Hyperspectral imaging can be a powerful tool for remote sensing of geologic, biologic, and ocean surfaces of atmospheres, and of rocket plumes. A hyperspectral imager provides a 3D (two spatial and one spectral) description from a sequence of 2D images. Common hyperspectral approaches using narrow band filters or imaging spectrometers are inefficient because photons outside the filter passband or the slit area are not detected. A new imaging technique called spectro-tomography collects all available photons and relies on computer tomography to reconstruct the 3D data cube of the image. A rotational spectro-tomographic (RST) imager is designed with a wide aperture, objective-grating camera, that is rotated in steps around its optical axis. The 2D projections of the object are analyzed using methods based on Fourier transforms. Both direct Fourier methods and filter-backprojection algorithms have been developed for 3D tomographic analysis. Numerical methods are employed to simulate and reconstruct a broad spectrum object with 64 spectral bands and 64 X 64 spatial resolution elements. For this example, the photon flux at the detector of the RST imager is 64 times that of a conventional spectral imager. The rotational spectro-tomographic imager has applications to detection of natural and artificial atmospheric emissions where large photon through-put is required.