F-Theta lens & spot size calculator
Estimate theoretical focused spot diameter, ideal scan width, F-number and depth-of-focus indicators from wavelength, focal length, beam diameter and beam quality.
- 355 nm to 10.6 µm wavelength presets
- Theoretical 1/e² spot estimate
- Ideal F-Theta scan width
- Aperture clipping check
Balance focused spot size with scan field
Enter the beam values at the lens entrance. This calculator estimates an ideal center-field result; always confirm the selected lens datasheet and edge-of-field performance.
Understand what the calculator estimates
The formulas describe an ideal Gaussian beam near the center of a flat-field lens. They are useful for comparing configurations before checking a real lens specification.
4 × M² × λ × f ÷ (π × D)Uses wavelength λ, focal length f and 1/e² input beam diameter D.
y ≈ f × θUses optical scan angle θ in radians. A full one-axis width is twice the radial image height.
f-number = focal length ÷ beam diameterA lower effective F-number generally corresponds to tighter theoretical focusing.
zR = π × w₀² ÷ (M² × λ)Uses the theoretical waist radius w₀ and indicates how quickly an ideal beam expands around focus.
Technical basis: SCANLAB F-Theta lens overview and Edmund Optics F-Theta fundamentals.
Longer focal length expands the field and enlarges the spot
For the same wavelength, beam diameter and M², focal length changes both the theoretical focus and the ideal scan field in direct proportion.
Working distance is not equal to effective focal length
Use the manufacturer’s specified working distance, flange distance and mechanical reference. Do not position the workpiece from focal length alone.
Check more than focal length and nominal field size
A lens must match the source, scanner, power level, environment and required result across the full working field.
Wavelength and coating
Choose optics designed for the laser wavelength and power. The wrong coating can reduce transmission, create heating or increase back-reflection risk.
- Design wavelength and bandwidth
- Average and peak power limits
- Back-reflection requirements
Aperture and mirror geometry
The beam must pass through the scanner and lens without harmful clipping over the requested scan angle.
- Scanner entrance and mirror aperture
- Maximum lens input beam diameter
- Optical versus mechanical scan angle
Center and edge performance
Real focused spot, telecentricity, field flatness and distortion can change across the image field.
- Edge spot growth and ellipticity
- Focus variation across the field
- Software correction file compatibility
Compare common focal lengths using your current inputs
The table recalculates with the wavelength, beam diameter, M² and scan angle entered above.
| Focal Length | Theoretical Spot | Ideal Full Width | Effective F-Number | Trade-Off |
|---|---|---|---|---|
| 100 mm | 14.9 µm | 69.8 mm | f/10.0 | Smaller spot / field |
| 160 mm | 23.8 µm | 111.7 mm | f/16.0 | Current input |
| 210 mm | 31.3 µm | 146.6 mm | f/21.0 | Larger field / spot |
| 254 mm | 37.8 µm | 177.3 mm | f/25.4 | Larger field / spot |
| 330 mm | 49.2 µm | 230.4 mm | f/33.0 | Larger field / spot |
Ideal width uses the entered optical half-angle and the F-Theta relation. A commercial lens may specify a smaller usable field to maintain spot quality, flatness, transmission and distortion limits.
Start lens selection from the required result
Use the calculator to narrow options, then confirm process evidence with the exact source, scanner, lens and material.
| Application Need | Lens Direction | Customer Priority | What To Confirm |
|---|---|---|---|
| Fine QR codes and small text | Shorter focal length or larger input beam | Small, stable spot and readable cells | Center/edge code grade, focus tolerance and fixture height |
| Large-area product marking | Longer focal length and specified larger field | Coverage without repositioning | Edge spot, distortion correction and marking time |
| Deep metal engraving | Field matched to required power density | Depth, speed and consistent hatch | Spot at power, thermal behavior and debris protection |
| Laser cleaning raster | Lens sized for beam, power and cleaning width | Uniform energy across a larger path | Coating damage threshold, field uniformity and protection window |
| Precision micromachining | High-quality short focal or telecentric optics | Small feature and controlled incidence angle | M², aberration, pulse dispersion and field flatness |
Confirm the lens with the actual laser and process
Share your wavelength, source model, beam diameter, M², scanner aperture, field requirement and target feature size. Oceanplayer can review the optical match before configuration.
Define the result
Material, feature size, field, depth, speed and acceptable variation.
Match components
Source, expander, scanner aperture, F-Theta lens and protection window.
Verify the field
Check center and edge samples, focus, distortion and process stability.
Continue your laser optics and process planning
Use spot size together with fluence, overlap and machine selection.
F-Theta lens and spot size questions
Practical answers for laser marking, cleaning and precision scanning projects.