Measurement of the atmospheric primary aberrations by 4-aperture DIMM
  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. 
Ramin Shomali, Sadollah Nasiri and Ahmad Darudi
astro-ph.IM physics.optics