How do the fine fringes on a hologram act like a diffraction grating?

In the context of holography, the fine, close-packed interference fringes recorded on a hologram act as a diffraction grating by bending or diffracting the light used to illuminate the hologram during the reconstruction process.1

When a coherent laser beam illuminates the hologram, these complex patterns—which store both the amplitude and phase information of the original object—interact with the light. The fringes function similarly to a diffraction grating by redirecting the light to reverse the original conditions of the coherent waves that created the hologram. This diffraction process allows the light to reconstruct the original optical field, forming both a virtual image and a real image of the object. By effectively manipulating the path of the light through these fine structures, the hologram is able to recreate a three-dimensional representation of the object that contains precise information regarding its depth and contours.12