# An Optical Sensor for Measuring In-Plane Linear and Rotational Displacement

## TL;DR

A new optical sensor measures in-plane movement and rotation between surfaces using light intensity changes from a color gradient wheel.

## Contribution

The sensor combines RGB and clear light intensity data with polynomial regression to detect linear and rotational displacement.

## Key findings

- The sensor achieved R2 values over 0.94 for linear and rotational displacement prediction using a hue-only wheel.
- Benchtop tests showed high accuracy with R2 values of 0.92 for a hue-and-saturation wheel.
- The sensor has potential for use in wearable medical devices to detect slippage or improper fit.

## Abstract

We developed an optoelectronic sensor capable of quantifying in-plane rotational and linear displacements between two parallel surfaces. The sensor utilizes a photo detector to capture the intensity of red (R), green (G), blue (B), and clear (C, broad visible spectrum) light reflected from a color gradient wheel on the opposing surface. Variations in reflected R, G, B and C light intensities, caused by displacements, were used to predict linear and rotational motion via a polynomial regression algorithm. To train and validate this model, we employed a custom-built positioning stage that produced controlled displacement and rotation while recording corresponding changes in light intensity. The reliability of the predicted linear and rotational displacement results was evaluated using two different color gradient wheels: a wheel with changing color hue, and another wheel with changing color hue and saturation. Benchtop experiments demonstrated high predictive accuracy, with coefficients of determination (R2) exceeding 0.94 for the hue-only wheel and 0.92 for the hue-and-saturation wheel. These results highlight the sensor’s potential for detecting shear displacement and rotation in footwear and wearable medical devices, such as orthotics and prostheses, enabling the detection of slippage, overfitting, or underfitting. This capability is particularly relevant to clinical conditions, including diabetic neuropathy, flat feet, and limb amputations.