Expanded performance opportunities for imaging spectrometers are described using φ-polynomial freeform surfaces in reflective and diffractive optics. The imaging spectrometers are generally of a type that include an entrance aperture for admitting radiation over a range of wavelengths, a detector array, a primary reflective optic with optical power, a secondary reflective diffractive optic, and a tertiary reflective optic with optical power for collectively imaging the entrance aperture onto the detector array through a range of dispersed positions. One or more of the primary reflective optic, the secondary reflective diffractive optic, and the tertiary reflective optic can include a φ-polynomial optical surface with no axis of symmetry and represented by a function that depends on both a radial component and an azimuthal