**1. Introduction**

Apples are known for their texture, flavor, visual effect, and nutritional value [1,2]. NIR spectroscopy has become the representative and main development direction of modern non-destructive testing with its unique advantages of simplicity, efficiency, and non-destructiveness, and is an effective way to solve the classification of agricultural products [3–6]. The application of NIR spectroscopy in fruit and vegetable quality inspection has been reported, mainly focusing on citrus, apple, pear, tomato, and other species [7–10].

Many scholars have studied the application of NIR spectroscopy in the internal quality of fruits. In terms of algorithms, Travers et al. [11] developed partial least squares (PLS) models based on spectra in the wavelength ranges of 680–1000 nm and 1100–2350 nm, respectively, after extracting the characteristic wavelengths using the competitive adaptive re-weighted sampling algorithm (CARS) for predicting the dry matter (DM) and SSC of pears. The feature wavelengths selected by CARS successfully highlighted the differences between the prediction models based on the two different spectral ranges. In near infrared spectroscopy research, the relationship between near-infrared reflectance and transmittance spectra of kiwifruit and soluble solids was investigated by Schaare et al. [12]. The analysis showed that modeling using transmittance spectra was better than reflectance, with a test set correlation coefficient of 0.961 and a test set root mean square error of 0.8%. Tian et al. [13] used NIR spectra to predict nuclear mold in apples of different fruit sizes, correcting the NIR spectra of apples with different degrees of disease. The accuracy of apple

**Citation:** Jiang, X.; Zhu, M.; Yao, J.; Zhang, Y.; Liu, Y. Calibration of Near Infrared Spectroscopy of Apples with Different Fruit Sizes to Improve Soluble Solids Content Model Performance. *Foods* **2022**, *11*, 1923. https://doi.org/10.3390/ foods11131923

Academic Editors: Zhiming Guo, Zhao Zhang and Dong Hu

Received: 4 June 2022 Accepted: 24 June 2022 Published: 28 June 2022

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disease degree prediction established by the corrected spectra was up to 90%. In terms of actual testing, Arana et al. [14] examined the soluble solids of white grapes and the method chosen was NIR spectroscopy, which achieved a good prediction of the soluble solids of white grapes. Jha et al. [15] examined the internal quality of seven Indian mangoes by NIR spectroscopy between 1200 nm and 2200 nm for both soluble solids and acidity and established PLS with Rp of only 0.715 and 0.703. Liu et al. [16] developed a generalized UVE-PLS model for apple brix by collecting diffuse transmission spectra of red Fuji apples from three different locations, namely Qixia, Luochuan, and Huining, highlighting the potential of spectroscopic techniques for fruit quality detection in different origins. Antonucci et al. [17] conducted a study on the internal quality of oranges by spectroscopic techniques and achieved good results in predicting their acidity and soluble solids by regression analysis using the PLS model, with correlation coefficients of 0.843 and 0.812 for soluble solids and acidity of oranges, respectively. Ni et al. [18] performed the NIR spectral model transfer of different instruments by filtering the wavelength information of different NIR instruments. Two datasets of maize and scutellaria samples measured by different NIR instruments were used to test the performance of the method, where the overall prediction performance of the SWCSS-PLS model for the secondary measurement samples was much better than that of the full-wavelength PLS model. Meng Qinglong et al. [19] collected the reflection spectra of fresh "Fuji" apples from 400 to 1000 nm, and used different pretreatment and different characteristic wavelength screening methods to establish various models to predict the SSC content of apples. It can be better used for the detection of apple SSC. The above studies did not consider the sample size. Ideally, the samples for NIR modeling should include all of the variables affecting the NIR spectra, but this is very difficult for the detection of complex variables in the internal quality of apples. If more variability samples are included in the model, the prediction accuracy of the model decreases and further confirmation is needed to meet the requirements. In this paper, it was found that the light intensity of the transmittance spectra of the internal pulp of apples showed a log-linear relationship with their fruit diameter. Therefore, a size-correction method for apples is proposed, based on which the NIR spectra of all apples with different fruit diameters are transformed into a single spectrum that is used to eliminate the effect of size on the performance of the apple SSC prediction model. Compared with the apple soluble solids content prediction model without size correction, the proposed apple size correction method effectively solves the problem of poor prediction accuracy of apple SSC model due to apple size.
