Abstract Aperture, pin-hole and collimator detection systems are often used in plasma diagnostics, for example in soft x-ray detection and bolometer systems. In this paper the simultaneous optimization of viewing-beam overlap and light yield is considered in multi-channel aperture and collimator systems for two-dimensional (2D) tomography. This paper briefly highlights the relation between beam-width overlap and spatial aliasing in tomography, and how aliasing can be avoided in theory and in practice. Three-dimensional (3D) single-channel aperture and collimator systems can be approximated by a combination of two planar systems if the aperture is rectangular. Three ways to optimize beam-width overlap and light yield for planar aperture and collimator systems are considered in detail: overlap of the angular étendue at the Full-Width at Half-Maximum (FWHM), overlap of the geometric function at the FWHM a certain distance from the aperture, and arbitrary overlap for a given maximum beam width. The combination of 2D effects from all three optimization methods were used in the design of 3D apertures for a new mult i-channel bolometer camera on the JET (Joint European Torus) tokamak. The resulting apertures are complex, but the new camera has several advantages over the previous.