Evaluate beam quality using waist, divergence, or datasets. See M squared, waist, and focus location. Export clean reports for labs, audits, and publications today.
| z (mm) | w (mm) | Comment |
|---|---|---|
| -40 | 0.85 | Farther from waist |
| -20 | 0.60 | Approaching focus |
| 0 | 0.42 | Near waist |
| 20 | 0.60 | Leaving focus |
| 40 | 0.88 | Farther from waist |
Tip: Use at least 5–7 points spanning both sides of the waist.
The calculator uses the standard beam quality relationship: M² = (π · w₀ · θ) / λ, where w₀ is the waist radius (1/e²), θ is the far-field divergence half-angle, and λ is the wavelength.
In data-fit mode, it fits w(z)² to a quadratic and maps it to the Gaussian propagation form to estimate w₀, z₀, θ, and M².
M squared (M²) compares a real laser beam to an ideal Gaussian beam. A perfect Gaussian has M² = 1, while higher values indicate extra divergence or a larger focus spot. It summarizes how well the beam can be focused for cutting, imaging, coupling, or sensing.
The beam parameter product (BPP) is waist radius times divergence half-angle. For a fixed wavelength, BPP scales with M² and appears in many specifications. Lower BPP supports tighter focusing, longer depth of focus at a chosen spot size, and better coupling.
If you know waist radius w₀ and far-field divergence half-angle θ, compute M² = (π w₀ θ) / λ. This is useful for fast alignment checks and comparison testing. Choose diameter only when your instrument reports 2w, and choose full-angle only when it reports 2θ.
With measured spot size w at several positions z, data-fit mode estimates M² by fitting w(z)². Use at least five points spanning both sides of the waist for stability. Keep the same width definition across all points to avoid inflated results.
Common wavelengths include 1064 nm, 532 nm, and 1550 nm. Divergence is often in mrad, while waist size may be micrometers for fiber beams and millimeters for free-space beams. Example: w₀ = 0.50 mm and θ = 1.2 mrad at 1064 nm yields M² about 1.77.
The Rayleigh range zR describes how quickly the beam expands near the waist. Higher M² typically reduces zR for the same waist size, meaning the beam spreads faster after focus. A shorter zR reduces depth of focus and increases sensitivity to lens placement.
Avoid clipping the beam on apertures, because truncation changes divergence and corrupts fits. Record background levels, prevent detector saturation, and average consistently. If the beam is elliptical, measure both axes separately because Mx² and My² can differ.
Use M² to estimate achievable focus size for a lens, compare sources, and set tolerances. Lower M² enables smaller spots at the same focal length, while higher M² may require larger optics or shorter focal lengths. Export CSV or PDF outputs to document acceptance tests and lab notebooks.
A near-Gaussian beam is close to 1. Many industrial single-mode sources are around 1.1–1.5. Multimode or shaped beams can be much higher, depending on the application and optics.
Use radius when you have w (1/e² radius). If your instrument reports beam diameter, select diameter so the calculator converts it to radius internally.
M² uses the half-angle divergence θ. If your measurement system outputs full-angle divergence (2θ), select full-angle so the calculator halves it before computing M².
Common causes include mixed width definitions, clipped beams, saturation, too few z points, or points only on one side of the waist. Improve sampling around focus and confirm consistent w units.
It assumes the 1/e² intensity radius. If your beam profiler uses FWHM or another definition, convert to 1/e² radius before fitting for best consistency.
Yes. Use micrometer units for waist and appropriate divergence units. For fiber sources, ensure the waist and divergence correspond to the same propagation axis and measurement method.
This page estimates a single M² value from the provided inputs. For elliptical beams, run the analysis twice using the horizontal and vertical widths to report separate Mx² and My².
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.