Vortices in optical beams have been the subject of extensive study since their status as a generic feature of light was established. They have found extensive use in optical trapping systems, astronomy, microscopy and are being investigated for free space communication systems. Related to optical vortices are correlation vortices in the coherence functions of partially coherent beams. Partially coherent beams have attracted interest as information carriers because of their resistance to scrambling on propagation. However, their analysis is more difficult than that of fully coherent beams due to the necessity of using correlation functions which increases the dimensionality of the integrals needed. In this dissertation we demonstrate a complete description of a partially coherent vortex beam on propagation, and derive a new partially coherent beam class based on Laguerre-Gauss beams. We also give an analytic description of diffraction through any polygonal aperture, and demonstrate the triangular aperture case. We conclude with a study of fully coherent, partially coherent and incoherent beams propagated through turbulence.
