Adaptive Optics Calculator
Adaptive optics in Kolmogorov turbulence: Noll's residual after J corrected Zernike modes, deformable-mirror fitting error, the Strehl ratio and the stroke needed, from D/r₀.
r₀ grows as λ^(6/5): r₀ = 10 cm at 500 nm is 11.2 cm at 550 nm and 59 cm at 2.2 µm.
Results
The modal and DM rows are two separate estimates of perfect correction, not terms to add: a mirror with N actuators across corrects roughly the first (π/4)N² modes. Strehl = e^(−σ²) + (1 − e^(−σ²))/(1 + (D/r₀)²), the coherent core plus the seeing halo. The stroke row assumes the tip-tilt (σ² = 0.134 (D/r₀)^(5/3)) is taken by a separate mirror. Servo lag, noise and anisoplanatism are left out; the free-space AO calculator adds the servo lag.
Strehl ratio vs Zernike modes corrected
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Kolmogorov turbulence (infinite outer scale) with perfect correction of the chosen modes or by the mirror; servo lag, wavefront-sensor noise and anisoplanatism are left out. The Strehl ratio adds the Parenti–Sasiela seeing halo to the Maréchal core. Aberrations from a sample in microscopy do not follow Kolmogorov statistics.
- Noll R. J. (1976). Zernike polynomials and atmospheric turbulence. J. Opt. Soc. Am. 66, 207–211. Residual variance Δ_J after J corrected modes (Table IV). doi:10.1364/JOSA.66.000207
- Hudgin R. H. (1977). Wave-front compensation error due to finite corrector-element size. J. Opt. Soc. Am. 67, 393–395. Fitting error κ(d/r₀)^(5/3). doi:10.1364/JOSA.67.000393
- Parenti R. R., Sasiela R. J. (1994). Laser-guide-star systems for astronomical applications. J. Opt. Soc. Am. A 11, 288. Strehl ratio with the seeing halo. doi:10.1364/JOSAA.11.000288
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