UMH Texture Rendering Methods

• The paper presents a UMH texture rendering method using three ultrasonic components—static pressure, 30 Hz, and 150 Hz vibrations—to target distinct cutaneous mechanoreceptors.
• It employs amplitude modulation and focus rotation techniques to synthesize a textured continuum, validated through quantitative perceptual studies and real material comparisons.
• Experimental results show high discriminability and tunable roughness and friction outputs, advancing applications in haptic VR, teleoperation, and non-contact interfaces.

Texture rendering in Ultrasound Midair Haptics (UMH) refers to the generation of distinguishable tactile sensations—perceived as texture, roughness, or friction—on the bare skin in free space using focused ultrasound. The approach leverages the distinct response profiles of cutaneous mechanoreceptors (SA-I, FA-I, FA-II) to synthesize textures by orchestrating static pressure and vibratory components with targeted temporal and spatial modulation of the ultrasound field. The recently introduced method utilizes three fundamental ultrasonic stimulus components—static pressure via focus rotation (SA-I analog) and sinusoidal vibrations at 30 Hz (FA-I analog) and 150 Hz (FA-II analog)—to synthesize a range of textural sensations, with systematic evaluation against physical material references and quantitative perceptual studies (Morisaki et al., 23 Jan 2026).

1. Biophysical and Perceptual Foundations

The UMH texture rendering method is explicitly receptor-oriented. Human tactile perception of textures is mediated by three major mechanoreceptor classes in glabrous skin:

• SA-I (Merkel cells): Sensitive to static or slowly varying indentation, encoding spatial pressure and fine form.
• FA-I (Meissner corpuscles): Respond strongly to low-frequency vibrations (~30 Hz), conveying flutter/low-frequency roughness.
• FA-II (Pacinian corpuscles): Activated by high-frequency vibrations (~150 Hz and above), critical for perceiving fine roughness and frictional microtextures.

The UMH method designs ultrasonic stimulus primitives that directly and independently target these receptive profiles by manipulating the radiation force field in air above the skin.

2. Ultrasonic Stimulus Components and Signal Design

2.1 Static Pressure Component (SA-I)

Static pressure is rendered using a “Local Motion” (LM) stimulus: five ultrasound foci are simultaneously arranged in a circle (radius 3.3 mm) about the nominal contact point on the user’s palm, with each focus completing a 5 Hz rotation. This spatially multiplexed focus pattern suppresses perception of lateral “sliding” while producing a composite, quasi-static normal force (typically ≈0.2 N). The instantaneous drive signal on transducer $n$ for the $i$-th focus is: $$s_n(t) = A(t)\,e^{j(2\pi f_c t - \sum_{i=1}^5 \phi_{n,i}(t))}$$ where $A(t)$ is the amplitude envelope (constant for pure pressure), $f_c=40$ kHz is the carrier, and $\phi_{n,i}(t)$ is the time-varying phase to focus at location $p_i(t)$.

2.2 Vibration Components (FA-I, FA-II)

Low- and high-frequency vibration modalities are synthesized by amplitude-modulating the entire multi-focus pressure stimulus: $$A^{\text{mod}}(t) = (1-\mathrm{AM}) + \mathrm{AM} \Bigl[\lambda\,\Phi_{30}(t) + (1-\lambda)\,\Phi_{150}(t)\Bigr]$$ where

$\Phi_{f}(t) = \frac{1+\cos(2\pi ft)}{2}$

with $f=30$ Hz (FA-I) or $f=150$ Hz (FA-II), $\mathrm{AM}\in[0,1]$ setting the overall modulation depth, and $\lambda\in[0,1]$ weighting between 30 Hz and 150 Hz. AM=0 yields pure static pressure; higher AM values synthesize vibration at the selected frequency ratio. These settings are selected for faithful mechanoreceptor targeting.

2.3 Texture Synthesis via Component Mixing

Combining the components enables continuous interpolation between perceptual endpoints: pure smoothness (static pressure only), low-frequency “flutter” (FA-I dominant), high-frequency “roughness/friction” (FA-II dominant), and mixtures. The amplitude modulation and frequency weights determine rendered roughness:

• AM=0, any λ: glassy/slippery (pressure only)
• AM>0, λ=1: fluttery/velvety (30 Hz dominant)
• AM>0, λ=0: rough/frictional (150 Hz dominant)
• Intermediate λ: composite textures

3. Experimental Setup and Stimulus Parameterization

The apparatus comprises eight 256-element phased-array ultrasound emitters (total 1,992 transducers, 40 kHz carrier), real-time tracking of hand position (Leap Motion, Intel RealSense), and software control at 1 kHz spatial update. A virtual interaction paradigm renders contact between the user’s palm and a moving virtual object, with tactile stimuli emitted when a predefined region of the palm is in contact.

Six canonical “texture” stimuli were constructed: | Label | AM | λ | Dominant Perceptual Mode | |-----------|-------|----|---------------------------| | S-LM | 0 | – | Static Pressure (glass) | | S-30Hz-w | 0.5 | 1 | Weak 30 Hz vibration | | S-30Hz-s | 1.0 | 1 | Strong 30 Hz vibration | | S-150Hz-w | 0.3 | 0 | Weak 150 Hz vibration | | S-150Hz-s | 1.0 | 0 | Strong 150 Hz vibration | | S-Mix2 | 1.0 | 0.7| Mixed (30 Hz-biased) |

4. Perceptual Evaluation: Methods

Rigorous psychophysical studies established discriminability and mapped the rendered sensations onto physical reference materials (glass marble, cotton textile, 100-grit sandpaper, artificial turf). Methods included:

• Detection thresholds: Interleaved staircase procedures determined minimum AM for vibration salience at both 30 Hz and 150 Hz. Thresholds were lower for 150 Hz (≈0.23) than for 30 Hz (p<0.005).
• Intensity scaling: Visual analog scale (VAS) ratings (0–100) as a function of AM. Vibration intensity increased linearly with AM (coefficients: a_{150Hz}=93.4, a_{30Hz}=67.3).
• Texture discrimination: 6-alternative forced choice (6-AFC) across the six canonical stimuli yielded >82% correct; pressure-only was perfectly discriminated.
• Comparative matching: Subjects rated roughness (R), friction (F), and stiffness (S) of each rendered stimulus vs. reference objects (VAS –100 to +100 scale; zero indicates perceptual identity with reference).

5. Quantitative Outcomes and Stimulus-Percept Mapping

• Roughness: The S-LM condition (AM=0) was statistically indistinguishable from an actual glass marble in roughness (p>0.05), confirming the efficacy of pure static pressure for glassy/smooth rendering. Adding 30 Hz vibration (FA-I) significantly increased roughness ratings (p<0.0005 vs. S-LM), with further increments produced by 150 Hz vibration (FA-II). The S-150Hz-s stimulus achieved roughness ratings not significantly different from 100-grit sandpaper (p>0.05), spanning the perceptual roughness continuum.
• Friction: Only the high-frequency (150 Hz) component caused statistically significant friction increases (p<0.05 vs. pressure-only and 30 Hz). S-150Hz-s friction was not significantly different from high-friction textiles.
• Stiffness: Variations in AM or λ produced minimal changes in perceived stiffness (Δmedian |S|<30 points), with all ultrasound stimuli rated softer than glass marble (p<0.05).
• Statistical analysis: Two-way ART–ANOVA for roughness yielded F(6,108)=48.7 (p=1.6×10^-28) for stimulus and F(3,54)=74.1 (p=3.9×10^-19) for reference material; friction showed a similar response.

A perceptual continuum was visualized in (R, F) space, anchored from marble-like smoothness (AM=0) to sandpaper-equivalent roughness (AM=1, λ=0), with intermediate friction and roughness tunable by the mixture parameter λ.

6. Technical and Methodological Significance

This texture rendering approach provides direct parametric control over tactile quality in UMH, with at least six perceptually distinct sensations spanning real-world material analogs. The static pressure component enables highly smooth, slippery textures resembling glass, while vibration amplitude and frequency control enable frictional and rough textures. Notably, the sensitivity difference for 150 Hz versus 30 Hz supports prior understanding of FA-II receptor lower thresholds and high discriminability of frictional microtextures.

The fact that all six canonical conditions were discriminated above chance and that roughness/spatial friction can be modulated in a continuous and physically grounded manner marks a significant advance in UMH-based texture rendering, with direct applicability in haptic VR, teleoperation, and non-contact interface design.

7. Comparative and Future Perspectives

Unlike conventional device-based or wearable haptic interfaces, this approach harnesses airborne radiation force, enabling texture rendering without user instrumentation and with full hand mobility. The ability to span a continuum from glass-smooth to sandpaper-rough, and to manipulate friction percepts independently, aligns with the state-of-the-art in tactile VR systems. A plausible implication is further refinement of midair tactile rendering through additional frequency components or spatial-temporal amplitude shaping, permitting more nuanced representations of anisotropic and spatiotemporally dynamic textures. The findings support a paradigm in which the synthesis of tactile “primitives” aligned with peripheral neurophysiology yields predictable, robust, and scalable perceptual outcomes (Morisaki et al., 23 Jan 2026).