Multi-channel synchronous vibration measurement method based on spatial heterodyne interferometry

This paper proposes a multi-channel synchronous vibration measurement method based on beam splitting utilizing a diffractive optical element (DOE) combined with angular division multiplexing technology. In this approach, a DOE is employed to generate an array of measurement beams, enabling the efficient extraction of vibration signals via frequency-domain separation techniques. The study provides an in-depth analysis of the effects of beam defocusing and detector quantization depth on the system's measurement performance. Furthermore, the theoretical limit on the maximum number of channels under ideal conditions is derived based on the Rayleigh criterion and the Nyquist sampling theorem. Building upon this theoretical framework, numerical simulations and experimental investigations regarding the first-order vibration mode of a metal plate were conducted. A comparative analysis between the proposed method and a conventional single-point scanning laser vibrometer demonstrates that the proposed approach offers both feasibility and effectiveness in high-fidelity vibration field reconstruction. Experimental results show that the measurement error ranges from 0.057 to 0.49 nm, and the system achieves synchronous measurement of up to 19,200 points under ideal conditions.