Spectral Decomposition Methods for Coherent Raman Spectroscopy

Journal of the Optical Society of America B, 1990

We present a numerical method to calculate the real and imaginary parts of the complex third-order Raman susceptibility in the case when the squared modulus of the susceptibility is known.

ACS Omega

Raman spectra are molecular structure-specific and hence are employed in applications requiring chemical identification. The advent of efficient handheld and smartphone-based Raman instruments is promoting widespread applications of the technique, which often involve less trained end users. Software modules that enable spectral library searches based on spectral pattern matching is an essential part of such applications. The Raman spectrum recorded by end users will naturally have varying levels of signal to noise (SN), baseline fluctuations, etc., depending on the sample environment. Further, in biological, forensic, food, pharmaceuticals, etc., fields where a vast amount of Raman spectral data is generated, careful removal of background is often impossible. In other words, a 100% match between the library spectrum and user input cannot be often guaranteed or expected. Often, such influences are discounted upon developing mathematical methods for general applications. In this manuscript, we carefully examine how such effects would determine the results of spectral similarity-based library search. We show that several popular mathematical spectral matching approaches give incorrect results under the influence of small changes in the baseline and/or the noise. We also discuss the points to be carefully considered while generating a spectral library. We believe our results will be a guiding note for developing applications of Raman spectroscopy that uses a standard spectral library and mathematical spectral matching.

Talanta, 2007

Fourier transform Raman spectra of eight mixtures of four organic solids, namely dicyandiamide, melamine, acetamide and urea were measured. Matrices formed from these spectra were first subjected to singular value decomposition to obtain the right singular vectors. The right singular vectors were then subjected to blind source separation using band-target entropy minimization (BTEM), thus no a priori information (i.e. involving the nature of the components present, their spectra, nor their concentrations) was included in the analysis. The recovered pure component spectra are of exceptionally high quality and are consistent with pure reference spectra. Various empirical and statistical tests, such as the Euclidean norm and target transform factor analysis, were employed to assess the quality of the recovered spectra. The present results indicate the applicability of combined Raman and BTEM analysis for solid mixtures.

Spectrochimica Acta Part A: Molecular Spectroscopy, 1993

This paper reviews some of the differences between dispersive and Fourier transform (FTJ Raman spectroscopy with the goal of highlighting some of the advantages and disadvantages of FT-Raman spectroscopy. In particular, the use of filters, Connes advantage, trading rules and the size of the multiplex and throughput advantages are discussed. INTRODUC~I~N THE introduction of Fourier transform (FT) Raman spectroscopy [l-4] has brought a new impetus to Raman spectroscopy. It has allowed the study of materials that were previously "impossible" because of laser induced fluorescence and provides ready access to the extensive data handling facilities that are available with a commercial FT-IR spectrometer. The use of Fourier transform methods for Raman spectroscopy is conceptually different from classical methods that employ monochromators, although the end result, the spectrum, is the same. It is the purpose of this paper to review some of the differences between dispersive and FT-Raman spectroscopy and in the process to highlight some of the advantages and disadvantages of FT-Raman spectroscopy. DISCUSSION The use of filters Perhaps the most striking feature of the Raman effect is its intrinsic weakness. Typically,-1 in 103 photons is Rayleigh (elastically) scattered and only between-1 in 106 and 1 in 109 photons is Raman (inelastically) scattered. The result is that most of the light that enters the spectrometer is at the same frequency as the laser and only a very small proportion is of relevance to the Raman experiment. The problem is to observe the Raman signal in the presence of the huge background. One of the major differences between dispersive and interferometric Raman spectroscopy is the way that the laser line is rejected. On the dispersive instrument, this is accomplished by tuning the monochromator away from the laser line so it never reaches the detector. In FT-Raman spectroscopy it is reduced or eliminated by the use of a set of filters, such that the optical density at the laser line is at least six and usually nine or greater. The reason that the laser line has to be reduced to this extent lies in the type of noise it generates in the spectum. Figure 1 shows the root mean square (r.m.s.) noise in a FT-Raman spectrum, as a function of the square root of the laser power at the sample, measured in a spectral region free from Raman bands. The graph may be divided into two parts: at low laser powers the noise is independent of the signal, thus detector noise is the dominant noise source. However, at laser powers greater than about 150 mW, for this sample, the noise becomes dependent on the square root of the laser power and thus shot noise is now the dominant noise source. The key question is how does shot noise manifest itself in the spectrum? In dispersive spectroscopy the spectrum is recorded in the frequency domain and the noise is l Author to whom correspondence should be addressed.

2009

Raman spectroscopy is a powerful and effective technique for analyzing and identifying the chemical composition of a substance. Two types of Raman spectra estimation algorithms exist: supervised and unsupervised. In this paper, we perform a comparative analysis of five supervised algorithms for estimating Raman spectra. We describe a realistic measurement model for a dispersive Raman measurement device and observe that the measurement error variances vary significantly with bin index. Monte Carlo analyses with simulated measurements are used to calculate the bias, root mean square error, and computational time for each algorithm. Our analyses show that it is important to use correct measurement weights and enforce the nonnegative constraint in parameter estimation.

Applied Spectroscopy

Raman spectroscopy is used in a wide variety of fields, and in a plethora of different configurations. Raman spectra of simple analytes can often be analyzed using univariate approaches and interpreted in a straightforward manner. For more complex spetral data such as time series or line profiles (1D), Raman maps (2D), or even volumes (3D), multivariate data analysis (MVDA) becomes a requirement. Even though there are some existing standards for creation, implementation, and validation of methods and models employed in industry and academics, further research and development in the field must contribute to their improvement. This review will cover, in broad terms, existing techniques as well as new developments for MVDA for Raman spectroscopic data, and in particular the use associated with instrumentation and data calibration. Chemometric models are often generated via fusion of analytical data from different sources, which enhances model discrimination and prediction abilities as ...

Zeitschrift für Physikalische Chemie, 2011

A wavenumber and intensity calibration procedure of Raman spectra by using chemometric techniques is presented. This approach allows the fine tuning of calibration parameters and routines with the final goal to eliminate setup dependent differences within experimentally recorded Raman spectra. This seems to be necessary since more and more Raman databases are needed for different analytical tasks, like identification of minerals or bacteria. Minimizing the impact of the applied experimental Raman setup on the reference (database stored) Raman spectra allows the databases to be enlarged very easily by feeding the database with Raman spectra recorded with different setups. Furthermore the chemometric analysis performance increases due to the larger number and better quality of reference spectra.

Optics Express, 2006

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. Another important advantage of this method is that no a priori information regarding the vibrational resonances is required in the analysis. This permits, for the first time, the quantitative analysis of CARS spectra and microscopy images without any knowledge of e.g. sample composition or Raman response.

Journal of Molecular Structure, 1995

Spectrum of Raman noise level was studied on a multichannel spectrometer with LN cooled CCD detector. A mixture of Y-AMP and NiCl, in water was used as a model system containing Raman active molecules (N?+ Y-AMP*-macrochelates) in both dissolved and crystalline form. It has been find that the noise spectral dependence corresponds to the superposition of luminescence background spectrum and narrow bands at positions of the main difference between Raman spectra of the two forms.

Sosiaalipedagoginen aikakauskirja

Utopiat ja toisenlaisten maailmojen kuvittelu ovat tärkeitä yhteiskuntakritiikin välineitä. Kuvittelu ei kuitenkaan synny itsestään, vaan se on taito, joka vaatii harjoittelua. Tässä käytäntökuvauksessa tarkastellaan sitä, miten kuvittelua voi opettaa yliopistossa. Kuvaus pohjautuu sosiologian maisteriopiskelijoille suunnattuun "Harjoituksia poliittisessamielikuvituksessa" -opintojaksoon. Kuvauksessa pohditaan konkreettisten esimerkkien avulla taiteen piirissä kehitettyjen harjoitteiden soveltamista yhteiskuntatieteelliseen ajatteluun ja opetukseen sekä kriittisen ajattelun valmiuksien kehittämiseen. Pohdinta perustuu harjoitusten kuvauksiin, tutkijoiden opetustilanteista kirjoittamiin kenttäpäiväkirjoihin ja opiskelijoiden kurssipalautteisiin. Kuvittelu auttaa edistämään yhteiskunnallista muutosta sekä haastaa etsimään toisenlaisia tietämisen tapoja. Kuvittelu ja sen opettaminen edellyttää mahdollisen pedagogiikkaa, joka ei tarjoa valmiita vastauksia vaan etsii tapoja kur...