Conventional spectrometers are limited in the amount of light they accept because of the requirement for narrow input apertures. A trade-off must generally be made between spectral resolution and input aperture width. This is especially a problem for performing spectroscopy on diffuse sources, such as with tissue, from which signal light has a broad spatial distribution. We introduce a method for achieving good spectral resolution from a fiber bundle input. The image of a fiber bundle has a characteristic structure. By distorting this image optically, we generate a pseudo-orthogonal intensity mask at the input of the spectrometer. The pseudo-orthogonal properties of the mask then allow decoupling at the detector plane of wavelength from spatial position. As long as the distorted image of the fiber bundle is well known, a spectrum can be recovered with spectral resolution equivalent to that of a conventional slit-based spectrometer. We demonstrate successful recovery of narrowly spaced spectral features as well as Raman spectra from a highly scattering sample with this method. This method enables probes with much higher throughputs and add fiber bundle-based spectroscopy to endoscopic designs.