3. Spectroscopy

Ferenc FirthaCorvinus University of Budapest

Faculty of Food ScienceDepartment of Physics and

Control

1. Colour: what like?

quick, but contact :-> average RGB/Lab/Lch

remote sensing + data reduction: -> position: colour, shape, pattern

2. Image processing: where?

4. Spectral imaging: where and what?

remote + stat. analysis + image processing-> position: distribution of compounds

contact + statistical analysis:NIR -> water, fat, oil, protein,…

3. Spectroscopy: what?

Place of spectroscopy

Light as

Electromagnetic wave:

ν excitation frequency + c velocity λ wavelength:

~ 300 000 km/s

Some ranges:• radio (30kHz–30MHz): λ big 30MHz• TV (50-1000MHz), GSM (380-1900MHz)300MHz• radar / WiFi, LAN, SAT 3GHz• microwave oven (water: 18-27GHz) 30GHz• IR, VIS, UV 300THz• X-ray (<1nm), gamma (<1pm): E big 300PHz

Photon:

Quantum theory: Energy of wave packet andν frequency:

h: Planck constant

Mass:

vc

vhE

2cmE

Electromagnetic ranges

Interactions of light

Absorption: of chemical components

Transmission: getting through

Reflection: specular (reflexió)diffuse (remisszió)scattering (physical properties)

Emission: after inducing (atomic level)

Measuring:

Transmission Absorbance

Reflection Absorbance

Fraunhofer lines (1814)

absorption lines in sunlight thousands of lines

Transmission spectrum of blue sky

- emission spectra- absorption spectra, absorption lines

Explanation: energy levels of hydrogen atom:

1. Atomic emission spectroscopy

Flame or inductively excited atoms and ions emit EM radiation. Spectrum is characteristic to the different energy levels of electrons, atomic components

emission spectraof elements (VIS)

2. Refraction

•refraction of X-ray or electron ray

CT: Computed Tomography3D type of x-ray by examining slices from various angle

3. Raman spectroscopy

sample is illuminated with a laser beamradiation from the illuminated spot is collectedwavelength of laser (Rayleigh scattering) is filtered outshift of frequency is measured

Energy-level diagram (line thickness is proportional to the signal strength)

4. Scattering

•Scattering image of laser beamis characteristic to the physical structure,like cell walls, rheological properties

5. Absorption spectroscopy

Let’s go back to the sunlight: there are also valleys, not only absorption lines

Explanation

In a molecule, the atoms can rotate and vibrate respectively to each other. These vibrations and rotations also have discrete energy levels, which can be considered as being packed on top of each electronic level.

Water absorption:

- electronic: UV < 200nm Intramolecular transitions restricted by hydrogen bonds:

- vibrations: IR 1µ-10µ

- rotations FIR 10µ-1mm

- intermol. vibrations MW 1mm-10cm

1. Spectral lines are broader causing overlap of many of the absorption peaks

2. Overtones and combinations also appear

VIS 380-780nm

flavonoid, anthocyaninblackberries, red grapes, red cabbage, red onions, beets, radishes

carotenoidcarrot, tomato, lemon,orange, spinach, corn

quinone mushroom

pyrrole chlorophile

melaninskin

Chem: http://www.kfki.hu/chemonet/hun/eloado/kemia/festek2.htmlKép : http://www.healthymoncton.com/taste-the-rainbow-why-we-want-to-eat-fruits-veggies-from-all-of-the-colours-of-the-rainbow/

Cranberry juice (anthocyanin)

β,β-carotene degradation

melanin

VIS

chlorophyll

NIR range (NIR: 780-2500nm, MIR: 2,5-15µm, FIR: 0,015-1mm)

Absorption comes from the O-H, C-H, N-H bonds: water, hydrocarbon, lipid, protein, alcohol, etc. Food Science

lipids:triacilglicerin (fat)

alcohol: metil,etil,propil…

protein

water free / bound: HDW (hydrofil) / LDW (hydrofob)

amid, amin

secondary amid

aromatic alcohol: e.g. benzyl

NIR 900–1700nmOH: 970, 1450, 1980Fiber: 1100, 1300, 1350, 1403, 1483, 1500, 1534Cellulose: 1490Lignin (wood): 1170, 1410, 1417, 1420, 1440

aromatic hydrocarbon: e.g. benzene

dckeII )(0

TI

IA 0lgdcII )(

0 10

303.2k ε: molar absorptivity (moláris abszorpciós tényező)

dcA

Absorbance: Lambert-Beer law

Absorbance is proportional:

to length (Bougue, 1729)

and concentration (Beer, 1852)

How to measure absorption?

1.Absorption spectroscopy:

Transmittance:

let’s suppose that reflectance is zero

TI

I

TA 0lg

1lg

0I

IT T

2. Reflection spectroscopy:

Absolute reflectance: all reflected / incidence

Reflectance (reflection factor): sample / standard

RI

I

RA 0lg

1lg

0I

IR R

0I

IR x

xI

I

RA 0lg

1lg

Questions: non-homogen grain inspected uneven surface sample rotated

Reflection spectroscopy

geometry:

•45/0 (illumination/observation)

•d/8

angle of view: usually 2 or 10 degree

Reflectance standards (VIS..NIR) d/8 geometry

Instrumentation

Snell (1620) refractionNewton (1666) spectrum: birth of spectroscopyBougue, Lambert (1729) absorbance

1. Spencer spectrometer (1868), spectroscope Hartley (1880) chemical analysis of mixturesBeer (1852)

A gas jet (C) is positioned at the right hand side of the picture along with a sample holder (B).In the foreground a candle (F) is illuminating an arbitrary scale that is reflected off the back surface of the prism and is superimposed on the spectrum when viewed through the telescope.

Some laws of spectroscopy

Kirchhoff (1860) 1.radiation of solid is continuous (black body)2.radiation of gas consist of lines3.solid in gas: has missing lines

Stefan (1879) black-body radiant exitance is proportional to the fourth power of its Th. temperature

Wien (1896) Displacement is inversely proportional to the temperature. Distribution:

Planck (1900) describes the complete spectrum of thermal radiation:

2. Spectrophotometer

Light source: electrically heated Nernst glower ()Mirror,lens,cuvette: alkali-halid glass (alkáli-halogenidből)Monochromator: gratingDetector: thermal / pyroelectric / photoconducting

3. FT-NIR (Fourier transform infrared spectroscopy)Interferometer:

Combination of wavelengths interferogram Responses to different combinations recontruction of spectrum

interferogram

How to process spectrum?

normalization: get spectra set to same level•Standard Normal Variate (SNV): subtract mean and devide by variance

smoothing: before differentiation•Moving average•Savitzky-Golay: polinomial regression

derivatives: to eliminate shift of peaks 1. kind of normalization 2. curvature (görbület)

assignation: of compounds - statistical models, like PLS, DA - artificial neuron network

Statistical analysis of spectral data

a.) Principal Component Analysis (PCA): Dimension reduction (not supervised)Finds the main axes (eigenvalues) of data space, those separate best data points.These PCs come as the linear combination of n dimensional source space.

PCA:

b.) Fisher’s Discriminant Analysis (FDA): Dimensionality reduction and classificationFinds a linear combination of features, which separates two or more classes.Steps: finds linear/quadratic classifier -> dimensionality reduction -> classification

•Analysis of Variance (ANOVA): categorical independent and continuous dependent variables•Fisher’s Discriminant Analysis (FDA): continuos independent and categorical dependent variables•Discriminant Correspondence Analysis: categorical independent and categorical dependent variables•Partial Least Squares (PLS) continuous independent and continuous dependent variables

LDA: QDA:[loadings,scores] = princomp(X); % coeff of linear combinations[Z,W] = FDA(X, Y, 2); % dimensionality reduction by FDA scriptcqs = fitcdiscr(X,Y,'DiscrimType','quadratic'); % create classifier

c.) Partial Least Squares (PLS) regression builds a linear modell between

• X source space (independent variables) and absorbance on different bands• Y target space (dependent, predicted variables) like moisture, fat, protein content

Inside, it makes a PCA on X space, a PCA on Y space, then builds a linear regression between the first p dim (latent variables, factors) of two PCA spaces.

The optimal number of latent variables are determined by cross validation (building model on calibration data set, then checking prediction on validation set) on the base of minimal Root Mean Squared Error of Prediction(RMSEP):

n

oyRMSEP ii

2)(

number of latent variables[XL,YL, XS,YS, beta, PCTvar, mse] = …plsregress(X,Y, LVno, 'cv',20, 'mcreps',10000);

The coefficient of determination (r2) characterizes the efficiency of PLS model.

The significant wavelengths can be assigned by the loading values of regression.

Loading values of enzym and fat content in cheese

d.) Partial Least Squares Discriminant Analys (PLS DA): variant for classification

PLS-DA consists in a classical PLS regression,where the response variable is a categorical one (replaced by the set of dummy variables describing the categories) expressing the class membership.

PCA space is rotated so that a maximum separation among classes is obtained, and to understand which variables carry the class separating information. (Camo)

3D score plot of a two-class PLS-DA model of GREEN versus RED/BLUE:

e.) Orthogonal PLS DA (OPLS-DA)

Class-orthogonal variation is combinedwith traditional PLS-DA.It gives better performance if such within-class variation exists.(J.of Chemometrics)

pls_model = pls(x,y,vl,'da');

Matlab toolboxes, like Eigenvector

other chemometric tools: SIMCA-P, Unscrambler, R (gnu), …

Artificial neural networks (ANN): for industrial application

used to connect some input cells (sensors) with some output cells (actuators). •like statistical models they are teached on calibration set, then tested on validation set•contrary to statistical models they use non-linear relations, with much more efficiency

ANN is a black box. We don’t exactly know, how it works, but it works well. They are used therefore mostly not in scientific work, but for industrial applications.

Multilayer back-propagation neural network (MBPN):Using calibration data set, weight values of synapses are set backwards (output to input) in every cycle to get less error in prediction.

logistic function:HIDDEN layers

Some NIR application on food:

moisture, protein in cereals (Norris, 1950) moisture, fat, protein in meat (Kaffka, 1983)

sugar, acidity in fruits, sorting systems food quality control in lab: any compound

Thank you for your attention