A total of 140 “Golden Delicious” apples with similar size and being free of visible defects were purchased from a local fruit supermarket at the city of Hangzhou. Physical properties (i.e., weight, diameter, and height) of the apples are measured and summarized in Table 1. To complete the acquisition of SFDI and the measurement of quality attributes for all the apples, the experiments were designed and conducted, with the flowchart shown in Figure 1. The intact apples were cut lengthwise to generate a slice with the thickness of about 15 mm. The slice (left in Figure 1) was used for juicing measurement to get the corresponding SSC value, while the other part (right in Figure 1) was subjected to the color measurement, SFDI measurement, and puncture test, respectively, from which the color parameters (L*, a*, b*, C*, and H°), optical property mapping, and firmness parameters [slope, flesh firmness (FF), and maximum force (Max.F)] were obtained. The measured optical property mapping was then used for data interpretation, correlation analysis, and quality prediction. During the experiment, apples were kept at room temperature (∼22°C) with no humidity control and the experiment was completed within 5 days.

Spatial-frequency domain imaging of the apples was acquired using a laboratory-developed SFDI system, as shown in Figure 2. A detailed description of the SFDI system and its calibration procedure were given in our previous study (Hu et al., 2016). The SFDI system mainly consists of a light source, a digital projector, and a color camera. The light source, combined with the DLP-based projector, is used to generate structured patterns for illuminating the apples. The reflected light is received by the camera, which produces SFDI under different frequencies and phases. The neutral density filter mounted with the projector could reduce light intensity uniformly to avoid burning on the apples, while the bandpass filter placed in front of the camera is used for wavelength dispersion, constituting a multispectral SFDI system. A number of two crossed linear polarizers are mounted in the projection and detection arms to reduce specular reflection from the apple surface. 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). To remove the effect of apple peel (with the thickness about 1 mm) on optical property mapping, six spatial frequencies with the values of 0, 0.04, 0.08, 0.12, 0.16, and 0.20 mm^–1 were utilized in this study.

The captured SFDI of apples was processed using appropriate algorithms for extracting optical property mapping, among which image demodulation and inverse estimation are the two key steps (Figure 3A). Great efforts have been made to develop and improve the demodulation and inverse estimation methods (Lu et al., 2016; Hu et al., 2018, 2019; Sun et al., 2022). In this study, the conventional three-phase demodulation coupled with non-linear curve-fitting (TP-CF) method was applied for extracting optical property mapping of apples due to its high accuracy. To implement the TP-CF method, three-phase images at the same frequency were first demodulated to generate one alternative component (AC) image. Then, the non-linear curve-fitting method was used to extract the optical property (μ_a and μ_s′) mappings of apples on a pixel-by-pixel fashion. It should be noted that two AC images are at least needed for curve fitting. The essential nature of the curve fitting is continuously iterative computing until the difference between the measured reflectance from the AC image and the computed reflectance based on the initially guessed optical properties is within the preset threshold (Figure 3B). In this occasion, dynamic adjustment is carried out to update the initial optical properties until the reflectance present a convergent pattern. To investigate the effect of ROI size on the optical property measurement, four ROIs with different sizes (i.e., 10 × 10, 30 × 30, 60 × 60, and 100 × 100 pixels, corresponding to 3 × 3 mm², 9 × 9 mm², 18 × 18 mm², and 30 × 30 mm² approximately) were selected, and the average value was taken as the optical property.

All the 140 apples were subjected to the measurement for different quality attributes. Juice of apple fruit was extracted from the apple slice (left in Figure 1), and SSC was measured using a handheld digital refractometer (model PR-101, Atago Co., Tokyo, Japan). Apple color was measured from the other part (right in Figure 1) using a colorimeter (CR-400, Konica Minolta Sensing, Inc., Tokyo, Japan) for the L*, a*, b*, C*, and H° values in triplicate, and average values were recorded for further analysis. As shown in Figure 1, apple firmness was measured from the surface area in quadruplicate with the distance between the center of puncture points and the external contour of apple about 10 mm, and the average values were recorded. Puncture tests were carried out using the texture analyzer (Model TA.XT plus, Stable Micro System, United Kingdom) equipped with a 5-mm cylindrical Magness-Taylor probe at a test speed of 4 mm/s and the penetration depth was set as 8 mm. A number of three parameters related to the firmness, which include slope in N/mm, FF in N, and Max.F in N, were then determined from the force–displacement curve. The slope was measured between the point of initial displacement and the point corresponding to the Max.F, while the FF was defined as the average force over the puncture distances between the rupture point and maximum puncture depth (8 mm).

Pearson’s linear correlation analysis was performed on the relationship among all quality parameters and the absorption and reduced scattering coefficients as well as their combinations (i.e., μ_a, μ_s′, μ_a × μ_s′, and μ_eff = [3μ_a (μ_a + μ_s′)]^1/2) using the software of IBM SPSS Statistics 25. μ_a × μ_s′ is the multiplication of μ_a and μ_s′, and it was reported to be more effective for predicting quality of tomatoes than using individual μ_a and μ_s′ (Huang et al., 2018). μ_eff is a useful parameter for comparing light transmittance characteristics of different tissues and their wavelength dependence (Flock et al., 1987). To further explore the relationship between optical properties and quality parameters of apples (i.e., SSC, firmness and color), prediction models were established based on μ_a, μ_s′, μ_a × μ_s′, and μ_eff using support vector machine (SVM), multiple linear regression (MLR), and partial least squares (PLS) at the four wavelengths. The models of SVM, MLR, and PLS were developed by the Unscrambler X 10.4 software. All the 140 apple samples were randomly divided with 75% for the calibration set and the remaining 25% for the validation set. The performance of the prediction models was evaluated using the statistic parameters of correlation coefficient of prediction (r_p) and root mean square error of prediction (RMSEP).

The statistical data of SSC, firmness (slope, FF, Max.F), and color (L*, a*, b*, C*, and H°) for all tested apples are summarized in Table 1. There was no relatively large variation for all the nine quality indexes based on the standard deviation (SD) and coefficient of variation (CV), since all the 140 apples were purchased from the same batch with similar properties. It was observed that the distributions of apple SSC and color were relatively narrow than the firmness, with the CV values close to or smaller than 10%. This observation brought great challenges for predicting SSC and color parameters, which will be discussed in the following section.

Correlations among the SSC, firmness, and color parameters for all apples are summarized in Table 2. It was observed that the overall correlation among these quality parameters was not strong, with most of the coefficients smaller than 0.50. This might be due to the fact that the apples used in this study were similar in appearance and had no difference in maturation stage or shelf life, thus causing narrow distribution of quality attributes. It should be noted that the correlation coefficient between the Max.F and FF was as high as 0.80, because the FF was defined as the average force over the puncture distances between the rupture point (Max.F) and puncture depth. This phenomenon was also reported by Huang et al. (2018) when studying tomato fruit based on spatially resolved spectroscopy. The correlation coefficient between b* and C* was 1.00, because the two parameters were very close to each other.

To determine the optical property mappings of apples, the TP-CF method was carried out, and the resulting absorption and scattering properties are displayed in Figures 4A,B, respectively. The numbers labeled below the sub-pictures are the average values of μ_a or μ_s′ for the marked ROI with the size of 30 × 30 pixels. It should be noted that the circular part is sliced apple tissue with relatively flat surface, while the surrounding part, which has a more uniform color distribution, is the sample holder made of aluminum material with blackening treatment. There was a decreased tendency of the μ_a and μ_s′ along the four wavelengths. Comparing the scattering properties at a wavelength, like 527 nm in Figure 4B, a spatial variation of μ_s′ for the apple tissue between 0.996 and 1.152 mm^–1 was noticed. The complex apple tissue formed by different components with different physicochemical characteristics and the performance of structured illumination (e.g., non-uniformity), as well as data processing algorithm for optical property estimation, are the potential factors that cause the variation. A similar variation also occurs for the μ_a mappings in Figure 4A. It was observed that the spatial variation of optical properties at 710 nm was less pronounced than the other three wavelengths, which demonstrates that wavelength plays a non-negligible role when estimating apple optical properties.

Figure 5 shows the average optical properties of four different ROI with the sizes of 10 × 10, 30 × 30, 60 × 60, and 100 × 100 along the four wavelengths. The μ_a and μ_s′ for different sizes of ROI are quite similar, but still, a difference can be observed. In general, the optical property value in small size ROI (10 × 10) was slightly different from the value in large size ROI, which might be caused by the spatial variation mentioned above. For the three larger ROIs, the average optical properties were close to each other, with the differences of 6.94–19.0% and 1.56–3.51% for μ_a and μ_s′, respectively. Considering the fact that larger-size ROI means more cost of time, the ROI with the size of 30 × 30 was chosen for averaging the μ_a and μ_s′ and would be used in the following sections.

To our knowledge, this is the first time that the optical properties of apple tissue were determined from different sizes of ROI. Based on SFDI measurements of “Braeburn” apples, Lohner et al. (2021) recently observed that μ_a was about 0.01–0.04 mm^–1 for the cortex tissue at 656 nm, which covers the μ_a range at 630 nm in this study (0.021–0.024 mm^–1), if the value from the ROI of 10 × 10 is excluded. As known from the previous work, the wavelength of 656 nm is mainly related to the presence of chlorophyll b (Merzlyak and Solovchenko, 2002), and it is thus reasonable that the μ_a value is larger than the present results. Our results are also comparable to the published integrating sphere measurements by other researchers. For example, Wei et al. (2020) measured the optical properties of cold-stored “Fuji” apples over 400–1,100 nm and reported that the μ_a was in the range of about 0.02–0.13 mm^–1, whereas the μ_s′ was between 1.0 and 1.75 mm^–1 for the flesh tissue, which are comparable with the present results.

Table 3 presents the relationships between the average optical properties and apple quality parameters. The correlations between the optical properties and their combinations at 527 and 630 nm measured by SFDI and apple quality parameters are not reported as non-significant. Better correlations were observed between μ_a and quality parameters, compared with μ_s′, which is in general agreement with the previous studies for apples, tomatoes, and peaches (Do Trong et al., 2014; Huang et al., 2018; Sun Y. et al., 2020). The μ_{a_460} was negatively related to a* and C* and positively related to b*, slope, FF, and Max.F, whereas μ_{a_710} was only positively related to b* and negatively related to a*, C*, slope, FF, and Max.F. As for scattering, no significant correlations were found between μ_s′_{_460} and quality parameters, whereas μ_s′_{_710} was positively and negatively related to b* and C*, respectively. It was observed that the combinations of μ_a × μ_s′_{_460}, μ_a × μ_s′_{_710}, μ_{eff_460}, and μ_{eff_710} resulted in better correlation results, compared with the individual optical properties. This is especially true for the correlations between the color parameters of a*, b*, C*, and μ_a × μ_s′_{_460}, μ_a × μ_s′_{_710}. For example, using μ_a × μ_s′_{_710} improved correlation coefficients of a*, b*, and C* by 14.8, 25.4, and 25.4%, compared with the correlation analysis based on the μ_{a_710}. Moreover, a noticeable improvement was found for SSC when using the combinations of optical properties (Table 3). These results demonstrated that optical property measurement can provide useful information about the apple quality.

The resulting r_p and RMSEP from SVM, MLR, and PLS based on μ_a, μ_s′, μ_a × μ_s′, and μ_eff are summarized in Table 4. Overall, the prediction result performs not well with the r_p-values of 0.24–0.86 and 0.19–0.82 for the SVM and MLR, respectively. The result predicted by PLS is worse and not reported. It could be observed that color parameters of b* and C* achieved the best prediction performance (r_p = 0.86), followed by the firmness parameters with the r_p-values of 0.68, 0.73, and 0.79 for slope, FF, and Max.F, and finally, SSC was the most challenging for the prediction (r_p = 0.66). The prediction results for all the apple quality parameters based on μ_a were far better than that based on μ_s′, which is consistent with the findings of Pearson’s correlation analysis above. The combinations of μ_a × μ_s′ and μ_eff gave better prediction results, compared to the individual μ_a or μ_s′. For example, using μ_a × μ_s′ for predicting the parameter of slope by the SVM resulted in r_p of 0.68, which represents 17.2% improvement, compared with the individual μ_a. It should be mentioned that the combinations improved the prediction of SSC significantly (> 34.0%), which also agrees well with the correlation analysis.