This article is motivated by a problem from experimental solid mechanics. The grid method permits to estimate in-plane displacement and strain components in a deformed material. A regular grid is deposited on the surface of the material, and images are taken before and after deformation. Windowed Fourier analysis then gives an estimate of the surface displacement and strain components. We show that the estimates obtained by this technique are approximately the convolution of the actual values with the analysis window. We also characterize how the noise in the grid image impairs the displacement and strain maps. Finally, the metrological performance of the grid method is enhanced with deconvolution algorithms. This work is potentially of interest in optical interferometry, since grids are particular fringe patterns.