Using a scanning electron microscope-molecular beam epitaxy system, detailed near-equilibrium growth processes of island nucleation, coalescence, and step motion are clearly observed for the growth of GaAs on (111)A substrates. These observations allow the quantitative analysis of the growth processes on the basis of the BCF theory that provides the standard model for crystal growth. As an example, the Ga adatom surface diffusion length is directly measured from the dependence of measured step velocity on the Ga arrival rate. The presence of denuded zone in the distribution of two-dimensional nuclei is clearly confirmed, quantitativelly showing good agreement with the diffusion length obtained from the step velocity.