A backlight, comprising: a front and back reflector forming a hollow light recycling cavity, the front reflector being partially transmissive to provide an output illumination area; a component that provides the cavity with a desired balance of specular and diffuse characteristics, the component having a transport ratio greater than 15% at a 15 degree incidence angle to a surface normal and less than 95% at a 45 degree incidence angle to the surface normal, wherein the front or back reflectors can be or include the component, or the component can be distinct from the front and back reflectors; and one or more light source members (24a-c) disposed to emit light into the light recycling cavity over a limited angular distribution relative to a plane parallel to the output illumination area; wherein the front reflector has a hemispherical reflectivity for unpolarized visible light of R f hemi, and the back reflector has a hemispherical reflectivity for unpolarized visible light of R b hemi, and R f hemi * R b hemi is at least 0.70, wherein hemispherical reflectivity is the total reflectivity of a component when light is incident on it from all possible directions; wherein the transport ratio for the component, for light of a given incidence angle, equals (F - B)/(F + B), where F is the amount of light scattered into directions upon interaction of the incident light with the component that are parallel to the direction of the incident light in a plane parallel to a surface of the component, and B is the amount of light scattered into directions upon interaction of the incident light with the component that are anti-parallel to the direction of the incident light in the plane parallel to the surface of the component. a front and back reflector forming a hollow light recycling cavity, the front reflector being partially transmissive to provide an output illumination area; a component that provides the cavity with a desired balance of specular and diffuse characteristics, the component having a transport ratio greater than 15% at a 15 degree incidence angle to a surface normal and less than 95% at a 45 degree incidence angle to the surface normal, wherein the front or back reflectors can be or include the component, or the component can be distinct from the front and back reflectors; and one or more light source members (24a-c) disposed to emit light into the light recycling cavity over a limited angular distribution relative to a plane parallel to the output illumination area; wherein the front reflector has a hemispherical reflectivity for unpolarized visible light of R f hemi, and the back reflector has a hemispherical reflectivity for unpolarized visible light of R b hemi, and R f hemi * R b hemi is at least 0.70, wherein hemispherical reflectivity is the total reflectivity of a component when light is incident on it from all possible directions; wherein the transport ratio for the component, for light of a given incidence angle, equals (F - B)/(F + B), where F is the amount of light scattered into directions upon interaction of the incident light with the component that are parallel to the direction of the incident light in a plane parallel to a surface of the component, and B is the amount of light scattered into directions upon interaction of the incident light with the component that are anti-parallel to the direction of the incident light in the plane parallel to the surface of the component.