A method for determining the focal ratio degradation of optical fibres for astronomy

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Abstract
We present a method for measuring the degree of focal ratio degradation (FRD) of an optical fibre and characterizing its performance by a single parameter, which can be used to model accurately the fibre's FRD performance in most astronomical spectroscopic applications. By using a known theoretical model for microbending-induced beamspreading, we have modelled the far-field output of an optical fibre for various input beams including collimated beams, uncollimated input beams and uncollimated pencil beams tilted with respect to the fibre's optical axis. This theory characterizes the FRD with a single parameter D. We have tested the validity of our model by observing the far-field output of a fibre in the laboratory and comparing it with the model's predictions. For the case of a collimated input beam (a laser beam), we measured the beamspreading as a function of the input beam angle and determined the parameter D by finding the best fit to the data. By using this value of D, we successfully predict the results of other experiments where the far-field output beam is recorded for input pencil beams of varying f-ratio. We therefore propose that the complete FRD performance of any fibre can be accurately predicted using a theoretical model and the appropriate value of D, which can be determined by a simple experiment. Finally, we suggest that the use of a single parameter to describe FRD will allow workers in the field to compare the performances of various fibres in a simple, well-defined way.

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