Smart mirrors have emerged as a new form of augmented reality (AR) interface for home environments. However, due to the parallax in human vision, one major challenge hindering their development is the depth misalignment between the 3D mirror reflection and the 2D screen display. This misalignment causes the display content to appear as if it is floating above the mirror, thereby disrupting the seamless integration of the two components and impacting the overall quality and functionality of the mirror. In this study, we introduce 3D-Mirrorcle, an innovative augmented reality (AR) mirror system that effectively addresses the issue of depth disparity through a hardware-software co-design on a lenticular grating setup. With our implemented real-time position adjustment and depth adaptation algorithms, the screen display can be dynamically aligned to the user's depth perception for a highly realistic and engaging experience. Our method has been validated through a prototype and hands-on user experiments that engaged 36 participants, and the results show significant improvements in terms of accuracy (24.72% $\uparrow$), immersion(31.4% $\uparrow$), and user satisfaction (44.4% $\uparrow$) compared to the existing works.
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