The utilization of ultrashort pulsed laser radiation enables the precise generation of microstructures and the processing of a wide variety of materials. However, for massive parallel processing, the raw intensity distribution of the beam emitted by the laser source usually has to be transformed into an arrangement of multiple laser beams with specific intensity distributions. Here, sophisticated, application-adapted optical systems serve as a key technology. This paper gives an overview of the optical design fundamentals of multi-beam optics. It also investigates the causes for one of the main challenges in the use of multi-beam optical systems: the distortion of the spot-array on the work piece. The distortion leads to individual spot position errors and can heavily limit the processing accuracy. Finally, active and passive concepts and technologies to reduce or eliminate distortion in multi-beam systems are presented.
The utilization of ultrashort (<10 ps) pulsed laser radiation enables the precise manufacturing of structure sizes in the micrometer range for a wide variety of materials. But despite their precision, ultrashort pulsed laser applications often lack the productivity for large scale industrial use.1 Today, commercially available picosecond laser systems approach average powers of up to 1 kW. However, the usable power in most ultrashort processes lies in the range of 1–10 W for single beam processing. The reasons for this are physical limitations by the actual structuring/ablation process and/or undesired heat accumulation in the work piece in conjunction with the limited scanning speed of a galvanometer based laser scanner.2
For single beam processing, these limitations can be overcome by increasing the scanning speed using a so-called polygon scanner. A fast rotating polygon mirror enables scan velocities in the range of several 100 m/s and a spatial separation of individual pulses even for repetition rates in the megahertz range.2,3 Another approach is beam splitting. Splitting the beam into partial beams reduces the power per beam while still fully utilizing the available laser power. State-of-the-art beam splitters allow for hundreds of partial beams, enabling high throughput parallel processing of periodic structures or several work pieces at once.4
II. OPTICAL DESIGN FUNDAMENTALS FOR MULTI-BEAM SYSTEMS
The main components of a typical multi-beam system are illustrated in Fig. 1. The beam of a laser source is split into several partial beams (also called beamlets) by a beam splitting element. A relay-system spatially separates the individual beamlets and feeds the beam-array into a beam deflection system. Finally, the beam-array is focused onto the work piece via a focusing element. Each of those components, except for the laser source, will be discussed in more detail in Subsections II A–II C.
A. Beam splitting
The splitting of a single beam into two or more beams is required in a variety of optical systems. Typically, an incoming beam is split into two beams via a beam splitting cube or prism. While a combination of these elements can also be used to create a larger number of beams, this is not feasible for a multi-beam system with tens or even hundreds of beams.
A different approach is the use of microlens arrays. As the name implies, these arrays consist of miniaturized lenses and are used to segment an incoming beam into a large number of beamlets (one for each lens) that are focused into a plane behind the array. With fill factors up to 100% and lenslet sizes down to tens of micrometers,5 microlens arrays allow for the precise generation of a large number of beamlets. However, the power within each beamlet depends on the power impinging on the corresponding lenslet. Nonuniform intensity distributions of the initial beam, therefore, lead to partial beams with varying power and, therefore, inhomogeneous processing results.4,6 With the typical (near-)Gaussian intensity distributions of pico- and femtosecond laser sources, microlens arrays are usually not suitable as a beam splitting element for material processing.
Alternatively, beam splitting can be realized via diffractive optical elements (DOEs). A targeted manipulation of the phase front of the incoming beam is used to control the intensity distribution behind the DOE. A typical DOE for beam splitting consists of a periodic diffraction grating. A one-dimensional periodic grating with period length d leads to partial beams under the angles given by
with the wavelength and the diffraction order n (assuming perpendicular incidence).7 A two-dimensional periodic grating leads to corresponding diffraction angles in two dimensions. A major advantage of DOE beam splitters is that the beam profile of each beamlet is a copy of that of the incoming beam. The power of each diffraction order is determined by the structure within each grating period. Typically, the goal is to have a uniform distribution of power to all desired diffraction orders and to suppress unwanted diffraction orders.
The most common form of a DOE for beam splitting is a structured glass substrate [cf. Fig. 2(a)]. The height/phase profile of the DOE structure is usually designed for a maximum phase change of 2π.9 The height profiles can be binary, multilevel or continuous. Figure 2(b) shows an exemplary height/phase profile of a 4 × 4 beam splitter DOE with four discrete height levels. The number of different height levels directly influences the two main evaluation criteria of a DOE: efficiency and uniformity error.
The efficiency of a beam splitting DOE is defined as the share of the total input power that is distributed into the N desired diffraction orders with respective powers ,10
The efficiency of commercially available beam splitting DOEs typically ranges between 70% and 90%.
The uniformity error describes the power or peak intensity difference between the desired orders,
with the highest power across all desired orders and the power of the lowest power spot .4,11
The efficiency increases with an increasing number of height levels of the height profile. However, with an increasing number of height levels, production inaccuracies and thus the uniformity error increase as well. For each DOE design, a compromise between efficiency and uniformity must be found.12,13
As an alternative to structured glass substrates, liquid crystal based DOEs allow for a dynamic adaptation of the phase mask. A more thorough explanation of this technology is given, e.g., in Ref. 14. These dynamic DOEs were already successfully implemented into multi-beam systems for material processing.15,16 Yet, state-of-the-art liquid crystal DOEs with active cooling are limited to laser powers <130 W. Above this power, thermal effects within the liquid crystals distort the phase mask and limit the phase modulation.17 Thus, dynamic DOEs are currently not suited to fully utilize the available laser power of modern short and ultrashort pulse laser sources.
A relay-system for multi-beam optics consists of (at least) two relay lenses and allows to spatially separate the beams after the DOE (cf. Fig. 3). As discussed in Sec. II A, around 10%–30% of the initial laser power is diffracted into unwanted diffraction orders. These are mostly higher orders but, depending on the desired beam-array, can also consist of the 0th or intermediate diffraction orders. As the unwanted orders can impact the processing results, they usually need to be filtered out.
The first relay lens focuses the partial beams into an intermediate focus. A mask in or near the intermediate focus then allows to filter out any unwanted orders. A movable mask even enables the dynamic selection of individual rows or columns within the beam-array.4 Depending on the power blocked by the mask, active cooling of the mask may be required. The second relay lens couples the beam-array into the following beam deflection system. A typical relay design is the so-called 4f-setup: The DOE is placed in the front focal plane of the first relay lens. This moves the intermediate focus into the back focal plane of the first relay lens and leads to telecentricity between the relay lenses, i.e., the chief rays of all beamlets are parallel to each other (cf. Fig. 3). The second relay lens is then positioned in such a way that the intermediate focus lies in its front focal plane, imaging the DOE (minus the masked out orders) into the back focal plane of the second relay lens.
Relay-systems are not absolutely necessary for multi-beam optics. For example, Haupt et al. placed a rotatable DOE directly in front of a galvanometer scanner.18 While this simplifies the optical system, it focuses all diffraction orders of the DOE onto the work piece, potentially negatively impacting the processing results.
C. Beam deflection and focusing
Laser surface processing requires a relative movement between beam (array) and work piece. Mirror-based beam deflection systems have established themselves in most areas of laser-based material processing. The high deflection speed and dynamics are key advantages of these systems compared to axis-based lateral movements of the work piece. The 2D-deflection of the beams is usually realized via two consecutive, rotatable deflection mirrors [cf. Fig. 4(a)] in so-called laser scanners.4
The spatial separation of the two rotation axes leads to a dependence of the beam deflection by the second mirror on the beam deflection by the first mirror. While, with the correct alignment, the incoming beam is always perpendicular to the rotation axis of the first mirror, this is not the case for the rotation axis of the second mirror. Any movement from the first mirror changes the angle between the beam and the rotation axis of the second mirror. Thus, movement of the second mirror generally does not lead to a straight trajectory of the beam on the work piece.20,21
Figure 4(b) schematically shows the distortion of the scanning field inherent to two-mirror beam deflection.
To focus the laser beam onto the work piece, a focusing lens is usually placed behind the laser scanner. An ideal flat-field focusing lens is corrected for field curvature and allows to focus the beam onto a flat work piece independent of the deflection from the laser scanner.22 Such a lens has, per definition, no distortion and does not further influence the scanning field. However, nearly all commercially available laser focusing lenses are so-called f-θ-lenses. F-θ-lenses are flat-field focusing lenses with intentional barrel distortion so that the distance of the beam on the work piece from the middle of the scanning field d is given by
with the focal length f of the lens and the total beam deflection angle . This allows for a constant scanning speed on the work piece with a constant rotation speed of the deflection mirror.
However, this is only true for 1D-scanning as the total deflection angle depends nonlinearly on the individual deflection angles for two scanner mirrors.21 Additionally, the barrel distortion of f-θ-lenses further impacts the 2D-scanning field, as shown in Fig. 5. In modern laser scanners, the distortion of the scanning field and the individual scan positions are compensated via the control software of the laser scanner. A model- and/or measurement-based calibration allows to precisely position the beam on the work piece.23 But these compensations only work for a single beam. For a multi-beam array (or any extended intensity distribution), the center of the array may be correctly positioned, but the shape of the array is distorted. This distortion, and therefore the positioning errors for the individual beams, increases with increasing scan angles (cf. Fig. 6). Such a distortion of the beam-array on the work piece is usually not tolerable, heavily limiting the usable scanning angles for high-precision applications.2,4
Yet even in the center of the scanning field or without a laser scanner, the spot-array is nonequidistant when using periodic DOEs as described in Sec. II A. There is a mismatch between the nonlinear relation between diffraction angles and diffraction order [cf. Eq. (1)] and the linear relationship between spot position and angle for an f-θ-lens [cf. Eq. (4)]. This results in a distorted spot-array even in systems that only consist out of DOE and focusing lens. However, for small spot-arrays (a few millimeters in size) and thus small diffraction angles, the small-angle approximation applies and this distortion is negligible.2,4
III. NEW OPTICAL DESIGN APPROACHES
As shown in Sec. II, the distortion of the spot-array caused by the laser scanner and focusing lens heavily limit the usable size of the scanning field and the spot-array. To improve the productivity of multi-beam processes, optical design approaches that inherently reduce or eliminate that distortion of the spot-array are required. If that is not possible or feasible, a dynamic compensation of the distortion based on the scanning position is needed.
A. Passive optical systems
As explained in Sec. II, a regular spot-array gets distorted even without a laser scanner due to the mismatch between the diffraction angles of the DOE and the imaging properties of the focusing lens.
One possible approach is, therefore, the adaptation of the focusing lens to match the diffraction pattern of standard periodic DOEs. Due to the relation between diffraction angles and diffraction order [cf. Eq. (1)], it may seem plausible to use an f-sin(θ)-lens, defined by the relationship
The second approach is the adjustment of the diffraction angles of the DOE. Diffraction angles as defined via Eq. (1) are a result of the periodic structure of most DOEs. Aperiodic structures allow for basically arbitrary diffraction angles that can be adapted to the process as well as to the focusing lens.25,26 The corresponding spot-arrays are still subject to the scanner-induced distortion.
To avoid the scanner-induced distortion of the spot-array, Büsing developed an optical system that tackles the cause of the distortion: the lack of perpendicularity between the beams and the rotation axes of the deflection mirrors (cf. Sec. II C). The system consists of two nested cylindrical relay-systems and a separate focusing in x- and y-directions using cylindrical f-θ-lenses (cf. Fig. 7). The separation of the beam deflection in x- and y-directions fully eliminates the scanner-induced distortion as all partial beams are perpendicular to the rotation axes of the deflection mirrors. The disadvantage of this design is the required size of the deflection mirror and the second f-θ-lens (MX and FTX in Fig. 7). As all beams must hit the rotation axes of the second deflection mirror perpendicularly, the size of the deflection mirror (and the following f-θ-lens) in the direction of its rotation axis must be as large as the scanning field in that direction.4,27
B. Active optical systems
As an alternative to the passive compensation described in Sec. III A, the distortion of the spot-array can also be actively compensated.
Büsing investigated a possible compensation of the scanner-induced distortion by dynamically rotating the DOE as the spot-array seems to mainly rotate for increasing scan angles (cf. Fig. 6). This allowed to reduce the deviations of the spot positions from a regular grid by up to 50% for large scanning angles. “Large” here refers to scan angles that are larger than the maximum diffraction angle of the DOE.4
To fully compensate for the scanner-induced distortion, a dynamic positioning of individual beams is required. This also allows to process 3D-surfaces, as the required spot positions change dynamically and cannot be passively compensated. Büsing developed a concept for a spot positioning unit consisting of two rotatable plane parallel windows for each partial beam between two telecentric relay-modules (cf. Fig. 8). The rotation of a window leads to a transverse offset of a partial beam after the glass window and also on the work piece. The combination of two windows gives full control of the 2D position of a partial beam within the deflection range of the glass windows.4,28 Hofmann et al. developed a corresponding prototype for a 2 × 2 beam-array.28,29 Each beam can be laterally shifted in each direction by ±900 μm, allowing to fully compensate the scanner-induced distortion. Figure 9 shows a close-up of that spot position control unit. The windows are rotated via galvanometer motors enabling the same dynamics and position accuracy as the actual laser scanner.
A different approach is pursued within the MultiFlex project:30 A 8 × 8 spot-array with 5 mm spot distance on the work piece illuminates nearly the whole scan field of a standard 2D-laser scanner and focusing lens at once. The laser scanner allows to move the spot-array by one spot distance so that each point on the work piece can be reached by at least one beam. Due to the size of the spot-array, the spot-array will be noticeably distorted even without any scanner movement. A vector analysis of the beam distortion4 predicts positioning errors (compared to a regular grid) of at least 24 μm for the beams at the edges of the spot-array. At the edges of the scanning field, these errors increase to 55 μm. However, the desired positioning accuracy for the process is 4 μm or less. Therefore, each beam will be individually switched on and off (i.e., deflected on the work piece or a beam dump) via an array of acousto-optic modulators when the beam is at the right, precalculated position. The concept is illustrated in Fig. 10.
The active optical systems presented above allow to fully compensate and/or overcome the distortion of multi-beam arrays. The key approach in these systems is the individual manipulation of each partial beam based on the position of the spot-array on the work piece. However, this requires larger, more complex, and more expensive optical systems compared to “simple” multi-beam systems as described in Sec. II. For each application, a compromise between the beam positioning accuracy, the size of the scan field, and the expenses for the optical system must be found.
Multi-beam systems are a key technology to fully utilize the potential of state-of-the-art ultrashort pulse laser sources. So far, multi-beam applications are limited to small spot-arrays and scanning fields. For larger spot-arrays and/or scanning fields, the inherent distortion of state-of-the-art 2D-laser scanners and focusing lenses deforms the spot-array, heavily limiting the positioning accuracy of the process. New design approaches for beam splitting elements and optical systems allow to eliminate the distortion of the spot-array on a fundamental level. Active optical systems enable the dynamic compensation of the distortion by manipulating individual beams and even allow for the multi-beam processing of 3D-surfaces.
The authors thank the German Federal Ministry of Education and Research for funding within the Research Campus “Digital Photonic Production” (No. 13N13710) and the European Commission for funding within the projects “ultraSURFACE” (H2020-ICT2015, No. 687222) and “MultiFlex” (H2020-ICT2018-2, No. 825201). Oskar Hofmann is part of the Max Planck School of Photonics supported by BMBF, Max Planck Society, and Fraunhofer Society.