Akin to functional magnetic resonance imaging (fMRI), diffuse optical imaging (DOI) is a noninvasive method for measuring localized changes in hemoglobin levels within the brain. When combined with fMRI methods, multimodality approaches could offer an integrated perspective on the biophysics, anatomy, and physiology underlying each of the imaging modalities. Vital to the correct interpretation of such studies, control experiments to test the consistency of both modalities must be performed. Here, we compare DOI with blood oxygen level-dependent (BOLD) and arterial spin labeling fMRI-based methods in order to explore the spatial agreement of the response amplitudes recorded by these two methods. Rather than creating optical images by regularized, tomographic reconstructions, we project the fMRI image into optical measurement space using the optical forward problem. We report statistically better spatial correlation between the fMRI-BOLD response and the optically measured deoxyhemoglobin (R=0.71, p=1×10-7) than between the BOLD and oxyhemoglobin or total hemoglobin measures (R=0.38, p=0.04|0.37, p=0.05, respectively). Similarly, we find that the correlation between the ASL measured blood flow and optically measured total and oxyhemoglobin is stronger (R=0.73, p=5×10-6 and R=0.71, p=9×10-6, respectively) than the flow to deoxyhemoglobin spatial correlation (R=0.26, p=0.10).