Abstract

The Vernier effect can amplify the sensitivity of the sensor, but its effective spectral range is usually limited to one free spectral range (FSR). Once the envelope shifts beyond one FSR, it will lead to the misidentification of the wavelengths with different orders. In this article, we present a method for calibrating the order of Vernier spectral envelope based on least square algorithm to solve this problem. Theoretically, the squared envelope extracted by Hilbert transformation is a cosine-shaped function. And the interval between the adjacent minima of the curve calculated by the least square method is equal to the harmonic central wavelength λ₀. It is deduced that the shifted position of a peak can be tracked by the order change of λ₀. The calculation result is further verified by both simulation and experiment. The result shows that the effective measurement range is expanded by 4.6 times. Therefore, the proposed method can expand the effective measurement range of the sensor based on Vernier effect under the condition of the same sensitivity.

Secondary envelope extraction based on multiple Hilbert transforms for laser self-mixing micro-vibration measurement

Xiangyu Cui, Chunsheng Li, Yuhan Geng, Weijie Ge, Lingling Kan, and Zihua Zhang
Appl. Opt. 58(34) 9392-9397 (2019)

Holographic particle sizing and locating by using Hilbert–Huang transform

Danjie Cai, Xiaojuan Zhao, Yuting Cen, Chujun Zheng, and Peng Han
J. Opt. Soc. Am. A 31(8) 1747-1753 (2014)

Robust Kramers–Kronig holographic imaging with Hilbert–Huang transform

Xuyang Chang, Cheng Shen, Sitian Liu, Dezhi Zheng, Shuai Wang, Changhuei Yang, Norden E. Huang, and Liheng Bian
Opt. Lett. 48(15) 4161-4164 (2023)

Phase demodulation using adaptive windowed Fourier transform based on Hilbert-Huang transform

Chenxing Wang and Feipeng Da
Opt. Express 20(16) 18459-18477 (2012)

Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis

Maciej Trusiak, Łukasz Służewski, and Krzysztof Patorski
Opt. Express 24(4) 4221-4238 (2016)