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Low-Cost LED Array-Based Optical Time Grating With Submicron Resolution
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DOI：10.1109/tim.2026.3714610.png)
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Abstract
En 中文
Using a uniformly spaced LED array composed of approximately Lambertian emitters, this article presents a low-cost optical time grating for noncontact linear displacement measurement. Four phase-shifted harmonic commands are applied to the LEDs in each period to synthesize an optical traveling wave, and displacement is reconstructed from the phase variation of the intensity signal detected by a photodetector (PD) above the array. To address practical LED nonidealities, a physical measurement model is established by considering the brightness, angular divergence, and mounting errors of individual LEDs. The model parameters are identified through direct measurements and numerical optimization, and the calibrated phase–displacement relationship is then used for error compensation. Experiments over a 20 mm range show that the measurement nonlinearity is reduced from 2.4 % to 0.074 %. Using the calibrated model without additional parameter adjustment, independent validation measurements in the forward and reverse directions yield maximum residual errors of 18.83 and $15.42~\mu \mathrm {m}$ , respectively. The system achieves a repeatability of $0.79~\mu \mathrm {m}$ ( $\sigma $ ) and resolves $0.5~\mu \mathrm {m}$ displacement steps. These results demonstrate that the proposed LED-based optical time grating provides a simple and cost-effective optical measurement solution for compact medium-precision motion-control applications.
Keywords:
LED array
linear displacement measurement
model-based calibration
optical time grating
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