The illumination channel of an endoscope uses a light-source objective of numerical…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Beams, resonators and guided-wave photonics

Optics and Photonics, Ch Optical fibres in communication and endoscopy

Problem

The illumination channel of an endoscope uses a light-source objective of numerical aperture NAobj=0.18\mathrm{NA}_{\mathrm{obj}} = 0.18 (Chapter 2 definition) to launch light into the unordered illumination fibre bundle. Each fibre in the bundle has NAfibre=0.24\mathrm{NA}_{\mathrm{fibre}} = 0.24 and core index n1=1.50n_1 = 1.50. The illumination cable is L=8L = 8 km long (a long feed cable in a laboratory test rig) with absorption coefficient α=1.15×10−5 m−1\alpha = 1.15\times10^{-5}\ \mathrm{m^{-1}} (Chapter 5 definition). Neither end face is coated. ((a)) Assuming the objective delivers its power uniformly over its solid angle (small-angle approximation), what fraction of the launched power falls within a fibre's acceptance cone? ((b)) Find the total loss budget in decibels, combining the normal-incidence Fresnel reflectance (Chapter 6) at both end faces with the absorption over the full 8 km.

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