Traditional slit-based spectrometers have an inherent trade-off between spectral resolution and throughput that can limit their performance when measuring diffuse sources such as light returned from highly scattering biological tissue. Recently, multielement fiber bundles have been used to effectively measure diffuse sources, e.g., in the field of spatially offset Raman spectroscopy, by remapping the source (or some region of the source) into a slit shape for delivery to the spectrometer. Another approach is to change the nature of the instrument by using a coded entrance aperture, which can increase throughput without sacrificing spectral resolution.In this study, two spectrometers, one with a slit-based entrance aperture and the other with a coded aperture, were used to measure Raman spectra of an analyte as a function of the optical properties of an overlying scattering medium. Power-law fits reveal that the analyte signal is approximately proportional to the number of transport mean free paths of the scattering medium raised to a power of -0.47 (coded aperture instrument) or -1.09 (slit-based instrument). These results demonstrate that the attenuation in signal intensity is more pronounced for the slit-based instrument and highlight the scattering regimes where coded aperture instruments can provide an advantage over traditional slit-based spectrometers.