Discrimination of real and virtual surfaces with sinusoidal and triangular gratings using the fingertip and stylus.

Two-interval two-alternative forced-choice discrimination experiments were conducted separately for sinusoidal and triangular textured surface gratings from which amplitude (i.e., height) discrimination thresholds were estimated. Participants (group sizes: n = 4 to 7) explored one of these texture types either by fingertip on real gratings (Finger real), by stylus on real gratings (Stylus real), or by stylus on virtual gratings (Stylus virtual). The real gratings were fabricated from stainless steel by an electrical discharge machining process while the virtual gratings were rendered via a programmable force-feedback device. All gratings had a 2.5-mm spatial period. On each trial, participants compared test gratings with 55, 60, 65, or 70 µm amplitudes against a 50-µm reference. The results indicate that discrimination thresholds did not differ significantly between sinusoidal and triangular gratings. With sinusoidal and triangular data combined, the average (mean + standard error) for the Stylus-real threshold (2.5 ± 0.2 µm) was significantly smaller (p <; 0.01) than that for the Stylus-virtual condition (4.9 ± 0.2 µm). Differences between the Finger-real threshold (3.8 ± 0.2 µm) and those from the other two conditions were not statistically significant. Further studies are needed to better understand the differences in perceptual cues resulting from interactions with real and virtual gratings.

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.