Signal-modelling methods applied to the free-field calibration of hydrophones and projectors in laboratory test tanks

In reverberant laboratory tanks, free-field acoustic calibrations using hydrophones and projectors are limited by the arrival of boundary reflections, and by start-up transients caused by the resonant behaviour of the transducers. This paper describes the application of a signal modelling method which enables measurements to be undertaken at acoustic frequencies below the limits imposed by the echo-free time of the test tank. In the approach, the signals obtained during calibration are modelled, initially by a simple model for the steady-state transducer response, and then by an extended model consisting of terms that are used to describe both the steady-state and resonant behaviours of the device(s). This model may be further extended to include terms that describe the response both to the direct signal and to reflections of the signal from the tank boundaries. A non-linear least-squares problem involving data for all discrete frequencies of measurement is then solved to provide improved estimates of the model parameters and echo arrival times. The method is applied to the calibration of low Q-factor transducers such as hydrophones in the frequency range 250 Hz–1 kHz, and to high Q-factor source transducers in the frequency range 1 kHz–5 kHz, using measurements undertaken in a modest-sized tank where the echo-free time does not allow steady-state conditions to be reached. The calibrations were validated by comparison with both pressure calibrations in a small coupler, and free-field calibrations at an open water facility, with the agreement obtained of better than 1 dB, well within expanded uncertainties (which range between 0.5 and 1.2 dB).