Adaptive Aberration Correction for Laser Processes Improvement

Abstract

The ultrafast laser processing of three-dimensional structures characterized by highly spatially resolved features is more efficiently realized by implementing adaptive optics. Adaptive optics allow for the correction of optical aberrations, introduced when focusing inside the machined material, by tailoring the focal intensity distribution for the specific texturing task, in a reduced processing time. The aberration corrections by adaptive optics allow for a simplified scan strategy for the selective laser micromachining of transparent materials using depth-independent processing parameters, overcoming the limits related to the previously necessary pulse energy adjustment for different z positions in the material volume. In this paper, recent developments in this field are presented and discussed, mainly focusing on the use of dynamic optical elements—deformable mirrors and liquid crystal spatial light modulators—to obtain a high degree of laser processing control by an in-time correction of optical aberrations on different workpieces and mainly of transparent materials.

1. Introduction

Ultrafast lasers utilize extremely short pulses (tens to hundreds of femtoseconds) that allow for high precision in material processing. The rapid energy absorption minimizes thermal effects, leading to reduced heat-affected zones (HAZs) and enabling the creation of intricate 3D features. However, the effectiveness of this process can be significantly hindered by optical aberrations, which distort the laser focus over varying depths within a material. Thus, the efficiency and accuracy of the machining process require the optimization of the laser beam profile to ensure precise focal placement. The implementation of adaptive optics (AO) has demonstrated significant improvements in the fidelity of laser-written structures, particularly in complex materials such as diamond and silica. This includes the real-time correction of the disturbed wavefronts, which also reduces the cost of power supply necessary for processing the material due to the defocus of the laser beam. This is mainly performed by manipulating the spatial distribution of light energy for structured and wide-area fabrication, and by modulating the phase, amplitude and/or polarization of the laser beam [1]. The integration of adaptive optics with ultrafast laser technology is poised to revolutionize three-dimensional fabrication. As research continues to explore new adaptive elements and configurations, the potential for creating even more intricate and functional microstructures expands. This synergy not only enhances existing applications but also opens doors for innovative uses in fields such as integrated optics and lab-on-a-chip technologies.

This work reviews recent advances in this field, with a particular emphasis on using dynamic optical elements—adaptive optics—to achieve precise control over laser processing. First, we report some information about AO technologies, their configurations as well as the core principle of AO, which involves measuring distortions and applying corrective measures to restore the wavefront to its ideal shape. Subsequently, we report the main concepts regarding the integration of AO into wavefront shaping systems. We have outlined the significant advancement in high-power laser applications, offering improved precision, efficiency, and versatility essential for modern technological demands.

However, challenges such as improving robustness and reliability still remain critical for unlocking the full potential of AO technologies. Ultimately, this review aims to provide guidelines to analyze potential technological innovations that could further extend the capabilities of AO in industrial or scientific applications (e.g., to optimize the extreme parallelization of laser beams to increase processing speed), stimulating new ideas on how to exploit AO in yet-unexplored contexts (e.g., improving energy efficiency in AO-enabled laser processes) by taking into account the environmental impact.

2. Adaptive Optical Technologies

Aberrations affect the quality and accuracy of an optical system, reducing the images’ resolution and contrast. As reported extensively in Appendix A, in geometrical optics, aberrations arise when light rays deviate from their ideal path due to lens shape and alignment. The wavefront approach describes these aberrations in terms of wavefront shapes, where deviations from a perfect wavefront indicate the presence of aberrations. The order of geometrical aberration corresponds to the symmetry of wave aberration, with the latter geometry being one order higher. The definition of geometrical aberration is the deviation of a real imaging point from the ideal one. Using the power-series polynomial representation, the geometrical aberration order is given by the sum of the order of the angle and distance between the beam and the optical axis. Instead, the order of the wave aberration is obtained by adding the value 1 to the geometrical aberration order. For instance, the two-fold astigmatism is represented by the first- and second-order aberration in terms of the geometrical and wave aberrations, respectively. Some approaches are used to compensate or reduce aberration effects. One of these methods adopt multiple optical elements in combination, such as achromatic and apochromatic lenses or aspherical and toroidal mirrors [2]. Sawant et al. [3] suggest the use of hybrid components, combining the optical power of a refractive and a diffractive optical system, to realize compact doublet lenses that correct various aberrations. Figure 1 shows the scheme of the hybrid lens-metacorrector and the theoretical and experimental results obtained, showing that the overall device efficiency of the fabricated metasurface is around 10–25% in the wavelength range of 600 to 800 nm.

2.1. Adaptive Optics: Key Developments and Their Impact

Recently, adaptive optics (AO) is largely implemented for multiphoton, stimulated emission depletion and selective plane illumination microscopies, offering a significant improvement in resolution over conventional light microscopy approaches [4,5,6,7]. AO concept was first proposed by Horace W. Babcock in 1953, aiming to improve astronomical imaging by using a deformable mirror to correct wavefront errors in real-time. The initial applications were primarily military, driven by the need for clear images of satellites during the Cold War, which led to significant advancements in the technology. In the late 20th century, particularly during the 1990s, advances in computer technology made AO systems more practical and widespread [8]. This period saw the introduction of laser guide stars, which created artificial points of light in the atmosphere to measure distortions more effectively, allowing astronomers to observe fainter celestial objects [9].

The application of AO to ophthalmology began in the late 1990s, with pioneering work by researchers such as David R. Williams at the University of Rochester. This initial research demonstrated the potential of AO to correct ocular aberrations, allowing for high-resolution imaging of the retina and its cellular structures, which were previously only observable through histological techniques [10,11,12]. AO ophthalmoscopy allows us to visualize cellular-sized structures within the living human retina, such as photoreceptors, nerve fibers and capillaries (see Figure 2).

A detailed review regarding the optical wavefront technologies used to improve patient quality of vision and meet clinical requests has already been written by the authors (see ref. [13]). AO clinical applications are nowadays expanding. Among the current uses, they include (i) assessing retinal diseases where traditional imaging falls short, such as identifying lesions undetectable by standard fundus exams; (ii) developing objective visual function tests that monitor both photoreceptors and retinal vasculature, potentially aiding in managing ocular and systemic vascular diseases; and (iii) supporting gene therapy trials by providing detailed insights into cellular structures affected by genetic disorders. Thus, the ability to visualize individual cells and quantify cell loss has significant implications for early diagnosis and treatment planning [14]. On the other hand, the development of ultrafast AO systems has marked a significant leap forward. These systems can correct dynamic aberrations at much higher frequencies (up to 30 times faster than previous systems), improving imaging performance under clinically relevant conditions [15]. This advancement enhances the ability to capture high-resolution images even during normal eye movements [16]. The implementation of microelectromechanical systems (MEMSs) contributed significantly to the development of smaller and cost-effective AO systems [17] by enabling high-resolution wavefront correction. As an example, Figure 3 shows two AO systems with the same elements but using one (Figure 3a) or two (Figure 3b) different types of deformable mirrors (DMs). In the first case, a flat mirror was used in combination with an AlpAO DM with 69 actuators [18]; in the other case, an AOptix bimorph deformable mirror with 35 actuators, for low- and high-stroke correction, was used together with a Boston Micromachines MEMS DM (140 actuators) for high-order correction [19].

In vision science, MEMS technology has facilitated the development of scanning laser ophthalmoscopes that utilize adaptive optics to enhance retinal imaging quality. Various control algorithms have been compared to optimize the performance of these systems, demonstrating that MEMS DMs can effectively suppress wavefront errors and improve image quality [20]. Despite the great advantages of AO applications, AO imaging typically requires more time compared to conventional methods. The process of scanning patients can be lengthy, making it challenging to incorporate AO into routine clinical workflows, especially in busy practice settings. Moreover, AO systems often image only a small area of the retina at a time. This limitation can make it difficult to assess larger retinal regions or to conduct comprehensive examinations without multiple scans, which further extends the time required for each patient visit [10]. Furthermore, current AO systems may struggle with dynamic aberrations and require faster correction capabilities to accommodate real-world clinical scenarios where eye movement and other factors can introduce additional distortions [16,21]. Hence, ensuring robust performance under various conditions remains a challenge.

2.2. How Adaptive Optical Systems Work: Components and Principles

AO principle is based on the change in shape or position in response to the aberrations detected by a sensor, which analyzes the wavefront of the light, allowing to correct the aberrations in real-time [22]. Critical components in modern optical systems, particularly in adaptive optics applications, are the slit illumination and the deformable mirrors which play crucial roles in compensating wavefront aberrations. Slit illumination control optimizes light distribution across the aperture. By controlling the illumination profile, it improves the signal-to-noise ratio in wavefront sensing, leading to more accurate measurements of wavefront distortions. Consequently, this allows for more effective adjustments using adaptive optics components, resulting in better overall image quality and performance in optical systems. Improved spatial resolution and dynamic range can be achieved by employing pyramid wavefront sensors and by using phase diversity methods. Instead, real-time increased sensitivity and reduced latency were obtained with high-speed cameras and spatial light modulators (SLMs). These latter modulate the amplitude, phase and polarization of an incident light beam thanks to their quasiplanar geometry (see Figure 4).

Deformable mirrors are fundamental adaptive optics elements that can dynamically correct optical aberrations. Working principles of the Shack–Hartmann sensor (S-H), SLMs and of deformable mirror (DM) are extensively described in ref. [13]. Here, we report only a schematic representation of S-H and pyramid sensors in Figure 5 as well as of SLM and DM in Figure 6 together with a brief description.

Deformable mirrors (DMs) correct wavefront aberrations by dynamically adjusting their reflective surface shape, thereby ensuring that the light converges accurately to form a circular cross-section in the focal intensity distribution. This is achieved through numerous actuators that deform the mirror to create a wavefront that is the negative of the aberrations encountered. As light reflects off the DM, it compensates for distortions, thus restoring the focus to an optimal circular cross-section. For example, a hybrid DM can employ piezoelectric and magnetostrictive materials to manipulate its reflective surface, correcting both lower- and higher-order Zernike modes, which is crucial for maintaining a circular intensity distribution. This adaptability enables the transformation of Gaussian beams into desired shapes while preserving spatial characteristics.

Near-diffraction limited fabrications (at nominal depths of up to 50 $\mathrm{\mu }$m) were reached by combining SLM and DM, allowing for a net increment of about 10 $\mathrm{\mu }$m achievable depth without aberration correction: the unaberrated focal spot dimensions were maintained and the laser power was reduced [29,30]. For laser beam-shaping applications, Kuang et al. [31] realized parallel laser micro-structures using the synchronization of SLM and computer-generated holograms (CGHs). The same goal was reached using two adaptive mirrors to independently control the focus diameter and the focus position of the laser beam in cutting, welding and scanning systems [32].

2.3. Adaptive Optics Systems: Common Architectures

Adaptive optics configurations vary widely in complexity and application, from simple single-conjugated systems to sophisticated multi-conjugated setups. The choice of configuration depends on specific requirements such as the nature of distortions, the desired imaging quality, and budget constraints. Each system plays a vital role in enhancing optical performance across various fields, including astronomy, laser processing, and biomedical imaging. An adaptive optics system typically consists of three main components:

• Wavefront sensors: These devices measure the aberrations in the incoming light wavefront. They can be either direct sensors or sensorless systems that infer distortions from image quality.
• Tip-tilt mirror (TTM): TTM corrects the tilts of the incoming wavefronts in two dimensions. It achieves this by making small rotations around two axes, effectively realigning the light path to reduce distortion. The TTM is typically placed in front of the wavefront sensor. This configuration allows for a closed system, where the sensor continuously measures wavefront distortions and sends corrective signals to the TTM [33] (Figure 7).
  The TTM is particularly effective at correcting low-order aberrations (such as tilt and defocus), which account for a significant portion of the distortion caused by atmospheric conditions. By addressing these errors first, higher-order aberrations can then be corrected using more complex deformable mirrors.
• Deformable Mirrors (DMs): DMs are critical components that adjust their shape in real-time to compensate for detected aberrations. They can have varying numbers of actuators, allowing for precise control over the wavefront correction [34]. Recent advancements include the development of liquid crystal spatial light modulators and MEMS-based deformable mirrors (Figure 8).
  These latter mirrors consist of a flexible membrane supported by an array of actuators that can adjust the mirror’s shape in real-time to correct for wavefront distortions caused by atmospheric turbulence or optical imperfections. For instance, an MEMS DM with 489 actuators has been shown to effectively generate individual Zernike polynomials, which are essential for correcting aberrations [35].
• Control Algorithms: Algorithms, such as hill-climbing or other feedback mechanisms, optimize the adjustments made by the DMs to enhance image quality.

As extensively reported in ref. [1], several reconfigurable optical elements act to modify the beam profile. Salter and Booth also report several examples of laser processing to generate chiral surface, nanostructures, 3D nanoarray, etc., outlining the benefits of using AO technologies. These components can be configured in either an open-loop or closed-loop system. In an open-loop system, the sensor does not receive feedback on the effectiveness of corrections, while a closed-loop system continuously adjusts based on real-time measurements, allowing for more precise corrections despite potential instabilities [36]. The AO key configurations are as follows:

• Single-conjugate adaptive optics (SCAO), which is the simplest configuration, consisting of a single wavefront sensor and a single wavefront corrector. It measures wavefront distortions and applies corrections in a straightforward manner, typically using a deformable mirror placed in a pupil–conjugate plane to counteract atmospheric turbulence effects. It is commonly used in ground-based telescopes to enhance image quality by correcting for atmospheric disturbances (e.g., see Figure 2a and Figure 6b).
• Multi-Conjugate Adaptive Optics (MCAO) configuration employs multiple wavefront sensors and correctors located in different planes that are not mutually conjugate (Figure 9a). MCAO can better address aberrations originating from various directions [37]. While it offers superior performance, it significantly increases system complexity and cost, making it less common than SCAO.
• Sensorless adaptive optics (SAO) uses pre-existing knowledge about the expected image features to optimize corrections dynamically, which can be beneficial in certain imaging scenarios where sensor data are difficult to obtain. It usually considers iterative procedures that may involve the use of Deep Neural Networks (DNNs) [38] and Deep Reinforcement Learning (DRL) with policy gradients [39] (Figure 9b).
• Segmented mirror systems utilize an array of smaller mirrors that can be individually controlled to form a larger effective aperture. Each segment can be adjusted to correct for local aberrations, enhancing overall image quality. This configuration is often modeled using advanced optical design software to simulate and optimize performance.

Figure 9. (a) Schematic of MCAO equipped with two DMs and two WFs to perform correction over an extended field of view. Figure reprinted from ref. [40] under the terms of the Creative Commons Attribution-Non-Commercial-NoDerivs 3.0 Germany License. (b) Tissue phantom images from a scanning laser ophthalmoscopes aberrated (left) and corrected (right) [39]. Figure reprinted from ref. [39] under the terms of the OSA Open Access Publishing Agreement.

Figure 9. (a) Schematic of MCAO equipped with two DMs and two WFs to perform correction over an extended field of view. Figure reprinted from ref. [40] under the terms of the Creative Commons Attribution-Non-Commercial-NoDerivs 3.0 Germany License. (b) Tissue phantom images from a scanning laser ophthalmoscopes aberrated (left) and corrected (right) [39]. Figure reprinted from ref. [39] under the terms of the OSA Open Access Publishing Agreement.

3. Emerging Trends in Laser Material Processing: Opportunities and the Role of PSF and Zernike Polynomials

Ultrashort laser pulses and strong focusing conditions generate high peak intensities greater than 10¹³ W/cm², which, in turn, lead to ionization due to nonlinear absorption mechanisms in transparent dielectrics like glasses for visible and near-visible wavelengths [41]. The highly localized absorption regions determine volume modifications in transparent dielectrics. The short duration of the pulse offers several further advantages over longer-duration laser pulses such as eliminating plasma creation and, therefore, plasma reflections, thereby reducing collateral damage through the small component of thermal diffusion and other heat transport effects during the much shorter time scale of such laser pulses [42,43]. The generation of aberrative effects limits the laser processing performance. For example, in fused silica, the undesired morphological/structural modifications lead to reduced resistance to etching agents such as aqueous KOH or HF. Thus, etching channels in fused silica with selectivities of more than 1400:1 can be achieved by direct laser writing with a subsequent wet chemical etching process [44]. In these cases, for constant focusing conditions, the intensity profile changes depending on the focusing depth due to spherical aberrations. One way to eliminate this effect is the utilization of spherical aberration-corrected optical systems for a fixed depth. Another way is to adjust the pulse energy as a function of focusing depth. However, the material machining requires higher pulse energies to reach the modification threshold for an extended volume. A performing technical solution for the customized correction of spherical aberrations for ultrashort laser processing is the use of spatial light modulators (SLMs), whose principal mechanism has been described in previous paragraphs. Bisch et al. [45] applied a liquid crystal spatial light modulator (LC-SLM) for aberration correction, enabling the fabrication of low-loss single-mode borosilicate glass-based waveguides over a depth range greater than 1 mm. Kratz et al. [46] reported a depth-independent scanning strategy for generating complex 3D geometries in transparent materials. The authors compared the results of the laser process with the aberration-corrected beam profile using AO elements with those without aberration correction: the main results concern the pulse energy conservation, the uniform etching channel precision in laser propagation direction for all the investigated glass thicknesses, and a depth-independent processing method due to the decoupling of scan strategy from pulse energy (Figure 10).

Recent studies indicate that to reconstruct and simultaneously correct the distorted wavefront, Fourier Transform iterative calculations are necessary. However, some limitations still occur for a real-time analysis. These technical issues are partly resolved by combining the measured wavefront with the “ideal image” reproduced by a machine learning approach that allows for the prediction of the wavefront starting from a distorted point spread function (PSF) image.

In an optical system, the object complex amplitude $u_0$ is related to the corresponding image $u_i$ by the convolution with the PSF of the system [47]:

$$u_i(x,y)=PSF(x,y)⊛u_0(x,y).$$

(1)

In turn, the $PSF$ can be written as the square modulus of the Fourier transform ($FT$) of the pupil function (P) of an objective lens described in polar coordinates:

$$PSF(x,y)={\left|FT\left\{P(r,\theta )\right\}\right|}^2.$$

(2)

The analytical expression of the aperture function, describing how light waves are influenced when transmitted through an optical imaging system including the human eye, is given by

$$P(r,\theta )=A(r,\theta )e^{i\left\{\varphi \right(r,\theta )+\omega (r,\theta \left)\right\}},$$

(3)

in which A, $\varphi$ and $\omega$, respectively, represent the amplitude, phase and wavefront aberration with respect to the pupil plane. In detail, $\omega$ can be written in terms of the Zernike polynomials, as discussed in Appendix A.1:

$$\omega (r,\theta )=\sum _{m=1}^{\infty }{a}_m{z}_m(r,\theta ),$$

(4)

where $z_m$ is the Zernike polynomials and $a_m$ the corresponding Zernike coefficients for the given Zernike mode m.

As detailed in Appendix A.1, the decomposition of these aberrations into a series of modes, specifically Zernike polynomials, allows for effective analysis and correction. Zernike polynomials provide a systematic way to represent wavefront errors. Each polynomial is characterized by two indices nn (radial order) and mm (azimuthal frequency), and they are orthogonal over a unit circle. The coefficients associated with these polynomials, denoted as z(n,m)z(n,m), quantify the contribution of each mode to the overall wavefront error. For example, lower-order aberrations (LOAs) include modes such as defocus and astigmatism, which are critical for basic optical corrections. For instance, the first three rows of the Zernike pyramid (Figure A1) correspond to LOAs, where the highest radial term is 2. Instead, higher-order aberrations (HOAs) are defined by a radial order of 3 or higher and can include more complex distortions, like spherical aberration and coma. Higher-order modes often contain lower-order terms within their expressions, complicating their interpretation [48,49].

The hierarchy of wavefront aberrations, shown in Figure A1, is adopted as a classification reference when considering the effects of the optical aberration in laser processing. In this case, we start to consider that wavefront aberrations can be categorized into lower-order and higher-order aberrations, which significantly influences the performance and accuracy of laser micromachining processes. Lower-order aberrations include spherical aberration, coma and astigmatism. Aberrations primarily affect the overall focus and alignment of the laser beam, leading to a broader focus spot and reduced resolution in micromachining applications. Higher-order aberrations are more complex and include terms like trefoil and quadrafoil. These can lead to significant focal distortions that are detrimental to precision micromachining. For instance, they can result in focal splitting, where different parts of the laser beam focus differently, complicating the machining process.

So, the significance of Zernike coefficients and their associated basis functions in adaptive optics lies in their ability to provide a robust framework for analyzing and correcting optical aberrations. This capability is especially vital in high-precision applications like laser scribing, where even minor deviations can lead to significant errors in material processing outcomes. Specifically, the Zernike coefficients (a set of orthogonal functions defined over a unit circle) quantify the contribution of each Zernike polynomial to the overall wavefront aberration. Each coefficient corresponds to a specific mode of aberration (e.g., tilt, defocus, astigmatism) and is computed from the measured wavefront data. The independence of these coefficients allows for a clear interpretation of how much each mode contributes to the total root-mean-squared (RMS) wavefront error. Higher-magnitude coefficients indicate greater contributions to optical performance degradation, which is critical in applications like laser scribing where precision is paramount. Ultimately, the basis functions $z_m(r,\theta )$ derived from Zernike polynomials serve as mathematical tools for reconstructing wavefronts. In adaptive optics systems, these functions can be employed to model and correct distortions in real-time. The orthogonality of these functions ensures that they can effectively represent complex wavefront shapes without redundancy, allowing for efficient computation and in-time correction strategies during laser processing to obtain products with sub-micron resolutions.

4. AO as a Transformative Technology When Integrated in a Wavefront Shaping System for a High-Power Laser Source

The scaling of the productivity using ultrafast lasers is very demanding and needs simultaneous or sequential process parallelization as well as advanced control over beam shaping, focus correction, and real-time feedback mechanisms [50,51,52,53]. Also, in this case, adaptive optics represent a transformative technology in laser processing, leading to higher precision and efficiency in various manufacturing processes. In detail, the main advantages of integrating AO into micromachining setups are as follows [1,54,55]:

• Improved Beam Quality: Adaptive optics can modify the Gaussian beam shape typical of lasers into more suitable profiles for specific applications, such as a flat-top or ring-shaped intensity distribution. This modification can enhance the quality of laser marking and drilling processes by providing a more uniform energy distribution at the focus (Figure 11a–c).
• Aberration Correction: When lasers are focused inside materials, aberrations can distort the beam, leading to inefficiencies in machining. Adaptive optics can correct these aberrations dynamically, ensuring that the laser maintains its diffraction-limited performance throughout the machining process. This is particularly beneficial for ultrafast laser applications where precision is critical.
• Parallel Processing: Adaptive optics can facilitate parallelization by generating multiple foci from a single laser beam, significantly reducing processing times for high-resolution tasks. This capability is especially advantageous for large-scale or complex three-dimensional fabrications (Figure 11d,e).
• Dynamic Control: The ability to adjust the beam shape and focus dynamically allows for complex structuring of materials during processing [56]. This flexibility enables manufacturers to tailor the laser’s properties in real-time, accommodating various fabrication tasks without needing to change equipment (Figure 11f–h).
• Enhanced Material Interaction: By controlling the intensity distribution at the focus, adaptive optics can optimize interactions with different materials, leading to improved outcomes in terms of precision and surface finish.

However, some considerations should be made against using adaptive optics. Implementing adaptive optics adds complexity to the laser micromachining setup, requiring additional components such as wavefront modulators (e.g., deformable mirrors or spatial light modulators) [57]. This complexity can lead to increased costs and maintenance requirements. Moreover, the dynamic nature of adaptive optics systems may introduce stability issues during machining processes, particularly if not properly calibrated or synchronized with the laser operation.

In ultra-short pulsed laser, a master oscillator/power amplifier (MOPA) configuration uses the master oscillator to generate a low-power optical signal that is then amplified by the power amplifier to produce the laser beam. Unfortunately, high-power laser systems with MOPA configurations can face degradation of the overall quality of the output beam due to the deviation of the beam of the master oscillator relative to the power amplifier, as well as for the thermally induced distortion occurring in the gain medium of the power amplifier. These optical aberrations introduce a change in the focal intensity distribution (focal distortion) from its ideal diffraction-limited nature affecting the quality of the textured/scribed materials. Specifically, the focal splitting is related to focusing inside birefringent media, where different polarization modes couple to different refractive indices [1,58,59,60,61]. The challenge is to reach the maximum wavefront compensation in terms of spatial shaping of the laser beam in phase, amplitude and/or polarization. For example, when the laser processing occurs inside a material transverse to the optic axis, an asymmetrical elliptical shape of the diffraction-limited focus is observed. In this case, AO elements, controlling the illumination of the slit placed before the focusing objective lens, generate a circular cross section structure. Thus, the focal intensity will spread in a direction orthogonal to the slit axis, keeping the same axial resolution.

Figure 11. Three-dimensional images of Gaussian (a), flat (b) and inverted-Gaussian (c) laser beam profiles, reprinted from ref. [62] under the terms of the CC BY license. Representative two- and three-dimensional fabrication by parallel processing: (d) the microletter array of ‘N’ fabricated with 28 exposure points in two dimension through the relay lens of a 150 mm focal length; and (e) a three-dimensional microspring array fabricated with the relay lens of an 80 mm focal length (corresponding insets focus on individual structures). Reprinted from Kato et al. [63], with the permission of AIP Publishing. Schematic of dynamic ring fabrication (f) and corresponding images of the same circular trajectories fabricated at depths of 1 $\mathrm{\mu }$m (g) and 7 $\mathrm{\mu }$m (h) both with and without simultaneous compensation of aberration. Reprinted by ref. [64] under the terms of the OSA Open Access Publishing Agreement.

Figure 11. Three-dimensional images of Gaussian (a), flat (b) and inverted-Gaussian (c) laser beam profiles, reprinted from ref. [62] under the terms of the CC BY license. Representative two- and three-dimensional fabrication by parallel processing: (d) the microletter array of ‘N’ fabricated with 28 exposure points in two dimension through the relay lens of a 150 mm focal length; and (e) a three-dimensional microspring array fabricated with the relay lens of an 80 mm focal length (corresponding insets focus on individual structures). Reprinted from Kato et al. [63], with the permission of AIP Publishing. Schematic of dynamic ring fabrication (f) and corresponding images of the same circular trajectories fabricated at depths of 1 $\mathrm{\mu }$m (g) and 7 $\mathrm{\mu }$m (h) both with and without simultaneous compensation of aberration. Reprinted by ref. [64] under the terms of the OSA Open Access Publishing Agreement.

Figure 12 shows the scheme of a wavefront shaping system equipped with a small-aperture DM, a laser source and a Shack–Hartmann sensor.

The input beam, having a wavefront distribution ${\phi }_{in}(x,y)$, is reflected by the DM and, passing through the laser system, reaches the Shack–Hartmann wavefront sensor. The interaction between the input beam ${\phi }_{in}(x,y)$ and DM is crucial for achieving optimal wavefront shaping before the beam reaches the Shack–Hartmann sensor. To clarify the role played by each element, we describe each step of the wavefront shaping process:

• Input beam characteristics: The input beam ${\phi }_{in}(x,y)$ typically exhibits some level of distortion or non-uniformity in its wavefront. This could be due to imperfections in the laser source or optical components in the system.
• Role of DM: DM is strategically placed to manipulate the wavefront of the incoming beam. It consists of an array of actuators (often mechanical pistons) that can adjust the shape of the mirror’s surface. By altering this shape, the DM can compensate for wavefront aberrations present in ${\phi }_{in}(x,y)$ [66].
• Wavefront correction: As the input beam interacts with the DM, it undergoes a transformation that aims to flatten or optimize its wavefront. The specific adjustments made by the DM are determined based on feedback from the Shack–Hartmann sensor, which measures the wavefront shape and identifies deviations from an ideal planar wavefront [57].
• Feedback loop: The Shack–Hartmann sensor captures the modified wavefront after it has been shaped by the DM. It analyzes the positions of focal spots created by an array of microlenses, allowing it to calculate parameters such as tip, tilt and curvature of the wavefront [67]. These data are then used to iteratively refine the DM’s adjustments, creating a closed feedback loop that continuously improves wavefront quality.
• Optimal wavefront shaping: The goal is to achieve a near-perfect wavefront before it reaches any subsequent optical components or processing stages in the laser micromachining setup. This ensures maximum efficiency and precision during laser ablation or machining processes, as a well-shaped beam can more effectively interact with materials [68].

The entire process is mathematically described as follows:

$${\phi }_{in}(x,y)+2S_{DM}(x,y)+F(x,y)={\phi }_{out}(x,y)$$

(5)

where $S_{DM}(x,y)$, $F(x,y)$ and ${\phi }_{out}(x,y)$ are the DM surface distribution, the induced laser wavefront distortion function and the output wavefront distribution, respectively [69]. The relationship between the input and the output wavefront through the laser system is linear and can be described in terms of the transmission function $H(x,y)$:

$$H(x,y)={\phi }_{in}(x,y)+F(x,y)$$

(6)

If the initial conditions were expressed by the output wavefront ${\phi }_{out}(x,y)$ and the DM surface $S_{DM}^{\left(0\right)}(x,y)$, the first compensation DM surface distribution $S_{DM}^{\left(1\right)}(x,y)$, representing the wavefront shaping in the laser system, can be calculated as follows:

$$\left\{\begin{array}{cc}\hfill H(x,y)& ={\phi }_{out}(x,y)-2S_{DM}^{\left(0\right)}(x,y)\hfill \\ \hfill S_{DM}^{\left(1\right)}(x,y)& ={\displaystyle \frac{1}{2}}\left[{\phi }_{aim}(x,y)-H(x,y)\right]\hfill \end{array}\right.$$

(7)

by considering the wavefront distribution ${\phi }_{aim}(x,y)$ and the transmission function $H(x,y)$. When the laser system itself (i.e., the aberrations) is linear, the output flattening wavefront distribution cannot be obtained after the first wavefront correction. So, the iterative method should be applied:

$$S_{DM}^{(n+1)}(x,y)={\displaystyle \frac{1}{2}}\left[{\phi }_{aim}(x,y)-{\phi }_{out}^{\left(n\right)}(x,y)\right]+S_{DM}^{\left(n\right)}(x,y)$$

(8)

where $S_{DM}^{\left(n\right)}(x,y)$ represents the DM surface distribution at the $n^{th}$ iteration, and for $n=0$, it represents the initial DM surface; ${\phi }_{out}^{\left(n\right)}(x,y)$ represents the $n^{th}$ output wavefront distribution, and for $n=0$, it represents the initial wavefront [70].

Hence, the dynamical adjustment of the laser beam profile by the simultaneous AO correction of aberration effects is essential to induce material removal and surface modification with sub-micron accuracy. This enables adaptive welding strategies, such as seam tracking and gap bridging. In fact, ultrafast lasers combined with AO can track seams with high precision due to their ability to rapidly adjust focus and intensity. This is particularly useful for materials with intricate geometries or uneven surfaces [1]. AO excels in handling complex weld geometries (e.g., curved seams) due to its ability to dynamically adjust beam parameters. Moreover, AO allows ultrafast lasers to adaptively bridge gaps by modifying the beam profile or oscillating the focal point. This ensures consistent energy delivery across varying material separations. With increased tolerance to joint gaps, AO reduces the need for precise machining or clamping during part preparation. This lowers manufacturing costs and shortens production times. In particular, ultrafast lasers excel in processing transparent materials (e.g., glass) through nonlinear absorption mechanisms. AO enhances this capability by enabling precise 3D structuring and deep penetration welding, such as forming molten structures up to 5 mm deep in quartz glass [71]. Furthermore, parallelization enabled by AO reduces processing times by allowing for the simultaneous processing of multiple areas or rapid switching between focal positions [1]. All these advancements make adaptive optics a transformative technology in laser welding, offering unparalleled precision, efficiency, and adaptability for industrial applications.

In laser scribing, AO systems that implement piston, tip, and tilt corrections allow for the following: (1) the stabilization of the beam position and focus; (2) compensation for disturbances such as jitter or mechanical vibrations; and (3) enhanced dynamic response performance through advanced control methods [33]. Below are further details on piston, tip, and tilt parameters as critical components in adaptive optics (AO) systems. Piston, tip, and tilt parameters are crucial in adaptive optics (AO) for defining the reference surface and correcting wavefront aberrations. The piston parameter in AO significantly impacts wavefront correction by addressing the average optical path length discrepancies across the wavefront. It effectively shifts the entire wavefront up or down, ensuring that all parts of the wavefront are aligned to a common reference plane. This adjustment is crucial for achieving coherent light propagation and minimizing overall wavefront error, particularly in systems with segmented mirrors. Proper piston correction enhances image quality by reducing residual aberrations, thereby improving the system’s ability to deliver diffraction-limited imaging. Tip and tilt adjust the wavefront’s angle, addressing misalignments that affect image quality. By accurately aligning the wavefront, tip correction enhances the point spread function (PSF), leading to increased resolution and contrast in the final image. This correction is particularly important in dynamic environments, such as astronomy and vision science, where even minor shifts can significantly impact image clarity and details. Moreover, by adjusting the tilt of the wavefront, tip–tilt mirrors align the incoming light beams to a common focal point in view of various processing applications. Tip–tilt stages allow for precise control over the angular position of laser beams. By adjusting the tilt and tip angles, these systems can compensate for variations in alignment and surface flatness, ensuring that the laser remains focused on the desired target area [33].

A further optimization of these processes is now achieved by the integration of machine learning with Shack–Hartmann and pyramidal sensors. For instance, using reinforcement learning with pyramidal sensors has shown superior performance in challenging conditions, outperforming traditional methods. The use of Bessel beams and acousto-optic deflectors (AODs) in laser processing has advanced significantly, enabling faster, more efficient, and precise fabrication techniques. Bessel beams are non-diffractive optical beams with self-healing properties, making them ideal for high-precision laser processing tasks such as to fabricate high-aspect-ratio structures in two-photon polymerization (TPP). This approach enables volumetric printing without the need for point-by-point scanning, thereby overcoming traditional limitations in serial processing [72]. On the other hand, Acousto-optic deflectors (AODs) are critical for achieving extremely fast beam deflection in laser systems. AODs use sound waves to dynamically modulate the refractive index of a medium, enabling rapid beam steering with microsecond response times. This capability is essential for applications requiring precise and fast beam positioning, such as 3D printing. Then, the combination of AODs with Bessel beams allows for ultrafast scanning over large areas while maintaining the unique properties of the Bessel beam. This integration is particularly useful in GHz burst-mode femtosecond lasers for cutting dielectrics or other challenging materials [73,74]. Additionally, machine learning aids in mitigating nonlinearities in wavefront sensing, further enhancing image quality and system robustness. This synergy enables AO systems to achieve higher fidelity in real-time corrections. Recently, advances in machine learning, particularly deep learning, have led to innovative solutions for depth estimation and image restoration from defocused images captured across different axial planes. For example, defocus segmentation techniques aim to distinguish between sharp and blurred regions within an image. Using algorithms like Pulse Coupled Neural Networks (PCNNs) combined with Local Binary Patterns (LBPs) can effectively segment focused areas from defocused ones, facilitating further processing or analysis of specific regions within an image [75,76,77]. A recent study introduces the Two-headed Depth Estimation and Deblurring Network (2HDED:NET), which simultaneously addresses depth estimation and image deblurring. This model utilizes a shared encoder for both tasks, allowing it to leverage the relationship between depth information and defocus characteristics. It has shown superior performance on benchmark datasets such as NYU-v2 and Make3D, outperforming traditional models that treat these tasks separately [78].

Nevertheless, some efforts are still necessary to (i) accurately predict the low-order aberrations (mainly astigmatism and spherical aberration) versus the Zernike-mode coefficients and the number of datasets; (ii) reduce the data transfer speed of the image sensor [47]; and (iii) avoid long processing times for high-resolution tasks, which is still an issue due to the point-based nature of laser processing when creating multiple foci simultaneously, even though adaptive optics is able to enhance processing speed through parallelization. The need for continuous adjustments to maintain focus across three-dimensional structures adds to this challenge [1].

5. Metasurfaces for Aberration Correction in Laser Scribing Processes

Recent advancements in metasurfaces have significantly improved wavefront aberration correction. These two-dimensional optical materials manipulate light through subwavelength structures, allowing for efficient phase control and reduced chromatic aberration compared to conventional optics [79]. Dielectric metasurfaces, in particular, have shown enhanced performance by achieving steep phase gradients and enabling functionalities that combine multiple optical components into a single device. Recent developments have integrated metasurfaces with conventional optical components, enhancing imaging systems and enabling functionalities like beam steering and polarization control. These advancements facilitate applications in high-end imaging and computer vision, demonstrating the potential for real-time wavefront correction in various optical devices.

Furthermore, metasurfaces have shown great promise in correcting optical aberrations by providing precise control over the phase of transmitted or reflected light [80]. Specifically, by customizing the geometry of the meta-atoms, metasurfaces can introduce tailored phase shifts that counteract aberrations [81]. A specific application of metasurfaces is in metalenses, which utilize arrays of nanoscale structures to focus light. These lenses can be engineered to compensate aberrations by adjusting the phase distribution across the lens surface (Figure 13). In addition, metasurfaces can achieve diffraction-limited focusing across a broad wavelength range, maintaining high efficiency. This is particularly important in laser scribing, where precise energy delivery is essential for effective material processing. For instance, certain metasurfaces have demonstrated focusing efficiencies of up to 90% at specific wavelengths [82]. Recent developments have introduced active metalenses with reconfigurable focusing capabilities. These systems can adjust the focal spot’s position in three-dimensional space, allowing for greater flexibility during laser scribing operations. By mechanically tuning the arrangement of multiple metalenses, users can achieve precise control over the focal point [83]. The capability of metalenses to focus laser beams with exceptional precision (no aberration effects) allows for accurate scribing of transparent materials like glass and polymers without leading to micro-cracks around the scribed area.

Metasurfaces used for aberration correction can be either passive, with fixed functionalities, or active, allowing for tunable and reconfigurable functions. Using metasurfaces can lead to more compact optical systems and enable novel properties and applications [80]. One approach involves using cascaded metasurfaces to achieve adaptive aberration corrections coordinated with focus scanning. This method allows for precise dynamic control of electromagnetic waves. In detail, by rotating two cascaded transmissive metasurfaces, adaptive aberration corrections can be achieved in tandem with focus scanning [85]. The rotation of the metasurfaces globally changes their phase profiles (Figure 14). By adjusting the mutual rotation angle between two layers in twisted metasurfaces, the reflected EM wave can be focused on a specific location. This allows for dynamic control of the focal spot in both two-dimensional and three-dimensional spaces.

In laser texturing setups, metasurfaces can be mounted on spherical surfaces to correct coma aberrations. Attaching metasurfaces to the surfaces of refractive optical elements allows for the analytical derivation of the desired phase profile; this setup can compensate for 80% of chromatic and 70% of spherical aberration. In these cases, the metasurface layer consists of an array of dissimilar cylindrical amorphous silicon nanoposts with different diameters placed on a subwavelength periodic hexagonal lattice and embedded in a flexible polydimethylsiloxane substrate. An aluminium oxide layer is located between the polydimethylsiloxane and the amorphous silicon post. The arbitrary shape of the object surface distorts the wavefront of transmitted light, but the metasurface corrects this [86].

Metasurfaces, which are engineered surfaces with subwavelength features, can manipulate light at unprecedented levels. Their integration with Vertical-Cavity Surface-Emitting Lasers (VCSELs) allows for custom-tailored optical wavefront shaping, enabling functionalities such as beam collimation, steering, and the generation of complex beam profiles (e.g., Bessel and vortex beams) directly from the laser output. By shaping the emitted laser beam more effectively, they ensure that the light interacts with the material in a more controlled manner, leading to improved scribing quality [87,88].

In summary, the integration of metasurfaces into laser scribing processes presents a cutting-edge solution for overcoming optical aberrations, enhancing precision and efficiency in various applications.

6. Conclusions

Adaptive optics integration leads to substantial progress in high-power laser applications, providing enhanced precision, efficiency and versatility that are crucial for contemporary technological requirements. By dynamically adjusting the laser beam’s wavefront, AO systems allow the identification and correction of the various optical aberrations, particularly depth-dependent spherical aberrations, that can be complicated due to the non-uniform refractive index of materials. However, the integration of AO systems with an existing laser processing setup is still a primary challenge because it requires precise alignment and calibration, which can be technically demanding. Moreover, the cost of adaptive optical elements and their complexity may hinder widespread adoption, especially in smaller manufacturing environments.