Diffractive optical elements (DOEs) have been proposed for many applications. One of the principle limitations of these lenses is abundant chromatic aberration that prohibits broadband use without design compensation. I present a novel configuration that exploits this typically unwanted effect to create an image spectrometer for visible or IR applications. The DOE provides both imaging and dispersion. A monochromatic CCD is scanned along the optical axis through a region described by the image locations of the desired wavelengths. Each detector position is an image location of one wavelength. However, the images captured by the CCD are a superposition of this infocus image and the images of the other wavelengths at various stated of defocus. Post-detection processing with computer tomography techniques is used to remove the unwanted blurred components, leaving an image for each spectral componenet. This paper presents the design, algorithms, experimental demonstration, and computer simulations of this image spectrometer's performance.