Mathematical Analysis of Dynamic High-Power Laser Beam Shaping Using Galvanometer Scanners or Deformable Mirrors by the University of Twente (Netherlands)

Mathematical Analysis of Dynamic High Power Laser Beam Shaping Using Galvanometer Scanners or Deformable Mirrors (by University of Twente, Netherlands, published in Optics & Laser Technology)

01 Introduction

In various high-power laser material processing applications—such as laser cutting, welding, and surface treatment—beam shaping plays an essential role in optimizing processing quality and production efficiency. Studies have shown that adjusting the spatial intensity distribution of the laser beam can improve weld geometry, reduce spatter, and enhance joint stability. Currently, two primary devices used for dynamic beam shaping are Galvanometer Scanners (GS) and Deformable Mirrors (DM). However, there is a lack of systematic comparison between these methods in terms of resolution, shaping capability, and error distribution. This study proposes a new mathematical framework to quantify and compare the performance of GS and DM in dynamic beam shaping applications.

02 Overview

This paper investigates the performance of dynamic beam shaping technologies in high-power laser processing. Using mathematical models, it quantifies the beam shaping capability and error distribution of two main devices: Galvanometer Scanners and Deformable Mirrors. The study defines three typical target beam profiles (split, horseshoe, and square) and evaluates the performance differences between devices through simulation and experiments. Results indicate that galvanometer scanners perform better in shaping split and horseshoe beams by utilizing high-frequency path scanning to achieve the desired beam shape, although path errors and intensity fluctuations occur due to frequency limitations. The performance variance between the two devices for different target beams reflects the limitations in their dynamic control capabilities. This research provides theoretical support for applying dynamic beam shaping in laser processing and identifies future optimization directions, including increasing galvanometer scanning speed and improving deformable mirror precision to meet complex processing demands.

03 Figures and Analysis

Figure 1 illustrates the spatial definition of the shaping function and the top view of the unshaped beam, outlining the shaping region.

Figure 1. Schematic optical layouts of dynamic beam shaping systems using (a) Galvanometer Scanner or (b) Deformable Mirror.

Figures 2 and 3 show that galvanometer scanners achieve a split beam shape through periodic scanning paths. Error analysis demonstrates that ideal galvanometers can fully replicate the target beam, though actual devices introduce minor errors due to frequency constraints.

Figure 2. (a) Visualization of the shaping function S and the unshaped beam IU; (b) Shaped beam IS for the “Split” beam profile with a resolution of D/df = 3.

Figure 3. Simulated shaped laser intensity distributions and deviations from the desired “Split” beam profile using: (b), (c) Ideal Galvanometer Scanner; (d), (e) Practical Galvanometer Scanner; (f), (g) Ideal Deformable Mirror; and (h), (i) Practical Deformable Mirror.

Figure 4 displays the horseshoe-shaped beam defined by a curved shaping function. Simulations show comparable performance between GS and DM in replicating curved shapes, but with different error distributions.

Figure 4. (a) Visualization of the shaping function S and the unshaped beam IU; (b) Shaped beam IS for the “Horseshoe” beam profile with a resolution of D/df = 3.

Figures 5 and 6 indicate that deformable mirrors outperform in square beam shaping. However, due to surface curvature limits, slight intensity deviation appears at the corners. GS suffers from intensity fluctuations along the x-direction due to scanning path limitations.

Figure 5. (a) Visualization of the shaping function S and the unshaped beam IU; (b) Shaped beam IS for the “Square” beam profile with a resolution of D/df = 3.

Figure 6. Simulated shaped laser intensity distributions using: (b), (c) Ideal Galvanometer Scanner; (d), (e) Practical Galvanometer Scanner; (f), (g) Ideal Deformable Mirror; and (h), (i) Practical Deformable Mirror.

04 Conclusion

The conclusions of this paper are as follows:

1. Mathematical analysis shows that the resolution of galvanometer scanners is inversely proportional to the wavelength and beam quality of the incident laser, and directly proportional to the galvanometer’s angular range and the diameter of the collimated beam. However, both devices are limited by their ability to achieve higher scanning frequencies. Achieving higher scan frequencies requires faster power modulation of the laser source to realize the desired intensity distribution in the focal plane.

2. Similar to GS, the resolution of deformable mirrors is also inversely proportional to the laser beam wavelength and quality. The study shows that both GS and DM are capable of creating split, horseshoe, and square beam profiles in the focal plane. While the average deviation from the desired intensity distribution is similar for both devices, the error distribution across the focal plane differs. Due to its beam path characteristics, the galvanometer scanner performs best for curved beam shaping functions.

Source: https://doi.org/10.1016/j.optlastec.2024.112356

**--Cite the article published by 高能束加工技术 on April 14, 2025, in the WeChat public account "High-Energy Beam Processing Technology and Applications."