Analytical propagation formula of Gaussian-Schell model beams passing through Young’s double slits

By expanding the window function of double-slit aperture into a finite sum of complex Gaussian functions and from the Collins formula, the approximate analytical propagation equation of Gaussian-Schell model (GSM) beams passing through Young’s double silts and ABCD optical system is derived. The validity region of the approximate analytical formula is given by comparing the results obtained from the analytical formula with those from the Collins formula. The effect of the spatial correlation length of GSM beams and the central obstruction ratio of Young’s double slits on the validity region of the approximate analytical formula is studied, and the application prospect of the formula is also presented.