An apparatus for measuring a spatially under-sampled Bidirectional Reflectance Distribution Function (BRDF) of a surface (202, 302, 400, 600, 700, 906), the apparatus comprising: a first light source directed to illuminate the surface (202, 302, 400, 600, 700, 906) from a first illumination direction; a plurality of sensors positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906), wherein the plurality of sensors comprises: a first sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a first reflectance direction; a second sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a second reflectance direction; and a third sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a third reflectance direction, wherein the first, second, and third directions (206, 208, 210) are not coplanar; and a computer in communication with the plurality of sensors, wherein the computer is configured to convert light sensed by the plurality of sensors into a first appearance property of the surface (202, 302, 400, 600, 700, 906) considering the first, second, and third reflectance directions (206, 208, 210), wherein the first appearance property is a plurality of weighted directional responses of the surface (202, 302, 400, 600, 700, 906), wherein each directional response is for a different wavelength or range of wavelengths, characterized in that each of the plurality of weighted directional responses is a vector sum of all of each of the sensed light intensities and reflectance directions (206, 208, 210) over a given wavelength or wavelength range. a first light source directed to illuminate the surface (202, 302, 400, 600, 700, 906) from a first illumination direction; a plurality of sensors positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906), wherein the plurality of sensors comprises: a first sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a first reflectance direction; a second sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a second reflectance direction; and a third sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a third reflectance direction, wherein the first, second, and third directions (206, 208, 210) are not coplanar; and a first sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a first reflectance direction; a second sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a second reflectance direction; and a third sensor positioned to receive light reflected by the surface (202, 302, 400, 600, 700, 906) in a third reflectance direction, wherein the first, second, and third directions (206, 208, 210) are not coplanar; and a computer in communication with the plurality of sensors, wherein the computer is configured to convert light sensed by the plurality of sensors into a first appearance property of the surface (202, 302, 400, 600, 700, 906) considering the first, second, and third reflectance directions (206, 208, 210), wherein the first appearance property is a plurality of weighted directional responses of the surface (202, 302, 400, 600, 700, 906), wherein each directional response is for a different wavelength or range of wavelengths, characterized in that each of the plurality of weighted directional responses is a vector sum of all of each of the sensed light intensities and reflectance directions (206, 208, 210) over a given wavelength or wavelength range.