A hyperspectral imager provides a 3-D data cube in which the spatial information (2-D) of the image is complemented by spectral information (1-D) about each spatial location. A static, high-throughput spectrometer design previously developed by our group can be used as the spectral engine in a high-throughput hyperspectral imager that avoids the Fourier undersampling issues present in previous dispersive designs. We present the theory for both pushbroom and tomographic operation and describe experimental results from our proof-of-concept implementation of a hyperspectral microscope.