Based on the point spread function of the off-axis Fresnel digital holographic system with pre-magnification, the phase
aberration introduced by microscope objective is obtained. Using a collimated light as reconstructing wave, the phase
aberration introduced by the difference between the reconstructing wave and the reference recording wave is analyzed.
This method is very simple, and it is very different from the one proposed by T. Colomb et al. The phase mask that can
be used to compensate automatically the phase aberration in the phase reconstruction is obtained. According to the
principle of digital holography, it must be pointed out that for Fresnel digital holography, the recording distance must be
determined accurately before compensating automatically the phase aberration. This is done by an automatic focusing
procedure, which is based on image-gray-entropy-method. The simulation result for a special three-dimensional micro
object, which is polluted by a random noise, is presented. The percentage error of the reconstructing distance obtained by
the focusing procedure is below 0.6 for SNR = 25. Then an automatic aberration compensation procedure, which is the
same as that one proposed by T. Colomb et al., is applied to reconstruct the phase image. The results show that for a
weak noise the above method is very effective; for a stronger noise the procedure described here is applied iteratively,
starting from the initial values provided by the first evaluation; while for a very strong noise the procedure fails at all.
Moreover, after applying a median filter to the primary reconstructed phase image, the aberration of the phase image
obtained by further iteration decreases, at the same time the noise is strengthen.