Hilbert C*-systems for actions of the circle group

An error analysis of two-wavelength absorption-based fibre-optic sensors is presented in this paper. A general formulation to express the measurement error and the error induced by the instability of the light power input into the absorbing sample to be measured is derived. Using this formulation, two common and important errors in this type of sensor, temperature fluctuation of light sources and bending optical fibres, are numerically discussed as illustrative examples. The analyses can be applied to both transmission-type and reflection-type absorption-based fibre-optic sensors.