Researches on the factors influencing the cat's eye effect on the echo intensity distribution of a gaussian beam

On the basis of the ABCD Collins-matrix theory and the idea of expanding the aperture function into a finite sum of complex Gaussian functions, an analytical propagation formula for a Gaussian beam through a cat's eye optical lens is deduced. Using a series of numerical simulations we studied how the propagation distance, parameters of the cat's eye optical lens and transmitting laser beam influence the intensity distributions at the receiving screen. The results reveal that with the increase of propagation distance, diffraction effect appears and the intensity distribution would change from the Gaussian pattern into symmetrical profile and finally approximately Gaussian pattern. Moreover, the intensity distribution is closed related to the parameters of the cat's eye optical lens including defocusing amount, focus and calibre. Defocusing amount would lead to an intensity transfer and decrease, also the intensity distribution is different at positive and negative defocusing amount. It is the ratio of defocusing amount and focus that directly influences the intensity distribution. The shift of calibre of the cat's eye optical lens would cause a shift of intensity distribution by influencing the retro-reflective angle.