## 3 Results and Discussion
### Optical Properties of Gala Apples at Different Depths and Time During Storage  
We measured the absorption and reduced scattering coefficients at two wavelengths and two SDSs of six apples. Figure 4 shows the average amplitude and phase of all apples at 660 and 980 nm. The frequency range employed in the fitting was from 10 to 500 MHz because the data collected at modulation frequencies higher than 500 MHz were noisy and therefore neglected for this set of measurements. The optical properties of apples recovered at 660 nm wavelength at SDSs of 1 and 5 mm 1, 7, and 14 days after purchase are displayed in Figure 5. The decrease over time in the \(\mu_{a}\) and \(\mu_{s}\)' at 660 nm indicate the breakdown of chlorophyll and the enzyme of the cell walls of the apple skin [19; 20]. Figure 5a shows that the \(\mu_{a}\) at 660 nm and 1 mm SDS decreased by 34% after the first 7 days, and 20% from Day 7 to Day 14, which indicates that the trend of breakdown of the chlorophyll  
Figure 3: (**a**) Absorption and (**b**) reduced scattering coefficients of an apple recovered at 660 nm wavelength (green bar) and 980 nm (blue bar) at source–detector separation (SDS) of 1 mm and 5 mm. decelerates gradually. We observed that the decreasing rates of the \(\mu_{a}\) at 1 mm SDS were more pronounced, which is 47%, than that at 5 mm SDS, which is 24%. This demonstrates that the change in chlorophyll can be detected more prominently at 1 mm. The \(\mu_{a}\) variation at 660 nm wavelength and SDS of 5 mm was not as notable as at 1 mm, possibly because the concentration of chlorophyll is much lower in the apple outer flesh than in the skin. Figure 5b shows that the \(\mu_{s}\)' at 660 nm wavelength at SDSs of 1 mm and 5 mm decreased in 14 days; this finding agrees with the phenomenon reported in some studies, where the decrease in the \(\mu_{s}\)' was associated with apple softening during ripening [21]. [PERSON] et al. [22] found that the enzymatic breakdown in the cell walls leads to an increase in air-filled pores and cell size reduction. The presence of these additional air spaces also suggests the softening of the fruit. In Figure 6a, the \(\mu_{a}\) at a wavelength of 980 nm at 5 mm SDS decreased by 43% after 14 days, reflecting the reduction of the water concentration in the apple outer flesh. The rapid decrease of \(\mu_{a}\) might be affected by the storage condition (apples were uncovered in the air-conditioned room). Moreover, it was also probably due to a coupling effect between the scattering and absorption quantification in  
Figure 4: (**a**) Amplitude and (**b**) phase of apples verse the source modulation frequencies generated from different source–detector separations (SDSs) and wavelengths: 1 mm at 660 nm (), 5 mm at 660 nm (), 1 mm at 980 nm (), and 5 mm at 980 nm (). Figure 5: (**a**) Absorption and (**b**) reduced scattering coefficients of an apple recovered at source–detection separation (SDS) of 1 mm (black squares) and 5 mm (red circles) 1, 7, and 14 days after purchase at a wavelength of 660 nm. the frequency-domain fit. Such coupling appears when the diffusion model's assumptions are not sufficiently fulfilled [23]. The structure of apple skin and the deeper flesh tissue could be a possible source of deviation from the model. The coupling between \(\mu_{a}\) and \(\mu_{s}\)' caused by inaccurate modeling could be alleviated by incorporating more accurate photon transport models such as Monte Carlo method based models. Figure 6b shows the \(\mu_{s}\)' at a wavelength of 980 nm at SDS of 5 mm also decreased in 14 days, as consistent with apple softening during ripening [21]. In Figure 6a,b, we observed the error bars of the \(\mu_{a}\) and \(\mu_{s}\)' at 1 mm were large; this fact suggests that the water distribution in the skin could be nonhomogeneous. In general, the water content is low in the apple skin, and we speculate that the water absorption signal may come from the superficial flesh.