Laser-beam apodization with a graded random phase window

Experiments and analysis indicate that graded random phase modulation can be used to apodize a laser beam. In the case of an obscuration or a hard edge it can prevent the formation of Fresnel-diffraction ripples. For example, here the interaction of a 1-microm-wavelength laser beam with a central obscuration of half-width a = 100 microm is studied theoretically. It is found that if the exit surface of a window, placed immediately downstream of the obstacle, is randomly modulated with a Gaussian amplitude transverse correlation length l = 50 microm and a mean-square amplitude that decreases exponentially from a peak height of ~1 microm(2) away from the center of the obscuration with transverse scale length L = 500 microm, then the Fresnel-diffraction ripples normally produced by the obscuration are eliminated. The scaling of these results is also discussed. The calculations are in general agreement with experimental results.