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.

What is the CCD / CMOS Image Scale Calculator?

Enter camera pixel size in microns and telescope focal length to compute image scale in arcsec per pixel, then compare to your seeing conditions to check for optimal sampling. For astrophotographers matching cameras to scopes. It runs free in your browser on Gera Tools, with nothing uploaded.

CCD / CMOS Image Scale Calculator

Name: CCD / CMOS Image Scale Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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)

Worked examples with real camera and scope combinations

Example 1 — Short refractor, large pixels

A 480 mm focal-length refractor paired with a camera with 3.76 µm pixels:

image_scale = 206.265 × 3.76 / 480 = 1.61 arcsec/px

Under typical 3-arcsecond suburban seeing this falls in the well-sampled range (1/3 to 2/3 of 3 arcsec = 1.0–2.0 arcsec/px). Excellent for wide-field nebulae and galaxy clusters.

Example 2 — Long SCT, small pixels

A 2,000 mm focal-length SCT with 2.4 µm pixels:

image_scale = 206.265 × 2.4 / 2000 = 0.25 arcsec/px

Under 2-arcsecond seeing the target range is 0.67–1.0 arcsec/px. At 0.25 arcsec/px this setup is heavily over-sampled — stars spread across many dim pixels, requiring longer exposures with no resolution gain. Binning 2×2 effectively makes the pixel 4.8 µm and the scale 0.50 arcsec/px, placing it back in range.

Common fix: binning and focal reduction

Problem	Likely fix
Heavy over-sampling	Bin 2×2 (software) or add a focal reducer (0.63× or 0.8×)
Under-sampling with wide FOV (intentional)	Leave it; wide-field is often the goal
Under-sampling wanting more detail	Barlow lens (2× doubles the focal length) or smaller-pixel camera

Tips for matching hardware

Most backyard sites have 2 to 4 arcseconds of seeing, which makes image scales around 1 to 1.5 arcsec/px a sweet spot for deep-sky work at typical amateur apertures. Field of view is the other constraint: a sensor’s field in arcminutes equals (sensor_size_mm / focal_length_mm) × 3438. A large sensor on a short scope gives a rich wide field; a small sensor on a long scope gives a tight planetary or globular view. Run the image-scale and FOV calculations together to make sure both fit your targets before buying.