Focused Laser Spot Size and Depth of Focus Calculator
Laser marking, micromachining and fiber alignment all depend on how small a spot you can focus and how tightly the focal plane must be held. This calculator links focal length, input beam size and M squared to the spot and depth of focus.
Your numbers
Your results
Ideal aberration-free lens and Gaussian beam. Spherical aberration and clipping at the lens aperture increase the real spot.
Focused spot diameter (um) vs input beam diameter (mm)
Sweeps Collimated beam diameter at lens (1/e2) from 2 to 30, holding your other inputs fixed.
Store laser process recipes against routings
Optional expert review of how to link focus and power settings to ERP routings and work orders.
Optional. The tool and every export work without this. No spam.
How to use the calculator
Enter the laser wavelength, the lens focal length, the 1/e2 diameter of the collimated beam entering the lens and the M squared of the beam. The spot diameter output is for a Gaussian beam with the standard focusing relation. The Airy disk is shown for comparison and applies to uniform illumination of a circular aperture. The chart sweeps beam diameter to show that a larger beam on the same lens gives a smaller spot, until you hit the lens aperture limit.
- Make the lens clear aperture at least 1.5 to 2 times the 1/e2 beam diameter to avoid clipping.
- Shorter focal length also gives smaller spot and a much shorter depth of focus.
- Check scan lenses: their quoted spot already includes field flatness limits.
The formulas
For a Gaussian beam focused by a lens, the focused spot diameter is 4 M2 lambda f / (pi D), where D is the 1/e2 input diameter. The waist radius is half of that and the Rayleigh range follows as pi w0^2 / (M2 lambda). Depth of focus is taken here as twice the Rayleigh range. The Airy diameter 2.44 lambda f / D describes the first dark ring for a top-hat beam. In a Gaussian beam with no aperture clipping there are no rings.
Worked example
A 532 nm laser with M squared of 1.2 and an 8 mm beam through a 100 mm lens focuses to about 10 um diameter, with a depth of focus near 0.3 mm. That means a part height variation of 0.3 mm degrades the spot noticeably. Cutting the beam to 4 mm doubles the spot to about 20 um but quadruples the depth of focus, which is a common trade for processes on non-flat parts.
Common mistakes
Using the output diameter of the laser head rather than the actual beam on the lens misses any expander or truncation upstream. Another error is treating the calculated spot as the process feature size: thermal diffusion, threshold effects and material response often make the machined feature larger or smaller than the optical spot. Verify against a burn test or a camera at the work plane, and store the settings with the job routing in your ERP or MES.
Frequently Asked Questions
Why does a larger beam give a smaller spot?
Spot diameter scales with wavelength times focal length divided by beam diameter. A wider beam fills more of the lens, which means a higher numerical aperture and a tighter diffraction-limited focus, until the lens aperture or aberrations take over.
Is the Airy disk or Gaussian spot correct for my laser?
Most lasers have near Gaussian beams without hard aperture clipping, so use the Gaussian result. Use the Airy figure for uniformly illuminated apertures, such as a heavily overfilled lens or an imaging system.
How do I count for lens aberration?
Use the calculated spot as a lower bound. Choose lens designs rated as diffraction limited at your wavelength and f-number, such as aspheric singlets or multi-element objectives, and confirm with a beam profiler at the focus.
What about focal shift with temperature?
High-power lenses and protective windows show thermal focal shift. Compare the depth of focus above with your expected shift; if the shift is a significant fraction, plan focus tracking or lower the numerical aperture.
Netray can help move laser process settings and verification results out of spreadsheets and into your routing and quality records, on-prem if required.
Related Tools
Gaussian Beam Spot Size and Rayleigh Range Calculator
Find Rayleigh range, spot size at any distance and divergence for a real laser beam using waist radius, wavelength and the M squared beam quality factor.
Industry TemplatesLaser Pulse Energy, Peak Power and Fluence Calculator
Turn average power, repetition rate, pulse width and spot size into pulse energy, peak power, peak fluence and peak irradiance.
Industry TemplatesBeam Expander Magnification and Divergence Calculator
Choose beam expander focal lengths and see output diameter, divergence reduction and the beam size at a working distance.
Discrete ManufacturingLaser Pulse Overlap and Heat Input Calculator
Work out pulse spacing, overlap and line energy for a scanning or moving pulsed laser from speed, repetition rate, spot size and power.
More Industry Templates tools
See all- Fiber Coupling Efficiency and Mode Mismatch Calculator
- Thin Film Quarter-Wave AR Coating Calculator
- Distributor Free Freight Policy Template
- Job Shop Quote Cover Letter Template
- Monthly Operations Review Meeting Pack Template
- OEE Improvement A3 Charter Template
- Sheet Metal Job Traveler Template
- Press Brake Setup Sheet Template
- Sheet Metal Cut List and Material Takeoff Worksheet