Numerical Simulation on Spatial-Frequency Domain Imaging for Estimating Optical Absorption and Scattering Properties of Two-Layered Horticultural Products

Abstract

Spatial-frequency domain imaging (SFDI) is a wide-field, noncontact, and label-free imaging modality that is currently being explored as a new means for estimating optical absorption and scattering properties of two-layered turbid materials. The accuracy of SFDI for optical property estimation, however, depends on light transfer model and inverse algorithm. This study was therefore aimed at providing theoretical analyses of the diffusion model and inverse algorithm through numerical simulation, so as to evaluate the potential for estimating optical absorption and reduced scattering coefficients of two-layered horticultural products. The effect of varying optical properties on reflectance prediction was first simulated, which indicated that there is good separation in diffuse reflectance over a large range of spatial frequencies for different reduced scattering values in the top layer, whereas there is less separation in diffuse reflectance for different values of absorption in the top layer, and even less separation for optical properties in the bottom layer. To implement the nonlinear least-square method for extracting the optical properties of two-layered samples from Monte Carlo-generated reflectance, five curve fitting strategies with different constrained parameters were conducted and compared. The results confirmed that estimation accuracy improved as fewer variables were to be estimated each time. A stepwise method was thus suggested for estimating optical properties of two-layered samples. Four factors influencing optical property estimation of the top layer, which is the basis for accurately implementing the stepwise method, were investigated by generating absolute error contour maps. Finally, the relationship between light penetration depth and spatial frequency was studied. The results showed that penetration depth decreased with the increased spatial frequency and also optical properties, suggesting that appropriate selection of spatial frequencies for a stepwise method to estimate optical properties from two-layered samples provides potential for estimation accuracy improvement. This work lays a foundation for improving optical property estimation of two-layered horticultural products using SFDI.

Optical Property Mapping of Apples and the Relationship With Quality Properties

“…On the other hand, and surprisingly enough, the prediction of firmness parameters based on the absorption properties was far better than that based on the scattering properties. This unexpected outcome could be attributed to the fact that SFDI is limited to light penetration depth (2–3 mm) ( Lu and Lu, 2019 ; Hu et al, 2021 ), while the firmness measurement by the texture analyzer probed the flesh much deeper (8 mm). In addition, the wavelengths used in this study are near to the characteristic wavelengths with absorption peaks, while the scattering properties have no features in those wavelengths.…”

“…In this study, four wavelengths of 460, 527, 630, and 710 nm are used. When spatial frequency of the structured illumination is 0.20 mm –1 , the light penetration depth within apple tissue is approaching 1 mm ( Hu et al, 2021 ). High-frequency illumination has a relatively shallow light penetration depth, which could be interpreted by the depth-varying feature ( Hayakawa et al, 2018 ; Lu and Lu, 2019 ).…”

A Method for Obtaining Optical Properties of Two-Layer Tissue such as Thin-Skinned Fruits by Using Spatial Frequency Domain Imaging

“…When the penetration depth is greater than the thickness of the skin layer (z > d), the flesh layer of the two mediums begins to show differences in the results of the light-medium interaction due to the different optical properties of the two mediums. According to the literature [14], it is known that the influence of the flesh layer optical properties changing on the total reflectance are far less than those of the skin layer optical properties changing. Assuming the second scattering and second absorption of light in the tissue are not considered, the amount of light energy loss in the skin layer of the two mediums is the same.…”

“…However, due to the singleness of the research object, the results obtained by such models cannot be widely used in the optical properties detection of various fruits. Hu et al [14] aggregated the optical properties of various fruits for MC simulations in order to study the effect of four parameters (the skin layer absorption coefficient µ a1 , the skin layer reduced scattering coefficient µ s1 , the flesh layer absorption coefficient µ a2 and the flesh layer reduced scattering coefficient µ s2 ) on the prediction of reflectance. They found that the sensitivity of µ a2 and µ s2 changes was very small and difficult to separate at all spatial frequencies.…”