Influence of the size and skin thickness of apple varieties on the retrieval of internal optical properties using Vis/NIR spectroscopy: A Monte Carlo-based study

Abstract

Visible/near-infrared spectroscopy is a well-established method to measure optical properties of tissues, assuming that a light propagation model can be used to recover absorption and reduced scattering coefficients from non-invasive probing. Spectroscopic measurements have achieved success in non-destructive assessment of apple optical properties and quality attributes. However, the spectroscopy of apples must consider the size of the fruit and the presence of the thin skin layer that surrounds the flesh, to correctly read the signals acquired on the boundary. In this research, the fruit was modelled as a two layer spherical structure with various radii and finite thickness of the upper skin layer. Monte Carlo computations were performed to generate time-resolved reflectance and spatially-resolved reflectance measurements. Simulated data were then fitted using a procedure based on Levenberg-Marquardt algorithm with specific semi-infinite models. The errors in the retrieved optical properties of the flesh (absorption coefficient l a , and reduced scattering coefficient l 0 s ) were studied as functions of apple radius, skin thickness, and source-detector distance, for given optical parameter sets assigned to the flesh and the skin. The results suggest that the time-resolved reflectance spectroscopy may probe optical properties of the flesh regardless of the skin layer, when a sufficient source-detector distance (15 mm) is used for the measurements. Similar results were found in case of using the spatially resolved spectroscopy, because measurements extend up to 15-29 mm by steps of 1 mm or 2 mm. The computations also show that the curvature of the boundary has noticeable effect on the errors in the retrieved optical coefficients of the flesh. However, results from time-resolved spectroscopy are more influenced by the size of apples, compared with the spatially-resolved spectroscopy.

Numerical Study of Light Transport in Apple Models Based on Monte Carlo Simulations

“…These probabilities depend on the optical parameters µ s , µ a , g and n, which are assigned to the tissues. Here we used a Monte Carlo code described in a previous paper [20] that was adapted to both imaging setups displayed in Figure 1a,b.…”

“…Moreover, the peak intensity is practically not affected by the absorption coefficient of the skin. According to [20], the skin acts like a screen which confines the diffused photons in the sub-surface (skin-flesh). In this case, more backscattering photons can escape the boundary (skin-air), and then contribute to increase the peak intensity of the spatial diffuse reflectance.…”

“…These assumptions may not be well appropriate because most fruits are at least composed of two layers of tissues, i.e., skin and flesh, and also present a local curvature (or size) that cannot be assimilated to a plan boundary. Therefore, it seems more realistic to develop a two-layer or multi-layer model with curved boundary to study light propagation in whole fruit, and quantify the effect of the surrounding layer (skin) on the assessment of the flesh optical properties [20]. Several studies have provided analytical solutions to diffusion problem for layered media [21][22][23].…”

“…Other works have described numerical methods based on finite element [24][25][26] and Monte Carlo (MC) [6,[27][28][29][30][31][32][33][34] models to simulate light transport in various complex multilayered biological structures. The Monte Carlo method has also been successfully used in the context of food and agricultural products for predicting optical features related to apples [20,35], kiwi fruit [36], and onion bulbs [37]. Although the MC method requires the propagation of substantial numbers of photons and large amounts of computing time to obtain statistically reliable results, it can solve the radiative transfer equation [38] without the limitations of complex sample geometries and optical properties.…”

Experimental Study of Light Propagation in Apple Tissues Using a Multispectral Imaging System

“…As a result, CW spatially-resolved measurements reflect the optical properties of the skin and subsurface [31,32], unless the photons probe deeply in the flesh by increasing the source-detector distance. Recently, Vaudelle and L'Huillier (2015) [33] and Askoura et al (2016) [34]; considered this question by assuming the apple as a two-layer spherical model comprising the skin and flesh tissues. Numerous simulations based on a Monte Carlo code have been performed in order to generate time-resolved and spatially-resolved reflectance measurements.…”