What is image scale in arcsec per pixel?

Image scale is the slice of sky that one pixel covers. It is found by image_scale = 206.265 times pixel_size_microns divided by focal_length_mm. A scale of 2 arcsec per pixel means each pixel spans 2 arcseconds of sky.

What is optimal sampling for astrophotography?

The Nyquist guideline says you want roughly 2 to 3 pixels across the smallest detail your seeing allows. A practical target is an image scale of about one-third to one-half of your seeing in arcseconds, so 2-arcsecond seeing pairs well with about 0.7 to 1.0 arcsec per pixel.

What does under-sampled mean?

Under-sampled means each pixel covers too much sky, so stars look blocky and fine detail is lost because the sensor cannot record what the optics deliver. It happens with large pixels on a short focal length. Wide-field setups are often intentionally under-sampled to maximize field of view.

What does over-sampled mean?

Over-sampled means pixels are smaller than the detail the atmosphere allows, so you spread a blurry star over many pixels with no gain in resolution, just dimmer pixels and longer exposures. Very long focal lengths with small pixels over-sample under average seeing.

Does binning change image scale?

Yes. Binning 2x2 combines four pixels into one, effectively doubling the pixel size and the image scale while quadrupling sensitivity. If you are over-sampled, binning is a free way to reach better sampling and shorter exposures, though on CMOS it is usually done in software.

CCD / CMOS Image Scale Calculator

Matching a camera to a telescope comes down to one number: image scale, the amount of sky each pixel sees. Get it right and stars are crisp and round; get it wrong and you either throw away detail or waste exposure time on empty resolution. This calculator computes arcseconds per pixel and grades it against your local seeing.

How it works

The image scale formula uses the small-angle approximation, where 206,265 is the number of arcseconds in one radian:

image_scale (arcsec/px) = 206.265 * pixel_size_microns / focal_length_mm

The factor 206.265 already folds the micron-to-millimeter conversion into the 206,265 arcsec/radian constant, so pixel size goes in as microns and focal length as millimeters directly.

Judging the sampling

A widely used target is to keep image scale near one-third to one-half of the seeing:

scale > 2/3 of seeing → under-sampled (blocky stars, but wide field)
scale between 1/3 and 2/3 of seeing → well sampled
scale < 1/3 of seeing → over-sampled (no extra detail, dimmer pixels)

Tips

Most backyard sites have 2 to 4 arcseconds of seeing, which means image scales around 1 to 1.5 arcsec/px are a sweet spot for deep-sky work. If you land far on the over-sampled side, try binning 2x2 or a focal reducer; if heavily under-sampled and you want more detail, add a Barlow or a camera with smaller pixels. Field of view, not just sampling, should also guide the final choice.