Inclusion of deformed wavefronts into correction of holographic concave gratings

Abstract

We derive the general form of the light path function for corrected holographic concave gratings until the third order of the pupil coordinates. The waves used for recording and reconstruction deviate until the third order from spherical waves. From this we derive the transformation properties of the coma-parts of the wavefronts by grating diffraction and the propagation formula for deformed wavefronts in homogeneous media. These tools can be used for the correction of single gratings and systems containing gratings and as guidelines for intentions to correct diffractive elements with wavefronts deformed by synthetical holograms. The contributions of the third order terms to the ray tracing are given by analytic formulae. Applications are given. Deformed wavefronts can be recommended if there are external constraints by spatial arrangement to the grating configuration or if the spectral range is arranged below the recording wavelength.