Paraxial propagation of partially coherent flat-topped beam

The propagation of flat-topped beam passing through a paraxial optical ABCD system is extended to partially coherent case and has been studied in detail. Based on Wigner distribution function (WDF), the irradiance distribution of partially coherent flat-topped beam is derived. Furthermore, two propagation parameters, such as M2-factor and Power in Bucket (PIB) are illustrated analytically and numerically.