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Analytical beam-width characteristics of distorted cat-eye reflected beam

The analytical expression of beam-width of distorted cat-eye reflected beam under far-field condition is deduced using the approximate three-dimensional analytical formula for oblique detection laser beam passing through cat-eye optical lens with center shelter, and using the definition of second order moment, Gamma function and integral functions. The laws the variation of divergence angle and astigmatism degree of the reflected light with incident angle, focal shift, aperture size, and center shelter ratio are established by numerical calculation, and physical analysis. The study revealed that the cat-eye reflected beam is like a beam transmitted and collimated by the target optical lens, and has the same characteristics as that of Gaussian beam. A proper choice of positive focal shift would result in a divergence angle smaller than that of no focal shift. The astigmatism is mainly caused by incidence angle.