in the figure above, where two such slices are represented in purple and red), one can understand these projections as a partial spread of the stack of slices, similarly to a magician spreading his cards in order for an audience member to pick one of them. It is important to note that for typical spectral dispersions and the typical size of a sensor, the spectral information of a given slice is heavily overlapping with the one from other neighboring slices. In the "5" image, one can see in the side projections that the number is not clearly readable (loss of spatial information), but that some spectral information is available (i.e. some wavelengths appear brighter than others). Hence, the image contains multiplexed information regarding the datacube. The number and layout of the projections depend on the type of diffracting element employed. In particular, more than one order of diffraction can be captured. Datacube reconstruction The resulting image contains all of the information of the datacube. It is necessary to carry out a reconstruction algorithm to convert this image back in the 3D spatio-spectral space. Hence, the CTIS is a computational imaging system. Link to X-ray computed tomography Conceptually, one can consider each of the projections of the datacube in a manner analogous to the X-ray projections measured by medical X-ray computed tomography instruments used to estimate the volume distribution within a patient's body. Hence, the most widely-used algorithms for CTIS reconstruction are the same as the one used in the X-ray CT field of study. In particular, the algorithm used by Descour is directly taken from a seminal work in X-ray CT reconstruction. Since then, slightly more elaborate techniques have been employed, in the same way (but not to the same extent) X-ray CT reconstruction has improved since the 80s. Difficulties Compared to the X-ray CT field, CTIS reconstruction is notoriously more difficult. In particular, the number of projections resulting from a CTIS acquisition is typically far less than in X-ray CT. This results in a blurrier reconstruction, following the projection-slice theorem. Moreover, unlike X-ray CT where projections are acquired around the patient, the CTIS, as all imaging systems, only acquires the scene from a single point of view, and hence many projection angles are unobtainable. References External links A fast reconstruction algorithm for computed tomography imaging spectrometer (CTIS) is documented in the paper: Larz White, W. Bryan Bell, Ryan Haygood,