A method for the holographic reconstruction of an acoustic field from a finite sound source is discussed in detail. It is often experienced that the holographic reconstruction based on the angular spectral method gives unexpectedly erroneous reconstruction. This is due to the fact that the singularity of the transfer function in the spatial frequency domain cannot be treated accurately by the discrete system. [Waag et al., ``Cross-sectional measurements and extrapolations of ultrasonic fields,'' IEEE Trans. Sonics Ultrason. SU- 32, 26--35 (1985)]. In this paper, a reconstruction is proposed that is based on the convolution of observed data and the transfer function rather than the direct manipulation of data in the frequency domain. It is shown that when the observed data are backpropagated to the plane that includes the finite sound source, the sampling interval of the data can be taken to be significantly larger than the half-wavelength. On the other hand, by taking the pixel interval of the reconstructed source image as less than or equal to the half-wavelength, the acoustic field at an arbitrary point in the space can be evaluated by the successive forward propagation of the source image. The effect of observing an aperture on the resolving power is also discussed.