The computed tomography imaging spectrometer (CTIS) is a snapshot imaging spectrometer which can produce in fine the three-dimensional (i.e. spatial and spectral) hyperspectral datacube of a scene. History The CTIS was conceived separately by Takayuki Okamoto and Ichirou Yamaguchi at Riken (Japan), and by F. Bulygin and G. Vishnakov in Moscow (Russia). The concept was subsequently further developed by Michael Descour, at the time a PhD student at the University of Arizona, under the direction of Prof. Eustace Dereniak. The first research experiments based on CTIS imaging were conducted in the fields of molecular biology. Several improvements of the technology have been proposed since then, in particular regarding the hardware: dispersive elements providing more information on the datacube, enhanced calibration of the system. The enhancement of the CTIS was also fueled by the general development of bigger image sensors. For academic purposes, although not as widely used as other spectrometers, CTIS has been employed in applications ranging from the military to ophthalmology and astronomy. Image formation Optical layout The optical layout of a CTIS instrument is shown on the left part of the top image. A field stop is placed at the image plane of an objective lens, after which a lens collimates the light before it passes through a disperser (such as a grating or a prism). Finally, a re-imaging lens maps the dispersed image of the field stop onto a large-format detector array. Resulting image The information that the CTIS acquires can be seen as the three-dimensional datacube of the scene. Of course, this cube does not exist in physical space as mechanical objects do, but this representation helps to gain intuition on what the image is capturing: As seen in the figure on the right, the shapes on the image can be considered as projections (in a mechanical sense) of the datacube. The central projection, called the 0th order of diffraction, is the sum of the datacube following the spectral axis (hence, this projection acts as a panchromatic camera). In the image of the "5" on the right, one can clearly read the number in the central projection, but with no information regarding the spectre of the light. All the other projections result from "looking" at the cube obliquely and hence contain a mixture of spatial and spectral information. From a discrete point of view where the datacube is considered as a set of spectral slices (as