*4.2. Investigating Light Penetration Depth*

Table 1 showed the measured values of optical property parameters (*μa*, *μ <sup>s</sup>*) of apple slices without peel using the integrating sphere technique. By inputting the optical property values manually into the developed program, the light penetration depth for the apple tissue could be simulated by consulting a scaled lookup table derived from MC simulations to the radiative transport equation in the spatial-frequency domain. Figure 7 displays the simulated results for the apple tissue at six wavelengths (550, 600, 630, 675, 710, and 730 nm), in which the median sampling depth with a [25–75]% fraction of the total measured diffuse reflectance was recognized as the critical metric for light penetration depth [33]. It was observed in the simulation results that light penetration depths increased slowly with the wavelengths, which is similar to the findings reported by Zhao et al. [17]. At 550 nm, the median sampling depth with [25–75]% was slightly smaller than that of the other five wavelengths, which was approximately in the range of 0.6–2.2 mm. It demonstrated that

the 25–75% measured reflectance had the opportunity to interact with the tissue in the depth of 0.6–2.2 mm. Similarly, Lammertyn et al. [38] reported that the maximum light penetration depth in Jonagold apples at 692 nm was about 2 mm, which agrees well with the finding in this study. In the report of Binzoni et al. [39], the light propagation behavior is that the photons reaching the detectors do not go very deep and thus the information contained in the spectral images comes from a depth that does not exceed 2–3 mm. The above experimental results were all consistent with our simulation results. However, the light penetration depth (less than 400 μm) reported by Lu and Lu [21] was much smaller than the 2.2 mm. One potential reason is the evaluation level. Lu and Lu investigated the detection depth through demodulated images, while we studied the penetration depth from the aspect of optical property estimation. Furthermore, the custom-defined acceptable resolution and contrast would also affect the detection depth. Hence, it was concluded that the light penetration depths in apple tissues were close to each other at the six wavelengths, with values of no more than 2.2 mm.

**Figure 6.** Demodulated DC (direct component) and AC (amplitude component) images of the nylon sample at a sequence of spatial frequencies of 0, 0.01, 0.02, 0.04, 0.08, and 0.12 mm<sup>−</sup>1, from (**top left**) to (**bottom right**).


**Table 1.** Optical property parameters (*μa*, *μ <sup>s</sup>*) of 'Golden Cream Delicious' apple tissues measured by integrating sphere system at six different wavelengths.

**Figure 7.** Simulated median optical detection depth for the apple tissue at six wavelengths, which is estimated using a scaled lookup table derived from MC simulations to the radiative transport equation in the spatial-frequency domain [33]. The median detection depth is the depth that encloses the photon trajectories responsible for 50% of the detected light, and accordingly, the vertical-capped lines in the figure correspond to detection depths responsible for 25% (**lower**) and 75% (**upper**) of the detected light.

Figure 8A shows the contrast variation with frequencies for the DC and AC images of the USAF-1951 target covered with apple slices at 630 nm. For both the slices with and without peel, DC images gave almost a constant value of image contrast since they were independent of spatial frequency, while AC images showed much higher contrast values, which rose steadily with the spatial frequency. These findings indicated that AC images, which are unique to SFDI, enhanced image contrast compared to DC images, demonstrating that SFDI is superior to conventional uniform light imaging techniques in image contrast. Figure 8B shows the histogram results of image contrast for the DC images of the USAF-1951 target covered with apple slices at the wavelengths of 600, 630, 675, and 710 nm. It was noticed that the contrast values decreased with the thickness of apple tissue, as well as the wavelength. A special case occurs from 675 nm to 710 nm, in which there is a small rise of the contrast for some thicknesses. This is because the reflected signal intensity was generally poor in 630–690 nm due to strong absorption of chlorophyll. When removing the influence of the peel (right panel in Figure 8B), there was a steady decreasing trend for the image contrast with the wavelength, because the pigment had little effect on apple flesh tissue.

**Figure 8.** (**A**) Contrast variation with spatial frequencies for the direct component (DC) and amplitude component (AC) images of USAF-1951 target covered with apple slices with (left) and without peel (right); (**B**) histogram of contrast values for the DC images of USAF-1951 target covered with apple slice with (left) and without peel (right) in different thicknesses.

Figure 9 shows statistical results of contrast and PVR at 630 nm for the DC images of the USAF-1951 target covered with different-thickness apple slices. It was observed that the contrast values in the left chart decreased with the thickness of the apple slice. There was an approximate linear relation as the slice thickness ranged from 0.9 mm to 2.5 mm. A similar result was found when analyzing the image contrast in the right chart, with a narrow thickness range of 1.0–2.5 mm. It was noticed that the distribution of image contrast in the left chart (with peel) was more disperse and irregular than that in the right chart. This could be attributed to the influence of pores on the surface tissue of apple peel. On the other hand, PVR showed a gradual decreasing trend with the slice thicknesses. The black horizontal

bars of the USAF-1951 target were hardly recognized while PVR was reduced to a certain value. In order to determine the light penetration depth in apple tissue, the threshold value of PVR in the slice thickness range of 0.9–2.5 mm, in which a linear relationship between the contrast and slice thickness was observed, was tested by large-scale experiments and finally set as 1.2. From this aspect, the light penetration depths in apple tissues with and without peels were determined as 0–1.8 mm and 0–2.3 mm, respectively. These results were quite similar to those obtained in the simulation experiments (0–2.2 mm). The differences between the simulation and practical experiments could be caused by many factors. For example, the apple optical properties, which were taken as the inputs in the simulations, are prone to measurement errors of the integrating sphere system, and thus lead to deviations for the simulation results. In addition, it is challenging to consider all the experiment details completely, such as the minute space between the covered apple slice and USAF-1951 target, and they may cause potential effects on our data analysis and final results.

**Figure 9.** Contrast (left axis) and PVR (right axis) variation at 630 nm for direct component (DC) images of USAF-1951 target covered with different-thickness apple slices ((**left**) with peel; (**right**) without peel).

#### *4.3. Validation in Detecting Early-Stage Bruise of Apple*

Experiments on early-stage bruise detection of apples were conducted to validate the results of light penetration depth in apple tissues. The apple was peeled first to make the bruised tissue visible, and then it was covered with different-thickness apple slices with or without peels. Spatial-frequency domain images were acquired, followed with image demodulation and inverse estimation for generating optical property mappings. It was supposed that the bruised apple tissue could be detected if the light penetration depth was equal to or larger than the thickness of the covered apple slice. Figure 10 shows the demodulated images of the bruised apple covered with a 0.8 mm thick apple slice without peel. The AC images at certain spatial frequencies enhanced the bruised feature compared with the DC image. Strong contrast and surface texture variation were observed with the increased frequency. These findings indicated the enhanced capability of SFDI for detecting early-stage bruises of the apples, in comparison with the imaging techniques under uniform or diffuse illumination. It was believed that inverse parameter estimation for optical property mappings would provide more useful information for qualitative and quantitative analyses of bruise detection [32]. Therefore, the absorption and reduced scattering coefficient mappings were produced in our next step. The previous studies reported that bruising changed the optical properties of apples, particularly the reduced scattering coefficient, resulting in the difference between bruised and non-bruised tissues. The bruising detection based on the reduced scattering coefficient mapping was further analyzed to validate the results of light penetration depth in apples.

**Figure 10.** Demodulated images of the bruised apple covered with an 0.8 mm thick slice without peel at a sequence of spatial frequencies of 0, 0.01, 0.05, 0.10, 0.15, 0.20, 0.25, and 0.30 mm<sup>−</sup>1, from top left to bottom right.

Figure 11 shows the reduced scattering coefficient mappings of the bruised apple covered with pre-prepared apple slices, with the bruised tissue marked in red circles. It was noticed that the bruised apple tissue without being covered by any slice, as shown in Figure 11A, was clearly observed from the reduced scattering coefficient mapping. Figure 11B shows that the bruised apple tissue covered with the 1.2 mm thick slice with peel could still be easily recognized, revealing that the spatially modulated light could completely penetrate through the apple slices with peel with the thickness of 0–1.2 mm. The 1.5 mm thick slice cover without peel (Figure 11D) provided more difficulty for apple bruise detection than the 0.8 mm thick slice (Figure 11C), but both of them could still be penetrated by the light. Through data analysis of all the mapping results with different-thickness slices, it was concluded that the apple slice without peel could be completely penetrated with the thickness range of 0–1.5 mm.

According to the report of Binzoni et al. [39], the number of photons that visit a given tissue voxel situated at a depth larger than 2 mm represents less than the 1% of the total number of photons reaching the corresponding detection pixel. They made the conclusion that the light penetration depth was no more than 2 mm, which confirmed our findings. In addition, Lu and Lu [21] reported that the maximum light penetration depth was no more than three sheets of white paper (or less than 400 μm). In our study, the apple slice, instead of white paper, was used as the cover for experiments, which was more scientific and reasonable for investigating the light penetration depth in apples. It should be pointed out that the results of light penetration depth obtained in this study are based on the apple sample, SFDI system configuration, and data processing method. Zhao et al. [16] reported that shortwave-infrared illumination could penetrate thicker biological tissue than visible light, because there is decreased optical scattering in the shortwave-infrared region compared to visible wavelengths. Hence, the hardware of the SFDI system, including the camera, the light source, and wavelength range, as well as the image processing algorithm, could be improved to increase light penetration depth in the future.

**Figure 11.** The reduced scattering coefficient mappings of the bruised apple covered without any slice (**A**), with a 1.2 mm thick slice with peel (**B**), and with a 0.8 mm thick (**C**) and 1.5 mm thick (**D**) slices without peel.
