An imaging spectrometer includes an all-reflective objective module that receives an image input and produces an objective module output at an exit slit, and an all-reflective collimating-and-imaging module that receives the objective module output as an objective-end input and produces a collimating-end output, wherein the collimating-and-imaging module comprises a reflective triplet. A dispersive element receives the collimating-end output and produces a dispersive-end input into the collimating-and-imaging module that is reflected through the collimating-and-imaging module to produce a spectral-image-end output. An imaging detector receives the spectral-image-end output of the collimating-and-imaging module. The objective module may be a three-mirror anastigmat having an integral corrector mirror therein, or an all-reflective, relayed optical system comprising a set of five powered mirrors whose powers sum to substantially zero. The collimating-and-imaging module may be optimized to minimize spectral smile.