Brillouin light scattering (BLS) is an emerging method for cell imaging and characterisation. It allows elasticity-related contrast, optical resolution and label-free operation. Phonon microscopy detects BLS from laser generated coherent phonon fields to offer an attractive route for imaging since, at GHz frequencies, the phonon wavelength is sub-optical. Using phonon fields to image single cells is challenging as the signal to noise ratio and acquisition time are often poor. However, recent advances in the instrumentation have enabled imaging of fixed and living cells. This work presents the first experimental characterisation of phonon-based axial resolution provided by the response to a sharp edge. The obtained axial resolution is up to 10 times higher than that of the optical system used to take the measurements. Validation of the results are obtained with various polymer objects, which are in good agreement with those obtained using atomic force microscopy. Edge localisation, and hence profilometry, of a phantom boundary is measured with accuracy and precision of approximately 60 nm and 100 nm respectively. Finally, 3D imaging of fixed cells in culture medium is demonstrated.