Toroidal Diffraction Gratings

A toroidal diffraction grating is a sort of concave gratings. The toroidal shape is defined by two curvature radii at each central axis. Toroidal shapes where R_h is a horizontal curvature radius and R_v is a vertical curvature radius. The toroidal shapes are expressed in the following equation.

The paraxial focal positions of a toroidal grating in Fig.8 are defined by equations (17) and (18). Here r is the entrance length, r'_h is the horizontal focal length, and r'_v is the vertical focal length. α and β satisfy the grating equation (2)'.

Fig.8 The different focus of the Spherical diffraction grating

The spherical diffraction gratings are formed on spherical blanks( R_h=R_v ) that has two focal lengths(r'_h, r'_v ) has astigmatisms, The toroidal diffraction gratings are formed on toroidal (aspheric) blanks( R_h≠R_v ) that can correct astigmatisms.