Mapping of human brain function has revolutionized systems neuroscience. However, traditional functional neuroimaging by positron emission tomography or functional magnetic resonance imaging cannot be used when applications require portability, or are contraindicated because of ionizing radiation (positron emission tomography) or implanted metal (functional magnetic resonance imaging). Optical neuroimaging offers a non-invasive alternative that is radiation free and compatible with implanted metal and electronic devices (for example, pacemakers). However, optical imaging technology has heretofore lacked the combination of spatial resolution and wide field of view sufficient to map distributed brain functions. Here, we present a high-density diffuse optical tomography imaging array that can map higher-order, distributed brain function. The system was tested by imaging four hierarchical language tasks and multiple resting-state networks including the dorsal attention and default mode networks. Finally, we imaged brain function in patients with Parkinson's disease and implanted deep brain stimulators that preclude functional magnetic resonance imaging.