Telescope Resolution: Sharper Eyes

See how wavelength and aperture set a best-case resolution limit.

• Magnification isn’t the same as resolution.
• Shorter wavelength and larger aperture improve resolution.
• With atmosphere on, “seeing” can dominate unless AO helps.

• Diffraction-limited scaling: $$\theta_\mathrm{diff} \approx 1.22\,\frac{\lambda}{D}$$ where $\lambda$ is wavelength and $D$ is effective aperture.
• Atmosphere: without AO the resolution is $\max(\theta_\mathrm{diff},\,\theta_\mathrm{seeing})$. With AO the corrected point-spread function is a core of width $\theta_\mathrm{diff}$ inside a halo of width $\theta_\mathrm{seeing}$, so the resolution is $\theta_\mathrm{diff}$ and the Strehl ratio $S$ is the fraction of the light in that core, not a reduction of the seeing.
• Status cutoffs are didactic: resolved if separation $\ge \theta_\mathrm{eff}$, marginal if $\ge 0.8\,\theta_\mathrm{eff}$.
• Visualization: diffraction uses an Airy PSF $I(x)=[2J_1(x)/x]^2$; with atmosphere on we use a blurred PSF for clarity (not a full turbulence simulation).