This paper describes a technique that numerically reconstructs the complex acoustic amplitude (i.e. the acoustic amplitude and phase) of a compression acoustic wave in the interior volume of a specimen from a set of full-field optical measurements of the instantaneous displacement of the surface. The volume of a thick specimen is probed in transmission mode by short bursts of narrowband compression acoustic waves generated at one of its faces. The temporal evolution of the displacement field induced by the bursts emerging at the opposite surface is measured by pulsed digital holographic interferometry (pulsed TV holography). A spatio-temporal 3D Fourier transform processing of the measured data yields the complex acoustic amplitude at the plane of the surface as a sequence of 2D complex-valued maps. Finally, a numerical implementation of the Rayleigh–Sommerfeld diffraction formula is employed to reconstruct the complex acoustic amplitude at other planes in the interior volume of the specimen. The whole procedure can be regarded as a combination of optical digital holography and acoustical holography methods. The technique was successfully tested on aluminium specimens with and without an internal artificial defect and sample results are presented. In particular, information about the shape and position of the defect was retrieved in the experiment performed on the flawed specimen, which indicates the potential applicability of the technique for the nondestructive testing of materials.