This paper deals with the optimal pattern that can be used to retrieve displacement fields by minimizing the optical residual calculated over small regions of contrasted images. This minimization is generally performed in the spatial domain by processing speckle patterns with DIC. Another option is also considered here. It consists in switching this minimization to the Fourier domain. The benefit is that periodic patterns can be processed, which is generally not possible with DIC. It turns out that the optimal pattern in terms of sensor noise propagation is theoretically the checkerboard if it is correctly sampled, and this pattern is periodic. The reason why checkerboard is optimal is that the image gradient is maximum in this case. In addition, the minimization of the image residual in this case has a quasi-direct solution, which considerably speeds up the calculations. We first recall the basics of the different techniques used in the paper, namely classic subset-based DIC, and a spectral method called Localized Spectrum Analysis (LSA). A recent deconvolution procedure introduced to enhance the metrological performance of DIC and LSA is also briefly recalled and used in this study. Synthetic images are considered to assess in different cases the displacement resolution, as well as other sources of spurious spatial fluctuations observed in the displacement fields such as the pattern-induced bias with DIC. The main conclusion is that using checkerboards instead of random speckles leads to measurements featuring a better compromise between spatial resolution and measurement resolution.