A single-conjugate adaptive optics system on a telescope has a deformable mirror with…

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

A single-conjugate adaptive optics system on a telescope has a deformable mirror with actuator spacing d=0.20d = 0.20 m projected onto the pupil, and operates in a closed loop of bandwidth 100 Hz with a bright on-axis guide star giving a subaperture signal-to-noise ratio of 8. The site has r0=0.15r_0 = 0.15 m at 500 nm and a wind speed of 12 m s−1^{-1} across the pupil. Use the fitting-error term σfit2=0.34(d/r0)5/3\sigma^2_{\mathrm{fit}} = 0.34(d/r_0)^{5/3}, the temporal term σtemp2=(νG/ν3dB)5/3\sigma^2_{\mathrm{temp}} = (\nu_{\mathrm{G}}/\nu_{3\mathrm{dB}})^{5/3} with νG=0.43v/r0\nu_{\mathrm{G}} = 0.43v/r_0, and the noise term σnoise2=1/SNR2\sigma^2_{\mathrm{noise}} = 1/\mathrm{SNR}^2, with the on-axis anisoplanatism term zero. Recall that r0r_0 scales with wavelength as r0(λ)=r0(500 nm)(λ/500 nm)6/5r_0(\lambda) = r_0(500\ \mathrm{nm})(\lambda/500\ \mathrm{nm})^{6/5}. ((a)) Predict the Strehl ratio at λ=1.65 μm\lambda = 1.65\ \mu\mathrm{m} (H band). ((b)) With the hardware, wind and guide star unchanged, predict the Strehl ratio at λ=1.0 μm\lambda = 1.0\ \mu\mathrm{m} (Y band), and comment on which error term drives the difference.

Browse the problem library