When implementing the reconstruction of the sound field radiated directly from a source located in a half-space, the half-space basis functions need to be formulated with boundary impedance as a parameter. The boundary impedance is usually obtained via in situ acoustic impedance measurement techniques. In a reconstruction method based on expansion in half-space spherical wave basis functions, a hologram surface and a single reference microphone placed in the near-field are used to collect sound pressures. The sound pressure at the reference microphone is first reconstructed and the error of the reconstructed pressure relative to the measured pressure is then calculated. The sound pressure reflection coefficient corresponding to the minimum error is chosen as the estimated value of the reflection coefficient at each of the measurement points. Thus, this method is applicable to reconstructing the directly radiated sound pressures without knowledge of the boundary impedance, without the in situ acoustic impedance measurements necessary for conventional methods. The purpose of this work is to discuss the various parameters affecting the accuracy of reconstruction. Moreover, the boundary impedance is reconstructed based on the estimation of the reflection coefficient. In this way, an acoustic impedance measurement technique implemented via the near-field acoustical holography is proposed. Taking the source to be spherical, numerical simulations are conducted to verify the proposed method of reconstructing the boundary impedance and the directly radiated sound pressures. The influences of reference microphone coordinates, the effective flow resistivity of the boundary, and the rate of decrease of porosity with depth of the boundary on the accuracy of reconstruction are quantitatively analyzed.