Angular Resolution Calculator

Angular resolution measures the ability of an optical instrument to distinguish two closely spaced objects or fine details. The smaller the angular resolution value, the finer the detail the instrument can resolve. It is a critical property for telescopes, microscopes, cameras, and even the human eye.

The Rayleigh criterion gives the angular resolution as θ = 1.22 × λ / d, where θ is the minimum resolvable angle in radians, λ is the wavelength of light, and d is the diameter of the aperture. The factor 1.22 comes from the first zero of the Bessel function describing the diffraction pattern of a circular aperture.

The 1.22 factor arises from the mathematics of diffraction through a circular aperture. When light passes through a circular opening, it forms an Airy disk pattern. The first dark ring of this pattern occurs at an angle governed by the first zero of the first-order Bessel function, which evaluates to approximately 1.22. This is why the Rayleigh criterion uses 1.22 rather than 1.

The human eye has an aperture (pupil) of roughly 2–8 mm and is most sensitive to light around 550 nm (green). Using these values in the Rayleigh criterion gives an angular resolution of approximately 1–4 arcminutes, which matches the commonly cited value of about 1 arcminute for a healthy human eye under good lighting.

Larger apertures produce better (smaller) angular resolution because the minimum resolvable angle θ is inversely proportional to the diameter d. Doubling the aperture halves the minimum resolvable angle, allowing the instrument to distinguish twice as much fine detail.

Yes — angular resolution is directly proportional to wavelength. Shorter wavelengths (such as ultraviolet or blue light) yield better resolution than longer wavelengths (such as red or infrared). This is why electron microscopes, which use electrons with very short de Broglie wavelengths, can resolve structures far smaller than light microscopes.

The Hubble Space Telescope has a primary mirror diameter of 2.4 m. At a typical optical wavelength of 500 nm, the Rayleigh criterion gives an angular resolution of about 0.05 arcseconds. This extraordinary resolution, combined with the absence of atmospheric distortion in space, allows Hubble to image extremely fine detail in distant galaxies.

Angular resolution (θ) is the minimum angular separation an instrument can distinguish — a smaller value means better performance. Resolving power is often used as the reciprocal concept: higher resolving power means the instrument can separate finer details. In practice the two terms are closely related and are often used interchangeably, though resolving power may also refer to spectral resolution in spectroscopy.