Propagation of partially coherent off-axis flat-topped beam through aligned and misaligned optical systems

A new kind of partially coherent beam named partially coherent off-axis flat-topped beam is proposed. The cross-spectral density of this beam can be expressed as a finite series of off-axis Gaussian-Schell-model beams with different parameters. Analytical propagation formulae for the partially coherent off-axis flat-topped beam through aligned and misaligned optical systems are derived. As a numerical example, the propagation properties of the partially coherent off-axis flat-topped beam in free space are discussed.