Axial performance parameters developed for analytical design of center shaded filter in high aperture focusing system

In order to establish the explicit interrelation between the performance and structure parameters of a center shaded filter in high aperture focusing systems, approximate integral equations are proposed and further used to derive axial performance parameters, which are required for the evaluation of axial energy loss and focal depth extension. It has been derived that the axial intensity can be analytically expressed as a square of sinc function and the shaded angle of a center shaded filter can be explicitly calculated using either the expected Strehl ratio or axial gain. The developed axial performance parameters are proved through simulation to be precisely consistent with numerical evaluation results.