The WISDOM instrument concept was developed at MIT as part of a NASA-NSF funded study to equip the 3.5m WIYN telescope with an extremely precise radial velocity spectrometer. The spectrograph employs an asymmetric white pupil optical design, where the instrument is split into two nearly identical “Short” (380 to 750 nm) and “Long”" (750 to 1300 nm) wavelength channels. The echelle grating and beam sizes are R3.75/125mm and R6/80mm in the short and long channels respectively. Together with the pupil slicer, and octagonal to rectangular fibre coupling, this permits resolving powers over R = 120k with a 1.2” diameter fibre on the sky. A factor of two reduction in the focal length between the main collimator OAP and the transfer collimator ensures a very compact instrument, with a small white pupil footprint, thereby enabling small cross-dispersing and camera elements. A dichroic is used near the white pupil to split each of the long and short channels into two, so that the final spectrograph has 4 channels; namely “Blue,” “Green,” “Red” and “NIR.” Each of these channels has an anamorphic VPH grism for cross-dispersion, and a fully dioptric all-spherical camera objective. The spectral footprints cover 4k×4k and 6k×6k CCDs with 15 µm pixels in the short “Blue” and “Green” wavelength channels, respectively. A 4k×4k CCD with 15 μm pixels is used in the long “Red” channel, with a HgCdTe 1.7 μm cutoff 4k×4k detector with 10um pixels is to be used in the long "NIR" channel. The white pupil relay includes a Mangin mirror very close to the intermediate focus to correct the white pupil relay Petzval curvature before it is swept into a cylinder by the cross-dispersers. This design decision allows each of the dioptric cameras to be fully optimised and tested independently of the rest of the spectrograph. The baseline design for the cameras also ensures that the highest possible (diffraction limited) image quality is achieved across all wavelengths, while also ensuring insensitivity of spot centroid locations to variations in the pupil illumination. This insensitivity is proven to remain even in the presence of reasonable manufacturing and alignment tolerances. Fully ray-traced simulations of the spectral formats are used to demonstrate the optical performance, as well as to provide pre-first-light data that can be used to optimise the data reduction pipeline.