###### Abstract  
Autostereoscopic displays employing lenticular sheets have broad applications due to the high transmittance of lenticular sheet. However, due to the restriction of lens array design and processing, the imperfect image of lenses can reduce the quality experience of autostereoscopic displays. Stereo depth is one of the qualities of experience parameters, which relates to the three-dimensional effect. Therefore, to quantize the reduction effect of stereo depth caused by lens aberration is of great value. In this paper, we implement a binocular model of an autostereoscopic display system with lens array to analyze this effect, which is different from the previously used monocular model. Two receivers in the positions of viewer's eyes are set on the viewing plane, and a similar factor is defined to evaluate the difference of light spots perceived by the two receivers. When the similar factor exceeds a certain value, the two spots cannot be fused in the brain, thus restricting the perceived stereo depth. Both in simulation and experiment, a sudden decrease of the similar factor is observed when the viewing angle exceeds \(16^{\circ}\). In the subjective experiment, all the sixteen viewers feel a sudden decrease of stereo depth when the viewing angle exceeds \(16^{\circ}\), which further verifies the validity of the model. The model and the method are significant for improving the viewing experience of autostereoscopic displays and providing a guidance on autostereoscopic display system designing. L pacs: 97.10.  
perform the maximum SD, and are theoretically limited by their pixel pitch, because of the unperfect lenslets employed in the lenticular sheets. Due to the limitation of design and processing, most of the lenticular sheets employ simple cylindrical lenslets with low processing accuracy. Furthermore, the lenslets in the margin area of an AD suffer from large incident light beams and long imaging distance. This aberration may greatly reduce the viewer's depth sensation. The quantification of this effect is essential to both the design and evaluation of the ADs. SD is one of the three quality of experience parameters of a stereoscopic display, and the only one that relates to the 3D effect. Generally, the SD is considered to be a synthesized effect that can be affected by many factors together [9]. Several groups have studied the factors that impact the SD of ADs. A previous study shows that, although human depth perception can be obtained from different depth cues, binocular disparity is the most important one when viewing stereoscopic 3D displays [10]. Therefore, the reduction and disturbance to binocular disparity decrease the perceived SD. The influence of crosstalk to stereopsis was theoretically and experimentally studied [11]. The experimental results show that reducing crosstalk can improve the perceived SD [12; 13; 14; 15]. Crosstalk is a synthesized effect, which can be caused by installation errors, lens problems, etc. Therefore, it is difficult to derive the specific relationship between crosstalk and SD. In addition, the enhancement of angular resolution was reported to improve perceived SD [16], but the explicit relationship between angular resolution and the SD was not reported. It is of great significance if one influence factor on perceived SD can be analyzed quantitatively. The reduction effect of lens aberration on SD was quantitatively studied by using wave optics [17; 18]. A monocular model of the display system was implemented. In the model, a stereo point, represented by one pixel, was imaged by a lenslet in the lenticular sheet with aberration at the expected 3D point position. The work in References [17; 18] used the hypothesis that, if the image spot can be distinguished by the viewer's eye, the 3D point can be formed in the viewer's brain. It can be deduced that, when different 3D contents are loaded on an AD, the positions of the 3D point formed by a lenslet are different.