Parametric dependencies of high-diffraction-order achromatized aplanatic configurations that employ circular or crossed-linear diffractive optical elements

The parametric relationships of achromatized transmissive and reflective diffractive optical elements (DOEs) are explored for a number of configuration classes as a function of diffraction order, focal ratio, wavelength, and field angle. The necessity for blazing high-diffraction-order DOEs is elucidated. The ray image sizes are presented in dimensionless imaging space and thus are applicable to any size of optical system. Several aplanatic configurations are evaluated.