Monitoring the growth of nonuniform gratings written holographically by Gaussian laser beams

Interfering Gaussian laser beams are sometimes used to photochemically etch gratings into materials; the gratings which result are nonuniform since the groove depth varies over the grating cross section. The grating growth can be monitored in real time by observing the diffraction of the writing beams into their various orders. In order to relate the maximum groove depth to the observed diffraction efficiency, the grating nonuniformity must be accounted for. We present a short calculation which does this. The results are checked with measurements on actual gratings and good agreement is obtained. The results can help to interpret previously published measurements.