Angle transformer and its angle-dependent transmission efficiency щ(ф)

Aiming at reducing the transmission loss at large angles, a novel solid-core light guide with an angular transformer input end was put forward. The angular transformer has an input diameter of D1 = 7mm and an output diameter of D2 = 10,5mm. For the input rim angle of 37o (NA1 = 0.6), the output angle of 23o (NA2 = 0.5) was calculated by using the optical invariant: NA1 D1 = NA2 D2. Due to the refractions at the input surface and the total internal reflections at inclined and polished sidewall, the input rays of large angles are transformed into the output rays of small angles. The drastic reduction in angles means that there are much less imperfect reflections along the sidewall, hence the lower transmission loss (see Fig. 5). The length of the angular transformer determines whether the relations between the input and output angles can be determined precisely by optical invariant. A long transformer gives a better approximation to the invariant. For practical reasons, the length of 12cm was chosen. Careful grinding and polishing were done to ensure high transmission efficiency.