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Acoustic imaging from non-synchronous measurements is a powerful method that can achieve excellent performance of a densely sampled large array by using an arbitrary prototype array. It has attracted significant interest recently since it is beyond the fundamental limitation of the working frequency determined by the size and microphone spacing of an array. One basic assumption of the non-synchronous measurements theory is the spatial continuity of the acoustic field, which is implemented by introducing the spatial basis function. Nevertheless, a comprehensive investigation of spatial basis function in the context of non-synchronous measurements is still missing. Two kinds of methods are proposed to construct spatial basis functions based on the homogeneous Helmholtz equation solution in this paper. One is the generalized harmonic polynomials (GHPs) and the other is the plane wave expansion (the quasi-uniform plane wave and the non-uniform plane wave). Comparisons of their spectral matrix completion errors show that the proposed construction methods of spatial bases can both yield low errors. Moreover, the construction of the proposed bases is simple to be implemented with only one dimension parameter to be chosen and suitable for the complex sound field. The effectiveness of the proposed bases in the non-synchronous measurements is also validated with simulations and an experiment. [ABSTRACT FROM AUTHOR]