Scanning mirrors are essential components of laser scanning optical systems in microscopy, remote sensing, display, and manufacturing. Currently, there are two main strategies for 2D area scanning: (1) tilting a single mirror about two axes using a gimbal and (2) combining two single-axis scanning mirrors [1,2]. The choice of 2D scanner is application-dependent, requiring consideration of a number of technical specifications, including aperture size, speed, angular resolution, scanning range, and beam path geometry [1]. Because both strategies have some limitations, trade-offs between the design specifications often bottleneck certain performances of optical systems.

A major advantage of the gimbaled mechanism is single-pivot scanning, free of scan-path-related artifacts [2]. This is ideal for pre-objective scanning requiring low spot variation, aberration, and high telecentricity. However, building two rotational degrees of freedom into a single steering mirror often leads to high mechanical complexity, ultimately limiting performance and affordability. In contrast, single-axis scanning mirrors are more popular, owing to their high technical maturity and price/performance ratio. Some device types also provide certain cutting-edge technical specifications (e.g., speed of resonance) [1]. A common 2D scanning configuration using two single-axis scanners places two scanners close to each other [2]. This “galvo pair” configuration is simple and cost-effective. While it is acceptable for many applications, the two distant rotational axes complicate the beam path geometry and introduce spot variation, displacement jitters, and telecentric errors [3,4]. This is a major problem for applications sensitive to beam path fluctuations. Simultaneously achieving single-pivot, high-speed, large-range 2D scanning has been of great interest in optical design research, but there has been no simple solution.

Here, we introduce a simple but novel geometry to perform virtual single-pivot scanning using two conventional single-axis scanners (Fig. 1 and Visualization 1). Ideally, the first mirror (M1) is a single-axis scanner with a rotational axis distant from the mirror (e.g., a polygon scanner). The second mirror (M2) is a single-axis scanner with a rotational axis near the mirror surface (e.g., a galvo). The axes of M1 and M2 are orthogonal. The incident beam is pointed at the axis of M1, reflected toward the axis of M2, and reflected back to M1. The virtual pivot (P) is the mirror image of the reflecting point on M2, which is always located where the incident and exiting beams intersect.

 

Fig. 1. (a) 3D representation of scanner design. The beam enters from above M2 and exits below M2. (b) Vertical projection of the geometrical model: AD = kL, AR₁ = kLsec(θ), OR₁ = L − kLsec(θ), ∠OR₁R₂ = 2θ, R₁R₂ = (L − kLsec(θ))sec(2θ), OP = OR₁ + R₁R₂ = L − kLsec(θ) + (L − kLsec(θ))sec(2θ), OP/L =1− k(sec(θ) + sec(θ)sec(2θ)) + sec(2θ), ΔP = 1 + sec(2θ) − k(sec(θ)+ sec(θ)sec(2θ)) − [−2k + 2] = − 1 + sec(2θ) − k(sec(θ) + sec(θ)sec(2θ) − 2). Visualization 1 is an animation of the scanning.

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The system will behave as a single-pivot 2D scanner as long as P does not move during scanning. As M2 rotates, P remains fixed if the beam is centered at its rotation axis. However, as M1 rotates, the beam path length change between the mirrors will cause P to dislocate. Nevertheless, the extent of the dislocation varies with the geometrical arrangements. Under certain conditions, the displacement of P is small and even negligible, which provides an opportunity to achieve single-pivot scanning.

To better understand the behavior of the pivot dislocation, we derived an analytical solution for a set of desired scanner arrangements. Figure 1(b) shows a 2D projection normal to the axis (A) of M1 (BC) where θ is the rotation angle. For design practicality and model simplicity, we set the system to be symmetrical about the projection of the incident beam (i₀): both M1 and M2 (B′C′) are orthogonal to i₀ at the initial condition (θ = 0); M2 intersects i₀ at O; i₁ and i₂ are the reflecting beams between M1 and M2; i₁′ and i₂′ are mirror images of i₁ and i₂ in M1; i₃ is the exiting beam; and i₀ and i₃ are always collinear with i₁′ and i₂′, respectively. Point A is a unit length (L) away from M2. A single geometrical parameter k defines the distance between M1 and its pivot (AD = kL). The length of OP is i₀+ i₁′, which is a function of θ and k. Let P[θ, k] equal the length of OP divided by L; P[θ, k] = 1 + sec(2θ) − k(sec(θ) + sec(θ)sec(2θ)). The dislocation function of the virtual pivot is derived as ΔP[θ, k] = (P[θ, k] − P[0, k]) = sec(2θ) + 2k(1 - cos(θ)sec(2θ)) − 1.

Plotting ΔP versus θ for different values of k, Fig. 2(a) reveals that ΔP varies minimally under certain conditions. When k = 0.6684, the variation of ΔP is less than ±0.005% for θ within ±11.25° (90° optical deflection range). For reference, if M1 is a polygon scanner with kL equal to 10 mm and M2 is placed L = 14.96 mm away from the M1 axis, the resulting virtual pivot fluctuation is within ΔP = 0.79 µm. At higher tolerance, the variation in ΔP is less than ±0.1% for k between 0.660 and 0.677, still negligibly small for most circumstances. Using the same 10-mm polygon mirror, when L is between 14.77 and 15.15 mm, the virtual pivot fluctuation is within 15 µm. At smaller scanning angles (θ within ±2.5°), the variation in ΔP is less than ±0.1% for a large range of k, between 0.5 and 0.85. The configuration can well accommodate machining errors, vibration, and thermal expansion. For more details, Figs. 2(b) and 2(c) can be used as references to determine the performance and tolerance of the system.

 

Fig. 2. (a) Plot of ΔP as a function of θ between −11.25° and 11.25° at selected values of k. (b), (c) Contour plots of ΔP at selected ranges of k.

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At higher tolerance and smaller scan angles, the double-reflection strategy even applies to a galvo pair (e.g., k = 0, Visualization 2). Although the pivot dislocation is greater than the aforementioned polygon-scanner-based design, it is still significantly better than the conventional galvo pair arrangement. In this case, M1 should be the slow axis and M2 should be the fast axis. Mirror M2 could also be a resonance scanner to achieve higher scanning speeds. For θ within ±4° or ±2.5°, ΔP is within ±1% and ±0.24%. For reference, two galvo mirrors placed 10 mm apart would result in 0.1 mm and 24 µm maximum pivot shifts at 32° and 16° optical deflections, whereas the shifts in the second mirror are 2.8 and 1.4 mm in a conventional galvo pair. The diminutive pivot shift is comparable to the scan field waist of paddle and golf-club scanners at the same scale (see Marshall and Stutz [1] or Li [2] for details), providing a great alternative to these specialized mechanics. More interestingly, this strategy could be implemented in existing orthogonal galvo pairs by simply modifying the initial galvo angles and beam paths.

The main advantages over a typical gimbaled scanner include high scanning speed, large optical deflection, and low cost. Under this design concept, a ∼10,000-rpm scanner (e.g., Eagle Eye from Precision Laser Scanning LLC) with 30 facets can produce a ∼5 kHz fast-axis rate with ∼48° optical deflection. Moreover, the slow axis of our design uses a galvo, which can generally provide better angular resolution and positional feedback than current commercial dual-axis scanners. It also provides an easy way to actively cancel the repeatable wobbling error of the polygon scanner through a lookup table, which is a common strategy in conventional polygon–galvo scanning systems [5]. Key specifications of some current commercial scanners are provided in Table 1 for comparison.

Table 1. Fast-Axis Specifications of Selected Commercial Scanners^a

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Compared with current scanning artifact correction strategies to correct scanning artifacts in a galvo pair, this double-reflection configuration is simpler and more robust. Previously, a common strategy to remove the displacement jitter from a galvo pair was to conjugate the galvo with a 4f relay [4]. However, this strategy introduces at least two extra optical elements, increasing the footprint, complexity, loss, and aberrations of the system. Other strategies include using special scanner geometries, such as paddle and golf-club scanners [6], and implementing free-form scan lenses [7]. Unfortunately, these special designs require significant customization and are not widely accessible. Besides, they only provide moderate improvement to the pivot shift. In contrast, the presented design only requires two widely available commercial single-axis scanners. Because the configuration is fully reflective with flat mirrors, it does not introduce any dispersion or aberrations, compared with the 4f-relay strategy, making it ideal for multiwavelength and ultrafast applications.

The system can be treated practically like a gimbaled scanner with an inaccessible pivot because the system behaves approximately the same as a single-pivot scanner. Although the virtual pivot is inaccessible, an equivalent point is located on M2. Therefore, the system can be aligned by aiming the beam toward the center of both mirrors, and adjusting the elevation or altitude angle of the beam, so that the beam intersects the center of M2. When M1 is a polygon scanner, it generates unidirectional scanning at a constant angular velocity. This is advantageous for some raster scan applications, but continuous scanning may result in a fixed scan range and some beam clipping at the beginning and end of each scan cycle. The design will eliminate the pincushion distortion of a typical single-axis scanner pair. Instead, it will introduce fan distortion like a conventional gimbal scanner [2].

A minor design drawback is the relatively large M1 area with respect to the beam diameter, which leads to reduced beam size or greater mirror inertia. Mirror M1 has to be a beam diameter wider than ∼2kLtan(θ_max) to avoid beam clipping, where θ_max is the desired one-way maximum scan angle. Nevertheless, because the scan speed and angular response are doubled as the beam is reflected twice by M1, a mechanical rotation of θ can lead to a 4θ optical deflection, twice as much as 2θ in a typical single reflection. In fact, multiple reflections were previously reported to improve angular sensitivity and scanning speed for 1D scanning [8,9]. Although the trade-off is less meaningful for 1D scanning, it remediates the problem in our case. Moreover, the width of M2 is also larger than the beam diameter by (L − kLsec(θ_max))tan(2θ_max); for instance, it is ∼22% larger at 50° optical deflection. This may result in a reduction in the scan speed when M2 is used as the fast axis.

Two strategies can help manage the larger mirror area problem. Because the required areas of both M1 and M2 scale with the maximum scan angle, reducing the angular range helps reduce the mirror size. For instance, a 25° optical deflection only requires an ∼11% greater M2 area. Alternatively, it is possible to significantly reduce the M1 size by orienting i₁ perpendicular to M2 when θ = 0 (Visualization 3). In this case, the incident and exiting beam paths overlap. Additional optical elements (e.g., beam splitters) are required to separate the beams.

It is worth noting that the actual performance of a double-reflection scanner is dependent on the choice of hardware components. Like other scanner technologies, there are trade-offs between price, speed, size, range, accuracy, etc. For instance, without considering the cost of a polygon scanner, an air-bearing motor can outperform a ball-bearing motor, and a beryllium polygon mirror can outperform an aluminum mirror in scanning speed [1]. High-precision roller bearings will create much smaller non-repeatable jitters than will conventional ball bearings. Therefore, without well-defined design constraints for a specific application, it is difficult to make a fair comparison with existing technologies. For example, a microelectromechanical system (MEMS) scanner is much more compact. A mechanical gimbal can support a large mirror aperture. A conjugated galvo pair better utilizes the mirror aperture and offers higher speed. The presented design does not guarantee top performance in particular specifications. It rather broadens the design parameter space of beam steering applications.

It is also worth noting that this double-reflection configuration can be a universal strategy for improving the scan quality of polygon scanners. Polygon scanners are reliable and cost-effective solutions for high-speed raster scanning. However, they have limited use in high-quality pre-objective scanning applications because the reflecting point on the polygon mirror is constantly shifting, even during 1D scanning [2]. This introduces pupil shifting and complex beam paths that are difficult to compensate for with spherical optics. With the double-reflection geometry, this 1D scan artifact is eliminated, even when M2 is a static mirror, which enables the potential use of polygon scanners in a broader range of applications.

In summary, we demonstrated that two single-axis scanning mirrors could generate near-perfect, single-pivot 2D scanning with a simple double-reflection arrangement. This arrangement is established with widely available single-axis scanners, providing an easy and robust solution for low distortion and high-speed pre-objective scanning in various applications. We believe that this finding will benefit many optical applications requiring high-speed, high-quality beam steering in the future.