Sixteen patterned surfaces ranging in surface wavelength from 270 nm up to 90 μm, as well as two blank surfaces, were prepared in duplicate by employing surface wrinkling29,30,31 as depicted in Fig. 1. They were characterised as described in the methods section and the topographic parameters associated with the systematic, sinusoidal wrinkle pattern are shown in Table 1S. Figure 2 displays images of 4 of these surfaces, showing that essentially identical patterns are achieved at different length scales which are independent of the imaging techniques used [atomic force microscopy (AFM) for the smaller wavelengths and profilometry for the larger wavelengths]. A colour code has been used to simplify the distinction between the surfaces, from smaller (red) to larger wavelengths (blue). Blank surfaces were templated from unwrinkled polydimethylsiloxane (PDMS) specimens and thus have no systematic wrinkled topography.

Figure 1 Schematic diagram outlining the fabrication procedure of wrinkled surfaces. (1) Original PDMS substrate with initial length L. (2) Stretching of the PDMS by ΔL using a strain stage. (3) Surface treatment of the PDMS either by UVO or OP treatment. (4) Spontaneous wrinkling occurrence after releasing the pre-strain. (5) Replica moulding of the wrinkled PDMS substrate onto an UV-curable adhesive. Full size image

Figure 2 Wrinkled-patterned surfaces ranging from nanometers to micrometers. Representative 3D images of sinusoidal-patterned surfaces of identical material spanning two orders of magnitude in wavelength (λ) with varying amplitudes (z in this figure) fabricated by the combination of surface oxidation, surface wrinkling and replica molding techniques (Fig. 1): (a) WS2, (b) WS8, (c) WS11 and (d) WS15 (for details of surfaces included, see Table 1S). (e) An approximate colour scale for the representation of wavelengths. Full size image

The surfaces were presented pairwise in psychophysical experiments where 20 participants (blindfolded) scaled perceived similarity of all the randomly presented pairs [201 pairs in total including test-retest comparisons (Supplementary Fig. 1S)]. The participants probed the surfaces with the index finger of their preferred hand in a designated direction (perpendicular to the grooves) for as long as they wished and at loads and speeds that they established themselves, where the average duration of one comparison was approximately 10 s. Each surface pair was assigned a self-determined similarity value on a percentage scale from completely similar (100%) to totally dissimilar (0%). The similarity values were transferred to a dissimilarity scale for each subject and submitted to mapping by individual differences scaling (INDSCAL)32,33. A two-dimensional “tactile space” was generated from the dissimilarity matrices of the individual subjects, where each pair of stimuli obtains a unique subject weight. The Cartesian distribution of the surfaces according to the resulting two perceptual dimensions for the group is shown in Fig. 3a. Despite their inherent material similarity, the different stimulus surfaces are well distributed in the perceptual map, indicating that they were confidently differentiated perceptually. The distribution of the stimuli in the map shows that surface WS1 (270 nm in wavelength) was not distinguished from the blank surfaces whereas surfaces WS2 and WS3 were (760 and 870 nm in wavelength, respectively). Moreover, the amplitude of the minimum pattern distinguished was only 13 nm, showing that the human finger with its coarse fingerprint structure in the sub-millimetre range is capable of dynamically detecting surface structures many orders of magnitude smaller. This value is much smaller than the previously reported value of 1 μm21. It is generally assumed that it is the fast adapting mechanoreceptors, i.e. the Pacinian Corpuscles that are involved in fine texture perception (surface features smaller than 100 μm). Brisben et al.34 showed that these Pacinian Corpuscles respond to vibratory amplitudes as low as 10 nm applied to the skin. The nanometre sensitivity of a finger moving over a surface suggested by Fig. 3, corresponds well to the amplitude sensitivity when a hand is mounted on a vibration table34. In this report, the vibration is provided by sequential collisions of the skin with the nanoscale structures rather than a globally homogeneous external vibration.

Figure 3 2D INDSCAL solution and interpretation of dimensions. (a) Two-dimensional tactile space (for the group of the first 10 participants) based on perceived similarities among 18 surfaces; the closer the points in the map, the more similar the surfaces are perceived. (b) Finger friction coefficient versus wrinkle wavelength. Colour symbols are based on wrinkle wavelength (red is smallest and blue largest wavelengths; open symbols are “blank” reference surfaces), for details see Table 1S. The point distributions in (a) and (b) are distinctly similar, suggesting that friction and wrinkle wavelength are cues for surface similarity (a third order polynomial fits these data well). The WS1 (λ = 270 nm) surface was not perceived as different to the reference surfaces (BS1 and BS2), whereas the WS2 (λ = 760 nm) and WS3 (λ = 870 nm) surfaces were. The respective amplitudes of the latter two are 13 nm and 22 nm, respectively. The data in (b) are presented as the arithmetic mean ± s.d. Full size image

The scree-plot (depicted in Supplementary Fig. 2S and an indicator of how many dimensions the INDSCAL solution has) shows little improvement of the model fit past three dimensions (zero stress means a perfect correspondence between the similarity data and the INDSCAL configuration whereas a value of one means no fit). Although the stress values of the INDSCAL solutions indicate that both the 2D and 3D solutions represent the individual dissimilarity data matrices well, we here choose the 2D solution on the following grounds. It was supported by a principal components analysis (PCA) of the similarity matrix of the group, which resulted in only two components with eigenvalues larger than one. For the 2D INDSCAL solution, average stress over matrices was 0.332 (RSQ = 0.476), a relatively high value. It is probably caused by the unusually low and narrow range of the stimulus patterns used in this experiment combined with a relatively large between-subject variance in haptic sensitivity. The error though is random and the scale values are proportionally over- and underestimated, which is not reflected in the stress value33.

The issue of potential damage to the surfaces and thus the possibility of gradual changes in topography during the experiment has been addressed. Images of the surfaces were taken before and after the experiments and a certain amount of detritus could be observed trapped in the troughs between the peaks, while the sinusoidal pattern remained unchanged (Supplementary Fig. 4S). The surfaces were thus robust to interrogation with the fingertip. One surface was irreversibly scratched by the fingernail of participant 11 however, showing that they are not completely impervious to hard handling. In the Supplementary Information we show a comparison of the data from the first 10 and last 10 participants in Fig. 3S. The results are demonstrably very similar, but not identical so we have chosen to exclude the later participants to be sure that the slight flattening caused by the detritus does not skew the results.

The fact that the “tactile space” is well described by only two dimensions shows that the participants distinguished the surfaces with respect to two basic perceptual aspects, which cannot however, a priori be related to physical quantities. It is generally held that perceptual dimensions are not linearly related to physical quantities, or even combinations thereof. For comparison, Fig. 3b shows a plot of two of the distinguishing physical quantities of the stimulus surfaces; these are the finger friction coefficient (ordinate) and the wrinkle wavelength (abscissa). The spatial distribution of points is highly reminiscent of that in the perceptual dimension plot, suggesting that in fact the two perceptual dimensions of Fig. 3a are related to, or determined by, the two physical dimensions in Fig. 3b. Considering the different units of measurement involved the similarity is striking, but for the presence of two outliers, WS2 and WS3 (wavelengths of 760 and 870 nm, circled). This unprecedented result presumably arises from the very narrow distribution of stimuli, leading to the isolation of a limited number of perceptual outcomes. The good fit of the two tactile-space dimensions with the physical measures (wavelength and finger friction) further validate the INDSCAL and PCA solutions. Inspection of Fig. 3 reveals that the distribution of the data points along the respective curves is different, indicating that the relationship between the perceptual dimensions and the physical quantities is not a rectilinear one.

As mentioned earlier, multidimensional scaling studies report mainly “rough-smooth” and “hard-soft” perceptual dimensions19,23,24,25, with a “sticky-slippery” dimension reported as a possible third dimension23. The results obtained in the present study suggest a “rough/smooth” dimension as well as a “sticky-slippery” dimension. The reason that a “hard-soft” dimension is not observed is that we have deliberately chosen stimuli to isolate the effect of topography, so all the stimuli are equally hard. These results confirm that “sticky-slippery” is an important dimension that can be physically measured by tactile (finger) friction. It is reasonable that once the possibility to distinguish surfaces based on hardness/softness is limited, friction is used as a cue to distinguish surface feel to a higher extent (at least for fine textures where larger differences in friction are obtained).