Fig. 2. Schematic of angle sensing in 2D and 3D space.

a Schematic of single slit aperture for calculating field energy using Rayleigh–Sommerfeld diffraction theory. b Plot of total energy ratio between two equally divided regions (A and B) for different incident angles. Calculation based on full-wave simulation and Rayleigh–Sommerfeld diffraction theory are in good agreement. c The electric field intensity profile of a plane wave incident on a PEC slab with an open aperture of 2.5$\lambda$ width. The intensity profile is a strong function of the incident angle $\theta$. d The scattered field by the open aperture. It is calculated by subtracting the incident field from the total field. The incident field is defined as the field without the open aperture but with a perfect PEC reflector. e Schematic of angle sensor with an aperture on four photodetectors labeled by A, B, C, and D. The map of energy ratio $\frac{\left(A-C\right)}{\left(A+C\right)}$ for different incident angles is shown on the hemisphere. Each point on the hemisphere represents one combination of polar angle $\theta$ and azimuthal angle $\varphi$. f The map of energy ratio $\frac{\left(B-D\right)}{\left(B+D\right)}$. g Contour lines extracted from hemisphere in e and f. A unique incident angle can be determined when two ratios $\frac{\left(A-C\right)}{\left(A+C\right)}$ and $\frac{\left(B-D\right)}{\left(B+D\right)}$ are measured by the four photodetectors.