Optical Path Difference in Off-Plane Quasi-Littrow Dispersion Mountings

The present paper analyzes the relative relation between the meridian and sagittal rays in off-plane quasi-Littrow (OP-QL) dispersion mountings. It's concluded that the off-plane angle will cause the rotation of the beam and result in the mismatch between the sagittal beams on different optical elements. Therefore the total optical path difference (OPD) should be an accumulation of corresponding beams instead of the sagittal beam of each element itself. Then, a directional derivative based method is put forward to calculate the OPD for spherical mirrors in various directions. Based on the method, the numerical OPD for OP-QL mountings is solved. Finally, this methodology is validated with both echelette and echelle examples.