  The present paper investigates and discusses the ability of the Hartmann test
with 4-aperture DIMM to measure the atmospheric primary aberrations which, in
turn, can be used for calculation of the atmospheric coherence time. Through
performing numerical simulations, we show that the 4-aperture DIMM is able to
measure the defocus and astigmatism terms correctly while its results are not
reliable for the coma. The most important limitation in the measurement of the
primary aberrations by 4-aperture DIMM is the centroid displacements of the
spots which are caused by the higher order aberrations. This effect is
negligible in calculating of the defocus and astigmatisms, while, it cannot be
ignored in the calculation of the coma.
