Diffraction by a Finite Sinusoidal Phase Grating

The exact expressions for the diffraction pattern produced by a single sinusoidal groove and for finite gratings have been derived and compared with the expressions commonly used. We have shown that the usual approximations are valid only in the limit of gratings with an infinite number of grooves. Attention is given to the case of color thermoplastic recording, where the number of grooves is expected to be few.