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 Rh is a horizontal curvature radius and Rv 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

Fig.8 The different focus of the Spherical diffraction grating

 

The spherical diffraction gratings are formed on spherical blanks( Rh=Rv ) that has two focal lengths(r'hr'v ) has astigmatisms, The toroidal diffraction gratings are formed on toroidal (aspheric) blanks( RhRv ) that can correct astigmatisms.