Phase Function Effects on Identification of Terahertz Spectral Signatures Using the Discrete Wavelet Transform

Area of Science:

• Spectroscopy and Spectrometry
• Signal Processing
• Materials Science

Background:

• Terahertz (THz) spectroscopy is valuable for material identification.
• Extracting characteristic absorption signatures from THz spectra can be challenging due to scattering.
• Wavelet transforms offer potential for signal analysis in complex spectral data.

Purpose of the Study:

• To apply the Discrete Wavelet Transform (DWT) for extracting material absorption signatures from THz reflection spectra.
• To evaluate the performance of different mother wavelets (Daubechies, LA, Coiflet) in this application.
• To develop a phase correction method for accurate spectral analysis using DWT.

Main Methods:

• Application of Discrete Wavelet Transform (DWT) to terahertz reflection spectra.
• Comparison of Daubechies, Least Asymmetric (LA), and Coiflet mother wavelets.
• Calculation of advancement coefficients for zero-phase DWT.
• Testing with alpha-lactose monohydrate/polyethylene samples with varying surface roughness.

Main Results:

• Wavelet and scaling filter phase functions cause spectral shifts in the wavelet domain.
• A method for achieving zero-phase DWT using advancement coefficients was developed.
• The DWT-based algorithm successfully extracted 0.53 and 1.38 THz resonant signatures.
• Extraction was effective even with significant surface scattering effects.

Conclusions:

• DWT is a powerful tool for analyzing terahertz spectra.
• Phase correction is crucial for accurate spectral signature extraction using DWT.
• The DWT analysis provides a robust method for material identification in terahertz non-destructive evaluation (NDE).