Non–invasive techniques for the study of human brain function based on changes of the haemoglobin content or on changes of haemoglobin saturation have recently been proposed. Among the new methods , near–infrared transmission and reflection measurements may have significant advantages and complement well–established methods such as functional magnetic resonance imaging and positron emission tomography. Near–infrared measurements can be very fast, comparable in speed to electrophysiological measurements, but are better localized. We will present the demonstration of measurements of millisecond signals due to brain activity in humans following stimulation of the visual cortex. However, major unresolved questions remain about the origin of the signals observed. Optical measurements on exposed cortex in animals show that both the absorption and the scattering coefficient are affected by neural activity. Model calculations show that the signals we detected may originate from rapid changes of the scattering coefficient in a region about 1 to 2 cm below the scalp. We discuss our measurement protocol, which is based on a frequency–domain instrument, and the algorithm to separate the absorption from the scattering contribution in the overall optical response. Our method produces excellent separation between scattering and absorption in relatively homogeneous masses such as large muscles. The extrapolation of our measurement protocol to a complex structure such as the human head is critically evaluated.