## 5 Conclusions  
This paper presents a theoretical analysis of intrinsic properties of the two-layered diffusion model and inverse algorithm through numerical simulation, including effect of optical parameter on reflectance prediction and optical property extraction, estimation accuracy of different curve fitting methods, and relationship between penetration depth and spatial frequency, in order to improve optical property estimation accuracy of two-layered horticultural products using SFDI technique. Reflectance prediction results indicated that there is good separation in diffuse reflectance over a large range of spatial frequencies for different \(\mu_{s1}\)' values, whereas less separation in diffuse reflectance for different \(\mu_{a1}\) values, and even less separation for different values of \(\mu_{a2}\) and \(\mu_{s2}\)', which is in agreement with accuracy for estimating optical properties. Evaluation of parameter estimation accuracy for all the five curve fitting strategies suggested to apply the stepwise method for estimating optical properties of two-layered samples, which estimated \(\mu_{a1}\) and \(\mu_{s1}\)' using the one layered model first, followed with the estimation of \(\mu_{a2}\) and \(\mu_{s2}\)' using the two-variable fit. Investigation on the factors influencing the extraction of \(\mu_{a1}\) and \(\mu_{s1}\)', and relationship between penetration depth and spatial frequency offered great guidance for optimizing the frequency region for optical property estimation. Future work can be done on exploring the full potential of depth-varying features in SFDI for reducing or eliminating the effect of the top layer on estimating optical properties of the bottom layer.  
The following are available online at [[https://www.mdpi.com/2076-341](https://www.mdpi.com/2076-341)]([https://www.mdpi.com/2076-341](https://www.mdpi.com/2076-341)) 7/11/2/617/s1, Figure S1: Absolute error contour maps for estimating \(\mu_{a1}\) (left panel) and \(\mu_{s1}\)' (right panel) of four representative two-layered simulation samples with varying values of \(\mu_{a1}\)/\(\mu_{a2}\) by using the stepwise method with different start and end frequencies, Figure S2: Absolute error contour maps for estimating \(\mu_{a1}\) (left panel) and \(\mu_{s1}\)' (right panel) of four representative two-layered simulation samples with varying values of \(\mu_{s1}\)'/\(\mu_{s2}\)' by using the stepwise method with different start and end frequencies, Table S1: Twenty two-layered simulation samples with different combinations of \(\mu_{a1}\), \(\mu_{a1}\)', \(\mu_{a2}\), \(\mu_{s2}\)' and top-layer thickness \(d\) for investigating the effects of optical properties on reflectance prediction and comparing the estimation performance of diverse curve fitting methods, Table S2: Two-layered simulation samples with varying values of \(\mu_{a1}\)/\(\mu_{a2}\), Table S4: Two-layered simulation samples with varying values of \(\mu_{s1}\)'/\(\mu_{a2}\)', Table S5: Two-layered simulation samples with varying values of \(\mu_{s1}\)'/\(\mu_{a1}\)'.  
Conceptualization, D.H. and Y.H.; methodology, D.H. and T.S.; software, D.H.; validation, Y.H. and Q.Z.; writing--original draft preparation, D.H.; writing--review and editing, D.H., Y.H., Q.Z. and T.S.; supervision, L.Y. and Z.Y.; funding acquisition, D.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of Zhejiang Province (LQ20C130002), the Natural and Science Foundation of China (32001414), the Project of Key Laboratory in the Ministry of Agriculture and Rural Areas (2016 NYZD18003) and the Startup Project of Zhejiang A&F University (2034020090).  
The authors gratefully thank [PERSON] in the U.S. Department of Agriculture Agricultural Research Service (USDA/ARS) for his great guidance and valuable advice.  
The authors declare no conflict of interest.