A neutron supermirror is a highly polished, layered material used to reflect neutron beams. Supermirrors are a special case of multi-layer neutron reflectors with varying layer thicknesses. The first neutron supermirror concept was proposed by Ferenc Mezei, inspired by earlier work with X-rays. Supermirrors are produced by depositing alternating layers of strongly contrasting substances, such as nickel and titanium, on a smooth substrate. A single layer of high refractive index material (e.g. nickel) exhibits total external reflection at small grazing angles up to a critical angle \theta_c. For nickel with natural isotopic abundances, \theta_c in degrees is approximately where \lambda is the neutron wavelength in Angstrom units. A mirror with a larger effective critical angle can be made by exploiting diffraction (with non-zero losses) that occurs from stacked multilayers. The critical angle of total reflection, in degrees, becomes approximately, where m is the "m-value" relative to natural nickel. m values in the range of 1–3 are common, in specific areas for high-divergence (e.g. using focussing optics near the source, choppers, or experimental areas) m=6 is readily available. Nickel has a positive scattering cross section, and titanium has a negative scattering cross section, and in both elements the absorption cross section is small, which makes Ni-Ti the most efficient technology with neutrons. The number of Ni-Ti layers needed increases rapidly as \propto m^z, with z in the range 2–4, which affects the cost. This has a strong bearing on the economic strategy of neutron instrument design.