Focusing a Laser Beam: Spot Size, Depth of Focus and Damage

How to focus a laser beam to a chosen spot: the focused spot size from wavelength, focal length, input beam diameter and M², the trade against depth of focus, choosing and orienting the lens, peak irradiance and fluence at the focus, damage thresholds, and how to measure the spot.

Published September 27, 2026Updated October 6, 20266 min read

Scope

This article brings together what sets the size and shape of a focused laser spot and what the focus can do: the spot size formula, its trade against depth of focus, lens choice and aberrations, the irradiance and fluence at the focus, and the damage thresholds that limit them. It is written for collimated input beams focused by a single lens, the usual case on the bench and in materials processing. The Gaussian Beam Calculator computes the same quantities for any input, and the reverse task, making a diverging beam parallel, is covered in How to Collimate a Laser Beam.

Focused spot size formula

A collimated Gaussian beam of $1 / e^{2}$ diameter $D$ at a lens of focal length $f$ focuses to a waist of $1 / e^{2}$ diameter

2 w_{0} = \frac{4 λ f M^{2}}{π D},

where $M^{2}$ is the beam quality factor, 1 for an ideal Gaussian beam and larger for real multimode beams (see M² Beam Quality Measurement). The spot shrinks with a shorter focal length or a larger input beam, which is why a beam expander is placed before a focusing lens when a small spot is needed. The ratio $f / D$ is the working f-number of the focus.

Spot size versus depth of focus

The distance over which the focused beam stays within $\sqrt{2}$ of its waist radius is twice its Rayleigh range,

2 z_{R} = \frac{2 π w_{0}^{2}}{λ M^{2}},

which falls as the square of the spot size. For a 1064 nm beam of 6 mm diameter with $M^{2}$ = 1:

Focal length	Spot diameter $2 w_{0}$	Depth of focus $2 z_{R}$
50 mm	11.3 μm	0.19 mm
100 mm	22.6 μm	0.75 mm
200 mm	45.2 μm	3.0 mm

Halving the spot size cuts the depth of focus by four. A process that needs a tolerant focus, such as cutting thick material or working on an uneven surface, therefore uses a larger spot than the smallest the optics could give.

Lens choice and orientation

The formula above assumes the lens adds no aberration. For a singlet this holds when the working f-number is large; as it falls toward a few, spherical aberration enlarges the spot beyond the Gaussian value and spreads the focus along the axis.

Plano-convex singlets give their smallest aberration for a collimated input when the curved side faces the collimated beam.
Best-form and aspheric lenses reduce spherical aberration further; an asphere can reach the diffraction limit at small f-numbers where a singlet cannot.
Achromatic doublets correct chromatic aberration as well, which matters for broadband or multi-wavelength beams.
Windows and cover glasses between the lens and the focus shift the focus away from the lens by $t (1 - 1 / n)$ for a plate of thickness $t$ and index $n$ , and add spherical aberration at small f-numbers.

A clear aperture 1.5 times the beam's $1 / e^{2}$ diameter passes 98.9% of the power but already widens the focused spot by 11 to 15% (in its $1 / e^{2}$ and half-maximum widths), and twice the diameter widens it by only 1.7 to 3.1%. A smaller aperture clips the beam harder, adding diffraction rings around the spot; if the beam is truncated hard, the focus approaches the Airy pattern of a uniformly filled aperture rather than a Gaussian spot.

Irradiance and fluence at the focus

The peak irradiance of a Gaussian spot of power $P$ is twice the power divided by the area inside the $1 / e^{2}$ radius:

I_{0} = \frac{2 P}{π w_{0}^{2}} .

For pulses of energy $E$ the peak fluence is, likewise, $F_{0} = 2 E / (π w_{0}^{2})$ . For the 100 mm case above ( $w_{0}$ = 11.3 μm), 1 W of continuous power gives a peak irradiance of 5.0 × 10⁵ W/cm², and a 100 μJ pulse gives a peak fluence of 50 J/cm², about 70,000 times the fluence of the 6 mm collimated beam. An optic placed at or near the focus meets that whole increase, so no window, filter or second lens belongs there; the thresholds to compare against are described in the next section.

Laser-induced damage thresholds (LIDT)

Laser-induced damage thresholds (LIDT) are quoted as a fluence (J/cm²) for pulsed beams, at a stated wavelength, pulse duration and repetition rate, and often as a linear power density (W/cm, power divided by beam diameter) for continuous beams, where the failure is thermal. Two conventions make comparisons treacherous:

Peak or average fluence. A threshold quoted as an average fluence, the energy divided by the $1 / e^{2}$ area, is half the peak fluence of the same beam. Compare the beam's peak fluence with a threshold only when the threshold is also defined at the peak.
Pulse duration. For pulses in the nanosecond range, vendors commonly scale thresholds with the square root of the pulse duration. The rule is approximate, and it does not hold for picosecond and femtosecond pulses, where the damage mechanism changes.

A working margin of a factor of two below the specified threshold is common practice; contamination and defects lower the real threshold of an optic in use.

Measuring the spot

A focused spot of tens of micrometers spans only a few pixels of a typical camera sensor, too few to measure its width reliably. Three approaches work:

Knife edge through the focus, as in the knife-edge method, which resolves spots of a few micrometers.
A camera with magnification, imaging the focal plane onto the sensor with a microscope objective of known magnification, while keeping the irradiance on the sensor below saturation.
The caustic scan of the M² measurement, which fits widths through the focus and gives the waist, its position and $M^{2}$ together.

Common questions

How do you calculate the spot size of a focused laser beam?

For a collimated beam of $1 / e^{2}$ diameter $D$ and a lens of focal length $f$ , the focused $1 / e^{2}$ diameter is $4 λ f M^{2} / (π D)$ . A 6 mm beam at 1064 nm with $M^{2} = 1$ focuses to 22.6 µm with a 100 mm lens and to 11.3 µm with a 50 mm lens; a shorter focal length, a larger input beam or a lower $M^{2}$ gives a smaller spot.

What is the depth of focus of a focused laser beam?

It is the length over which the beam radius stays within $\sqrt{2}$ of its waist value, equal to twice the Rayleigh range: $2 π w_{0}^{2} / (λ M^{2})$ . Because it scales with the square of the spot size, the same 1064 nm beam has a depth of focus of 0.75 mm at a 22.6 µm spot and 0.19 mm at an 11.3 µm spot.

What is the peak intensity at the focus of a laser beam?

For a Gaussian spot the peak irradiance is $2 P / (π w_{0}^{2})$ , twice the power divided by the $1 / e^{2}$ area, and a pulse of energy $E$ has a peak fluence of $2 E / (π w_{0}^{2})$ . At an 11.3 µm waist radius, 1 W gives 5.0 × 10⁵ W/cm² and a 100 µJ pulse gives 50 J/cm².

How do you compare a focused beam with a laser damage threshold?

Compare peak fluence with a threshold that is also defined at the peak, because the peak fluence of a Gaussian beam is double the energy divided by its $1 / e^{2}$ area, and match the wavelength, pulse duration and repetition rate; thresholds for continuous beams are often given in W/cm. Keep a margin of about a factor of two below the specified value, because contamination and defects lower the threshold of an optic in use.

How do you measure a focused laser spot?

Scan a knife edge through the focus, which resolves spots down to a few micrometers; image the focal plane onto a camera through a microscope objective of known magnification, keeping the sensor below saturation; or fit beam widths through the focus with an M² caustic scan, which also gives the waist position and $M^{2}$ .

References: A. E. Siegman, Lasers (University Science Books, 1986), chapters on Gaussian beams; S. A. Self, "Focusing of spherical Gaussian beams," Applied Optics 22, 658 (1983); ISO 21254-1, Lasers and laser-related equipment: Test methods for laser-induced damage threshold.