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.

Camera Angular Resolution Calculator

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.

Example and tips

A 3.76 micrometre pixel behind a 400 mm lens yields about 1.94 arcseconds per pixel — a good match for average seeing. Watch the limiting factor: stopping a lens down past its diffraction limit only softens the image, while a pixel-limited system benefits from a longer focal length or finer-pitch sensor. For inspection work, multiply the per-pixel angle by the working distance to get the real-world size of one pixel.