## 2 Materials and Methods
### Optical Properties Measurement  
Typical diffuse reflectance spectroscopy (DRS) systems can work with photon transport models to determine the absorption coefficient (\(\mu_{a}\)) and reduced scattering coefficient (\(\mu_{s}\)') of tissues. The \(\mu_{a}\) and \(\mu_{s}\)' are calculated by the phase and amplitude of photon density waves which are derived from the diffusion equation with extrapolated boundary condition [16]. In the frequency-domain method, the source is sinusoidally modulated at frequency \(f\). The physically measured quantities in  
Figure 1: Schematic of the frequency-domain diffuse reflectance spectroscopy (DRS) system configuration.  
a frequency-domain DRS measurement are the phase change and the amplitude modulation of the light that has propagated through the tissue, which are given by:  
\[Amp(\rho,\omega)=\left\{\text{Re}[R(\rho,\omega)]^{2}+\text{Im}[R(\rho,\omega)] ^{2}\right\}^{1/2} \tag{1}\]  
\[Phase(\rho,\omega)=\tan^{-1}\frac{\text{Im}[R(\rho,\omega)]}{\text{Re}[R(\rho, \omega)]} \tag{2}\]  
Here, \(\omega=2\pi f\), \(\rho=\left(x^{2}+y^{2}\right)^{1/2}\) and \(R\) (\(\rho\),\(\omega\)) is the spatially resolved reflectance.  
However, at short SDS, as is essential for investigating superficial tissue volumes, most of the photon transport models are invalid. We constructed a database for the ANN training and calculated the diffuse reflectance for various optical properties and various modulation frequencies. We defined the ranges of \(\mu_{a}\) and \(\mu_{s}\)' to be from 0.001 and 0.1 mm\({}^{-1}\), and from 0.5 and 5 mm\({}^{-1}\), respectively. Other simulation parameters are listed below: the refractive index of sample was 1.33 for apple studies, the anisotropy factor was 0.9, and the phase function was the Henyey-Greenstein phase function. Thus, we used a Monte Carlo-based ANN to determine the sample optical properties from the frequency-domain diffuse reflectance collected at short SDS. We have carefully verified the ANN in our previous study [17].  
The source of the optical properties and the procedure for determining it is illustrated in Figure 2. The intensity-modulated light was launched into the tissue, thereby resulting in the propagation of diffuse photon density waves. Amplitude demodulation and phase delay detected by the network analyzer were compared with the diffusion model. Then, a Levenberg-Marquardt minimization algorithm was used to calculate the absorption and reduced scattering coefficients. The photon transport model assumes that the sample has a flat surface, and the source and detector fibers are flush with the sample surface. We found that 5 mm was the longest SDS at which the validity of this assumption may be confirmed for measuring apples. Thus, the longest and shortest SDSs were set to 5 and 1 mm, respectively. On all the measurement days, we collected 5 frequency-domain reflectance values at SDSs of 1 and 5 mm on a certain spot of each apple, and the source and detector fibers were replaced on the apple surface after each frequency-domain reflectance was collected. The \(\mu_{a}\) and \(\mu_{s}\)' were calculated from 5 reflectance values at 5 points separately by diffusion equation or ANN model. After that, the \(\mu_{a}\) and \(\mu_{s}\)' were averaged and then regarded as the optical parameters of each apple.  
Figure 2: Flowchart of the measurement of optical properties.