Fuzzy Logic And Raman Spectroscopy

Caiete Iesene, vol.1, ianuarie 2009, ISSN 2065-5576, pp.67-73

FUZZY LOGIC AND RAMAN SPECTROSCOPY By Laurenţiu Florin BUBUIANU Romanian Public Television, TVR Iaşi - Regional Television Station, 33 Lascăr Catargi, Iaşi, 700107, Romania, [email protected] (Received january 2009)

Abstract. Fuzzy logic is relatively young theory with the major advantage that it allows the natural description, in linguistic terms, of problems that should be solved rather than in terms of relationships between precise numerical values. This advantage (fuzzy logic can deal with complicated, undefined, vague systems, with a high degree of uncertainty in a simple way) is the main reason why fuzzy logic theory is widely applied in technique. In this paper we propose a fuzzy logic approach for sample differentiation using Raman spectroscopy in order to characterize various substances. Raman spectral imaging has been widely used for extracting chemical information from biological specimens, to provide information on chemical structures and physical forms and to identify substances from the characteristic spectral patterns. One of the challenges is to cluster the chemical groups from the vast amount of hyperdimensional spectral imaging data so that functionally similar groups can be identified. Raman spectra are relatively weak signals whose features are inevitably affected by various types of noises during its calibration process. Fuzzy logic has been widely used to solve uncertainty, imprecision and vague phenomena, and in this work a fuzzy filtering method is proposed to enhance the signal to noise ratio and for the classification of the substances into different categories. The further research objective is to create a real-time sensor for sample analysis using a Raman spectrometer for an autonomous robot. Keywords: A.I., Fuzzy Logic, Raman Spectroscopy, Filtering, Clustering, Pattern Recognition

1. Introduction Spectrometry is the spectroscopic technique used to assess the concentration or amount of a given substances based on interaction between radiation and matter as a function of wavelength. Spectroscopy / spectrometry are often used in physical and analytical chemistry for the identification of substances through the spectrum emitted from or absorbed by them. Most spectroscopic methods are differentiated as either atomic or molecular based on whether or not they apply to atoms or molecules. Along with that distinction, they can be classified on the nature of their interaction: absorption (atomic absorption, nuclear magnetic resonance etc.), emission (like luminescence and spectrofluorimetry) or scattering spectroscopy (measures the amount of light that a substance scatters at certain wavelengths, incident angles, and polarization angles). The scattering process is much faster than the absorption/emission process and one of the most useful applications of light scattering spectroscopy is Raman spectroscopy. Raman spectroscopy is a spectroscopic technique use in chemistry and physics to study vibrational and rotational modes in a system. When light interacts with matter, the photons which Fig. – Energy level diagram in Raman spectroscopy make up the light may be absorbed or scattered, or may not interact with the material and may pass straight through it. If the energy of an 1

Caiete Iesene, vol.1, ianuarie 2009, ISSN 2065-5576, pp.67-73

incident photon corresponds to the energy gap between the ground state of a molecule and an excited state, the photon may be absorbed and the molecule promoted to the higher energy excited state. It is this change which is measured in absorption spectroscopy by the detection of the loss of that energy of radiation from the light. Raman spectroscopy relies on inelastic scattering of monochromatic light (a laser beam in the visible, infrared or ultraviolet range); the laser lights interacts with systems resulting in the energy of the laser photons being shifted up or down (as shown in fig.1). Thus, the shift in energy gives valuable information about the phonon modes in the system. In physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. Phonon plays a major role in many of the physical properties of solids, including a material's thermal and electrical conductivities. Raman spectroscopy is commonly used in chemistry, since vibrational information is specific for the chemical bonds in molecules. It therefore provides a fingerprint by which the molecule can be identified. For instance, the vibrational frequencies of CO and CO 2 can be Fig.2 – Raman spectrum of polyethylene terephthalate identified (using notch or edge filters for laser beam) and assigned on the basis of normal coordinate analyses using infrared and Raman spectra. In fig.2 is shown the characterization of thin coatings on polyethylene terephthalate (PET) using Surface-enhanced Raman scattering (SERS) and in fig.3 the Raman spectrum of elemetal sulphur obtained with green argon laser (514nm) spectrometer. Raman gas analyzers have many practical applications, being commonly used in modern medicine for real-time monitoring of anaesthetic and respiratory gas mixtures during surgery. Samples can be examined as solids, liquids or vapours state, in hot or cold states. Raman scattering is less widely used than infrared absorption due to sample degradation and fluorescence, but the number of applications growth because instrument parameters are few, spectral manipulation is minimal and a simple interpretation of the data are sufficient. Within the past decades, several variations of Raman spectroscopy have been proposed and developed and many are used today. The usual purpose is to enhance the sensitivity, to improve the spatial resolution, or to acquire very specific information. The Raman spectra identification of an unknown substance is based on the Fig.3 – Raman spectrum of elemental sulphur obtained comparison between an unknown experimental with 514.5nm (argon laser beam) spectrometer spectrum, and pattern spectra. Frequently the comparison is made by the spectroscopist by visual inspection, but this is slow and imprecise and moreover the Raman spectrum is inevitably affected by noise (background, flicker, readout etc.) which introduces ambiguity into the correlation values. 2. Pattern-Recognition (in Raman Spectroscopy) using Fuzzy Logic Spectrometry is the spectroscopic technique used to assess the concentration or amount of a a particular substance in a sample. As we know Fuzzy Logic provides a simple way to draw conclusions from imprecise data, so we can design a fuzzy identification system based on the following statement: when the correlation between the unidentified and the pattern is enough high, the analysed substances is recognized as the chemical substances which corresponds to this pattern. 2

Caiete Iesene, vol.1, ianuarie 2009, ISSN 2065-5576, pp.67-73

The Raman instrument consist of the laser (in this case argon laser with excitation lines between 350nm and 700nm, usually 514nm and 60mW), optics, spectrometer, CCD or CMOS detector and computer. Laser beam is focused on the sample and the dispersed light is read and transmitted by the CCD/CMOS sensor to spectrometer for range detection. First we need to locate the wavenumber position of the Raman bands, automatically or even by hand (local maximum detection). After that, the identification of the unknown spectrum is done by searching the coincidence of the Raman bands of the reference spectra using fuzzy logic. Fuzzy Logic incorporates a simple, rule-based “IF X AND Y THEN Z” approach to a solving control problem rather than attempting to model a system mathematically. The fuzzy logic model is empirically-based, relying on an operator's experience rather than their technical understanding of the system. A fuzzy system is a static nonlinear mapping between its inputs and outputs. A fuzzy system is composed of the following four elements: • A fuzzification mechanism, which convert crisp inputs to into fuzzy sets • A set of If-Then rules (fuzzy rule base - a linguistic description of experts knowledge) • An inference mechanism (fuzzy inference engine) which emulates the expert’s decision making • A defuzzification interface which convert the fuzzy results from inference mechanism Fig.4 –Fuzzy system – block diagram to crisp outputs for the process The mapping of the inputs to the outputs for a fuzzy system can be characterized by a set of conditions (modus ponens):

If premise Then consequent The inference mechanism determine the extend to which rule is relevant to the current situation as characterized by the inputs and draw the conclusion using the inputs and the information in the rules-base. To estimate a the degree of similarity between two spectra we use a correlation coefficient computed as follows, using experimental data e( i) and library data sets l (i ) [1.1]

K el =

∑ ( e(i) − m ) ⋅ ( l (i) − m ) e

l

i

∑ ( e(i) − m ) e

i

2

⋅

∑ ( l (i) − m )

2

l

i

where me and ml represent the mean values of data sets e( i) and l (i ) . As we can see, the higher the coefficients are the more similar spectra are. The proposed fuzzy logic systems maps the nonlinearly crisp inputs (crisp data sets obtained using Raman spectroscopy), into a crisp outputs: identification or not of the analyzed substance. For fuzzification of correlation coefficient we chose three fuzzy logic linquistic variables Low, Medium, High, each of them defined with a membership function associated (as shown in fig.5). Similarly, for output we choose two linquistic variables identified and non-identified, defined with linear membership function (fig.6). The experimental Raman spectrum is read as a vector of N points where e(i ) correspond to the intensity for the defined wavenumber. Because the Raman bands depend on instrumental conditions (spot of the laser, wavelenght, time of exposure), which can change for different Fig.5 – Membership function for input data 3

Caiete Iesene, vol.1, ianuarie 2009, ISSN 2065-5576, pp.67-73

measurement, even with the same spectrometer, we first need to normalize the obtained data. In practical situations we can try to identify a complex substance, a mixture of two or more elemental chemical substances. In that case the measured Raman spectrum can contain a mixture of two or more individual spectrum, corresponding to elementary substances, and the value of membership function for output fuzzy variable is clearly between 0 and 1, so for calculation of the degree of similarity, between experimental and library spectrum, and correctly identify the chemical substances based on Raman spectrum we use the centroid method. 3. Conclusion Fig.5 – Membership function for output data

In this work we show a procedure used for substance detection, using Raman spectroscopy and fuzzy logic. The experimental results show that fuzzy logic offers a versatile technique, easily overcoming ambiguous situations which could be produced by noise or mixture of two or more elemental substances. Raman spectroscopy provides detail information on molecular structure and chemical composition of the samples and fuzzy logic provides the mathematical background for problem solving under the conditions of uncertainty and imprecision. The whole procedure includes experimental spectrum capturing and calibration, normalization of input data, noise filtering and pattern recognition using fuzzy logic. The further work objective is to develop a real-time sensor for sample analysis using a Raman spectrometer for an autonomous robot.

REFERENCES [1] Dennis H.Rouvray, Fuzzy Logic in Chemistry, Academic Press, 1997 [2] J.D.Wineforner, Raman Spectroscopy for Chemical Analysis, vol.157, Wiley, 2000 [3] Timmothy J.Ros, Fuzzy Logic With Engineering Applications 2nd Edition, Wiley, 2004 [4] Didier Dubois&, Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, Springer , 2005 [5] Jan Jantzen, Foundations of Fuzzy Control, Wiley, 2007 [5] J.G.Carbonell&, Applications of Fuzzy Sets Theory, 7th International Workshop on Fuzzy Logic, Springer , 2007 [7] Jyh Shing Roger Jang , Neuro-Fuzzy and Soft Computing, Prentice Hall, 1997 [8] Hung T.Nguyen&, A First Course in Fuzzy and Neural Control, CRC Press, 2003 [9] Markus C.Hemmer, Expert Systems in Chemical Research, CRC Press, 2008

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