An infrared spectrometer for operation in the mid-infrared spectral range is presented, where the spectrometer includes a Bragg-mirror-based spectral filter that is operative for providing an interrogation signal whose spectral content is dispersed along a first direction at a filter aperture. The filter aperture is imaged through a sample by a thermal-imaging camera to create a focused image that is based on the interrogation signal and the absorption characteristics of the sample. As a result, embodiments in accordance with the present disclosure can be smaller, less complex, and less expensive than infrared spectrometers known in the prior art.