Laser Beam Divergence: Formula, Spot Size and Range
Beam divergence is the single parameter most often misread in laser rangefinder datasheets. A smaller number is usually better, but it is not a range specification, and treating it as one leads to the wrong module choice.
The definition
Divergence is the angular spread of the beam, expressed in milliradians (mrad). One milliradian is one metre of spread per kilometre of propagation. For a beam with full-angle divergence θ in mrad at range R in km, the spot diameter is:
D (m) ≈ θ (mrad) × R (km)
This linear approximation is accurate enough for module selection work. The formal expression uses the half-angle: D = 2 · R · tan(θ/2). Datasheets vary on whether the figure is full-angle or half-angle — this is a common source of 2× disagreement between suppliers, and worth confirming explicitly. ERDI figures are full-angle unless the document states otherwise.
Spot size at range for ERDI modules
| Divergence | 1 km | 5 km | 10 km | 20 km | Models |
|---|---|---|---|---|---|
| 0.15 mrad | 0.15 m | 0.75 m | 1.5 m | 3.0 m | LR120K1, LDR80K2 |
| 0.2 mrad | 0.2 m | 1.0 m | 2.0 m | 4.0 m | LR160 |
| 0.3 mrad | 0.3 m | 1.5 m | 3.0 m | 6.0 m | LDR60K1, LDR80K1 |
| 0.6 mrad | 0.6 m | 3.0 m | 6.0 m | 12.0 m | LDR20K1 |
The practical reading: at 10 km, a 0.15 mrad beam puts all of its energy inside a 1.5 m circle, while a 0.6 mrad beam spreads the same energy over a 6 m circle. On a vehicle-sized target, the tighter beam returns far more energy — which is why divergence, not pulse energy alone, drives long-range performance on small targets.
Why tighter is not always better
Three situations favour a wider beam:
- Platform instability. A beam that is too tight for the platform's pointing jitter will partially miss the target at range. A gimbal with millimetre-level stabilisation and a 0.15 mrad beam is fine; the same beam on a hand-held unit is not.
- Target acquisition. Wide beams are easier to put on small or moving targets quickly. For designation against a moving target, some divergence is a feature.
- Atmospheric scintillation. In strong turbulence, a very tight beam can be steered off the receiver; a slightly wider beam averages the effect.
A well-chosen module matches divergence to the platform's stabilisation quality and the target size at the intended range.
Divergence and received energy
Received signal scales with the fraction of the beam that lands on the target. If the spot is much smaller than the target, all the energy is useful. Once the spot grows beyond the target, the received energy falls roughly as 1/D² — that is, as 1/(θ·R)².
Combine that with the inevitable 1/R² spreading loss and you can see why range grows only slowly with pulse energy. This is also why the maximum range specification must state the target: a 2.3 m × 2.3 m standard panel at 10 km fills a 0.15 mrad spot but is much larger than a 0.6 mrad spot.
Measuring it honestly
Divergence should be specified with the measurement convention:
- Is it full-angle or half-angle?
- Is it measured at the 1/e² intensity contour, or at a defined encircled-energy fraction (e.g. 86.5%)?
- Is it the design value or a measured value over temperature?
Two suppliers quoting "0.3 mrad" may be describing different things. Ask for the convention and, for a critical program, a measured beam profile.
Frequently asked questions
What is a good beam divergence for a laser rangefinder?
For long-range airborne and vehicle applications, 0.15 to 0.3 mrad is typical. Handheld and short-range modules commonly use 0.5 to 1.0 mrad, trading spot size for ease of aiming.
Does lower divergence increase range?
It increases the energy delivered to a small target at long range, which is often the limiting factor. It does not change the detector's sensitivity or the atmospheric loss, so it is one of several levers rather than a direct range multiplier.
What is the difference between beam divergence and beam waist?
The beam waist is the narrowest point of the beam, usually at the exit aperture or at a focus set by the optics. Divergence describes how quickly the beam widens after that point.
Can divergence be adjusted after delivery?
In most modules the transmit optics are fixed and aligned at build. Some designs allow a focus adjustment for a specific range band, but changing divergence is an optical reconfiguration, not a field setting.
Next: read how divergence interacts with energy and repetition rate in pulse energy, PRF and divergence, or compare modules on the laser rangefinder collection page.