Modeling light propagation for under-display sensing in a smartphone

Under-display sensing (UDS) is essential to achieve bezel-less smartphones (infinity display). However, light penetrating or reflected by the display panel is distorted, deteriorating UDS signals. Therefore, light propagation should be accurately modeled to analyze and optimize UDS. This study proposes a universal model that recognizes the light propagation mode using the Fresnel number. Under-display ambient light sensors (ALS), under-display cameras (UDC), and proximity sensors are identified to work in the geometric optics, Fraunhofer diffraction, and Fresnel diffraction regimes, respectively. A commercial smartphone is adopted to demonstrate the model's effectiveness and provide domain knowledge. First, regarding the angular response attenuation in under-display ALS, the geometric obstruction by the pixel layout is simulated after acquiring the display panel's microphotograph. Measured data agrees with the simulation with an error smaller than 10 degrees in the viewing angle's full width at half maximum. Next, the UDC is simulated using Fraunhofer diffraction to provide full-color pictures containing blurring caused by the pixel layout's diffraction, showing high similarity with photographs. Finally, Fresnel diffraction dominates the under-display proximity sensor, which utilizes a weakly collimated infrared beam. An approximate solution of the signal on the detector is a scaled Fraunhofer diffraction pattern whose magnification is determined by the sensor configuration. The source-detector orientation influences the background noise (the signal level when no user is present), which is simulated and compared with experimental data, providing an optimal orientation of 45 degrees. The gap between the sensor and the display panel is also investigated through simulation and experiment, demonstrating that Fresnel diffraction is more effective than geometric optics or Fraunhofer diffraction. The proposed model with solid experimental verification on a commercial smartphone can help rationally design UDS and provide insight into the light propagation problem in smartphones.