What pixel scale means
In astrophotography, the pixel scale (also called image scale or sampling) is the patch of sky each pixel of the camera covers, measured in arcseconds per pixel. It depends only on the size of the pixels and the focal length of the telescope.
The formula
Pixel scale (″/px) = 206.265 × pixel size (µm) ÷ focal length (mm)
The constant 206.265 comes from the number of arcseconds in a radian (206,265), divided by 1,000 to match the units. Binning 2×2 doubles the effective pixel size, and so doubles the scale.
With a camera of 3.76 µm pixels on a 600 mm refractor, the scale is 206.265 × 3.76 ÷ 600 = 1.29″ per pixel. A 6,248 × 4,176 pixel sensor then covers about 134.6′ × 90.0′, or roughly 2.2° × 1.5°: four full Moons side by side.
Matching the scale to the seeing
The atmosphere blurs every star into a disk whose width, the seeing (FWHM), is typically 2 to 3″ at an average site and 1″ or less on the best mountains. Sampling theory and experience suggest putting 2 to 3 pixels across the FWHM:
| Pixels per FWHM | Diagnosis | What to do |
|---|---|---|
| under 1.5 | Undersampled: square stars | Longer focal length or smaller pixels |
| 1.5 to 3.5 | Well sampled | Nothing |
| over 3.5 | Oversampled: signal wasted | Bin 2×2 or use a reducer |
Undersampling is not always a problem: wide-field nebula images often accept it to frame large targets. Dithering between exposures and drizzle integration recover some resolution.
Using the result
- Choose a focal reducer or Barlow by comparing the scale with your typical seeing.
- Check the field of view against the size of your target before buying a camera.
- Plate-solving software also needs the approximate scale to identify a star field quickly.
Remember to enter the effective focal length: a 0.8× reducer turns a 600 mm telescope into 480 mm.