Optical and terahertz spectra analysis by the maximum entropy method

Decoding 'Maximum Entropy' Deconvolution

For over five decades, the mathematical procedure termed "maximum entropy" (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian feature, obtaining expressions for the amount of sharpening and identifying how spurious structures appear. Illustrative examples are provided. These results enhance the utility of this widely used deconvolution approach to spectral analysis.

Extracting Complex Refractive Index from Polycrystalline Glucose with Self-Referenced Method for Terahertz Time-Domain Reflection Spectroscopy

A self-referenced method for extracting the complex refractive index of material was proposed. The method utilized signals reflected from the front and rear surfaces of a slice sample as reference and sample signals, respectively. Before using the self-referenced method, a hybrid filtering technique for eliminating systematic and random noises of time-domain terahertz reflection spectroscopy was used. A terahertz reflection spectrum of crystalline glucose was measured and three feature absorption peaks were obtained from 0.2 to 2.0 THz. We suggest that intermolecular vibrational modes may contribute to the observed absorption spectra in the THz frequency range.

Wavelet prism decomposition analysis applied to CARS spectroscopy: a tool for accurate and quantitative extraction of resonant vibrational responses

We propose an approach, based on wavelet prism decomposition analysis, for correcting experimental artefacts in a coherent anti-Stokes Raman scattering (CARS) spectrum. This method allows estimating and eliminating a slowly varying modulation error function in the measured normalized CARS spectrum and yields a corrected CARS line-shape. The main advantage of the approach is that the spectral phase and amplitude corrections are avoided in the retrieved Raman line-shape spectrum, thus significantly simplifying the quantitative reconstruction of the sample's Raman response from a normalized CARS spectrum in the presence of experimental artefacts. Moreover, the approach obviates the need for assumptions about the modulation error distribution and the chemical composition of the specimens under study. The method is quantitatively validated on normalized CARS spectra recorded for equimolar aqueous solutions of D-fructose, D-glucose, and their disaccharide combination sucrose.