How is angular resolution per pixel calculated?

For the small angles involved, one pixel subtends pixel pitch divided by focal length in radians. Multiplying by 206265 converts radians to arcseconds. A 3.76 micrometre pixel behind a 400 mm lens gives about 1.94 arcseconds per pixel.

What is a good arcseconds-per-pixel value for astrophotography?

Aim to sample at roughly one-third to one-half of your seeing disc. With typical seeing of 2 to 4 arcseconds, an image scale of about 1 to 2 arcseconds per pixel is a common sweet spot that avoids both under and over sampling.

What does diffraction-limited mean here?

If the lens's diffraction blur (the Rayleigh limit) is larger than one pixel, the optics, not the sensor, set the finest detail. The tool reports whether your system is pixel limited or diffraction limited so you know which to improve.

How is the diffraction limit computed?

It uses the Rayleigh criterion: 1.22 times the wavelength divided by the aperture diameter, in radians. The aperture diameter is the focal length divided by the f-number. Green light at 550 nm is a common reference wavelength.

Does this work for machine-vision inspection too?

Yes. The same image-scale maths tells you the smallest angle, and therefore the smallest feature at a known distance, that one pixel can resolve, which is the starting point for sizing an inspection camera and lens.

What is the Camera Angular Resolution Calculator?

Compute angular resolution in arcseconds per pixel from sensor pixel pitch and lens focal length, plus field of view and the lens diffraction limit. Useful for astrophotography sampling and optical inspection. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Camera Angular Resolution Calculator

Name: Camera Angular Resolution Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

Get one useful tool a week

Like this tool? Enter your email and we'll send you one genuinely useful Gera tool a week — plus a link to come back to this one. No spam, one-click unsubscribe any time.

This tool converts a camera’s pixel pitch and lens focal length into image scale — the angle that a single pixel covers on the sky or scene. It is the core number for choosing an astrophotography rig or sizing an optical inspection system.

How it works

Because the angle per pixel is tiny, the small-angle approximation applies:

angle per pixel (rad)    = pixel pitch / focal length   (same units)
angle per pixel (arcsec) = angle (rad) × 206265
horizontal FOV           = 2 × atan(sensor width / (2 × focal length))
diffraction (rad)        = 1.22 × wavelength / aperture diameter
aperture diameter        = focal length / f-number

The tool then compares the per-pixel angle with the diffraction blur to tell you whether the sensor (pixels) or the optics (diffraction) is the limiting factor.

Worked example

Take a Sony IMX571 sensor with a pixel pitch of 3.76 µm behind a 400 mm refractor at f/7.1:

angle per pixel = 3.76 / 400,000 × 206265 ≈ 1.94 arcsec/px
aperture         = 400 / 7.1 ≈ 56.3 mm
diffraction      = 1.22 × 0.00055 / 56.3 × 206265 ≈ 2.45 arcsec

The pixel resolves 1.94 arcsec while the diffraction limit is 2.45 arcsec — the optics are limiting, so the system is diffraction limited. Upgrading to a finer sensor pitch would not sharpen the stars; you would need to open the aperture or extend the focal length instead.

Sampling guidelines for astrophotography

Optimal sampling depends on the typical atmospheric seeing at your site. The broadly accepted rule is to aim for a pixel scale of roughly one-third to one-half the seeing disc diameter:

Typical seeing	Target image scale
1 arcsec (excellent, mountain site)	0.3–0.5 arcsec/px
2 arcsec (good suburban)	0.7–1.0 arcsec/px
3–4 arcsec (typical city)	1.0–2.0 arcsec/px

Under-sampling (too few arcsec per pixel) smooths stars into blobs; over-sampling (too many pixels per arcsec) adds noise without detail. The calculator lets you adjust focal length and sensor pitch to land in the right band for your site.

Using the diffraction limit output

The Rayleigh criterion — 1.22 × wavelength / aperture — gives the finest detail the optics can in principle deliver. If your pixel scale is much smaller than the diffraction limit, you are pixel-limited (sensor resolves finer than the optics). If your pixel scale is larger than the diffraction limit, you are diffraction-limited (optics can deliver more than the sensor captures). In practice:

Pixel-limited: use a Barlow or longer focal length to spread the diffraction disc across more pixels.
Diffraction-limited: a finer sensor pitch would help, but the gains are marginal — focus on seeing and guiding instead.

For machine-vision and optical inspection use the same formula. Multiply the per-pixel angle (in radians) by the object-to-lens working distance to find the real-world size one pixel resolves at that distance.