A 4 m telescope observes through air with Fried parameter m at 500 nm and a wind…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Electronics, Instrumentation & Communication · Fourier optics and image formation

What an Instrument Can See, Ch Keeping the phase: holography, wavefront modulation and adaptive optics

Problem

A 4 m telescope observes through air with Fried parameter

r_0 = 0.12

m at 500 nm and a wind speed of

v = 15

m s

^{-1}

across the pupil. A deformable mirror with actuator spacing matched to

r_0

is proposed, giving roughly

(D/r_0)^2 \times \pi/4

actuators across the pupil, and the Greenwood frequency is

\nu_{\mathrm{G}} = 0.43v/r_0

. ((a)) Estimate the number of actuators the deformable mirror needs. ((b)) Estimate the Greenwood frequency, and hence state, to the nearest order of magnitude, the closed-loop bandwidth the correction needs (a bandwidth several times

\nu_{\mathrm{G}}

is required for the temporal error to stay small).

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