Astronomy

Telescopes and light

Aperture, diffraction limit, collecting area, seeing versus space telescopes.

Basics

Aperture

Aperture is the diameter D of the main lens or mirror. Larger D gathers more photons and, ideally, a finer image. Mirrors scale large apertures more cheaply than lenses. The focal ratio f/D shapes field and exposure feel. Mount, tracking, and dome can cost as much as the optic. Cheap eyepieces that only raise magnification just enlarge a blur.

Diffraction limit

A circular aperture’s theoretical resolution is near θ ≈ 1.22 λ / D (radians). Longer wavelength or smaller D thickens the image. A 1 m visible telescope is theoretically ~0.1″, but the atmosphere usually wins first on the ground. Radio needs much larger D for the same θ because λ is large. Interferometers stitch baselines from many apertures.

Collecting area

Collected light scales roughly with area π (D/2)². Double D and the same star yields about four times the photons. Faint galaxies and distant supernovae live or die by area. Spectroscopy still needs photons after the slit, or noise wins. Exposure time trades against area in the plan.

Seeing and space

Atmospheric turbulence that makes stars dance is seeing. Even on good mountains, visible seeing is often an arcsecond or more. Adaptive optics uses laser guide stars and fast mirrors to approach the diffraction limit. Space telescopes have no seeing and open UV/IR windows, at high launch and servicing cost. Huge ground apertures and space platforms complement each other.

Formulas

Diffraction limit (rough)

θ ≈ 1.22 λ / D

Radians; ×206265 for arcseconds.

Symbols

  • λ wavelength
  • D aperture diameter

Collecting area

A = π (D/2)²

First-order scale for photon rate.

Symbols

  • A area

Light and time (sketch)

S/N ∝ √(A t Δλ) (배경 한계 스케치)

Area, exposure, and bandpass raise S/N.

Symbols

  • t exposure time
  • Δλ bandwidth

Key table

Hubble vs giant ground Hubble: no seeing. 30 m-class ground: area + AO compete
Seeing unit stellar FWHM in arcseconds; 0.5″ is excellent
Central obstruction a secondary blocking the centre tweaks contrast a little

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