# Measurement System for Finger Skin Displacement on a Textured Surface Using Index Matching
## 1 Introduction  
Tactile displays that produce realistic sensations are used for virtual reality (VR), teleoperation, and remote palpation applications. Research seeking to enable more realistic simulated tactile presentations (i.e., the sense of friction or roughness) as felt by the fingertip is actively underway. The aim is to improve the sense of immersion in VR and remote control. Past skin displacement studies focused primarily on temporal changes. However, to present a high-quality tactile sensation, it is not enough to only measure temporal changes; it is also necessary to measure spatial changes, such as those of skin displacement. In the past, accelerometers and force sensors have been relied upon to measure vibrations caused by friction [1] and fine textures [2], including artificial [3] and natural ones [4]. These measurements have focused on the activity of the slowly adapting type-II Pacinian corpuscle (PC) receptive fields, which fire relatively well at a combination of high frequency and low spatial resolutions. However, recent neurophysiological findings suggest that the slowly adapting type-I (SAI) mechanoreceptors (Meissner corpuscles) and the rapidly adapting type-I (RAI) mechanoreceptors (Merkels disk) are active at higher spatial resolutions when tracing textures [5]. Thus, in addition to temporal information, spatial information is clearly useful for reproducing vivid texture sensations of high quality. Although there have been efforts to measure spatial skin displacement, previous studies did not measure sensations of roughness, such as that of a flat surface. [PERSON] et al. [6] measured skin displacement on flat or very large uneven surfaces (3 mm ridge width) using a flat plate and a high-speed camera. However, the pitch width was not psychologically related to roughness perception, but was instead related to shape perception [7]. Although it has been suggested that spatial skin changes contribute to texture perception, the spatial behaviors of roughness perception measurements, which are inherently spatiotemporal in nature, have not been directly observed. To enable this, a spatiotemporal haptic measurement system is needed. To this end, we developed a measurement system for skin displacement on a wide range of textures that incorporates an index-matching method from the field of fluid dynamics. In the developed system, a transparent sample is submerged in oil with almost the same refractive index as the sample, and measurements are made when the interface is nearly optically transparent. In addition to 1D unevenness, this makes it possible to spatially measure the skin shear and vibration of the contact area when tracing a texture that accurately reproduces a natural acrylic texture sensation. The contributions of this paper can be summarized as follows:  
* We propose a method for directly observing skin displacement on coarse textured surfaces. * The texture shapes to which this method can be adapted are clarified via optical simulation based on [PERSON]'s law. * We verify the accuracy of the equipment that implements this method. A limitation of this system is the change in friction caused by the use of oil, because finger-skin conditions are different from those of dry conditions. Friction has been reported to have an effect on roughness perception [8]. Thus, the perceived roughness is likely to be reduced for measurements in oil compared with normal measurements. It is also known that the mechanical properties of finger skin change with humidity. [PERSON] et al. [9] showed that increasing fingertip humidity softens the fingertip belly and greatly affects the change in area when it comes into contact with an object. The data obtained by our measurement method are those of skin displacement in oil, which may differ from normal skin displacement. Thus, it may not be possible to reproduce the natural texture by simply reproducing the skin displacement in oil.