Calculation of ultrafast laser pulse overlap rate and its impact on processing quality.

In galvanometric scanning-based ultrafast laser processing (micro-cutting, scribing, and surface texturing), the Pulse Overlap Rate (O) is one of the most critical operational parameters. It determines the spatial distribution of successive laser pulses along the beam trajectory, directly affecting surface roughness (Ra), Heat-Affected Zone (HAZ) expansion, and overall processing throughput.

For system integrators, process development engineers, and industrial machine operators, optimizing the pulse overlap rate is essential for achieving smooth, recast-free surface finishes while maximizing removal efficiency.

1. Mathematical Formulas for Pulse Overlap Calculation

To calculate the pulse overlap rate, one must first determine the center-to-center distance (d) between two consecutive laser pulses along the scanning direction.

Pulse Center Distance (d)

d = v / f

• d: Distance between adjacent pulse centers (μm)

• v: Galvanometer scanning speed (mm/s)

• f: Laser pulse repetition frequency (kHz or Hz)

Pulse Overlap Rate (O)

O = 1 - d / D = 1 - v / f * D

• O: Pulse overlap rate (%)

• D: Focused laser spot diameter (μm)

2. Impact of Overlap Rate on Surface Morphology

Varying the overlap rate changes the energy deposition density along the scan path, leading to three distinct surface morphology regimes:

1. Low Overlap Rate (0 < O < 30%): Pulse spacing (d) is large relative to spot size (D). Individual pulse craters remain isolated or weakly connected, resulting in discontinuous textures, deep grooves, and high surface roughness.

2. Medium Overlap Rate (30% ≤  O ≤ 70%): Represents the Optimal Process Window. Consecutive pulses fill in adjacent crater rims evenly, yielding a smooth, uniform surface texture, minimal thermal diffusion, and reproducible depth control.

3. High Overlap Rate (O > 70%): Pulses overlap tightly ($d$ is very small). High pulse density traps energy within the interaction volume, causing localized thermal buildup, heavy material remelting, thick recast layers, and potential micro-cracks or voids.

3. Key Trends in Parameter Variation

① Scanning Speed vs. Pulse Distance & Overlap

Under fixed repetition frequency (f) and spot size (D), increasing scanning speed (v) increases pulse spacing (d) linearly while reducing the overlap rate (O).

Higher Scanning Speed (v ↑)   →  Larger Pulse Spacing (d ↑)  → Lower Overlap Rate (O↓)

② Overlap Rate vs. Surface Roughness (Ra)

The relationship between overlap rate and surface roughness follows a U-shaped curve:

• At low overlap (< 30%), roughness is high due to discrete pulse crater formation.

• At medium overlap (30% – 70%), roughness reaches its lowest point (smooth, polished finish).

• At high overlap (> 70%), roughness increases again due to thermal melting, spatter, and severe HAZ degradation.

③ Overlap Rate vs. Processing Efficiency (Removal Rate)

• At low overlap, energy utilization is low because pulses are too far apart to support cooperative material removal.

• At medium overlap, removal rate peaks as pulse energy overlaps constructively above the ablation threshold.

• At excessively high overlap, plasma shielding and debris clouds generated by preceding pulses block subsequent beam energy, causing overall efficiency to drop sharp.

4. Parameter Calculation Example

Consider a high-precision laser setup with the following parameters:

• Focused Spot Diameter ($D$): 30 μm

• Repetition Frequency (f): 500 kHz (500,000 Hz)

• Scanning Speed (v): 300 mm/s (300,000 μm/s)

Step 1: Calculate Pulse Distance (d)

d = 300,000 μm/s / 500,000 Hz = 0.60 μm

Step 2: Calculate Overlap Rate (O)

$$O = 1 - 0.60 μm / 30 μm = 1 - 0.02 = 0.98 (98%)

• Engineering Assessment: An overlap rate of 98% indicates extreme pulse overlap. In practical production, this speed/frequency combination would likely cause severe heat accumulation and thermal damage. To reach the target 50% overlap window, scanning speed should be increased or repetition frequency reduced.

Conclusion

Managing the pulse overlap rate (O = 1 - v / f * D) is crucial for balancing surface quality and processing throughput in ultrafast laser manufacturing. By selecting parameters within the optimal 30% – 70% overlap window, engineers can eliminate thermal recast layers, minimize surface roughness, and avoid plasma shielding inefficiency.