Log-Gaussian gamma processes for training Bayesian neural networks in Raman and CARS spectroscopies.

We propose an approach utilizing gamma-distributed random variables, coupled with log-Gaussian modeling, to generate synthetic datasets suitable for training neural networks. This addresses the challenge of limited real observations in various applications. We apply this methodology to both Raman and coherent anti-Stokes Raman scattering (CARS) spectra, using experimental spectra to estimate gamma process parameters.

Evaluating different deep learning models for efficient extraction of Raman signals from CARS spectra.

The nonresonant background (NRB) contribution to the coherent anti-Stokes Raman scattering (CARS) signal distorts the spectral line shapes and thus degrades the chemical information. Hence, finding an effective approach for removing NRB and extracting resonant vibrational signals is a challenging task. In this work, a bidirectional LSTM (Bi-LSTM) neural network is explored for the first time to remove the NRB in the CARS spectra automatically, and the results are compared with those of three DL models reported in the literature, namely, convolutional neural network (CNN), long short-term memory (LSTM) neural network, and very deep convolutional autoencoders (VECTOR).

Effect of non-resonant background on the extraction of Raman signals from CARS spectra using deep neural networks.

We report the retrieval of the Raman signal from coherent anti-Stokes Raman scattering (CARS) spectra using a convolutional neural network (CNN) model. Three different types of non-resonant backgrounds (NRBs) were explored to simulate the CARS spectra (1) product of two sigmoids following the original SpecNet model, (2) Single Sigmoid, and (3) fourth-order polynomial function. Later, 50 000 CARS spectra were separately synthesized using each NRB type to train the CNN model and, after training, we tested its performance on 300 simulated test spectra.

Bayesian Quantification for Coherent Anti-Stokes Raman Scattering Spectroscopy.

We propose a Bayesian statistical model for analyzing coherent anti-Stokes Raman scattering (CARS) spectra. Our quantitative analysis includes statistical estimation of constituent line-shape parameters, the underlying Raman signal, the error-corrected CARS spectrum, and the measured CARS spectrum. As such, this work enables extensive uncertainty quantification in the context of CARS spectroscopy.

Influence of Fano resonance on SERS enhancement in Fano-plasmonic oligomers.

Plasmonic oligomers can provide profound Fano resonance in their scattering responses. The sub-radiant mode of Fano resonance can result in significant near-field enhancement due to its light trapping capability into the so-called hotspots. Appearance of these highly localized hotspots at the excitation and/or Stokes wavelengths of the analytes makes such oligomers promising SERS active substrates.

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.

Optical and terahertz spectra analysis by the maximum entropy method.

Phase retrieval is one of the classical problems in various fields of physics including x-ray crystallography, astronomy and spectroscopy. It arises when only an amplitude measurement on electric field can be made while both amplitude and phase of the field are needed for obtaining the desired material properties. In optical and terahertz spectroscopies, in particular, phase retrieval is a one-dimensional problem, which is considered as unsolvable in general.

Phase retrieval of reflectance for nanoparticle optical identification.

We present a method for optical identification of dielectric and metal nanoparticles in a liquid matrix using phase retrieval of reflectance with TE- and TM-polarized light. A formula is derived for extracting the effective complex dielectric function of a nanoparticle colloid based on different complex reflectance components. The phase retrieval is performed using the maximum entropy method.

Causality-based method for determining the time origin in terahertz emission spectroscopy.

We propose a method for determining the time origin on the basis of causality in terahertz (THz) emission spectroscopy. The method is formulated in terms of the singly subtractive Kramers-Kronig relation, which is useful for the situation where not only the amplitude spectrum but also partial phase information is available within the measurement frequency range. Numerical analysis of several simulated and observed THz emission data shows that the misplacement of the time origin in THz waveforms can be detected by the method with an accuracy that is an order of magnitude higher than the given temporal resolutions.

Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy.

The ability to observe samples qualitatively at the microscopic scale has greatly enhanced our understanding of the physical and biological world throughout the 400 year history of microscopic imaging, but there are relatively few techniques that can truly claim the ability to quantify the local concentration and composition of a sample. We review coherent anti-Stokes Raman scattering (CARS) as a quantitative, chemically specific, and label-free microscopy. We discuss the complicating influence of the nonresonant response on the CARS signal and the various experimental and mathematical approaches that can be adopted to extract quantitative information from CARS.

Determination of the time origin by the maximum entropy method in time-domain terahertz emission spectroscopy.

We have developed a scheme for determining the time origin by the maximum entropy method (MEM) in time-domain terahertz (THz) emission spectroscopy. By applying the MEM to trial damped sinusoidal waveforms, we confirmed that the MEM gives true phase shifts across the resonance features and that its inherent uncertainty in determining the time origin is +/-15 fs for 100-fs-class excitation/sampling optical pulses. Furthermore, when the MEM was applied to a THz waveform recorded experimentally with a finite sampling interval for the Bloch oscillation in a semiconductor superlattice, a misplacement of the time origin was indeed detected with an accuracy limited by the worse of the MEM inherent uncertainty and the sampling interval.

Quantitative CARS spectroscopy using the maximum entropy method: the main lipid phase transition.

The maximum entropy method for phase retrieval of multiplex coherent anti-Stokes Raman scattering (CARS) spectra is described in detail and applied to the time-resolved measurement of the main lipid phase transition of small, unilamellar 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) vesicles subject to a 3 min temperature sweep. Since the--thus derived--imaginary part of the third-order CARS susceptibility can be directly related to the linear vibrational spectrum, the multiplex CARS spectral data can be analyzed quantitatively and without prior knowledge of the sample. It is shown that the maximum entropy model provides an exact description of the original data, including the noise, if all available autocorrelation functions are used.

Spectroscopic analysis of the oxygenation state of hemoglobin using coherent anti-Stokes Raman scattering.

A method for noninvasively determining blood oxygenation in individual vessels inside bulk tissue would provide a powerful tool for biomedical research. We explore the potential of coherent anti-Stokes Raman scattering (CARS) spectroscopy to provide this capability. Using the multiplex CARS approach, we measure the vibrational spectrum in hemoglobin solutions as a function of the oxygenation state and observe a clear dependence of the spectral shape on oxygenation.

Comparison of subtractive Kramers-Kronig analysis and maximum entropy model in resolving phase from finite spectral range reflectance data.

The maximum entropy model (MEM) and Kramers-Kronig (K-K) analysis were compared with the aim of phase retrieval from reflectance. The object was to test two different phase-retrieval methods when reflectance is known at a finite frequency range and data fitting is not performed beyond the finite frequency band. In addition, it was assumed that the phase is known only at one or two anchor points.

Direct extraction of Raman line-shapes from congested CARS spectra.

We show that Raman line-shapes can be extracted directly from congested coherent anti-Stokes Raman scattering (CARS) spectra, by using a numerical method to retrieve the phase-information hidden in measured CARS spectra. The proposed method utilizes the maximum entropy (ME) model to fit the CARS spectra and to further extract the imaginary part of the Raman susceptibility providing the Raman line-shape similar to the spontaneous Raman scattering spectrum. It circumvents the challenges arising with experimentally determining the real and imaginary parts of the susceptibility independently.

Simulation on wavelength-dependent complex refractive index of liquids obtained by phase retrieval from reflectance dip due to surface plasmon resonance.

A method for the calculation of the wavelength-dependent complex refractive index of absorbing liquid from reflectance in the vicinity of surface plasmon resonance (SPR) is presented. The calculation is based on the maximum entropy method (MEM). As an example, phase retrieval from a simulated SPR reflectance of a red colored liquid solution is carried out.