## 1 Introduction  
Nondestructive assessment of the quality of fruits and vegetables is important for production and sales. Apples have been the subject of many studies, because they are one of the most economically important fruits in the world. At present, the quality of apples can be qualitatively evaluated by observing their size, color, and shape, or quantitatively determined by chemical or optical methods. The charge-coupled device (CCD) image analysis, hyperspectral image analysis, and multispectral imaging with computer vision algorithms are commonly used for apple sorting and grading [1; 2; 3]. With advances in measurement systems and algorithms, the recognition rate of existing methods for grading healthy and defective apples is up to 90% [4]. However, these techniques are limited to obtaining information on the surface features of apples. Thus, imaging-based systems cannot easily detect damaged apples, especially those with recent bruises with a color similar to that of healthy apples [5]. The changes in the optical absorption and scattering in apple flesh need to be evaluated to monitor the interior condition of the apples. The optical properties of tissues could be indicative of their chemical and physical properties. Numerous studies on measuring the optical properties of fruits using advanced optical techniques that are mainly based on the radiative transfer theory have been conducted [6; 7; 8]. These optical methods have been widely applied for the noninvasive characterization of tissue properties through measurements of light-tissue interaction phenomena such as reflectance, propagation, and attenuation [7; 9]. Among the various optical methods, diffuse reflectance spectroscopy (DRS) is useful for monitoring apple quality. For example, [PERSON] et al. used a femtosecond pulse laser source, and measured the diffuse reflectance that indicates the pulse broadening effect caused by apples, to derive the absorption and scattering properties of the fruits [10]. [PERSON] et al. estimated the optical properties of apple skin and flesh in the wavelength range of 350-2200 nm [11]. [PERSON] et al. measured the absorption and scattering properties of apples using the spatial frequency-domain imaging to determine the difference between bruised and nonbruised apples [12]. However, the change in the optical properties of apple skin and flesh during ripening and postharvest storage has not been reported. In addition, no research has established the relationship between the sampling depth and optical properties at different parts of apples. Furthermore, there is no research exploring the difference in the optical properties between normal apples and injured apples over time. Photon absorption and scattering can be characterized by the absorption coefficient (\(\mu_{a}\)) and reduced scattering coefficient (\(\mu_{s}\)'), respectively. The absorption coefficient is related to the fruits' chemical components, including chlorophyll and water, and the absorption spectrums of chlorophyll-a and water manifest their absorption peaks at approximately 660 and 970 nm, respectively [13; 14]. The reduced scattering coefficient is related to the physical structure of fruits such as cell structure. Chlorophyll degradation mainly occurs during leaf senescence or fruit ripening [13]. The cell wall depolymerization and the dissolution of the middle lamella lead to cell separation during storage [15]. The optical properties are potentially useful for estimating the quality, freshness, and firmness of fruits through the detection of the differences in absorption and scattering based on the two natural changes. Light absorption is related to tissue chemical constituents, such as moisture content and fruit ripeness, while light scattering is influenced by physical and structural properties, such as firmness and cell size [8]. In addition, variations in the source-detector separation (SDS) settings would result in variations in sampling volumes and depths.