The Order Calibration of Vernier Squared Envelope Extracted by the Hilbert-Huang Transform

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.