An adaptive optics team is designing a system for a 10 m telescope at a desert site…

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

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

Problem

An adaptive optics team is designing a system for a 10 m telescope at a desert site where the Fried parameter is

r_0 = 0.12

m at 500 nm, and the wind speed relevant to the turbulence is

v = 15\ \mathrm{m\,s^{-1}}

. The science camera works at 1.0

\mu

m. ((a)) Using the

\lambda^{6/5}

scaling of the Fried parameter, find

r_0

at 1.0

\mu

m. ((b)) Estimate the number of deformable-mirror actuators needed across the pupil, using

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

. ((c)) Find the Greenwood frequency

\nu_G = 0.43\,v/r_0

for this wind speed and

r_0

, then find the minimum closed-loop bandwidth

f

that keeps the temporal error variance below

0.10\ \mathrm{rad^2}

, taking

\sigma_t^2 = (\nu_G/f)^{5/3}

. ((d)) The observatory's 633 nm alignment laser must be steered onto the wavefront sensor by

1.5^\circ

using a blazed phase ramp written on a liquid-crystal spatial light modulator whose pixel pitch is 6.4

\mu

m. Find the largest deflection angle the modulator can address at 633 nm, the grating period needed for the

1.5^\circ

deflection, and the number of pixels per period (rounded to the nearest whole pixel). State whether the required deflection lies within the addressable range.

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