Light intensity at the return place and encirclement power ratio for the distorted reflected beam based on cat-eye effect

Based on the definition of second order moment and the approximate three-dimensional analytical formula for probe detected laser beam passing through a cat-eye optical lens with center shelter and oblique detector, the analytical expression of the encirclement power ratio of the cat-eye effect reflected light under far-field condition has been deduced. Variable laws of light intensity at the return place and encirclement power ratio are performed by numerical calculation, and are analyzed physically. The results show that the light intensity at the return place decreases monotonically with the increases of the diameter, incidence angle, tilted angle of the detector and the center shelter ratio, but the relationships between these parameters and the encirclement power ratio are all nonmonotonic. The reasonable choice of the focal shift size would result in the largest light intensity at the return place and the largest erirclenent power ratio.