Lasers are good but not perfect
Learn how — and why — a pointer can't work from the Earth to the Moon with our laser beam divergence calculator! Keep reading to discover one of the most important features of a laser device. Here you will learn:
- An introduction to lasers and their operation;
- What the laser beam divergence is;
- How to calculate the divergence of a laser beam; and
- How the divergence of a laser affects the way it propagates.
You will also find some examples and, finally, why pointing at the Moon is rather tricky!
Explaining lasers at the speed of light
Lasers are devices that emit a highly coherent beam of monochromatic light thanks to a process of amplification of a single wavelength inside an energized medium. Laser beams have three main properties:
- Laser radiation is nearly monochromatic. The characteristics of the medium where the light gets amplified allow selecting almost exclusively a single wavelength of light.
- Laser radiation shows a high directionality. The propagation of a beam happens along an axis around which the light expands rather slowly, even over long distances.
- Laser light is highly coherent. The photons emitted by a laser device are in phase with each other over both time and distance. Coherence allows laser beams to show interference.
The properties of laser radiation made the technology fundamental in the second half of the 20th century. When first devised, lasers were famously called "a solution seeking a problem". Eventually the problems were found, and lasers became irreplaceable in medicine, optics, astronomy, manufacturing — you name it!
Inside the resonating chamber: the origin of beam divergence
Meet a laser. It looks like a uniform opaque cylinder from the outside, but you may notice a different material on one of the bases. That's where the radiation escapes the chamber — don't look at it when the device is on!
Inside the chamber, two mirrors sit on opposite, parallel sides. One of them (at the opening of the resonator) is partially transparent, while the other is fully reflective. Between the two mirrors lies a medium, the core of the device. If pumped with energy (electricity or light), it amplifies the light of a specific wavelength. After bouncing back and forth many times, the photons escape the chamber, amplified and coherent.
The beam acquires its properties inside the optical resonator. Ideal lasers are Gaussian beams: they move along a primary direction — or axis — with a cross-sectional intensity profile that follows a Gaussian curve. The same physics that builds the beam also sets a hard limit on how parallel it can stay: the divergence.
What is the divergence of a laser beam?
A real laser beam is never perfectly parallel. As it travels away from the source, its cross-section slowly grows. The beam divergence θ is the angle at which the beam widens in the far field. It is usually quoted as a full angle (the entire opening of the cone) and measured in milliradians (mrad), though it can also be expressed as a half angle, in degrees, or in arcminutes.
A small divergence means a tightly collimated beam that stays narrow over long distances; a large divergence means the beam spreads out quickly. Divergence is the direct consequence of diffraction: the smaller the beam waist and the longer the wavelength, the more the beam spreads.
How to calculate the laser beam divergence
If you measure the beam diameter at two points along its path, you can find the full-angle divergence directly:
θ = 2 · arctan[ (Df − Di) / (2 · L) ]
where:
- Di — the initial beam diameter (closer to the source);
- Df — the final beam diameter (farther from the source); and
- L — the distance between the two measurement points.
For small angles, this simplifies to θ ≈ (Df − Di) / L. Once you know θ, you can predict the beam diameter at any distance z with D(z) = Di + 2 · z · tan(θ/2).
How to use our laser beam divergence calculator
- Choose your unit system — metric (mm, m) or American (inches, feet).
- Enter the initial beam diameter Di measured near the source.
- Enter the final beam diameter Df measured farther away.
- Enter the distance L between the two measurements.
The calculator instantly returns the full-angle divergence (in mrad, degrees and arcminutes), the half-angle divergence, and — just for fun — how wide your beam would be by the time it reached the Moon.
Why can't we use a laser pointer from the Earth to the Moon?
A typical laser pointer has a divergence of roughly 1–2 mrad. That sounds tiny, but the Moon is about 384,400 km away. Even at 1 mrad, the spot would grow to hundreds of kilometers across by the time it arrived — spreading the already weak power of the pointer over an enormous area. The light that would reach a given square meter becomes vanishingly small, which is exactly why a handheld pointer can never "paint" the Moon. Try it yourself: enter a small divergence and watch the projected Moon spot in the results balloon to hundreds of kilometers!
Real Earth–Moon laser ranging experiments overcome this by using powerful lasers, large telescopes to collimate the beam to microradian-level divergence, and retroreflectors left on the lunar surface by the Apollo missions.
FAQs
What is a typical laser beam divergence?
Collimated gas and solid-state lasers reach about 0.5–2 mrad, while bare laser diodes can diverge by hundreds of mrad before a collimating lens. Specialized beams sent through large telescopes can reach the microradian range.
Is divergence a full angle or a half angle?
Both conventions exist. This calculator computes the full-angle divergence by default and also reports the half angle, so you can compare with any datasheet.
How do I reduce beam divergence?
Expand the beam with a beam expander or telescope. A larger beam waist diffracts less, so divergence drops in proportion to how much you widen the beam.
Does wavelength affect divergence?
Yes. For a diffraction-limited Gaussian beam, divergence is proportional to the wavelength: longer wavelengths (such as CO2 lasers at 10,600 nm) spread more than shorter ones for the same beam waist.