We aim to show that Dyson imaging spectrometers can be easily designed by applying the concept of the Rowland circle to refracting surfaces. This allows us to conceive an analytical procedure that is based on the removal of astigmatism at two wavelengths. Following this procedure, high-optical-quality spectrometers can be designed even for high speeds. Root-mean-square spot radii less than $2.5\mathrm{\mu m}$ are obtained for speeds as high as $f/1.5$ , slit lengths of $15\mathrm{mm}$ , and wavelength ranges of $0.4–1.7\mathrm{\mu m}$ . Design examples are presented for classical Dyson spectrometers in which the detector is glued to the glass plane surface and for spectrometers with an air gap between this surface and the image plane.