Imaging Equations for Toroidal Gratings Using Lie Transformations
李变换方法在超环面光栅成像理论中的应用

The Lie method to characterize imaging of a toroidal grating was presented.A brief introduction of Lie method was given.There are the five transformations to describe the imaging processes of a toroidal grating.The formulae for calculation of the coordinate and direction of light ray were obtained with the above Lie transformation, and its numerical results were compared with those by raytracing program of Shadow.An advantage of the Lie theory of optical imaging was that the pupil (aperture) coordinates did not appear in the Lie theory.The phase space variables x and y in the Lie theory provided for the extent of the object.The image equations show that the direction relationship between variables of the object space coordinate system and those of the image space coordinate system.