An endoscope is to show a feature anywhere in a field of view on tissue in front of…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Beams, resonators and guided-wave photonics

Optics and Photonics, Ch Optical fibres in communication and endoscopy

Problem

An endoscope is to show a

0.20\ \mathrm{mm}

feature anywhere in a

12\ \mathrm{mm}

field of view on tissue

30\ \mathrm{mm}

in front of its objective. The ordered bundle has a circular face

2.4\ \mathrm{mm}

across, and its fibres have

\mathrm{NA} = 0.24

. Treat the objective as a thin lens in air (Chapter 1), and count one line pair as two fibre pitches at the face. ((a)) Find the size of transverse magnification that fits the field on the face, and the focal length of the objective that gives it at the stated object distance. ((b)) Find the largest fibre pitch that resolves the feature, and the number of fibres across the face and in the whole bundle. ((c)) The objective's aperture is

2.0\ \mathrm{mm}

in diameter. Find its image-side numerical aperture (Chapter 2) and say whether every ray it delivers to the face is guided; then find the largest aperture diameter the bundle could accept without losing rays at the wall. ((d)) One fibre breaks. What size of object detail does the dark point it leaves correspond to, and why does the picture survive?

Browse the problem library