A long-exposure exoplanet-transit photometer is fed by a 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 long-exposure exoplanet-transit photometer is fed by a fibre of core diameter

8\,\mu\text{m}

and numerical aperture

\mathrm{NA} = 0.12

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

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

. ((b)) The star gives a signal of only

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

. The detector has dark current

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

and read noise

2\,\text{e}^-

(rms, once per exposure), and the integration time is

100\,\text{s}

. Find the signal-to-noise ratio and identify the dominant noise term. ((c)) An indicator LED at

620\,\text{nm}

used to flag the shutter state radiates

50\,\text{mW}

. Using

V(620\,\text{nm}) = 0.381

and

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

, find its luminous flux.

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