Telescopes & Observing
The optics of observing — angular resolution and the diffraction limit, magnification, image scale and field of view, limiting magnitude, and the photon shot-noise limit on signal-to-noise.
- Angular Resolution (Rayleigh)Telescopes & instrumentsθ = 1.22 λ / D
The finest detail a telescope can resolve, set by diffraction at its aperture — the Rayleigh criterion. Bigger apertures see finer detail; a 100 mm telescope resolves about 1.4 arcseconds in green light.
- Field of ViewTelescopes & instrumentsFOV = 3437.75 × sensor(mm) / focal(mm)
The angular extent of sky a camera frames, from the sensor size and focal length. A shorter focal length or a larger sensor takes in more sky.
- Image ScaleTelescopes & instrumentss = 206.265 × pixel(µm) / focal(mm)
How much sky each camera pixel covers, from the pixel size and focal length. Matching the image scale to the seeing (roughly 1–2″ per pixel) is the key to sharp astrophotography.
- Limiting MagnitudeTelescopes & instrumentsm_lim ≈ 2.7 + 5 log₁₀(D_mm)
A rule-of-thumb estimate of the faintest star an aperture can show under dark skies. Approximate — real limits depend on sky brightness, magnification, and the observer — so it is offered as a guide, not a guarantee.
- Photon Shot-Noise SNRTelescopes & instrumentsSNR = √N
The best signal-to-noise achievable when the only noise is the Poisson statistics of the photons themselves — the shot-noise limit. To double the signal-to-noise you must collect four times as many photons.
- Telescope MagnificationTelescopes & instrumentsM = f_telescope / f_eyepiece
The magnification of a telescope–eyepiece pair — the ratio of their focal lengths. Useful magnification is capped by the aperture and the atmosphere, not by the eyepiece alone.