Abstract: An acoustic field reconstruction method based on an expansion in half-space spherical wave functions is proposed to reconstruct the direct radiation generated by a source located in a half-space bounded by a surface with finite acoustic impedance.The half-space spherical wave basis functions are formulated firstly,based on the analytical solutions of the acoustic pressures generated by multipoles,where the boundary impedance is used as an independent variable.By solving the expansion coefficients of the half-space basis functions via an inverse calculation,the expansion coefficients of the basis functions in the free-space,corresponding to the directly radiated field,are obtained meanwhile.The direct radiation of the source is finally reconstructed by using the expansion coefficients.Numerical simulations are carried out to verify the proposed method,for the cases where the boundary impedance is known a priori and where it is not explicitly given.The impacts of various parameters on the performance of the method are analyzed.The proposed method is also verified by an experiment conducted in an anechoic chamber.The results show that,the direct radiation from both a spherical source and a planar source,which are the typical sources,can be reconstructed using the proposed method,and that the reconstruction accuracy and stableness of the method are better when the boundary impedance is known a priori than those when the boundary impedance is not explicitly given.