偏光立體投影系統中影像品質的優化

Abstract

在偏光立體投影系統(Polarized Stereoscopic System)中，是採用兩台投影機分別投射左右眼影像，經過偏振片與延遲片的光學元件，最後在觀察者端觀看到立體的影像。但在偏光式立體投影系統中，因為投影螢幕大小以及投影距離的限制，投影機光源入射螢幕的角度為斜向35度入射，在此光源投射的條件下，當觀察者頭偏角度過大會有交互干擾與色差的問題，造成影像品質變差。 研究上採用偏振片與四分之一波長延遲片的瓊斯矩陣，透過瓊斯矩陣的運算，以模擬的方法計算相對應的交互干擾。並透過色度圖CIE 1976與色差公式對影像的色差進行分析。在不同頭偏角度與光源入射角度下，對於:交互干擾與色差這兩項品質因子，利用延遲片角度的堆疊設計，達到影像品質的優化。 本論文對這兩項品質因子:交互干擾與色差，分別在各頭偏角度與各光源入射角度下，採用窮舉法找出最佳的延遲片角度設計，來達成交互干擾與色差的優化。針對交互干擾部分，欲壓低長波長波段的交互干擾，又不會造成短波長波段交互干擾的劣化，而提出交互干擾容忍量的設計方法，以此方法設計在頭偏角度15度時可以達到16%的改善程度，在頭偏角度45度時採用20%容忍量時可以達到60%的改善程度。針對色差部分可以利用延遲片角度設計，來達到有頭偏情況下色彩的表現與無頭偏時一樣好。當同時對色差與交互干擾作優化時，透過分析色差與交互干擾的重要性，得知交互干擾重要高於色差，以交互干擾影響程度為色差10倍條件去設計，色差變差，但差異值僅0.0001~0.0009的數量級，反觀交互干擾的最大優化量接近1。 在未來的研究中，不只可以改變延遲片的角度設計，也可以透過不同的延遲片材料與厚度設計方式，對交互干擾或是色差得到進一步的優化，來達成偏光立體投影系統中更好的影像品質。

We adopt two projectors to project left and right images separately in polarized stereoscopic system. The light passes through the optical components such as polarizers and retarders. Finally, the observers can watch the stereoscopic images. Because of the screen size and projection distance, light is projected from the projector with an oblique angle of 35 degrees in the polarized stereoscopic system. Under this situation, observers will suffer from worse image qualities due to crosstalk or color shift when they are with severe head rotation. We can use the simulation method to calculate crosstalk by using the representative Jones matrix of polarizer and quarter-wave retarder and calculating the product of Jones matrices for the system. We can evaluate the color shift for images by chromatic diagram and color shift formula based on CIE 1976. We can optimize the image qualities by designing the angles of stacked retarder for minimizing crosstalk or color shift under different angles of head rotation and light incidence. We can find the optimized retarder angles by using exhausted method to achieve the optimization of crosstalk and color shift under different angles of head rotation and light incidence. We want to reduce the crosstalk within long wavelength range, but we don't want the crosstalk to get worse within wavelength range during optimizing crosstalk. Due to the crosstalk problem, we propose a solution with a certain maximum residue levels of crosstalk. We can achieve 16% improvement ratio under head rotation of 15 degrees and 60% improvement ratio in head rotation of 45 degrees with 20% maximum residue levels. We can achieve color shift optimization under head rotation situation just as under no head rotation situation. When we want to optimize crosstalk and color shift simultaneously, we try to analyze the importance of crosstalk and color shift and conclude that crosstalk is more important than color shift in image qualities optimization. If we adopt the criterion of crosstalk being 10 times important than color shift, we can get the maximum optimized value of 1 for crosstalk. Instead of getting better crosstalk, we suffer from worse color shift. But the worse value of color shift is within the range of 0.0001 to 0.0009. The difference is negligible. We will not only tune the retarder angles but also design different materials and thickness to further improve crosstalk and color shift in the future and achieve better image qualities in polarized stereoscopic system.