We propose an autostereoscopic display system that ensures full resolution for multiple users by directional backlight and eye tracking technology. The steerable beam formed by directional backlight can be regarded as the result of sparsely sampling the light field in space. Therefore, we intuitively propose an optimization algorithm based on the characterization for the state of the steerable beams, which is computed in matrix form using the plenoptic function. This optimization algorithm aims to optimize the exit pupil quality and ultimately enhancing the viewing experience of stereoscopic display. Numerical simulations are conducted and the improvement in exit pupil quality achieved by the optimization scheme is verified. Furthermore, a prototype of the stereoscopic display that employs dual-lenticular lens sheets for the directional backlight has been constructed using the optimized optical parameters. It provides 9 independent exit pupils at the optimal viewing distance of 400 mm, with an exit pupil resolution of 1/30. The field of view is ±16.7°, the viewing distance range is 380 mm to 440 mm. At the optimal viewing distance 400 mm, the average crosstalk of the system is 3%, and the dynamic brightness uniformity across the entire viewing plane reaches 85%. The brightness uniformity of the display at each exit pupil is higher than 88%.
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