Assessing the metrological performance of the methods available for displacement field measurement is of primary importance in experimental mechanics. It often relies on synthetically rendered images of a specimen before and after deformation. In this context, the only varying quantity should be the displacement field in order to prevent any other phenomenon to bias the estimation of the metrological performance. Concerning digital image correlation (DIC), images of a random speckle pattern are needed. We propose a new algorithm to render such images with a classic model of stochastic geometry, namely the Boolean model.