How it is calculated
A pulsed laser moving at speed \(v\) and repetition rate \(f_\text{rep}\) places consecutive pulses a pitch \(\Delta x\) apart. Adjacent scan lines sit a hatch \(h\) apart:
Overlap is defined against the 1/e² diameter \(d = 2w_0\). Negative overlap means there are gaps between spots. The scan speed for a target overlap is \(v = d\,f_\text{rep}\,(1 - \text{OL})\).
Effective pulse number for a Gaussian beam
“Pulses per spot” counts circles, but a Gaussian beam delivers most of its fluence near the center. Summing the Gaussian fluence of every pulse that passes a point on the scan line gives the accumulated dose in units of the peak fluence \(F_0\):
For a hatched area the same integral runs in two dimensions: \(N_\text{eff,2D} = \dfrac{\pi}{2}\dfrac{w_0^2}{\Delta x\,h}\). Summing the discrete pulses numerically confirms both expressions. When \(\Delta x \le w_0\), the point-to-point ripple in the sum stays within about ±1.5 %. At larger pitch the dose varies along the line and \(N_\text{eff}\) is only an average.
\(N_\text{eff}\) is the right pulse count to use with incubation models (\(F_\text{th}(N) = F_\text{th}(1)N^{S-1}\)). The accumulated fluence \(N_\text{eff}F_0\) is a useful dose metric for comparing scan strategies.
Worked example
A 30 µm spot scanned at 1 m/s with 100 kHz pulses and a 15 µm hatch:
The line overlap is 50 %, so \(N_\text{eff,2D} = 2.36\). The coverage rate is 15 mm²/s, which fills 1 cm² in 6.7 s before jump and acceleration overhead. Reaching 90 % pulse overlap at the same repetition rate means slowing to 300 mm/s.
Choosing overlap in practice
- Continuous scribes and cuts usually need 50–90 % pulse overlap so the trench has no unablated bridges. The edge ripple period equals Δx.
- Very high overlap (> 90–95 %) raises the pulse count per point and can cause heat accumulation at high repetition rates. Check the thermal diffusion tool.
- Polygon and fast-galvo systems often run at low or zero overlap and build depth with multiple passes. This spreads the heat input over time.
- Galvo acceleration raises the effective overlap at line ends unless the controller skips pulses (“skywriting”) or uses position-synchronized firing.
Assumptions and limits
- Constant scan speed and repetition rate, straight parallel lines, and one pulse per trigger (no burst mode).
- Overlap is geometric, measured against the 1/e² diameter. Some groups define overlap against the ablated crater diameter instead, which depends on fluence.
- \(N_\text{eff}\) assumes a TEM₀₀ Gaussian focal spot. For top-hat beams, pulses per spot and \(N_\text{eff}\) coincide.
References
- J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7, 196–198 (1982).
- W. M. Steen and J. Mazumder, Laser Material Processing, 4th ed., Springer (2010).