Calculated Results
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Beam caustic graph
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Fit residuals
Formula Used
The waist-divergence method uses M² = πw₀θ / λ. Here, θ is the far-field half-angle divergence.
The BPP method uses M² = πBPP / λ. The Rayleigh method uses M² = πw₀² / (λzR).
Caustic fitting models w²(z) = w₀² + θ²(z − z₀)². A quadratic fit determines waist size, location, and divergence.
How to Use
Select the measurement method matching your available laser data. Choose consistent width, angle, distance, and wavelength units.
Enter X values for circular beams. Enable astigmatic geometry when X and Y differ.
For caustic fitting, add measurements around the beam waist. Review warnings before exporting or accepting the result.
Example Measurement Data
| Position | X diameter | Y diameter | Uncertainty |
|---|---|---|---|
| -0.60 m | 1.78 mm | 2.03 mm | 0.03 mm |
| 0.00 m | 0.70 mm | 0.82 mm | 0.02 mm |
| 0.60 m | 1.81 mm | 2.00 mm | 0.03 mm |
Beam Quality Guidance
An M² near one indicates nearly diffraction-limited propagation. Larger values indicate reduced focusability and increased divergence.
Values from one to 1.3 are often excellent. Values above five commonly indicate strongly multimode beams.
These ranges are practical guidance, not universal acceptance limits. Application requirements should define the final pass criterion.
Frequently Asked Questions
What is the M² beam-quality factor?
M² compares a real beam with an ideal Gaussian beam. It measures propagation and focusing performance.
Can an M² value be below one?
A physical free-space beam should not produce M² below one. Such results usually indicate conventions, calibration, or fitting problems.
What is a diffraction-limited beam?
It is a beam approaching ideal Gaussian propagation. Its M² value is approximately one.
Should divergence use a half-angle or full-angle?
The standard formula uses half-angle divergence with beam radius. This calculator converts full-angle inputs automatically.
Should beam waist use radius or diameter?
Either choice works when used consistently. The calculator converts diameter values into equivalent radii.
How is M² measured experimentally?
Measure beam widths at multiple axial positions. Fit the resulting caustic to determine waist and divergence.
What is the beam parameter product?
BPP is waist radius multiplied by far-field half-angle divergence. Smaller values indicate better focusability.
Why are M²x and M²y different?
Astigmatism, asymmetry, alignment, or optical aberrations can affect axes differently. Separate values describe those differences.
How does M² affect focused spot size?
Focused spot size scales approximately with M². Higher M² beams produce larger minimum spots.