Led light source with diffuser

A light source, comprising:

• a reflective substrate with a reflectivity, Rsub, greater than 0.90;
• an array of light-emitting diodes (LEDs) mounted on the reflective substrate, the array having a spacing, d, between adjacent LEDs, the LEDs having a reflectivity, RLED, greater than 0.7 and a width, WLED, less than d/2;
• a diffuser having a first diffusing layer of height h1 and a second diffusing layer of height h2, the first diffusing layer being bonded to the reflective substrate and the second diffusing layer being bonded to the first diffusing layer;
• and
• the first diffusing layer containing a plurality of first scattering centers embedded in a first transparent host material and the second diffusing layer containing a plurality of second scattering centers embedded in a second transparent host material, the first and second diffusing layers having a relationship wherein:
• γ′sc-2>γ′sc-1;
• γ′sc-1h1+γ′sc-2h2<10;
• and
• (γabs-1+α1)h1+(γabs-2+α2)h2<20×10−3
• where γ′sc-1 is the reduced scattering coefficient for the first diffusing layer;
• γ′sc-2 is the reduced scattering coefficient for the second diffusing layer;
• γabs-1 is the absorption coefficient for the first diffusing layer;
• γabs-2 is the absorption coefficient for the second diffusing layer;
• α1 is the host absorptivity for the first diffusing layer;
• and
• α2 is the host absorptivity for the second diffusing layer.