Title: A primary method for the complex calibration of a hydrophone from 1 Hz to 2 kHz
Abstract: A primary calibration method is demonstrated to obtain the magnitude and phase of the complex sensitivity for a hydrophone at frequencies between 1 Hz and 2 kHz. The measurement is performed in a coupler reciprocity chamber ('coupler'); a closed test chamber where time harmonic oscillations in pressure can be achieved and the reciprocity conditions required for a primary calibration can be realized. Relevant theory is reviewed and the reciprocity parameter updated for the complex measurement. Systematic errors and corrections for magnitude are reviewed and more added for phase. The combined expanded uncertainties of the magnitude and phase of the complex sensitivity at 1 Hz were 0.1 dB re 1 V and ±, respectively. Complex sensitivity, sensitivity magnitude, and phase measurements are presented on an example primary reference hydrophone.