Physical tactile diagrams have traditionally been available to make visual 2-D graphics accessible to individuals who are blind and visually impaired. However, the methods used have drawbacks for which dynamic haptic matrix display devices have been developed to overcome. As texture is a key component of many tactile diagrams, this study examined the psychophysical response of perceived roughness when square wave gratings were explored with a haptic matrix display by blind and sighted participants. Ridge width, groove width, and contact area were all found to be significant factors contributing to the sensation of roughness. When ridge width was held constant, perceived roughness was a decreasing and approximately linear function of groove width. With groove width held constant, however, perceived roughness was found to be an inverted U-shaped quadratic function of ridge width. The magnitude of the sensation of roughness was found to increase when contact area was increased. Finally, no difference was found between the performance of blind and sighted participants. The resulting information has implications for the effective creation of distinct textures using haptic matrix displays for virtual environments and tactile diagrams.