Judged Roughness as a Function of Groove Frequency and Groove Width in 3D-Printed Gratings

For different types of textures judged roughness has been shown to be an inverted U-shaped function of inter-element spacing when texture amplitude is low [1, 2]. This may be due to an interplay of two “components” that contribute to the skin’s spatial deformation, and thus to a spatial-intensive code to roughness [1, 3, 4]: (1) deformation increases with the depth of the finger’s intrusion between elements, which increases with inter-element spacing until the finger contacts the ground; and (2) skin deformation decreases with a decreasing number of inter-element gaps being simultaneously under the skin, i.e. with the texture’s spatial frequency (which is negatively correlated with inter-element spacing). The present study systematically tested these ideas. We presented participants different series of 3D-printed rectangular grating stimuli, in which the width of the grating’s grooves varied and the spatial frequency of grooves was constant, or vice versa. Participants touched the stimuli without lateral movement and judged roughness using magnitude estimation. As predicted and previously observed, judged roughness increased with groove width and groove frequency. However, the predicted increase with groove frequency, was only found for frequencies below about 0.5 mm⁻¹. For larger frequencies, roughness decreased with increasing frequency. The decrease is at odds with findings from earlier studies that used aluminum rather than plastic gratings [5]. The results corroborate the assumption that the area of skin deformation plays a crucial role for roughness, but at the same time, point to the influence of subtle differences between materials that should be investigated in the future.