## 1 Introduction  
Black goji berry from the Qinghai-Tibet Plateau is an abundant source of various nutrients--proteins, superoxide dismutase, vitamins, minerals, amino acids, polysaccharides [1]. Therefore, black goji berry brings immeasurable economic benefits and development value. Specifically, there is a large content of purple pigment (up to 3.88 mg/g in fresh fruits), which is a rare edible natural anthocyanin resource. It is expected to become a colorant for cosmetics, pharmaceuticals, beverages, and food [2]. In addition, it contains a variety of trace elements, confirming good medicinal plant resources. Meanwhile, black goji berry combines 18 essential amino acids and free amino acids. The amino acids accounted for about 50% of the total, making black goji berry a preferred high-quality protein [3]. More importantly, a natural wild fruit, black goji berry contains up to 5.04% of oligomeric proauthor-cyanidins (OPC), which is 10 and 18 times higher than that in Chinese wolfberry and natural blueberry, respectively [4]. Black goji berry is an essential natural antioxidant because OPC enhances the immune system by 22 and 25 times compared to vitamins C and E, respectively [5]. Therefore, black goji berry is considered to be a novel source of nutraceuticalals.  
An antioxidant, as a molecule, prevents other molecules' oxidation which is a chemical reaction that can generate free radicals, resulting in chain reactions that may impose harm to cells. However, antioxidants such as ascorbic acid or thiols can terminate these chain reactions [6]. Intake of antioxidants from fruit and vegetables protects humans from cancers. Phenolic compounds are among important antioxidants found in vegetable food and possess the major organoleptic characteristics (color and taste) of beverages and plant-derived food [7]. Our work will conduce to knowledge about the ideal conditions for obtaining the maximum yields of phenolics and antioxidants from black goji berry. The results may find applications in the development of industrial extraction processes.  
Mathematical models for optimizing extraction processes of target compounds are crucial in the field of natural product chemistry to effectuate economical design of actual operation [8]. Currently, the response surface methodology (RSM), which solves both linear and non-linear multivariate regression problems, is a useful tool for establishing a model to mimic and optimize the whole extraction process [9; 10].  
For phenolics and antioxidant extraction, many methods have been applied, such as ultrasound-assisted extraction (UAE), microwave-assisted extraction (MAE), and reflux extraction. However, there is no report, to the best of our knowledge, on the phenolics and antioxidants extraction from black goji berry with the help of the accelerated solvent extraction (ASE) method. ASE can automatically extract solid and semisolid samples quickly by applying common solvents. The temperature of the ASE is far above the boiling point of most solvents, whereas the high pressure keeps a solvent in a liquid phase. Hence, the ASE technique possibly achieves automation, low solvent volume and reduced extraction properties [7].  
The objective of the current study is to extract the maximum amount of total phenolics content (TPC) from black goji berry by means of the ASE technique. The RSM design was used to establish the model and optimize the extraction conditions. Under the optimal extraction conditions, antioxidant capacity tests of black goji berry were also performed with the 2,2\({}^{\prime}\)-azino-bis-(3-ethylbenzothazoline-6-sulfonic acid) (ABTS) radical scavenging assay, the DPPH free radical scavenging capacity assay, and the ferric reducing antioxidant capacity assay.