Using 1-D and 2-D (circular) prolate spheroidal wave functions ϕn(c,x) and ϕN,n(c,r) exp (iNϕ), the paper discusses the imaging by an optical system of a partially coherent light field produced by an extended incoherent quasi-monochromatic source. The process mechanism of the degrees of freedom transmission through 1-D and 2-D optical systems are explained in terms of two integral equations with respect to the illuminating system and imaging system and an expression for the degrees of freedom is developed.