Hyperspectral imaging is a method that is used in various fields such as industry, medicine and aerospace. Snapshot systems are more and more used for this purpose. They have the advantage that scenes can be captured quickly, without moving mechanics and without possible motion artifacts. However, one of the disadvantages is the often poor spectral and spatial resolution. With filter-based systems, as the number of spectral channels increases, an increasing proportion of the light is absorbed, thus relativizing the time advantage in acquisition. The Computed Tomography Imaging Spectrometer (CTIS), proposed in 1991, overcomes this problem. The image, which is limited in the camera by a field stop, is spectrally dispersed into different directions, for example by using a diffractive element. The final hyperspectral image has to be computed afterwards from the sensor image by computationally intensive reconstruction algorithms. We present recent advances in the optimization of such a system using modern components and methods.