Three-dimensional (3D) high resolution beamforming is made more difficult by high data rates. This can be overcome by two-step imaging approaches such as the synthetic aperture beamforming technique. In this technique the first step significantly reduces the data rate by line-based delay and sum, whereas the second stage recombines the data to a high resolution volume image. The second step is implemented using 3D Fast Fourier Transforms and an interpolation step in frequency-wavenumber domain. A proof of concept is shown using a scanning 1 MHz focused single element transducer. The resulting volume image had a maximum -6dB point spread function of 3 mm throughout the entire depth of 135 mm. The signal-to-noise ratio was improved by 20dB in the far field.