Time-resolved NIRS and non-destructive Titolo presentazione - PowerPoint PPT Presentation

Time-resolved NIRS and non-destructive Titolo presentazione assessment of food quality sottotitolo Lorenzo Spinelli, Alessandro Torricelli Milano, XX mese 20XX Dipartimento di Fisica – Politecnico di Milano Winter College on Applications of Optics and Photonics in Food Science 20 February 2019

Outline • Lecture 1 (Alessandro Torricelli) 9-10 am • Basics of TD NIRS • Lecture 2 (Lorenzo Spinelli) 10-11 am • Application of TD NIRS to food quality assessment • Coffee break 11:00-11:30 am • Discussion 11:30-12:30 • What does affect TD NIRS? • Questions & Answers 2

Outline • Lecture 1 (Alessandro Torricelli) 9-10 am • Basics of TD NIRS • Introducing the PHOOD lab @ PoliMi • Modelling light propagation in food • CW and TD NIRS • Instrumentation for TD NIRS 3

Politecnico di Milano (PoliMi) Teaching & Research University PoliMi since 1863 1863 – 2019 156 years Engineering Architecture Design 4

Photonics for Health, Food, and Cultural Heritage Dipartimento di Fisica – Politecnico di Milano Professor Emeritus: Rinaldo Cubeddu Full professors: Antonio Pifferi Paola Taroni Alessandro Torricelli Gianluca Valentini Associate Professors: Andrea Bassi Daniela Comelli Davide Contini Cosimo D’Andrea Alberto Dalla Mora Assistant Professors: Rebecca Re Laura Di Sieno IFN-CNR Lorenzo Spinelli (CNR) Andrea Farina (CNR) Austin Nevin (CNR) Post-Docs: Lina Qiu Alessia Artesani + PhD Students (11) + Facilities (mechanic and electronic workshop) 5

Photonics for Health, Food, and Cultural Heritage Dipartimento di Fisica – Politecnico di Milano Health  In vivo Tissue Spectroscopy  Optical Mammography  Tissue Oximetry and Functional Imaging of the Brain  Fluorescence Lifetime Imaging in biology and medicine Food  nondestructive assessment of internal defects by pulsed NIR  nondestructive maturity assessment at harvest Cultural Heritage  Photoablation and Material Processing  Fluorescence Spectroscopy and Imaging  Multispectral Imaging and Colorimetry 6

Photonics for Health, Food and Cultural Heritage Laboratories Time-resolved systems  mode-locking of dye, gas and solid state lasers  time-correlated single-photon counting (TCSPC)  time-gated imaging Spectral-domain  tunable laser sources  broadband detectors Spatial-domain  scanning systems or camera  multi-channel systems Temporal-domain  fast acquisition rate • functional near infrared spectroscopy - fNIRS Lab • diffuse spectroscopy - DiffS Lab • optical mammography - Mammot Lab • molecular imaging - Molim Lab • near infrared spectroscopy for food - NIRf Lab • imaging spectroscopy for cultural heritage - ARTIS Lab • ultras for biomedicine - UB Lab 7

Can light penetrate biological tissues? Georges de La Tour (1593 – 1652) St Joseph (1642) Louvre, Paris Thanks to Marco Ferrari (UnivAQ) 8

Light absorption in the near infra-red (NIR): biological tissue The therapeutic and diagnostic window 9

Light absorption in the near infra-red (NIR): fruit 10

Visible (VIS) and near infrared spectroscopy (NIRS) : continuous wave (CW) approach VIS: 400-700 nm (nondestructive assessment of EXTERNAL properties) NIR: 700-3000 nm (nondestructive assessment of INTERNAL properties) Rich Ozanich, Berkeley Instruments Inc., Richland, WA 11

Visible (VIS) and near infrared spectroscopy (NIRS) : continuous wave (CW) approach HL200 Ocean Optics ≈ 1000 € Notebook ≈ 1000 € USB4000 Ocean Optics ≈ 2000 € DA-meter, courtesy of P. Rozzi, Sinteleia (Italy) Spider, courtesy of Manuela Zude ATB Potsdam (Germany) 12

Light propagation in diffusive media: absorption and scattering clear diffusive Absorption: related to tissue components Absorption coefficient: µ a = 1/ l a (cm -1 ) Scattering: related to tissue structure Scattering coefficient: µ s = 1/ l s (cm -1 )  interplay between light absorption and light scattering 13

Lambert-Beer law Light attenuation in a THIN diffusive medium Clear medium Diffusive medium (b) turbid medium (a) clear medium I OUT = I IN exp(- µ a L) I OUT = I IN exp(- µ t L) I IN I IN µ t = µ a + µ s L L Scattering coefficient     I ( ) L I   = ln = µ   = ln = µ + µ out out Lambert A L A     a a s     I I in in µ = ε Beer C a Valid only if µ t L < 1 (Single scattering regime) • • Scattering coefficient is unknown = ε Lambert-Beer A CL • Pathlength is unknown 14

Modelling photon migration in diffusive media Radiative Transport Equation (RTE) Conservation of energy in a small volume dV in a given direction s [ n dV d v is the expected number of photons in the n = photon (angular) density volume dV about r, with velocity in d v about v , at time t] ∂ n ′ = − • ∇ − µ − µ + µ • ) Ω + ε ∫ ˆ ˆ ˆ v s n v n v n v p ( s s n d ∂ a s s t π 4 (1) (2) (3) (4) (5) Light source Photons absorbed Photons in Photons out s Photons scattered to dV another direction Photons scattered from another direction ( s ’) to direction of interest ( s ) 15

The RTE for the Radiance ∂ ) ˆ r s 1 L ( , , t ′ ′ = − • ∇ ) − µ + µ ) + µ • ) ) Ω + ) ˆ ˆ ˆ ∫ s s s ˆ ˆ ˆ ˆ s L ( r , s , t ( ) L ( r , s , t p ( L ( r , , t d q ( r , s , t ∂ a s s v t π 4 = ν ˆ ˆ L ( r , s , t ) h v n ( r , s , t ) [ W m -2 sr -1 ] [ W m -3 sr -1 ] = ν ε ˆ ˆ q ( r , s , t ) h ( r , s , t ) 16

Solutions of the RTE RTE Expansion methods • P N approximation: Stochastic methods P 0 = Diffusion (1989) • Monte Carlo (1987) P 1 = Diffusing Wave P 3 = … Hybrid methods Discretisation methods • Paasschens (1997) • Discrete ordinates • 2-flux or Kubelka-Munk • Adding-double method Note: The year represents the first use of the method in the field of Biomedical Optics • Finite Element Method (1993) 17

P N Approximation • Expansion of the RTE terms into spherical harmonics to separate the position and directional variables + ∞ + 2 l 1 l = φ ∑ ∑ ˆ ˆ L ( r , s , t ) ( r , t ) Y ( s ) π l , m l , m 4 = = − l 0 m l • P N approximation truncates the expansion to the N-th term obtaining a set of N+ 1 independent equations • P 1 approximation is typically used in Photon Migration studies 18

P 1 Approximation 1 ( ) 3 ( ) s ≈ Φ + • ˆ ˆ Φ = ∫ Ω L ( r , s , t ) r , t J r , t Fluence ˆ ( r , t ) L ( r , s , t ) d π π 4 4 4 π ( ) 1 ≈ ˆ q ( r , s , t ) S 0 r , t Flux = ∫ Ω π ˆ ˆ J r s r s 4 ( , t ) L ( , , t ) d 4 π 1 3 ′ s • ≈ + µ ˆ ˆ p ( s ) g π π 4 4 Inserting in the RTE and integrating over Ω we get ∂ Φ ) 1 ( r , t = −∇ • ) − µ Φ ) + ) (1) J ( r , t v ( r , t S ( r , t ∂ a 0 v t and integrating over Ω we get ˆ s Inserting in the RTE, multiplying by ∂ ) 1 J ( r , t 1 µ′ = − ∇ Φ ) − µ + ) ( r , t ( ) J ( r , t (2) ∂ a s v t 3 µ′ = − µ Reduced scattering coefficient [ m -1 ] ( 1 g ) s s 19

Diffusion Equation ∂ ) 1 J ( r , t 1 µ′ = − ∇ Φ ) − µ + ) ( r , t ( ) J ( r , t ∂ a s v 3 t Under the assumptions ∂ ) The relative variation of the flux is smaller than 1 J ( r , t µ′ << v ) ∂ s the scattering rate! J r ( , t t v= 0.03 cm/ ps, µ ’ s = 10 cm -1 , v µ ’ s = 0.3 ps -1 We obtain the Fick’s Law ( ) ) = − ∇ Φ ) = ′ µ Diffusion coefficient [ m] J ( r , t D ( r , t D 1/ 3 s Substituting into (1) we obtain the Diffusion Equation ∂ Φ ) 1 ( r , t − ∇ Φ ) + µ Φ ) + = ) 2 ( r , ( r , ( r , D t t S t a ∂ 0 v t 20

Steady state (or continuous wave, CW) Diffusion Equation Neglect time dependence − ∇ Φ ) + µ Φ ) = ) 2 D ( r ( r S ( r a 0 Point source solution for infinite medium   µ 1   ) = δ ) Φ ) = − − a S ( r ( r ( r exp r r   0 0 π − 0 4 D r r D   0 O r r 0 r-r 0 21

CW NIRS 1/2 Collimated source Point source solution ) = δ ) − δ − ) r S ( ( z ( z 0 0 0 z 0 r r z 0 z 0 = ( µ s ’) -1 = l s z z Cylindrical coordinate system with radial simmetry Φ ) = Φ ϕ ) = Φ ) r ( ( r, ,z ( r,z     µ µ ( ) ( )     − + − 2 − + + 2 2 2 a a exp r z z exp r z z     0 0 D D     1 1 Φ ) = − ( r π ( ) π ( ) 2 4 D 4 D + − + + 2 2 2 r z z r z z 0 0 22