Evaluation of Velocity Signals Measured by Laser in Hydrophone Calibration Based on a Normalized Dynamic Time-Warping Algorithm

Laser heterodyne interferometry plays a crucial role in measuring the velocity of water particles during the calibration of hydrophones with the optical method. The velocity of water particles acts as an indicator of acoustic-pressure variations and can be used to evaluate the stability of the acoustic field. The calibration of hydrophones requires a stable acoustic field environment; currently, though, the assessment of acoustic field stability is largely subjective. This study introduces the Normalized Dynamic Time-Warping (NDTW) algorithm, which objectively evaluates acoustic field stability. Sine-fitting is applied to the region of interest in the measured signal to obtain a reference signal. Subsequently, the NDTW algorithm is used to calculate the difference between the measured and reference signals, enabling the assessment of acoustic field stability. The NDTW algorithm effectively identifies subtle differences between signals and addresses the accumulation errors arising from varying signal lengths. The calibration results showed that for signals of high quality within the identified frequency band, the calibration outcomes obtained using the NDTW algorithm deviated from the reciprocity method by no more than 0.7 dB. For frequency bands with poor signal quality identified by the NDTW algorithm, the deviation between the calibration results and the reciprocity method exceeded 0.7 dB.