Beam spread calculator

How to use the calculator

1. Enter the wavelength of the light source in meters (e.g., 532e-9 for 532 nm). You can use scientific notation (e.g., 532e-9).
2. Enter the diameter of the beam aperture or lens in meters. If you don't know the exact diameter, you can estimate it from the beam's spot size.
3. Click the "Calculate" button to compute the beam spread.
4. The calculator will display the beam spread in both radians and degrees.

Understanding the formula

This calculator uses the Airy disk diffraction limit formula to calculate the theoretical beam spread:
θ = 1.22 × (λ / D)

Where:
θ = Half-angle beam spread (radians)
λ = Wavelength of light (meters)
D = Beam diameter (meters)

This formula is based on the physical principle that a beam of light passing through an aperture will spread due to diffraction, with the angular spread inversely proportional to the aperture diameter.

Example

If you have a laser with a wavelength of 632.8 nm (632.8e-9 meters) and a beam diameter of 2 mm (0.002 meters), the beam spread would be:
θ = 1.22 × (632.8e-9 / 0.002) = 0.0003888 radians = 0.0223 degrees

Applications

This calculator is useful for:

• Optical system design
• Laser beam characterization
• Understanding the diffraction limit of imaging systems
• Designing telescopes, microscopes, and other optical instruments