*Article* **Analysis of Light Penetration Depth in Apple Tissues by Depth-Resolved Spatial-Frequency Domain Imaging**

**Tongtong Zhou 1,†, Dong Hu 1,†, Dekai Qiu 1, Shengqi Yu 1, Yuping Huang 2, Zhizhong Sun 3, Xiaolin Sun 1, Guoquan Zhou 1, Tong Sun <sup>1</sup> and Hehuan Peng 1,\***


**Abstract:** Spatial-frequency domain imaging (SFDI) has been developed as an emerging modality for detecting early-stage bruises of fruits, such as apples, due to its unique advantage of a depthresolved imaging feature. This paper presents theoretical and experimental analyses to determine the light penetration depth in apple tissues under spatially modulated illumination. Simulation and practical experiments were then carried out to explore the maximum light penetration depths in 'Golden Delicious' apples. Then, apple experiments for early-stage bruise detection using the estimated reduced scattering coefficient mapping were conducted to validate the results of light penetration depths. The results showed that the simulations produced comparable or a little larger light penetration depth in apple tissues (~2.2 mm) than the practical experiment (~1.8 mm or ~2.3 mm). Apple peel further decreased the light penetration depth due to the high absorption properties of pigment contents. Apple bruises located beneath the surface peel with the depth of about 0–1.2 mm could be effectively detected by the SFDI technique. This study, to our knowledge, made the first effort to investigate the light penetration depth in apple tissues by SFDI, which would provide useful information for enhanced detection of early-stage apple bruising by selecting the appropriate spatial frequency.

**Keywords:** light penetration depth; apple; spatial-frequency domain imaging; depth-resolved; bruise; scattering
