The ratio of the period of a diffractive element to the input beam size is a critical parameter in a diffractive beam shaper. We measured and calculated the Fraunhofer diffraction patterns of a periodic hologram with an input beam size similar to the period of the hologram. The measured intensities show very complicated patterns and are strongly dependent upon the center position of the laser beam relative to the hologram. Using a diffraction formula for a periodic hologram, we calculated the diffracted light intensities and fit them to the measured ones. The measured and calculated intensities are in good agreement even when the beam diameter of the incident laser is similar to the period of the hologram. We can therefore use this formula to estimate the output of a periodic beam shaper even under such an extreme condition.
