## 4 Discussion  
Depth-varying characterization is the hallmark of SFDI technique under structured illumination with sinusoidal patterns, which is absent in conventional uniform illumination. However, the light penetration depth derived from Equation (4) does not always hold for actually detectable region for a general imaging system. In such cases, the light backscattered close to the illumination source contributes more to the detected signals, which correspond to a far more superficial depth of tissue interrogation than that derived from diffuse light attenuation. Moreover, due to the comprehensive consideration of imaging resolution, imaging contrast and signal-to-noise ratio, the factor of \(1/e\) for light decaying in tissues is not always appropriate in practical applications, such as the subsurface bruise detection of fruit sample [36]. Since one goal of this study is to explore the potential of accuracy improvement for estimating optical properties of two-layered horticultural products by selecting appropriate frequency region, the relationship between light penetration depth and spatial frequency was just roughly investigated here. A more realistic experimental setting, such as three-dimensional modeling of the target sample with more layers [37], should be taken into account in the future for quantifying the light penetration depth, as well as the sampling volume (i.e., spatial distribution of detector depth sensitivity). The cross effect of each layer is one of the challenging factors influencing optical property estimation of two-layered horticultural products. It is desirable to obtain the effective information of the target (top or bottom) layer when estimating the corresponding \(\mu_{a}\) and \(\mu_{s}{}^{\prime}\) without the interference of the other layer. The feature of depth-varying of SFDI provides a potential solution for solving this problem. The emitted optical signals under large spatial frequency carry more information related to the top layer, while those with  
Figure 6: Relationship between light penetration depth and spatial frequency for a homogeneous sample under structured illumination of sinusoidal patterns with four sets of optical properties. relatively small spatial frequency penetrate deep into the bottom layer. It is thus possible to quantitatively select a spatial frequency, under which the captured signal is only related to the top layer. Then, an operation of subtraction between this signal and another one with smaller frequency can be used to eliminate the effect of the top layer. In principle, the signal after this operation should be more related to the bottom layer, and thus improving the estimation accuracy for \(\mu_{a}\) and \(\mu_{s}\)' of the bottom layer. Take the apple fruit as a two-layered example with peel and flesh tissues. Subtraction operation for the demodulated reflectance between the small frequency and large frequency is expected to clear the peel information of apple sample, and the remaining reflectance will be more valuable for estimating \(\mu_{a}\) and \(\mu_{s}\)' of the flesh tissue. It should be noted that this method may be limited for the two-layered horticultural products with relatively thin top-layer thickness (e.g., apple, peach and tomato) due to restricted light penetration depth (\(\sim\)1-2 mm) under the spatial frequency of 0.15 mm\({}^{-1}\)[38]. The full potential of this method is worth exploring in the future research. Thanks to the characteristics of the one-layered model, the stepwise method does not require a priori knowledge of the top-layer thickness for estimating \(\mu_{a1}\) and \(\mu_{s1}\)', but the top-layer thickness is still required to be known when estimating \(\mu_{a2}\) and \(\mu_{s2}\)' using the two-variable fit through the two-layered model. However, the top-layer thickness is usually unknown or difficult to be measured accurately, which brings challenges for optical property estimations of the bottom layer.