## 5 Conclusions and Discussions  
The perceived stereo depth of a lenticular based autostereoscopic display system is reduced because of the lens aberration. In this paper, we present a new method based on human vision to evaluate the SD reduction effect caused by lens aberration for lenticular based autostereoscopic display system. Compared to the monocular models, our model simulates the true function of lenslets in autostereoscopic display systems, and the 3D fusion in human vision.  
To analyze the effect of lens aberration, we used wave optics theory to set up a binocular model and calculate the sizes of both light spots on the viewing plane formed by the light beams emitted by a pair of pixels and refracted by the corresponding lenslets with aberration. The two receivers on the viewing plane have a distance of 65 mm, which is the human average interpupillary distance, to simulate a viewer's eyes. Different from previous work, we believe that reduction of stereo depth by lens aberration happens because the images of two homonymy points in the corresponding eyes have large disparity, which makes the brain fail to fuse the points into a 3D point. Therefore, we define a similar factor to evaluate the width difference of the two stereo spots on the viewing plane. We explore the influence of viewing angle on the similar factor by simulation and experiment. It is found that the simulation keeps stable within a certain range and reduce sharply when the viewing angle is larger than 16\({}^{\circ}\), both in simulation and experiment. Finally, we conduct a subjective experiment to verify our theory. All the observers experience a sudden decrease in 3D effect when the viewing angle achieves the break point 16\({}^{\circ}\), which proves our theory.  
However, our model is only with monochromatic illumination. That's because the influence of color on human 3D vision is a very complex mechanism. We cannot simulate the color human 3D vision by our model, which employs a similar factor to simulate the fusion of stereo images. To focus on the lens aberration, we must limit the simulation into a monochromatic situation. For the same reason, we cannot do subjective experiments by using monochromatic stereo images simply extracted from color stereo images.  
Figure 11: Perceived stereo depth of “lotus” on the prototype at different viewing angle by 4 different elder viewers.  
The research is still of importance for evaluating the parameters and improving the viewing experience of lenticular-based autostereoscopic displays. The largest viewing angle can be calculated according to the proposed model with the specifications of a lenticular-based autostereoscopic display. Optimization of the lens shape by minimizing the lens aberration at large viewing angles can improve the similar factor and expand the viewing angles accordingly, although the result cannot be predicted.  
[PERSON] provided conceptualization and resources. [PERSON] was the supervisor providing fundings and administrating the project, and she wrote the original draft and did the formal analysis. [PERSON] did the investigation, methodology and the validation, wrote the software. [PERSON] did the formal analysis and reviewed and edited the manuscript.  
This work was supported by Basic Research Program of Shenzhen (JCYJ20170412171744267, JCYJ20160428182212366) and National Basic Research Program of China (2015 AA043302). [PERSON] also appreciates the State Scholarship Fund (201808440080) from China Scholarship Council. The APC was funded by JCYJ20160428182212366.  
The authors thanked [PERSON] and [PERSON] for conducting the subjective experiment by elder volunteers and edited some pictures.  
The authors declare no conflict of interest.