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The phase angle component of the complex frequency response of a sonar system operating near transducer resonance is usually distorted. Interpretation and classification of the received sonar signal benefits from the preservation of waveform fidelity over the full bandwidth. A calibration process that measures the phase response in addition to the amplitude response is thus required. This paper describes an extension to the standard-target calibration method to include phase angle, without affecting the experimental apparatus, by using dual-frequency transmission pulses and frequency-domain data processing. This approach reduces the impact of unknown range and sound speed parameters upon phase calibration accuracy, as target phase is determined from the relationship of the two frequency components instead of relying on a local phase reference. Tungsten carbide spheres of various sizes were used to simultaneously calibrate the amplitude and phase response of an active sonar system in a laboratory tank. Experimental measurements of target phase spectra are in good agreement with values predicted from a theoretical model based upon full-wave analysis, over an operating frequency of 50-125 kHz.

Phase calibration of sonar systems using standard targets and dual-frequency transmission pulses