Tomato maturity is important to determine the fruit shelf life and eating quality. The objective of this research was to evaluate tomato maturity in different layers by using a newly developed spatially resolved spectroscopic system over the spectral region of 550-1650 nm. Thirty spatially resolved spectra were obtained for 600 tomatoes, 100 for each of the six maturity stages (i.e., green, breaker, turning, pink, light red, and red). Support vector machine discriminant analysis (SVMDA) models were first developed for each of individual spatially resolved (SR) spectra to compare the classification results of two sides. The mean spectra of two sides with the same source-detector distances were employed to determine the model performance of different layers. SR combination by averaging all the SR spectra was also subject to comparison with the classification model performance. The results showed large source-detector distances would be helpful for evaluating tomato maturity, and the mean_SR 15 obtained excellent classification results with the total classification accuracy of 98.3%. Moreover, the classification results were distinct for two sides of the probe, which demonstrated even if in the same source-detector distances, the classification results were influenced by the measurement location due to the heterogeneity for tomato. The mean of all SR spectra could only improve the classification results based on the first three mean_SR spectra, but could not obtain the accuracy as good as the following mean_SR spectra. This study demonstrated that spatially resolved spectroscopy has potential for assessing tomato maturity in different layers.

Assessment of Tomato Maturity in Different Layers by Spatially Resolved Spectroscopy.

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.

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

As a new imaging inspection method with characteristics of a wide view field and non-contact, spatial frequency domain imaging (SFDI) is very suitable to evaluate the optical properties of agricultural products to ensure the sustainable development of agriculture. However, due to the unique forward scattering characteristics of fruit skin, only a few photons can return to the skin surface after interacting with the flesh, thus affecting the detection accuracy of the flesh layer. This study aims to propose a more accurate and wider applicable method to extract the optical properties of two-layer tissue from SFDI measurements. Firstly, a two-layer model was proposed by optimizing the reflectivity of the flesh layer through the optical properties and thickness of the skin layer. Secondly, the influence of the optical properties and thickness of different skin layers on the reflectivity optimization of the flesh layer was investigated by a Monte Carlo simulation, and then, the accuracy and effectiveness of the proposed model was evaluated for practical inspection by phantom experiments. Finally, this model was used to obtain the optical properties, layer by layer, of four thin-skinned fruits (pear, apple, peach and muskmelon) to verify its universality. The results showed that, for the skin layer, the average errors of the absorption coefficient (μa1) and the reduced scattering coefficient (μ′s1) were 10.87% and 7.91%, respectively, and for the flesh layer, the average errors of the absorption coefficient (μa2) and the reduced scattering coefficient (μ′s2) were 16.76% and 8.64%, respectively. This study provides the basis for the SFDI detection of optical properties of two-layer tissue such as thin-skinned fruits, which can be further used for nondestructive fruit quality evaluations.

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

The accurate estimation of the optical properties of turbid media by using a spatially resolved (SR) technique remains a challenging task due to measurement errors in the acquired spatially resolved diffuse reflectance (SRDR) and challenges in inversion model implementation. In this study, what we believe to be a novel data-driven model based on a long short-term memory network and attention mechanism (LSTM-attention network) combined with SRDR is proposed for the accurate estimation of the optical properties of turbid media. The proposed LSTM-attention network divides the SRDR profile into multiple consecutive and partially overlaps sub-intervals by using the sliding window technique, and uses the divided sub-intervals as the input of the LSTM modules. It then introduces an attention mechanism to evaluate the output of each module automatically and form a score coefficient, finally obtaining an accurate estimation of the optical properties. The proposed LSTM-attention network is trained with Monte Carlo (MC) simulation data to overcome the difficulty in preparing training (reference) samples with known optical properties. Experimental results of the MC simulation data showed that the mean relative error (MRE) with 5.59% for the absorption coefficient [with the mean absolute error (MAE) of 0.04 cm-1, coefficient of determination (R2) of 0.9982, and root mean square error (RMSE) of 0.058 cm-1] and 1.18% for the reduced scattering coefficient (with an MAE of 0.208 cm-1, R2 of 0.9996, and RMSE of 0.237 cm-1), which were significantly better than those of the three comparative models. The SRDR profiles of 36 liquid phantoms, collected using a hyperspectral imaging system that covered a wavelength range of 530-900 nm, were used to test the performance of the proposed model further. The results showed that the LSTM-attention model achieved the best performance (with the MRE of 14.89%, MAE of 0.022 cm-1, R2 of 0.9603, and RMSE of 0.026 cm-1 for the absorption coefficient; and the MRE of 9.76%, MAE of 0.732 cm-1, R2 of 0.9701, and RMSE of 1.470 cm-1for the reduced scattering coefficient). Therefore, SRDR combined with the LSTM-attention model provides an effective method for improving the estimation accuracy of the optical properties of turbid media. 

Optical parameters inversion of tissue using spatially resolved diffuse reflection imaging combined with LSTM-attention network

A sequential method for estimating the optical properties of two-layer biological tissues with spatially-resolved diffuse reflectance was proposed and validated using Monte Carlo simulations. The relationship between the penetration depth of detected photons and source-detector separation was first studied. Photons detected at larger source-detector separations generally penetrated deeper into the medium than those detected at small source-detector separations. The effect of each parameter involved in the two-layer diffusion model (i.e., the absorption and reduced scattering coefficients (μa and μs′) of each layer, and the thickness of top layer) on reflectance was investigated. It was found that the relationship between the optical properties and thickness of top layer was a critical factor in determining whether photons would have sufficient interactions with the top layer and also penetrate into the bottom layer. The constraints for the proposed sequential estimation method were quantitatively determined by the curve fitting procedure coupled with error contour map analyses. Results showed that the optical properties of top layer could be determined within 10% error using the semi-infinite diffusion model for reflectance profiles with properly selected start and end points, when the thickness of top layer was larger than two times its mean free path (mfp′). And the optical properties of the bottom layer could be estimated within 10% error by the two-layer diffusion model, when the thickness of top layer was

Aichen Wang

Papers

A sequential method for estimating the optical properties of two-layer agro-products from spatially-resolved diffuse reflectance: Simulation