency Recovering Method for Photonic Under-Sampling E-Field Measurement

An electric field measurement system with two optical pulse sources down-converts the high-frequency electric signal to the baseband through a probe exploiting the electro optic-effect. From that process, it is feasible to recover the measured frequency. However, the majority of the current studies focus on the case where the difference between the two repetition frequencies is quite small, while only a few involve larger frequency differences. Nevertheless, in a non-laboratory uncontrolled environment such as a field measurement, it is commonly unfeasible to guarantee a small frequency difference imposing further study on frequency recovery methods under larger frequency difference. Spurred by that, in this paper we propose a universal frequency recovery algorithm relying on the Remainder Matching (RM) technique, which is suitable for both large and small frequency differences. In our method, we employ the RM technique to determine the exact remainder combination in the first repetition frequency intervals and calculate the measured frequency. We also present the theoretical basis of RM, along with a summary of the system design rules, which have a significant impact on the performance of the measurement system. Finally, we challenge our RM-based solution on noise and analyze the corresponding false alarm rate metric. Our results demo nstrate that the proposed RM-based frequency recovery algorithm attains an appealing performance.