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We describe a multiple-frequency imaging system based on an electrically-tunable terahertz (THz) frequency quantum cascade laser (QCL). The transverse resolution of the system was measured using gold-on-quartz resolution targets, and shown to remain unchanged as the radiation wavelength increased. This was explained through measurement of the far-field emission profile of the QCL. Using this imaging system we determined the attenuation coefficients of the high-explosive pentaerythritol tetranitrate (PETN), together with a number of other polycrystalline materials, at five frequencies, and compared these results with those obtained using both THz time domain spectroscopy and high-resolution Fourier-transform infrared spectroscopy.