With the development of multimedia technology, Augmented Reality (AR) has become a promising next-generation mobile platform. The primary value of AR is to promote the fusion of digital contents and real-world environments, however, studies on how this fusion will influence the Quality of Experience (QoE) of these two components are lacking. To achieve better QoE of AR, whose two layers are influenced by each other, it is important to evaluate its perceptual quality first. In this paper, we consider AR technology as the superimposition of virtual scenes and real scenes, and introduce visual confusion as its basic theory. A more general problem is first proposed, which is evaluating the perceptual quality of superimposed images, i.e., confusing image quality assessment. A ConFusing Image Quality Assessment (CFIQA) database is established, which includes 600 reference images and 300 distorted images generated by mixing reference images in pairs. Then a subjective quality perception experiment is conducted towards attaining a better understanding of how humans perceive the confusing images. Based on the CFIQA database, several benchmark models and a specifically designed CFIQA model are proposed for solving this problem. Experimental results show that the proposed CFIQA model achieves state-of-the-art performance compared to other benchmark models. Moreover, an extended ARIQA study is further conducted based on the CFIQA study. We establish an ARIQA database to better simulate the real AR application scenarios, which contains 20 AR reference images, 20 background (BG) reference images, and 560 distorted images generated from AR and BG references, as well as the correspondingly collected subjective quality ratings. Three types of full-reference (FR) IQA benchmark variants are designed to study whether we should consider the visual confusion when designing corresponding IQA algorithms. An ARIQA metric is finally proposed for better evaluating the perceptual quality of AR images. Experimental results demonstrate the good generalization ability of the CFIQA model and the state-of-the-art performance of the ARIQA model. The databases, benchmark models, and proposed metrics are available at: https://github.com/DuanHuiyu/ARIQA.