LED の光は狭い範囲から効率よくでてくるのがあたりまえだときかされたていたが
見落としがあったかも。

Calculation of the external quantum efficiency of light emitting diodes with different chip designs

Cuong, T. V.; Cheong, H. S.; Hong, C.-H.
Physica Status Solidi (C), Applied Research, vol. 1, Issue 10, pp.2433-2437
External quantum efficiency of GaN light emitting diode (LED) with SiO2-coated grating patterned substrate and/or surface-textured structure were calculated theoretically. Our results show that the enhancement of the reflectance coefficient was obtained by a factor of about 30% in LED chip with SiO2-coated grating patterned substrate, compared to conventional LED chip. The grating parameters such as height and width should be optimized above h=w/4. Moreover, by employing surface-textured structure, the loss factor at top surface of LED was reduced dramatically by decreasing of total internal reflectance at GaN-epoxy interface as the incident angle is higher than the critical angle. Therefore, external quantum efficiency can reach up to about 60% if internal quantum efficiency corresponds to about 90% because of reducing the total loss parameter at top and bottom surface of LED.

これはチップレベルのレンズが大きな効果があったということか。