A star's light crosses the atmosphere as a flat wavefront, but turbulent air cells of varying refractive index bend it into a corrugated shape. This lab models that corrugation across a 1D telescope aperture as a sum of moving sine harmonics (a simplified Kolmogorov-like screen), and drives a deformable mirror (DM) with a finite number of actuators that tries to cancel it out:
φ_turb(x,t) = Σ (A/k^0.83)·sin(kπx + t·wind·k + φ0_k), k=1..5
φ_DM(x) = piecewise-linear fit through M actuator commands
residual(x) = φ_turb(x,t) + φ_DM(x)
Strehl = |Σ e^{i·residual(x_n)}|² / N² (Maréchal ratio)
Each actuator's target command is set to −φ_turb sampled at its own position; the mirror surface only relaxes toward that target at the chosen correction bandwidth, so a slow loop lags a fast-moving atmosphere. Too few actuators also leave high-spatial-frequency wrinkles the mirror simply cannot shape (fitting error) — both effects are visible directly as leftover ripple in the white residual curve and as a fatter, dimmer point-spread function below it.
- Wavefront pane — incoming turbulence (orange), the mirror's shape (cyan, dots = actuators), and what is left uncorrected (white).
- PSF pane — the star's diffraction image computed from the residual wavefront; a flat residual gives a tight diffraction-limited spike, a wrinkled one spreads light into a broad halo.
- Strehl ratio — peak image intensity relative to a perfect, aberration-free telescope; 1.0 is diffraction-limited, under ~0.1 the image is essentially destroyed by turbulence.