  A thin phase hologram with sinusoidal modulation of the refractive index is
considered. The applicability of the approach is discussed, in which it is
assumed that light passes through a hologram, as through a slide, which leads
to a sinusoidal modulation of the wave phase. A consequence of this
consideration are expressions for the diffraction orders amplitudes, which
coincide with the expressions obtained in the Raman-Nath theory of light
scattering by ultrasonic waves. The paper compares expressions for the
amplitude of the first order of diffraction, obtained in the framework of
several theoretical approaches, including perturbation theory in a rigorous
formulation of the boundary value problem. As the thickness of the hologram
tends to zero, the expression obtained in this way coincides with the
expression obtained in the two-wave approximation of the coupled-wave theory.
Both expressions satisfy the electrodynamic reciprocity theorem. Under the same
conditions, the expression obtained as a result of the slide-like consideration
does not satisfy the reciprocity theorem and differs from the indicated
expressions by a factor equal to the ratio of the cosines of the diffracted and
incident waves. It is concluded that considering a thin hologram as a slide can
lead to noticeable errors.
