A Frequency-Domain Analysis of Haptic Gratings

The detectability and discriminability of virtual haptic gratings were analyzed in the frequency domain. Detection (Exp. 1) and discrimination (Exp. 2) thresholds for virtual haptic gratings were estimated using a force-feedback device that simulated sinusoidal and square-wave gratings with spatial periods from 0.2 to 38.4 mm. The detection threshold results indicated that for spatial periods up to 6.4 mm (i.e., spatial frequencies >0.156 cycle/mm), the detectability of square-wave gratings could be predicted quantitatively from the detection thresholds of their corresponding fundamental components. The discrimination experiment confirmed that at higher spatial frequencies, the square-wave gratings were initially indistinguishable from the corresponding fundamental components until the third harmonics were detectable. At lower spatial frequencies, the third harmonic components of square-wave gratings had lower detection thresholds than the corresponding fundamental components. Therefore, the square-wave gratings were detectable as soon as the third harmonic components were detectable. Results from a third experiment where gratings consisting of two superimposed sinusoidal components were compared (Exp. 3) showed that people were insensitive to the relative phase between the two components. Our results have important implications for engineering applications, where complex haptic signals are transmitted at high update rates over networks with limited bandwidths.