Diffractively corrected counter-rotating Risley prisms.

Using the vector refraction equation and the vector diffraction equation, we obtain the expressions of the direction cosines of the refractive rays for the two wedge prisms, and the direction cosines of the diffractive rays for two wedge grisms, in which diffractive gratings were etched into the prism faces to correct the chromatic aberrations. A mathematical model between the two vector equations is proposed to compare the difference angle chromatic aberrations when the Risley prisms/grisms are rotating at different angles. We conclude that the use of diffractively corrected prisms offers a new method to correct chromatic aberrations in Risley prisms.