Adaptive Optics Telescope Simulator

Atmosphere

Fried parameter r₀ 10 cm

Telescope aperture D 2.0 m

Wind speed (turbulence drift) 1.0×

Correction

Strehl ratio

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D / r₀

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Natural seeing

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Residual WFE

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How it works

Starlight leaves a distant star as a flat wavefront, but turbulent pockets of air at different temperatures (and therefore refractive index) bend it by different amounts across the telescope's aperture by the time it arrives. The pupil is shown here as a grid of sub-apertures whose height encodes the local optical-path error; drag it and the bumps drift sideways — that's the "frozen turbulence" pattern blowing across the mirror at the wind speed you set. Each sub-aperture's local tilt bends its ray, spreading the focused star image out into the fuzzy blob shown at the focal plane instead of a single point — this blur is what astronomers call "seeing".

Strehl ≈ exp(−σ²)                (Maréchal approximation)
σ₀² = 1.03 (D/r₀)^(5/3)          uncorrected wavefront variance
σ²_tip-tilt = 0.134 (D/r₀)^(5/3) after removing global tip/tilt
σ²_AO = 0.28 (d_act/r₀)^(5/3)    fitting error, d_act = actuator spacing
seeing FWHM ≈ 0.98 λ / r₀ (rad)  natural, diffraction-free resolution limit

Fried parameter r₀ — the coherence length of the atmosphere: the aperture size over which the wavefront stays roughly flat. A calm night gives r₀ ≈ 15–20 cm at visible wavelengths; a turbulent one drops below 5 cm.
Aperture D — a bigger mirror collects more light but also spans more independent turbulent cells (higher D/r₀), so an uncorrected large telescope is actually blurrier, in relative terms, than a small one on the same night.
Tip-Tilt — a fast steering mirror that cancels only the whole-aperture average tilt (image wobble). Cheap and effective, but leaves all higher-order distortion untouched.
Full AO — a deformable mirror with many actuators reshapes the wavefront point-by-point; residual error then depends on actuator spacing, not telescope size, which is why modern giant telescopes only became sharp once adaptive optics matured.

Real-world relevance: this is the same physics behind the Keck, VLT and Gemini adaptive-optics systems, and behind why ground-based observatories are sited on high, dry, still mountaintops to maximize r₀ before any correction is even applied.

Pupil (aperture) Star image (focal plane) Incoming starlight

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