**1. Introduction**

Optical sensing techniques, such as near-infrared spectroscopy and hyperspectral imaging, have been extensively researched and increasingly utilized for detecting multiple defects of agro-food products [1–3]. The past decade has witnessed the development of spatial-frequency domain imaging (SFDI) for detecting various surface and subsurface defects of fruits [4–7]. As one of the typical defect types, surface bruises in apples often occur during harvest, transportation, storage, and sorting processes. Slight early-stage bruises are invisible to our naked eyes and are challenging to be recognized by traditional imaging techniques under uniform or diffuse illumination, which are more sensitive to the obvious surface properties. Thanks to frequency-dependent light attenuation within tissues, as depicted in Figure 1, SFDI enables acquiring depth-resolved information regarding tissue constituents and structure. Based on this remarkable feature, SFDI is proven to be capable of detecting the early-stage bruises of apples beneath the peels [6]. As opposed to the traditional uniform light imaging techniques, such as machine vision and hyperspectral imaging, spatially modulated light in a sinusoidal waveform is used in SFDI to acquire pattern images from samples. Through image demodulation and inverse estimation processing, SFDI produces 2-D optical property mappings in a pixel-by-pixel fashion, i.e.,

**Citation:** Zhou, T.; Hu, D.; Qiu, D.; Yu, S.; Huang, Y.; Sun, Z.; Sun, X.; Zhou, G.; Sun, T.; Peng, H. Analysis of Light Penetration Depth in Apple Tissues by Depth-Resolved Spatial-Frequency Domain Imaging. *Foods* **2023**, *12*, 1783. https:// doi.org/10.3390/foods12091783

Academic Editor: Corrado Costa

Received: 19 March 2023 Revised: 13 April 2023 Accepted: 23 April 2023 Published: 25 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

absorption coefficient (*μa*) mapping and reduced scattering coefficient (*μ <sup>s</sup>*) mapping. The differences of optical properties between non-bruised apple tissues and bruised ones can be directly used for early-stage bruise detection. It is well known that there are quite a lot of optical property measuring methods, e.g., time-resolved, spatially resolved, and integrating sphere, which have been employed for measuring optical properties of diverse agro-food products [8–11]. However, they are generally limited to point measurement and cannot attain depth-resolved information, resulting in great challenges in the nondestructive detection of early-stage bruises of apples [12,13]. In the technique of SFDI under the spatially modulated illumination, high-frequency light is more sensitive to the shallower tissue, while the low-frequency component has a much larger light penetration depth (~mm) [14,15], which provides a theoretical basis for detecting early-stage bruises of apples.

**Figure 1.** Schematic of light attenuation within a semi-infinite turbid medium under spatially modulated illumination.

Knowledge of light penetration depth sampled by SFDI is of high significance for clinical and preclinical applications in the field of biomedicine [16–18]. For instance, the thickness of burned skin dictates the treatment protocol, highlighting the importance of understanding the detection depth in skin tissue [19]. SFDI has also been explored in deeptissue applications, where it is essential to understand the penetration of collected photons in order to evaluate the maximum depth of measurable tumor contrast [20]. However, measuring light penetration depths in the field of biomedicine is not without limitations. The experiments generally require patients to remain completely still during a potentially long acquisition time in order to acquire full area scans. The exploration of the light penetration depth often requires prior knowledge about tissue optical properties that may not be valid in damaged tissue. Similar to that in the field of agricultural and food engineering, knowledge of light penetration depth is critical for enhancing the detection performance of early-stage bruises in apples by SFDI. Despite great progress being made for the bruise detection of apples, there still is a lack of exploration of quantifying light penetration depth in apple tissue. As mentioned above, SFDI has a remarkable advantage in subsurface (early-stage) bruise detection of apples, but the light penetration depth is reported to be limited in mm, implying that some internal bruises located in the region

of deep tissue cannot be detected. It is thus desirable and also necessary to quantify light penetration depths under varying-frequency spatially modulated illumination, so as to better explore the potential of SFDI for early-stage bruise detection of apples in different depths, as well as to assess the severity of apple bruising. Up to now, the maximum detection depth in apple tissue using SFDI has been uncertain and there are few research studies focusing on studying light penetration depth. Lu and Lu [21] reported that the maximum light penetration depth was confirmed to be no more than three sheets of blank printing paper (or less than 400 μm). Their study investigated the light penetration depth from the aspect of demodulated images, which is different from our research in optical property estimation through inverse computation. Apple is taken as the experimental material in this study, which has different properties from the blank printing paper. The estimated optical property mappings could provide quantitative information in bruise detection (specific values of optical properties for non-bruised and bruised tissues), and thus further exploration of the light penetration depth could be implemented through these quantitative information.

Therefore, in this study, a set of well-designed experiments from theoretical simulation to practical implementation was performed to quantify the light penetration depth (especially for the maximum value) in apple tissue under spatially modulated illumination. The objectives were to (1) explore the light penetrating capacity of demodulated direct component (DC) and amplitude component (AC) images to prove our SFDI system performance; (2) conduct the simulation and practical experiments to investigate the light penetration depths in 'Golden Cream Delicious' apples with and without peels; and (3) validate the conclusion of the maximum light penetration depth in apple tissues by evaluating the performance of bruise detection.
