Extension of aberration theory of grating systems from one- to two-dimension extended source

The aberration theory of grating systems is extended from one-dimension to two-dimension extended source. In deriving the aberration formulae, the concept that pupil in the meridional plane is separate from the one in the sagittal plane is applied and the principal ray is determined by a linear equation. Using the Seidel aberration for reference, the aberrations are classified into seven types according to the geometrical characteristics. The numerical simulation of imaging of one model optical systems is made with the aberration formulae and exact ray tracing to examine the accuracy of the aberration formulae.