Rapid estimation of optical properties from diffuse reflectance signalsLászló Baranyai*, Dénes Lajos Dénes, József Felföldi

SZIE Faculty of Food Science, Department of Physics and Control, H1118 Budapest, Somlói u. 14-16. http://fizika.etk.szie.hu/ *Corresponding: Baranyai.Laszlo@etk.szie.hu

Diffuse reflectance (backscattering) imaging is of great interest dueto the quick and non destructive measurement method. Opticalproperties of the biological material affect significantly the diffusereflectance signal. Refractive index, absorption- and scatteringcoefficients (1/cm), anisotropy factor can be used to build models ofbackscattering. Especially absorption- and scattering coefficients areknown to successfully describe maturity, moisture content, physicaldamage (bruising), soluble solids content (SSC) and similarimportant postharvest technology parameters. Inverse modeling wasapplied to estimate primary optical attributes of tissue and derivedparameters such as penetration depth and diffusion coefficient.Inverse modeling was performed with the reference of Farrell-Patterson-Wilson diffusion theory model. Descriptive signal featuresof Full Width at Half Maximum (FWHM), slope of logarithmic profile,and advanced feature of width of intensity range rings aroundincident point were utilized.Rapid calculation is required for practical applications instead ofaccurate but time consuming nonlinear curve fitting. Presentedmethods may offer new options to estimate optical properties of foodand raw material.

Materials and Methods

Analysis of light penetration into biological tissue was based on thediffusion theory model [1] and Monte Carlo simulation. Diffusiontheory model is calculating intensity as function of radius measuredfrom light incident point. The model has three important parameters:● absorption coefficient (1/cm): μ

a

● scattering coefficient (1/cm): μs’ = [1-g]×μ

s

● tissue optical property: AThe function is computed as:

where

and

More common parameters are derived from tissue optical properties:● diffusion coefficient: D ~ 1/μ

t

● penetration depth: H ~ 1/μe

Monte Carlo simulation was run to ray-trace photon packages [2,3].This technique takes additional attributes into account, such as lightbeam diameter, beam intensity distribution, internal structure,anisotropy factor. Computation of Monte Carlo simulation takeshours, it may be used only in inverse modeling, not suitable for curvefitting.

Statistical analysis was performed using R [4] and RStudio. Modelswere evaluated according to determination coefficient (R2), RMSEP,ANOVA F value, Durbin-Watson autocorrelation test.

References

[1] Farrell, Patterson & Wilson. Medical Physics, 1992, Vol.19(4):879- 888[2] Baranyai & Zude. Progress in Agricultural Engineering Sciences, 2008, Vol.4(1):45-59[3] Zude & Baranyai. Computers and Electronics in Agriculture, 2009, Vol.69(1):33-39[4] R Foundation for Statistical Computing. Vienna, Austria, 2016.

I (r)= a '4π [ 1μt (μe+ 1r1 ) exp (−μer1)

r12 +( 1μt + 4 A3μt )(μ e+

1r2 )exp (−μer2)

r22 ]

r1=[( 1μt )2

+r2]1/2

r2=[( 1μt+ 4 A3μt )2

+r2]1/2

μe=[3μa(μa+μs ' )]1/2μt=μa+μs 'a '=μ s ' /(μa+μs ' )

Results and Discussion

Absorption and scattering coefficients were selected close to values of appletissue [2]. It was observed that modified absorption and scattering coefficientshave effect on acquired intensity and gradient, respectively (fig.1).

Figure 1: Effect of absorption (left) and scattering (right) coefficientsμ

a = 0.2 – 0.6 cm-1, μ

s’ = 30 – 60 cm-1

According to the computation, there is strong relationship between absorptioncoefficient and penetration depth, scattering coefficient and diffusion (fig.2).

Figure 2: Relationship between tissue optical properties

First order descriptive parameters of intensity profile were used to estimateoptical properties (Table 1). Full Width at Half Maximum (FWHM), radius atintensity level of 25% (R

25), 75% (R

75), and middle 50% ring width (R

75-R

25) and

relative width (R75

/R25

) were utilized.

According to the results, diffusion coefficient is better estimated from normalprofile. Penetration depth was not successfully estimated, but logarithmicprofile seems to be suitable for the purpose. All quality parameters improved alittle bit with non-linear curve fitting using the same parameter set.

Conclusions

Diffusion coefficient and penetration depth are important features, they haverelationship with chemical compounds and physical state, respectively.Obtained simulation results confirmed that first order descriptive parameters ofintensity profile might be used to estimate optical properties. Since thesefeatures are calculated rapidly, they can be suitable for online qualityevaluation. Further investigation is required for more accurate predictionmodels.

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Diffusion coefficient, cm Penetration depth, cm

Linear model, normal profile

R2 = 0.9213R2

adj = 0.9211

F = 4944RMSEP = 0.00133

D-W = 0.8528

R2 = 0.2797R2

adj = 0.2780

F = 164RMSEP = 0.02355

D-W = 0.0314

Linear morel, logarithmic profile

R2 = 0.4643R2

adj = 0.4630

F = 366RMSEP = 0.00347

D-W = 0.4475

R2 = 0.7001R2

adj = 0.6994

F = 985.9RMSEP = 0.01519

D-W = 0.4268

Table 1: Estimation of optical properties from intensity profiles (N=1271)