Two formulations for determining the characteristics of an unknown source of acoustic waves using the measurement of its field at its near zone are presented. The measurement in both cases is to be performed on a spherical scan surface which encapsulates the source. The first is for an ideal probe which measures the field at its location. The knowledge of the field is sufficient; its normal derivative is not required. In the second formulation a realistic probe is considered. This time it is required only that the probe has an axially symmetric receiving characteristic. With this formulation, the time functions which characterize the source are found using only the signal at the output of the probe. Both formulations are such that they are not specific to the scan surface radius. Furthermore, they are entirely in the time domain, requiring no inverse Fourier transformations left to be performed.