Near-Infrared Spectroscopy (NIRS) and diffuse optical imaging (DOI) are increasingly used to detect hemodynamic changes in the cerebral cortex induced by brain activity. Until recently, the small number of optodes in NIRS instruments has hampered measurement of optical signals from diverse brain regions. Our new DOI system has 32 detectors and 32 sources; by arranging them in a specific pattern, we can cover most of the adult head. With the increased number of optodes, we can collect optical data from prefrontal, sensorimotor, and visual cortices in both hemispheres simultaneously. We describe the system and report system characterization measurements on phantoms as well as on human subjects at rest and during visual, motor, and cognitive stimulation. Taking advantage of the system's larger number of sources and detectors, we explored the spatiotemporal patterns of physiological signals during rest. These physiological signals, arising from cardiac, respiratory, and blood-pressure modulations, interfere with measurement of the hemodynamic response to brain stimulation. Whole-head optical measurements, in addition to providing maps of multiple brain regions' responses to brain activation, will enable better understandings of the physiological signals, ultimately leading to better signal processing algorithms to distinguish physiological signal clutter from brain activation signals.