Gratings for metrology and process control 1: A simple parameter optimization problem

A simple graphical method is developed for calculating modulation and groove-to-period ratio of a shallow lamellar grating from its diffraction spectra and for simultaneously checking its assumed shape. It applies to both reflection nd transmission and to the conducting or dielectric nature of both the grating and its substrate. The effect of noise and distortion is briefly discussed. The method is illustrated for the limiting case of a reflecting metallic grating. Uses will be presented in subsequent papers.