Effect of surface roughness of optical waveguide on imaging quality and a formula of RSE tolerance and incident angle

The optical waveguide is a lightweight and portable scheme for augmented reality near-eye display devices. However, the surface roughness of the waveguide affects its imaging performance, which has not been studied. In this work, we investigate the light scattering caused by the root-mean-square roughness of the waveguide surface and present two methods to numerically analyze the modulation transfer function (MTF) of the display system. Here, we consider the effects of different surface roughness, incident angle, and incident wavelength on the scattering distribution when other conditions are constant. For a simplified optical waveguide display system, the MTF degradation and the variation of the tolerance is calculated. And when the MTF (@ 40 cycles/mm) is required to be 0.3 and the incident angles of the total reflection surface are 45°, 55°, 65° and 75°, the random surface error (RSE) tolerances are 0.207λ₀, 0.255λ₀, 0.347λ₀ and 0.566λ₀ (λ₀=0.5461µm), respectively. We find a formula descripting the relationship between RSE tolerance and incident angle. If the RSE tolerance exceeds the value of the formula at an angle, the imaging quality of the system will drop significantly. The formula can predict tolerances and incident angles and provide basic tool for imaging quality analysis and manufacturing for optical waveguide AR/VR display systems.