A telescope guide camera is fed through a step-index fibre of core diameter and…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Photodetection, photonic sources and quantum optics

What an Instrument Can See, Ch Radiance, etendue and a throughput budget that is spent

Problem

A telescope guide camera is fed through a step-index fibre of core diameter

200\,\mu\text{m}

and numerical aperture

\mathrm{NA} = 0.15

. ((a)) Find the fibre's etendue

\Xi = \pi A\,\mathrm{NA}^2

, treating the exit face as a circular Lambertian aperture. ((b)) On a faint guide star the detector records

2\,\text{e}^-\,\text{s}^{-1}

over a

5\,\text{s}

exposure, with dark current

0.001\,\text{e}^-\,\text{s}^{-1}

and read noise

5\,\text{e}^-

(rms, once per exposure). Find the signal-to-noise ratio and identify the dominant noise term. ((c)) A calibration LED at

500\,\text{nm}

delivers

10\,\text{mW}

into the fibre. Using

V(500\,\text{nm}) = 0.323

and

K_m = 683\,\text{lm}\,\text{W}^{-1}

, find the luminous flux.

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