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 It is supposed that close optical contact exists between LED/PD surface and the lens.

Currently most of LEDs/PDs are equipped with Si lenses with diameter of 3.5 mm,

some diodes are made with larger lenses (KM type, D=10 mm, see photo on the right)

For additional information see

R.C. Jones, Appl. Opt. 1 (1962), 607.