Robust wide-range chirp rate measurement based on a flexible photonic fractional Fourier transformer

We propose a photonic-assisted approach to measure the chirp rate of a linear frequency modulation waveform (LFMW) with a long duration, based on tunable photonic fractional Fourier transform (FrFT). Since the FrFT order can be continuously tuned by varying the frequency shift in an optical frequency-shifting loop (FSL), a specific FrFT order leads the fundamental frequency component arising in the output electrical spectrum to reach its maximum value, after the photonic-to-electrical conversion. Based on the designated FrFT order and the corresponding fundamental frequency in the output electrical spectrum, the chirp rate measurement over a wide range can be accessed, even the signal-to-noise ratio (SNR) of the input LFMW is substantially low. Simulation results indicate that the chirp rate of a 0.16-ms LFMW over a frequency range from 20 GHz to 26 GHz can be precisely characterized, with a relative measurement error of less than 0.13%, under the SNR condition of 0 dB. Moreover, an unambiguous chirp-rate measurement within the range of -5200 MHz/µs to 550 MHz/µs can be achieved. Hence, the proposed chirp rate measurement is featured with broadband operation, robust noise tolerance, low-frequency detection, and long-duration LFMW characterization.