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Fibre Optics in Metrology With a carrier frequency of some 1014 Hz, light has the potential of being modulated at much higher frequencies than radio waves. Since the mid-1960s the idea of communication through optical fibres has developed into a vital branch of electro-optics. Great progress has been made and this is now an established technique in many communication systems. From the viewpoint of optical metrology, optical fibres are an attractive alternative for the guiding of light. An even more important reason for studying optical fibres is their potential for making new types of sensors. . | Optical Metrology. Kjell J. Gasvik Copyright 2002 John Wiley Sons Ltd. ISBN 0-470-84300-4 13 Fibre Optics in Metrology INTRODUCTION With a carrier frequency of some 1014 Hz light has the potential of being modulated at much higher frequencies than radio waves. Since the mid-1960s the idea of communication through optical fibres has developed into a vital branch of electro-optics. Great progress has been made and this is now an established technique in many communication systems. From the viewpoint of optical metrology optical fibres are an attractive alternative for the guiding of light. An even more important reason for studying optical fibres is their potential for making new types of sensors. LIGHT PROPAGATION THROUGH OPTICAL FIBRES More extensive treatments on optical fibres can be found in Senior 1985 Palais 1998 Keiser 1991 and Yu and Khoo 1990 . Figure shows the basic construction of an optical fibre. It consists of a central cylindrical core with refractive index n1 surrounded by a layer of material called the cladding with a lower refractive index n2. In the figure a light ray is incident at the end of the fibre at an angle 90 to the fibre axis. This ray is refracted at an angle 91 and incident at the interface between the core and the cladding at an angle 92. From Snell s law of refraction we have n0sin 90 n1 sin 91 where n0 is the refractive index of the surrounding medium. From the figure we see that 91 - 92 If 92 is equal to the critical angle of incidence cf. Section we have n2 sin 92 n1 308 FIBRE OPTICS IN METROLOGY Cone of acceptance Figure Basic construction of an optical fibre which combined with Equations and gives 00 0a sin 1 n2 n2 n0 13-4 For 00 0a the light will undergo total internal reflection at the interface between the core and the cladding and propagate along the fibre by multiple reflections at the interface ideally with no loss. For 00 0a some of the light will transmit into the cladding