Tool · Imaging and diffraction

Airy Disk Calculator

The diffraction pattern of a circular aperture, computed exactly from Bessel functions: Airy disk radius and diameter, FWHM, the dark and bright rings, encircled energy, the Rayleigh, Sparrow and Abbe resolution limits, angular resolution for telescopes and pixel sampling for cameras, for any wavelength and f-number, aperture and focal length, or numerical aperture. Background: Airy disk, diffraction limit, and point spread function.

Optical system

Wavelength λ (nm)

f-number N = f / D

image-side NA = 1 / (2N) for a lens in air (sine condition)

Aperture diameter D (mm)

Focal length f (mm)

Numerical aperture NA

Immersion index n

Magnification to camera M

object-plane pattern; NA = n sin θ is limited to the immersion index

Camera pixel pitch p (µm)

Energy probe radius (Airy radii)

reads the fraction of the total power inside a circle of this radius

Presets

Scalar diffraction theory for a uniformly illuminated, aberration-free circular aperture. NA = n sin θ under the sine condition, so NA = 1/(2N) for a lens in air. Above about NA 0.7 the vector treatment (Richards and Wolf 1959) elongates the spot slightly along the polarization direction; the values here are the scalar ones that the resolution criteria quote.

Readouts

Ring	Dark-ring radius	Energy inside	Bright-ring peak

Radial intensity profile

Encircled energy

Two-point resolution

separation × Rayleigh

source 1source 2incoherent sum

The pattern

Checked against

These checks run in your browser on every load. The Bessel functions are compared with the Abramowitz and Stegun tables, the ring positions with the tabulated zeros of J₁ and J₂, the encircled energies and the Rayleigh saddle with Born and Wolf, the Sparrow limit with its published value, and the unit conversions with the textbook 2.44 λN, 0.61 λ/NA and 138/D rules.

Check	Expected	Computed