Theory
Laser Focus and Beam Quality M² Calculator
This tool allows you to reverse-engineer your laser's optical parameters and find your true focal offset using the method described in the How to Find Your Laser's True Focal Point article. Enter your measured dimensions (square or rectangle, cut-out piece or hole) at different defocus levels to calculate $z_{offset}$, $w_0$, $z_R$, and $M^2$.
| Defocus $z_{meas}$ (mm) | Measured $X$ (mm) | Measured $Y$ (mm) | |
|---|---|---|---|
| Parameter | X-Axis | Y-Axis | Combined |
|---|---|---|---|
| Focus Offset $z_{offset}$ (mm) | -- | -- | -- |
| Spot Radius $w_0$ (mm) | -- | -- | -- |
| Rayleigh Range $z_R$ (mm) | -- | -- | -- |
| Beam Quality $M^2$ | -- | -- | -- |
| Fit Error (RMSE) | -- | -- | -- |
Recommended Action: --
Regression Details
The calculator fits the data to the general quadratic propagation equation: $$w(z)^2 = C \cdot z_{meas}^2 + B \cdot z_{meas} + A$$ This method finds the vertex of the parabola, which represents the location of the true focal point.