Beam Waist and Spot Diameter Calculator
Calculate laser spot diameter, beam diameter, and depth of field based on lens parameters, wavelength, and M² factor.
Calculation Results
Spot Diameter
How does the Laser Beam Waist and Spot Size Calculator work?
First, consider that there is a Gaussian laser passing through the converging lens. The beams will begin to converge and eventually reach the point of maximum concentration. At this point, the beam diameter will reach a minimum. This diameter is what we call the "spot size" (the "beam waist" is the same thing, but generally refers to the radius). Beyond the waist, the beam began to diverge again, and it became wider and wider as it went back. The position of the waist on the Z axis depends mainly on the focal length. Essentially, focal length is a numerical value that indicates how well a lens concentrates or diverges light. Therefore, the higher the convergence of the lenses, the smaller the focal length and the closer the waist is to the lens. Therefore, if the distance from the waist of the beam is known, the size of the beam can be determined. In addition, depth of field refers to a specific distance centered on the waist of the beam at which the diameter of the beam is significantly smaller compared to its spot size. This is also twice the distance of Rayleigh. Rayleigh length is defined as a distance with a beam radius of less than or equal to √2 times the radius of the waist. As a result, the depth of field tends to be smaller when the focal length is smaller than the incident beam size, and vice versa. Finally, M² corresponds to the mass factor. Basically, this is a measurement of beam performance compared to a perfectly shaped theoretical TEM₀₀ Gaussian beam. The value of "1" is considered perfect, and the farther away from this value, the less perfect it becomes.
Formulas for spot size, beam diameter, and depth of field
The assumption here is that once the laser beam passes through the lens, it passes through a homogeneous isotropic continuum forever. We also assume that the laser emits only one specific wavelength and can be expressed as a TEM₀₀ Gaussian beam. In addition to the light beam, the lens is also considered to be perfect and thin. As a result, there are no reflections on its surface, and the focal length is the same across the surface. Our calculations are derived from the quasi-axis approximation of the Helmholtz equation and the thin-lens approximation. In addition, the incident beam is considered to be perfectly collimated on the lens. Therefore, the position of the waist on the z-axis coincides with the focal point and is at the focal length of the lens. Finally, these formulas are not precise when calculating the far-field beam diameter. In this case, you should use our divergence calculator with an initial diameter of the punctual point (0) and directly in the focal plane.
\( \text{Beam diameter}(mm) = \text{Spot size}(mm) \times \sqrt{1 + \frac{(\text{Distance from lens}(mm) - \text{Focal length}(mm))^2}{(\text{Depth of field}(mm) \div 2)^2}} \)
\( \text{Depth of field}(mm) = \frac{2\pi \times (\text{Spot size}(mm) \div 2)^2}{\text{Wavelength}(mm) \times M^2} \)