Airy Disk Diffraction Calculator

Calculator Inputs

Calculation method

Wavelength

Wavelength unit

Refractive index

Aperture diameter

Aperture unit

Focal length

Focal length unit

Screen or target distance

Distance unit

F-number

Numerical aperture

Pixel pitch, µm

First minimum factor

Formula Used

For a circular aperture, the first dark ring is estimated with:

θ = sin^-1(1.22λ / D)

Here, θ is angular Airy radius, λ is wavelength in the medium, and D is clear aperture diameter.

Linear radius at a screen or focal plane is:

r = L tan(θ)

For an f-number calculation, the focal plane Airy radius is:

r = 1.22λN

Airy diameter is twice the radius. For numerical aperture, the calculator uses:

r = 0.61λ / NA

How To Use This Calculator

Select aperture mode for telescope, pinhole, or long-distance diffraction work.
Select f-number mode for camera lens diffraction at the sensor plane.
Select numerical aperture mode for microscope-style diffraction estimates.
Enter wavelength, refractive index, and the relevant optical dimensions.
Press the calculate button to view results above the form.
Use CSV or PDF export for records, reports, and design notes.

Example Data Table

Example	Wavelength	Main Input	Distance Or Focus	Expected Use
Telescope aperture	550 nm	100 mm aperture	10 m target	Angular resolution and projected spot
Camera lens	550 nm	f/8	Sensor plane	Diffraction blur diameter
Microscope objective	520 nm	NA 0.65	Lateral image plane	Resolution estimate
Laser bench	632.8 nm	2 mm aperture	3 m screen	Spot spread check

Understanding Airy Disk Diffraction

An Airy disk appears when light passes through a circular aperture. The aperture can be a lens, mirror, telescope pupil, microscope objective, or pinhole. Diffraction spreads the wavefront into a bright central spot with dim rings around it. The central spot sets a real limit on detail. Better glass cannot remove this limit. A larger aperture, shorter wavelength, or stronger numerical aperture makes the disk smaller.

Why The Calculator Matters

This calculator helps designers estimate that limit before building an optical system. It accepts aperture diameter, wavelength, focal length, screen distance, f-number, and numerical aperture. It then reports angular radius, Airy radius, Airy diameter, Rayleigh separation, and sampling in pixels. The result helps compare telescopes, cameras, projectors, laser benches, microscopes, and imaging sensors.

Practical Interpretation

The first dark ring is often used as the Airy radius. Two point sources are considered barely resolved when the center of one pattern falls on the first dark ring of the other. This is called the Rayleigh criterion. For camera work, the Airy diameter should be compared with pixel pitch. A very small disk may be undersampled. A very large disk may soften fine detail.

Inputs And Units

Use nanometers for visible light when possible. Blue light creates a smaller pattern than red light. Enter the refractive index when the light travels through water, oil, or glass. The tool converts the wavelength in the medium for aperture and f-number calculations. Numerical aperture results use the common microscope relation with the entered vacuum wavelength.

Advanced Use

For a telescope, choose aperture and distance. The angular result is usually most important. For a camera lens, choose f-number. The focal plane diameter shows diffraction blur on the sensor. For a microscope, choose numerical aperture. The lateral diameter gives the diffraction-limited spot size. Export the table when you need a repeatable record for reports, lab notes, or design checks.

Design Tips

Keep units consistent when comparing several lenses. Check both radius and diameter because catalogs may use different terms. Remember that manufacturing errors, defocus, vibration, seeing, and sensor filters can enlarge the measured spot. Use the calculated value as a diffraction baseline, then add real system tolerances during final optical review and testing decisions.

FAQs

What is an Airy disk?

An Airy disk is the central bright spot formed when light diffracts through a circular aperture. It is surrounded by weaker rings.

What does the first dark ring mean?

The first dark ring marks the first minimum in the diffraction pattern. Its radius is often used as the Airy radius.

Why does aperture size matter?

A larger aperture reduces diffraction spread. It creates a smaller Airy disk and improves theoretical angular resolution.

Why does wavelength matter?

Longer wavelengths diffract more. Red light creates a larger Airy disk than blue light when aperture size is unchanged.

What is Rayleigh separation?

Rayleigh separation is the angle or distance where two point sources are barely resolved by the diffraction pattern.

When should I use f-number mode?

Use f-number mode for camera lenses or focused optical systems. It estimates diffraction blur at the focal plane.

When should I use numerical aperture mode?

Use numerical aperture mode for microscope objectives and high-aperture imaging systems. It estimates lateral diffraction-limited spot size.

Can real images be sharper than this value?

Usually no. The Airy disk is a diffraction limit. Real systems may be worse because of aberration, defocus, vibration, and sampling.