**1. Introduction**

Apple fruit is highly valued by consumers for its crispy texture and sweet and sour taste. Soluble sugars in apple fruit largely affect sweetness, and they are the main components of soluble solids [1]. Compared with obtaining the content of soluble sugars, it is faster and more economical to measure soluble solids content (SSC). SSC is measured via the fruit juice. Therefore, SSC is used as a significant property for assessing the sweetness of sugars in apples, and the non-destructive evaluation of SSC by optical techniques have been investigated for many years [2–6], inclusive of near-infrared spectroscopy (NIR) and hyperspectral imaging (HSI).

Light transfer in tissues contains absorption or scattering, and the process of interaction mainly depends on the different chemical components and structures of tissues. By collecting light that is reflected back from or transmitted through the tissue based on NIR and HSI techniques, the chemical

as well as structural characteristics of tissues can be acquired [7]. The prediction models for SSC can be built based on chemometrics methods by using the captured spectra and the standard measurements, and some satisfactory results have been obtained [8–12]. The calibration models can then be used to predict new samples after establishing and validating. However, it leads to limitation in illustrating the chemical and structural properties of interest from the meaningful information presented in obtained spectra due to the overarching behaviors of absorption and scattering in tissues collected by NIR and HSI techniques which cannot separate these two properties [13]. Besides, the accuracy of NIR and HSI techniques is limited, because the techniques are based on the Lambert-Beer law, which often discards the scattering effect. Furthermore, the obtained properties of reflectance or transmittance are dependent on the instrument types and light source/detecting probe setup [14]. There are, in general, inherent shortcomings with NIR and HSI techniques, which present great challenge in internal quality assessment of agri-food products.

The optical parameters measurement resulted in separate and quantized information of the absorption and scattering properties by calculating the absorption coefficient (μ*a*) and reduced scattering coefficient (μ- *<sup>s</sup>*) [15,16]. The current measurement techniques are developed to measure absorption and scattering properties, mainly including integrating sphere (IS) [17,18], spatially-resolved (SR) [19], time-resolved (TR) [20] and frequency-domain (FD) [21]. In addition, the techniques are based on the light transfer theory, which involves inverse adding double (IAD), Monte Carlo (MC), and diffuse approximation (DA), and the optical properties can be obtained by IS with IAD [22,23]. Such methods have opened up the opportunity to attribute internal quality parameters, both chemical composition and structure information, to optical properties of tissues for investigating the one to one relationship between them [24–27]. He et al. [28] applied an automatic integrating sphere (AIS) system combined with IAD strategies to acquiring the μ*<sup>a</sup>* and μ- *s* spectra of pear tissues in 400–1150 nm. Using a single integrating sphere, Wang et al. [29] estimated the absorption and scattering properties of healthy and diseased onion skin and flesh over the range of 550–880 nm and 950–1650 nm.

Many studies in Vis-NIR (400–1100 nm) have been conducted. The findings showed that μ*<sup>a</sup>* around 525 and 675 nm were affected by anthocyanin and chlorophyll. In addition, μ*<sup>a</sup>* at 630 nm is attributed to total galacturonic acid (GA) in residue insoluble pectin (RIP), with an *r* of 0.64 [30]. μ*<sup>a</sup>* and μ- *<sup>s</sup>* at 675 nm are noticed for area and equivalent diameter of apple tissue cells (*r* = 0.581–0.941) [31]. Nowadays, there are few studies on optical properties in longer wavelength ranges (above 1100 nm). However, the absorption property features above 1100 nm contain more important and obvious bonds, C-H, O-H, C-C, than the features observed in the Vis-NIR range [24,32]. Thus, enhanced sensitivity of optical properties related to tissue components can be obtained compared to the wavelength range above 1100 nm [33,34]. The increase in SSC causes an increase in the signal of absorption at 1198 nm, while water cored tissue caused a characteristic decline in light scattering coefficients [35]. However, the relationship between them has not been quantified, and the relationships between absorption and scattering properties and the compositions in SSC are also not clear yet.

Therefore, this research aimed to comprehensively clarify the mechanism of detecting SSC by optical technology and provide information for accurately developing improved SSC detectors of Fuji apple during storage by optical technology. In the work, the μ*<sup>a</sup>* and μ- *<sup>s</sup>* of apple fleshes in longer wavelength range NIR (905–1650 nm) were calculated based on the AIS system with the IAD method, and internal quality (SSC and the contents of soluble sugars) was measured. Finally, relationships between μ*a*, μ- *s* and SSC, the contents of total soluble sugar (TSS), fructose, glucose and sucrose were investigated, then the potential for predicting the SSC was evaluated.
