Aberration theory of plane-symmetric grating systems

Aberration theory of plane-symmetric optical systems of mirror and grating has been developed based on the wavefront aberration method. A toroidal reference wavefront surface is used to define the wavefront aberration. Based on the ray geometry, the coordinate mapping relationships of the ray between the optical element and the incident and aberrated wavefronts are derived using a polynomial-fit method; this enables the resultant coefficients of the wavefront and the transverse aberration to be kept to the fourth-order accuracy of the aperture-ray coordinates. By setting up the transfer equations of the field and aperture rays, the contribution to wavefront aberrations from each mirror and grating can be added to make the aberration calculation of multi-element systems feasible. The theory is validated by the analytic formulae of the spot diagram.