A sequential method for estimating the optical properties of two-layer agro-products from spatially-resolved diffuse reflectance: Simulation
01 Sep 2019-Vol. 3, pp 69-78
TL;DR: In this paper, 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, and the relationship between the penetration depth of detected photons and source-detector separation was first studied.
Abstract: 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
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TL;DR: It is demonstrated that spatially resolved spectroscopy has potential for assessing tomato maturity in different layers and even if in the same source-detector distances, the classification results were influenced by the measurement location due to the heterogeneity for tomato.
Abstract: 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.
11 citations
Cites background from "A sequential method for estimating ..."
...Previous study reported the source-detector distance was similar to the light penetration depths for the sample [31], which meant when the light penetration depths about 6....
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TL;DR: In this paper, 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 the bottom layer.
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.
2 citations
Cites background from "A sequential method for estimating ..."
...(2019) studied the effects of five optical parameters (μa1, μs1, μa2, μs2 and top-layer thickness d) on reflectance prediction with the technique of spatially-resolved [7]....
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...It could be observed from Table 2 that five-variable fit performed the weakest for estimating μs1, followed by the four-variable fit, confirming that estimation accuracy improves as fewer variables are to be estimated each time [5,7]....
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TL;DR: In this article , a two-layer model was proposed by optimizing the reflectivity of the flesh layer through the optical properties and thickness of the skin layer, which can be further used for nondestructive fruit quality evaluations.
Abstract: 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.
TL;DR: In this article , a novel data-driven model based on a long short-term memory network and attention mechanism (LSTM-attention network) combined with spatially resolved diffuse reflectance (SRDR) is proposed for the accurate estimation of the optical properties of turbid media.
Abstract: 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.
References
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01 Jan 1995
TL;DR: A Monte Carlo model of steady-state light transport in multi-layered tissues (MCML) has been coded in ANSI Standard C; therefore, the program can be used on various computers and has been in the public domain since 1992.
Abstract: A Monte Carlo model of steady-state light transport in multi-layered tissues (MCML) has been coded in ANSI Standard C; therefore, the program can be used on various computers. Dynamic data allocation is used for MCML, hence the number of tissue layers and grid elements of the grid system can be varied by users at run time. The coordinates of the simulated data for each grid element in the radial and angular directions are optimized. Some of the MCML computational results have been verified with those of other theories or other investigators. The program, including the source code, has been in the public domain since 1992.
2,889 citations
TL;DR: A Monte Carlo model of steady-state light transport in multi-layered tissues (MCML) has been coded in ANSI Standard C; therefore, the program can be used on various computers as mentioned in this paper.
2,678 citations
01 Jan 1940
TL;DR: In this paper, it was shown that the observed intensity of the diffuse light may be explained as scattered radiation if the phase function governing the scattering of starlight by the interstellar matter is strongly forward-throwing.
Abstract: Observations have been obtained to verify the existence of diffuse interstellar radiation. A Fabry photometer, attached to the 40-inch refractor at the Yerkes Observatory, was used to measure the the brightness of regions over a wide range of galactic latitude. The intensities in the photographic region of the spectrum were calibrated by means of the Polar Sequence stars. The mean of four such runs across the Milky Way, on circles of constant latitude $\ell = 40^{\rm{o}}$, shows a maximum brightness of 80 stars of the tenth magnitude per square degree for the diffuse extra-terrestrial radiation. The mean of three runs near $\ell = 140^{\rm{o}}$ shows a maximum of 35 in the same units. It is shown that the observed intensity of the diffuse light may be explained as scattered radiation if the phase function governing the scattering of starlight by the interstellar matter is strongly forward-throwing. The concentration of the diffuse light toward the galactic circle is also in agreement with this property of the phase function. The observations also indicate that the scattering efficiency, or albedo, of the particles is greater than 0.3.
2,498 citations
TL;DR: In this article, it was shown that the observed intensity of the diffuse light may be explained as scattered radiation if the phase function governing the scattering of starlight by the interstellar matter is strongly forward-throwing.
Abstract: Observations have been obtained to verify the existence of diffuse interstellar radiation. A Fabry photometer, attached to the 40-inch refractor at the Yerkes Observatory, was used to measure the the brightness of regions over a wide range of galactic latitude. The intensities in the photographic region of the spectrum were calibrated by means of the Polar Sequence stars. The mean of four such runs across the Milky Way, on circles of constant latitude $\ell = 40^{\rm{o}}$, shows a maximum brightness of 80 stars of the tenth magnitude per square degree for the diffuse extra-terrestrial radiation. The mean of three runs near $\ell = 140^{\rm{o}}$ shows a maximum of 35 in the same units. It is shown that the observed intensity of the diffuse light may be explained as scattered radiation if the phase function governing the scattering of starlight by the interstellar matter is strongly forward-throwing. The concentration of the diffuse light toward the galactic circle is also in agreement with this property of the phase function. The observations also indicate that the scattering efficiency, or albedo, of the particles is greater than 0.3.
2,398 citations
TL;DR: A model based upon steady-state diffusion theory which describes the radial dependence of diffuse reflectance of light from tissues is developed and the optical properties derived for the phantoms are within 5%-10% of those determined by other established techniques.
Abstract: A model based upon steady-state diffusion theory which describes the radial dependence of diffuse reflectance of light from tissues is developed. This model incorporates a photon dipole source in order to satisfy the tissue boundary conditions and is suitable for either refractive index matched or mismatched surfaces. The predictions of the model were compared with Monte Carlo simulations as well as experimental measurements made with tissue simulating phantoms. The model describes the reflectance data accurately to radial distances as small as 0.5 mm when compared to Monte Carlo simulations and agrees with experimental measurements to distances as small as 1 mm. A nonlinear least-squares fitting procedure has been used to determine the tissue optical properties from the radial reflectance data in both phantoms and tissues in vivo. The optical properties derived for the phantoms are within 5%-10% of those determined by other established techniques. The in vivo values are also consistent with those reported by other investigators.
1,541 citations