Impact of measurement configurations on the performance of empirical pre-processing techniques used in NIR calibrations

1. Impact of measurement configurations on the performance of empirical pre-processing techniques used in NIR calibrations Suresh N. Thennadil

2. Goal • An integrated approach for maximal extraction of information of suspensions and powders using vis-NIR spectroscopy. • Combine: • Measurement strategies – Optimal configuration • Physics – Light propagation and scattering theories • Multivariate calibration techniques

3. Introduction • Multivariate calibration models (PCR, PLS) for estimating concentrations of chemical species in suspensions and powders using NIR spectroscopy. • Complications due to light scattering – Pathlength variations. • Non-linear and confounding effects. • Variations depend on particle size, size distribution, shape and particle concentration.

4. Introduction • Empirical pre-processing techniques to reduce/eliminate light scattering effects. • Derivatisation • Multiplicative Scatter Correction (MSC) • Extended Multiplicative Scatter Correction (EMSC) • Standard Normal Variate (SNV) • Orthogonal Signal Correction (OSC)

5. Introduction • Empirical pre-processing techniques fairly effective in cases where sample-to-sample scattering variations are not too large. • Range of applicability – Under what situations and how well they work. • Efficacy – Which one works best. • Reducing light scattering variations through judicious design of sample-instrument interface could improve performance of multivariate calibration models.

6. Measurement configurations • Transmission Measurement It I0 ℓ a– Absorption cross-section; s - Scattering cross-section; ρ- Number density (concentration).

7. Idt I0 I0 Idr Measurement configurations • Total Diffuse Transmission • Total Diffuse Reflectance

8. d1 d2 Measurement configurations • Fiber-optic Reflectance Configurations d2 d1

9. Objectives • Compare performances of pre-processing techniques and how they are affected by choice of measurement configuration. • Total Diffuse Transmittance • Total Diffuse Reflectance • Generate data for a model system using simulations.

10. Objectives • Detailed investigation of performance of pre-processing techniques and optimal configuration will require: • Extensive experimental data – difficult to obtain. • Simulations accurately mimicking light transport through particulate media. • Fundamental light propagation models and light scattering theories. • Necessary for long-term objective of integrated optical design.

11. Light Propagation -Theory • The exact Transport Equation: - Specific intensity. - Bulk extinction coefficient. - Bulk scattering coefficient; - Bulk absorption coefficient p(ŝ,ŝ’) - Phase function; - Source term

12. Light Propagation - Theory • The phase function is usually represented as a function of scattering angle θ and anisotropy factor g(= <cosθ>). • Henyey-Greenstein function: • a and scan be written in terms of the individual species in the sample: a– Absorption cross-section; s - Scattering cross-section;  - Wavelength of incident radiation; ρ - Number density (concentration).

13. Light Propagation - Theory • For spherical particles, exact values of Fandg from Mie theory. • For hard-spheres, the Percus-Yevick approximation for S. • Need n() and k().Given these a, s and g can be calculated and the equation of transfer can be solved. F - Differential scattering cross-section; D - Characteristic dimension of the particle; S- Static structure factor; f(D) - Fraction of particles of size D; m - Complex refractive index of particle: m() =n() + i k()

14. Solving the Transport Equation • The following methods have been used to solve the equation of transfer: • The Discrete-Ordinate Method • The Adding-Doubling Method • Monte Carlo Simulations • The Adding-Doubling method - Most convenient for calculating total diffuse Transmission (TD) and Reflectance (RD).

15. Model System • System consisting of 4 chemical species • Species A – spherical monodisperse particles suspended in a liquid mixture of species B, C and D. • Volume fraction of A varied from 0.01 - 0.1. Particle radius 100 – 500nm. • B: Vol. Fr. 0 – 0.015 (0 – 10 g/l). • C: Vol. Fr. 0.2 – 0.4 (220 – 442 g/l) • D: Vol. Fr. 0.52 – 0.77 (518 – 763 g/l)

16. Optical Constants of Model Species

17. Normalised Pure Component Spectra

18. Data Sets • Calibration set – 50 samples • Validation set – 20 samples • Test set – 40 samples • Wavelength range: 1450 - 1850nm • Total diffuse transmittance and reflectance through a 0.5 mm sample thickness. • Total diffuse reflectance for very thick (100mm) sample.

19. Total Diffuse Transmittance Spectra – 0.5mm sample thickness

20. Total Diffuse Reflectance Spectra – 0.5mm sample thickness

21. Total Diffuse Reflectance Spectra – 100mm sample thickness

22. Scatter correction methods considered • Multiplicative Scatter Correction (MSC) • Extended Multiplicative Scatter Correction (EMSCW) • EMSCWP

23. Modified EMSC - EMSCL • Scattered intensity as a function of wavelength for larger particles may be approximated by ab. • Then wavelength dependence term in log units will be d*log(). • Replacing quadratic wavelength dependence in EMSCW with log term:

24. “Noise-Free” Measurements - Td

25. “Noise-Free” Measurements – Rd (.5mm)

26. “Noise-Free” Measurements – Rd (100mm)

27. “Noisy” Measurements • RMS noise in absorbance units: • 0 – Dark current current RMS noise • I0 – Intensity of incident light • 0/ I0 = 4.5e-6 so that A≈ 20A at 1 Au. • Noise added at each  by drawing from a Gaussian distribution of mean 0 and standard deviation A.

28. “Noisy” Measurements - Td

29. “Noisy” Measurements – Rd (.5mm)

30. “Noisy” Measurements – Rd (100mm)

31. Summary and Conclusions • Simulations of diffuse transmission and reflectance measurements of a model system were carried out by solving the “exact” equation of light transport using the adding-doubling method. • Analysis indicates: • Performance of empirical pre-processing techniques could be significantly affected by measurement configuration. • It may be possible to obtain better calibration models by choosing the optimal measurement configuration. • An integrated approach to optical design which takes the pre-processing and calibration steps into consideration can lead to significant improvements in information extraction.

32. Acknowledgements • This work was funded by the Engineering and Physical Sciences Research Council (EPSRC).