Three-dimensional (3D) nanoprinting via two-photon polymerization, also called direct laser writing, offers unprecedented design freedom and precision for micro-optical elements and systems. Following the first demonstrations of single microlenses,1 the method has evolved rapidly, particularly in the last 5 years, with notable demonstrations of hybrid achromats and apochromats,2 diffractive lenses,3 flat-optics,4^,5 millimeter-sized lenses,6 catadioptric fiber-optic sensor heads,7 and photonic waveguides8 and bundles.9 The possibility of creating submillimeter-sized freeform optics and/or optical systems is proving particularly useful for endomicroscopy. For instance, Gissibl et al.10 demonstrated multilens objectives measuring only 120μm in diameter, which can be placed directly at the tip of a fiber bundle. 3D-nanoprinted lenses on fiber-tips were featured in optical coherence tomography (OCT) endomicroscopes with circumferential,11 and forward-looking12 scanning as well. Our group has shown that a 1-mm cubic phase plate printed directly on top of a GRIN lens can be used to generate biaxially accelerated static airy light sheets for axial sectioning in biomedical imaging.13 Enabled by a 3D-nanoprinted “lens-in-lens” structure, Li et al.14 developed an intravascular endomicroscopic probe and demonstrated OCT and fluorescence imaging of a mouse artery in vivo.

Although 3D nanoprinting of micro-optics is becoming a staple tool, its potential for dynamic micro-opto-electro-mechanical systems (MOEMSs) remained unexplored until very recently.15^–18 For miniaturized imaging systems such as multimodal endomicroscopes and multiphoton miniscopes for neural imaging on freely moving elements, MOEMSs are used for performing essential functions including remote focusing for axial scanning.19^,20 In addition to the complete design freedom it offers, the inherent mechanical alignment between optical and mechanical components in 3D nanoprinting can be a particular advantage over conventional clean-room-based manufacturing processes, where optical components are typically fabricated separately and integrated with the actuators through precision micro-assembly,21 polymer curing22^,23 or thermal reflow.24 These processes are not only complex but also prone to alignment errors that accumulate as the micro-optical system becomes more complex. Furthermore, their reliance on time-consuming and costly clean-room processes limits the number of practical design iterations. The first monolithically fabricated MOEMS with continuously translating microlens by up to 88.9μm was demonstrated by Rothermel et al.16^,25 This device featured a microlens with a diameter of less than 100μm at the distal end of a spring, which was actuated electromagnetically through the combination of a microchannel capillary-filled with an epoxy resin containing NdFeB microparticles and an external coil. Due to the omnidirectional compliance of the spring, however, the axial lens translation was accompanied by strong parasitic off-axis motion. Our group recently demonstrated a bistable microlens actuator that can switch between two stable predefined states for reconfigurable micro-optical systems.15 The device featured a three-dimensional intertwined spiral springs that facilitated the confinement of the lens motion in the axial direction, and was switched by electromagnetically actuating a soft-magnet deposited directly on it through current pulses, and did not consume any direct current (DC) power in rest states.

In this work, we present a 3D-nanoprinted lens actuator with a large optical aperture, ideal for remote focusing in miniaturized imaging systems. For example, miniaturized two-photon miniscopes, such as the one developed by Zong et al.,20 use micro-electro-mechanical system (MEMS) mirrors with diameters of up to 1.2 mm to cover a large field of view with high resolution. Our developed actuator uses ortho-planar linear motion springs with a monolithically integrated lens and a self-aligned micromagnet and is actuated by two external microcoils with opposite current directions to minimize torsional forces and facilitate uni-axial motion. It uses a sintered NdFeB micromagnet instead of nanoparticles dispersed in polymers to maximize mechanical force and is optimized for low power consumption with a resonant frequency of more than 300 Hz for mechanical robustness. The 1.4-mm-diameter lens profile is optimized through several iterations to minimize both surface roughness and shape errors. Despite the large lens, the entire device, including the coils, has a footprint of 5.74 mm in diameter. Following the manufacturing and a detailed analysis of the optical performance, we conduct a thorough characterization of the mechanical performance, including long-term measurements. Particular emphasis is placed on the effects of coil temperature and the viscoelastic properties of the polymer on actuation. Finally, we compare the performance of the 3D-nanoprinted actuator with that of actuators fabricated using conventional MEMS processes.

The proposed actuator consists of a spring-supported ring-shaped micromagnet with an integrated lens, positioned between two coils, as depicted in Fig. 1. The electromagnetic gradient generated by the coils exerts a force on the magnet, resulting in a displacement of the magnet-lens assembly along the optical axis.

The mechanical design is based on ortho-planar linear-motion springs. Four springs connect the lens to the base. Each of the four springs consists of one serpentine spring. Following the nomenclature outlined by Parise et al., this design is referred to as Quad 1-1SC.26 The planar nature of the springs enables the use of different manufacturing methods, whereas the use of curved springs results in a very compact design. In addition, the raising and lowering of the lens relative to the base is free of rotational movement,26 which would be advantageous for potential nonrotationally symmetric lens designs.

The device uses electromagnetic actuation to attain axial lens translation. If an external magnetic field is applied along the symmetry axis of the actuator, the force Fz,m created by the micromagnet along the same axis is given by Fz,m=1μ0BrV∂B∂z=1μ0Brmmρm∂B∂z,(1)where μ0 is the magnetic field constant, Br is the residual flux density of the micromagnet, B is the applied external field, and Vm, mm, and ρm are the volume, the mass, and the density of the magnet, respectively. This magnetic force is balanced by the force Fz,s of the spring given by Fz,s=keffΔz,(2)where keff is the effective spring constant of the four parallel serpentine springs and Δz is the displacement of the lens. Equating Eqs. (1) and (2) yields the displacement Δz as Δz=BrVμ0keff∂B∂z.(3)

As high power dissipation from Joule heating in the electromagnetic coil is one of the main disadvantages of electromagnetic MEMS actuation, this design aims to minimize power consumption for a target lens displacement. As the dissipated power is proportional to the square of the current through the coil and the current is proportional to the required magnetic field, it becomes evident that minimizing the required magnetic field gradient minimizes power dissipation. At the same time, a sufficiently high resonant frequency of the actuator is required to achieve high speed and resilience against environmental disturbances. To include this requirement in the design process, we model the actuator as a simple harmonic oscillator with the resonant frequency f0 given by f0=12πkeffm=12πkeffml+mm,(4)where m is the mass, ml is the mass of the lens, and mm is the mass of the magnet. Solving Eq. (4) for keff and substituting it into Eq. (3) allow us to define the magnetic field gradient ∂B˜∂z required to achieve a certain displacement Δz for a design with a defined resonant frequency f0 as ∂B˜∂z=(2πf0)2(ml+mm)Δzμ0ρmBrmm.(5)The following two conclusions can be drawn to minimize the required magnetic field gradient. First, the mass mm of the magnet must be substantially greater than the mass ml of the lens. This requirement arises from the fact that the term ∂B˜∂z∼ml+mmmm converges to 1 under these conditions. Second, the ratio of the residual flux density Br of the magnet to its density ρm should be maximized, as ∂B˜∂z∼ρmBr. Recently, magnets fabricated by filling cavities filled with a compound based on NdFeB microparticles and a low-viscosity 2-component epoxy have been demonstrated.15^,16 Calikoglu et al.15 reached a residual flux density Br of 300 mT at a density ρ of 5.1gcm−3. Compared with the use of compound magnets, the use of conventionally manufactured magnets (Br=1.4mT and ρ=7.6gcm−3) reduces the power consumption by a factor of ∼10.

The actuator designed in this work has a lens aperture of 1.4 mm. Assuming a lens mass of ∼0.4mg using IP-S photoresin, the mass of the magnet is set to 3 mg to fulfill the design condition of mm≫ml. The micromagnets, custom machined from pressed and sintered blocks of NdFeB VAC745HR (Audemars Microtec), reach a residual flux density Br of 1.44 T at a density ρ of 7.6gcm−3. The micromagnets have an inner diameter of 1.4 mm, an outer diameter of 2 mm, and a height of 250μm. When determining the geometrical dimensions of the springs and thus getting keff, the goal is to achieve a resonant frequency of 300 Hz of the first natural mode, which aligns with the intended actuation mode. By choosing 300 Hz, we ensure that the first natural mode is more than 3 times the frequencies commonly found in the ambient environment, which are typically below 100 Hz.27 This separation makes the actuator inherently robust against external movements and vibrations.

The design was optimized using finite element analysis (FEA) with COMSOL Multiphysics^® 5.6 Structural Mechanics module, assuming a Young’s modulus of 5.1 GPa28 for the IP-S resin and including geometric nonlinearities. Nonlinear and viscoelastic material properties were not taken into account in the simulations. The optimization aimed not only to achieve a resonant frequency of 300 Hz but also to achieve a linear relationship between force and deflection while ensuring that the stress remains below the tensile strength of IP-S, given by 65 MPa.28

The optimized beam thickness is 44μm, with a reduced thickness of 34μm at the spring center to reduce stress concentrations in regions prone to maximum strain during deformation. Detailed mechanical dimensions can be found in Fig. S4 and Table S1 in the Supplementary Material. The simulated displacement Δz of the lens as a function of force F is shown in Fig. 2(a). Until the target displacement range of ±100μm, the geometrical nonlinearities remain negligible. The corresponding spring constant k is 13.79Nm−1. The maximum von Mises stress is 29% of the yield strength of IP-S. The first four natural modes of the actuator depicted in Fig. 2(c) correspond to resonant frequencies of 303, 464, 473, and 2105 Hz.

A magnet under an external magnetic field experiences not only a force but also a torque directed to align the internal magnetization vector with the external field. For axial displacement of the lens, only the force along the symmetry axis of the actuator is desired, as any torque tilts the lens with respect to the optical axis, potentially introducing aberrations. As the torque τ→ is given as τ→=VM→×B→,(6)where V is the volume of the magnet, M→ is the magnetization vector, and B→ is the magnetic field vector, it becomes evident that the torque becomes zero if either B→ and M→ is parallel or antiparallel to each other, or B→ is equal to zero. As the first condition would require perfect alignment of the magnet to the magnetic field, the second condition was implemented by using two coils with opposite winding directions, similar to an anti-Helmholtz coil. In this configuration, the magnetic fields produced by the two coils cancel each other out at the midpoint, creating a near-zero magnetic field within the actuation region. Consequently, torque is minimized due to the negligible field magnitude, whereas the force is improved due to the increased magnetic field gradient.15

We optimized the coil pair to minimize power consumption. Because the inner radius of the coils is determined by the size of the actuator and the power consumption is independent of the wire diameter, the only variables that require optimization are the number of axial and radial windings for a given wire diameter.

The total magnetic field B(z) can be computed by applying the Biot–Savart law to each conductor loop of the coil. It is given as B(z)=∑i=0n∑j=0mμ02(R0+rc+jdc)2I[(R0+rc+jdc)2+(z+rc+idc)2]3/2,(7)where R0 is the inner radius of the coil, I is the current through the coil, and z is the position along the symmetry axis of the coil relative to the center. rc and dc denote the radius and the diameter of the copper wire including the enamel, and n and m denote the number of axial and radial windings, respectively. The coils are made from enameled copper wire with a copper diameter of 114μm. We determined the fill factor (i.e., the ratio of total conductor area to total coil area in the radial cross-section) of a typical coil to be 70% (see Fig. S1 in the Supplementary Material). Therefore, we assume that dc is 120μm to match the calculation with the empirically determined fill factor for hexagonal packing. For 20 axial and 10 radial windings, the power consumption reaches a local minimum (see Fig. S2 in the Supplementary Material). The resistance Rcoil of this coil pair is 11.5Ω. The peak current Ipeak required for reaching the required gradient of 3.03Tm−1 for an actuation range of ±100μm is 84 mA at a peak power consumption of 81 mW. The average power when driving the actuator with a triangular waveform is 27 mW. The weight of the coil pair including the coil holder is 505 mg. This weight makes the actuator suitable for integration into miniaturized two-photon microscopes, which typically weigh around 3 to 5 g.19^,20

The optimized coil design was verified using FEA in the COMSOL Multiphysics^® AC/DC module. We simulated the force created by the micromagnet for a current of 84 mA at different positions along the symmetry axis. As shown in Fig. S3(b) in the Supplementary Material, the simulated force is constant around 1.48 mN within the actuation range, which is close to the calculated force of 1.38 mN required for a displacement of ±100μm. The simulated force differs from the calculated force because the latter assumes a homogeneous magnetization across the entire magnet volume. By contrast, the simulation accounts for the finite geometrical shape of the magnet as well as spatial variations of the gradient within the coil pair [see Fig. S3(a) in the Supplementary Material].

In principle, any optical component that can be fabricated using two-photon polymerization can be integrated into the actuator. In this work, we opted for a plano-convex lens designed to focus collimated light with a wavelength of 850 nm, and a possible solution to perform remote focusing in a two-photon miniscopes, such as the one discussed by Zong et al.20 We used ZEMAX^® OpticStudio^® for the design and optimization of the lens, which has a diameter of 1.4 mm, matching the inner diameter of the magnet, and an image space numerical aperture (NA) of 0.2, resulting in a back focal length of 3.42 mm. The lens surface is aspherical with a radius R of −1.72mm and a conic constant κ of −2.25. The lens is optimized for IP-S photoresin with a refractive index of 1.5.29

The complete fabrication process, summarized in Fig. 3, consists of four subprocesses: substrate preparation, monolithic 3D nanoprinting of the actuator including springs and lens, lift-off, and assembly.

A 20-nm layer of polyvinylalcohol (PVA, 87% to 89% hydrolyzed, Mw 13,000 to 23,000, 363081, Sigma-Aldrich) was spin-coated at 1750 RPM from an aqueous solution (1% w/w) onto a silicon substrate using a static dispense [Fig. 3(a)]. When dissolved in water, the PVA facilitates lift-off.

The actuator is printed in the dip-in configuration using a commercial 3D nanoprinter (Nanoscribe GmbH, Photonic Professional Gt+) equipped with a 10×/0.3NA objective using IP-S photoresin (Nanoscribe GmbH) [Fig. 3(b)]. The printing parameters for the mechanical support, springs, and lens are summarized in Table 1. We printed the mechanical parts with a larger slicing distance, because an optical-quality surface is not required for these. The lens was printed in two stages. In the first stage, a coarse print with a large slicing distance allows for a fast printing of the lens volume. In the second stage, a shell with a thickness of 5μm was printed on top of the already printed lens using a small slicing distance to create an optical-quality surface. This printing strategy shortened the printing time of the lens by a factor of ∼3 compared with conventional printing, where the complete volume of the lens would be printed at a small slicing distance.

To account for shape deviations caused by shrinkage during the printing process, we printed multiple iterations of the lens. After each iteration, the shape was measured and the print file was adapted accordingly using standard Zernike polynomials, resulting in a shape-compensated lens. For example, if the defocus term of the printed lens is smaller than the targeted value, the defocus term of the compensated lens is increased to reduce the deviation.13 During this process, the lens was printed without springs or mechanical support.

Printing the long, overhanging springs using the standard layer-by-layer approach is not a suitable option because the layers printed without support are floating, leading to distorted or failed prints.30 To overcome this problem, we adapted the printing strategy developed by Marschner et al.,31 where the overhanging structure is divided into several small parallelepipeds that are printed sequentially along the radius of the spring. We used a block length of 20μm and a shear angle of 15 deg. Individual blocks overlap by 4μm. We developed a custom Python script for general writing language (GWL) programming. The GWL file defines the path the laser focus will trace within the resin. To avoid spring deformation due to capillary forces during developer evaporation, which might push the springs beyond their yield strength and potentially cause plastic deformation or destruction,32 we constrained the movement of the springs by connecting them to the passive mechanical structure of the actuator using safety pins. Those pins have a height of 20μm and a width of 5μm.

Following printing, we developed the actuator in propylene glycol monomethyl ether acetate (PGMEA) for 2 h [Fig. 3(c)], before rinsing with isopropyl alcohol (IPA) for 30 min to remove the PGMEA. To increase the cross-linking and reduce aging effects, we flood illuminated the structure with 365 nm light (Dr. Hönle AG, LED Pen 2.0) while still being submerged in IPA33^,34 [Fig. 3(d)].

The substrate is immersed in water to dissolve the PVA, resulting in the lift-off of the 3D-nanoprinted structure from the substrate [Fig. 3(e)]. Although still immersed in water, the actuator is placed onto the lower electromagnetic coil [Fig. 3(f)]. The coil holders are fabricated out of fused silica using selective laser-induced etching (SLE) using a commercial laser microscanner (LightFab GmbH). We used enameled copper wire (1570225, TRU Components, Conrad Electronics SE, Germany) and a custom winding machine to create the coil using orthocyclic winding. Water is exchanged with IPA to reduce capillary forces during the evaporation of the solvent [Fig. 3(g)].

Following the lift-off, we removed the safety pins constraining the springs by femtosecond laser multiphoton ablation35 using the same commercial laser microscanner (LightFab GmbH) equipped with a 20×/0.45NA objective (DIC N1 OFN22, Nikon Inc.) at a power of 100 mW and a scan speed of 80μms−1. Figure 4 provides a close-up view of the springs before and after pin removal. The micromagnet is placed in the actuator and secured using UV-curable adhesive (Panacol Vitralit^® UC 1618) [Fig. 3(h)]. Subsequently, the second coil is placed on the actuator and secured using the same glue [Fig. 3(i)]. Passive alignment structures ensure alignment (±20μm) of the two coils relative to each other.

For mechanical characterization, the coils were driven by a custom printed circuit board, implementing a bidirectional voltage-controlled current source (Howland current source). The drive signal was generated using an arbitrary function generator (Tektronix GmbH, AFG1022), and the displacement was measured using a single-point laser Doppler vibrometer (Polytec GmbH, VGo-200).

To evaluate the frequency response of the actuator, the input signal was swept from 10 to 700 Hz over a period of 10 s. This measurement was repeated for different drive currents. Figure 5 shows the complete frequency response for a drive current of 2 mA and the first resonant peak for four different drive currents. The resonant frequency of the first mode is 347.3 Hz, which is 14% higher than the design value. The device gain (i.e., displacement per unit drive current) is 0.91μmmA−1, which is 24% smaller than the simulated result of 1.19μmmA−1.

Both these results point to the spring constant of the device being larger than the design specifications, which is most likely due to the strong dependence of the Young’s modulus on the curing parameters.36^,37 The quality factor is 17. For increasing drive currents, the resonant peak shifts toward lower frequencies, e.g., from 347.3 Hz for 2 mA to 343.8 Hz at 10.8 mA, indicating spring softening. At 10.8 mA, the measured peak-to-peak displacement at the first mode was 172μm.

To evaluate the characteristics of quasi-static displacement, the actuator was driven using a triangular signal at 1 Hz with three different peak currents. At a peak current of 88.6 mA, a peak-to-peak displacement of 209.2μm was observed. The device’s response to the triangular wave has significant hysteresis, as shown in Fig. 6(a). To quantify the hysteresis and investigate its origin, the drive frequency was varied between 250 mHz and 20 Hz for a peak current of 48.3 mA. Two sample datasets are presented in Fig. 6(c). Figure 6(b) illustrates the hysteresis as a function of drive frequency, with a decrease toward higher frequencies. For instance, at 250 mHz, the hysteresis is 10.5μm, whereas at 20 Hz, it decreases to 2.9μm. With 1.11μmμA−1 at 250 mHz and 0.89μmmA−1 at 20 Hz, the gain follows a comparable trend, as shown in Fig. 6(d).

The hysteresis behavior and its evolution with excitation frequency can be explained by the viscoelastic material properties of the IP-S photoresin. At low drive frequencies, such as 250 mHz, the period of the drive signal is comparable to the viscoelastic time constant of the material, allowing both elastic and viscoelastic effects to contribute to the observed displacement. At higher frequencies, such as 20 Hz, the period falls well below the viscoelastic time constant,16 resulting in reduced viscoelastic contributions and thus reduced hysteresis and gain, which approaches the value derived from the frequency response (0.89 versus 0.91μmmA−1).

The response time of the device was quantified by measuring the step response at different drive currents. Figure 7(a) depicts the device’s response to a rectangular signal with bidirectional actuation for different currents. The average rise time τr from 10% to 90% is 0.51ms±0.02ms. Following the initial step, a brief period of ringing is observed as shown in more detail in Fig. 7(b), because the device works in the under-damped regime. The viscoelasticity is manifested as the creep that follows the ringing of the actuator.

To quantify the viscoelastic material properties, we fitted a general Kelvin–Voigt model (GKV) of second order38 to the step responses measured at three different current values, shown in Figs. 7(c)–7(e). In the GKV model, which is represented in Fig. 8, the displacement s as a function of time t can be described as s(t)=F[CE0I+CE1I(1−e−tτ1)+CE2I(1−e−tτ2)],(8)where F is the force, I is the second moment of area, C is the geometry-dependent constant determined in the simulation, E is the Young’s modulus, and τ is the time constant. The results are summarized in Fig. 8. Although the time constants are consistent with values reported in the literature, the Young’s moduli are higher.16 These deviations are expected, as the material properties depend on the printing parameters,36^,37 as discussed in Sec. 4.

Another important effect that strongly influences the Young’s modulus of polymers is temperature. Rohbeck et al.39 demonstrated the temperature dependence of the Young’s modulus for IP-Dip, a photoresin similar to IP-S. Because electromagnetic actuation is relatively power-hungry compared with methods like electrostatic or piezoelectric actuation, operating the device over extended periods would potentially lead to self-heating, and thus changing device behavior, as the decrease in Young’s modulus as temperature increases leads to a reduced spring constant and thus an increased gain. To evaluate the long-term stability of the device, we applied a 1-Hz sinusoidal drive signal at different peak currents for ∼1000 cycles each. Figure 9(a) depicts the displacement as a function of time for the first 10 cycles, whereas Fig. 9(b) shows the measured peak-to-peak displacement over the full number of cycles. To emphasize the long-term stability, we carried out 30,000 actuation cycles using a 10-Hz sinusoidal drive signal (see Fig. S6 in the Supplementary Material). The results indicate that the displacement remains stable over time. However, it is apparent that the displacement increases during the first few hundred cycles before stabilizing at a constant value.

Figure 9(c) illustrates the thermal drift, defined as the additional peak-to-peak displacement relative to the initial value, along with the coil temperature over time, which was measured using thermal imaging (ETS320, Teledyne FLIR LLC). The time constant for the drift of 52 s closely matches the time constant of the coil temperature of 59 s. There is a strong linear correlation between drift and coil temperature (R2=0.99), as depicted in Fig. 9(d). Similar analyses for increased drive currents show comparable results (see Fig. S5 in the Supplementary Material). The slopes of these curves can be used to extract the temperature coefficient α, which gives the temperature-dependent spring constant k(T) as k(T)=k0[1−α(T−T0)]. For the three currents used in the experiments (i.e., 45.1, 67.3, and 88.6 mA), α is calculated as 0.016, 0.016, and 0.021K−1. It should be noted that although the effects described above are caused by self-heating, ambient temperature leads to similar effects.

To characterize the lens tilt during actuation, the displacement of the magnet was measured at four radial positions on the magnet. As the micromagnet has an inner diameter of 1.4 mm and an outer diameter of 2 mm, we measured the displacement of 0.85 mm to the left, right, top, and bottom of the lens center. Using trigonometry, we can calculate the tilt along the two main axes and the axis of the largest tilt. Using a 1-Hz sinusoidal drive signal at peak current of 88.6 mA (i.e., ±100μm displacement), we measured a tilt of ±0.23deg in the horizontal axis and ±0.13deg in the vertical axis. Along the axis of the largest tilt, the tilt was ±0.26deg.

To examine the characteristics of the monolithically integrated lens, we first measured its shape, followed by an optical characterization.

The lens shape was measured using a 3D optical profiler (ZYGO NewView™ 9000) both before shape optimization (i.e., the uncompensated lens) and after shape optimization (i.e., the compensated lens). We measured the root-mean-square (RMS) roughness within a square region of 25μm×25μm, applying a Gaussian high-pass filter with a cutoff period of 25μm (EN ISO 25178:2012). Standard Zernike polynomials were fitted to both the measured and ideal surfaces to quantify the shape deviation.13

The results of the shape analysis, presented in Fig. 10, include the complete measured surface with a root mean square (RMS) roughness of 37 nm, as well as cross-sections in the x- and y-directions. The deformation of the lens upon release from the substrate is attributed to residual stress caused by polymer shrinkage during the printing process. Consequently, the deformation of the first (flat) surface is transferred to the second (aspherical) surface. Because the overall thickness profile determines the optical characteristics of the lens, the deviations in the first and second surfaces are combined. Comparing the combined shape deviation to that of the uncompensated lens reveals a significant improvement in shape accuracy. For instance, defocus decreased from 3.30 to −0.55μm, and spherical aberrations were reduced from 0.47 to 0.25μm. The total RMS shape deviation decreased by 80% from 4.65 to 0.94μm.

To evaluate the optical performance, the actuator was illuminated with a collimated 850-nm pigtailed laser (LDM-850-V-0.2, Bitline System Pty Ltd). The focal plane was imaged using a 0.55 NA objective lens (Plan Apo 50×, 378-805-3, Mitutoyo AC) in combination with an infinity-corrected tube lens (TTL200-A, Thorlabs, Inc.) and captured with a CCD camera (UI-1240SE-NIR, IDS GmbH).

The plane of best focus is located at 3.29 mm, which is close to the designed value of 3.42 mm. Figure 11 shows cross sections of the focal spot, focus images of the measurement and the simulation based on the measured lens shape, as well as still images of the focal plane while the actuator translates the lens along the optical axis. The spot size (FWHM) is 2.65μm in the x-direction and 2.54μm in the y-direction. The expected spot size for the designed lens is 2.40μm. The deviation between the measured and ideal spot size is associated with the shape deviation of the lens, which is in essence a combination of astigmatism, coma, and spherical aberrations. This shape deviation is also the cause of the aberrations, as shown in Fig. 11(c). The mismatch between the ideal and measured back focal length is related to the deviation of the defocus. The modulation transfer function of the lens is shown in Fig. S7 in the Supplementary Material.

The fabricated and characterized actuator achieves a displacement of ±100μm, aligning well with the design specifications. However, both the resonant frequency and gain deviate from the design, with an increase in the resonant frequency and a decrease in gain. This discrepancy is likely attributed to a higher-than-expected spring stiffness, which may arise from geometric mismatches in the spring profile or deviations in the Young’s modulus from the assumed value during design and simulation. Notably, the Young’s modulus of two-photon polymerized materials depends on printing parameters such as laser power, writing speed, hatching distance, and slicing distance.36^,37 A significant portion of the springs was manufactured with overlapping volumes for stitching, resulting in high cross-linking levels. This increased cross-linking correlates with an elevated Young’s modulus.36^,40 For instance, Pagliano et al.40 observed a need to adjust the Young’s modulus from 5.1 to 6.5 GPa to align simulation results with measured resonant frequencies. Nano-indentation tests on the fabricated springs could provide valuable insights into this aspect. Regarding spring thickness, single-point measurements revealed minor deviations (44.5 versus 44.0μm and 33.7 versus 34.0μm). Incorporating these deviations into the simulations increased the resonant frequency from 303 to 309 Hz. However, these measurements do not account for potential variations in thickness along the spring length. Characterization of the device’s quasi-static actuation and step response revealed hysteresis and mechanical creep, likely due to the viscoelastic properties of the material. Advances in material optimization could mitigate these issues, reducing hysteresis and improving mechanical performance.

Aging is an additional effect that distinguishes the polymer used from materials such as silicon. The frequency response measurement was repeated after ∼140 days of storage in a dark laboratory environment. In this measurement, we observed a shift in the resonant frequency of the first mode from 347.3 to 359.3 Hz. Possible reasons for this shift include changes in the ambient conditions, such as temperature or humidity,33^,41 or aging effects, although the actuator was flood illuminated with UV during fabrication to increase the cross-linking and reduce aging.33^,34 Further investigation is required to quantify the effect and identify the dominant cause. A change in optical performance over time is not to be expected, as a detailed characterization by Schmid et al.33 showed that aging only affects the refractive index of the polymer within the first days. No significant change was observed after longer periods of time.

The optical performance of the printed lens closely matches the design, with residual shape deviations causing slight discrepancies in spot size and focal length. Further iterations of shape compensation could refine the optical accuracy,6 bringing measurements and design into closer alignment.

To print the complete actuator within a reasonable timeframe and without mechanical support attached to the substrate, several strategies were used. First, different parts of the actuator were printed with different printing parameters to reduce the 3D nano-printing time without any drawbacks. Second, the springs were printed in the form of several small parallelepipeds, so that no mechanical support attached to the substrate was necessary. However, as previously discussed, this can lead to variations in cross-linking levels, which makes the precise control of the Young’s modulus more challenging. Lastly, safety pins constrained the springs to prevent them from being damaged by capillary forces during development. Although removing these pins after development added an extra fabrication step, this step had no drawbacks in terms of mechanical properties and did not affect the inherent alignment of the actuator.

When compared to conventionally manufactured lens actuators, which achieve scanning ranges of up to 480μm with electrostatic actuation,42418μm with electromagnetic actuation,43400μm with thermal actuation,21 and 430μm with piezoelectric actuation,44 the performance of 3D nano-printed actuators is comparable. A significant advantage of 3D nano-printing lies in its ability to monolithically integrate the lens during fabrication. In contrast, conventional actuators typically require post-fabrication integration of the lens through methods such as polymer droplet curing,22^,23 glass reflow,24 or pick-and-place assembly.21 These approaches either constrain design freedom for the optical element or introduce aberrations due to placement tolerances.

To increase the maximum displacement of the actuator, several factors must be considered. In the design presented in this paper, a compromise is made between the maximum power consumption, and thus the operating temperature, and the resonance frequency. A larger displacement can be achieved both by increasing the current through the coil or by lowering the resonance frequency. However, as the current increases, the power consumption increases and the temperature approaches the polymer’s glass transition temperature of 46°C,28 which significantly alters the mechanical properties of the springs. With the second approach, i.e., a reduction in the resonance frequency, a greater displacement can be achieved for the same power consumption. However, the actuator becomes more sensitive to environmental vibrations.

In conclusion, we discussed a MEMS scanner with a monolithically integrated optical lens, fabricated via two-photon polymerization. The design ensures mechanical stability with a resonant frequency larger than 300 Hz while maintaining a low peak power consumption of 81 mW. The combination of an inherently aligned lens with near diffraction-limited performance, mechanical robustness, and low power consumption is expected to enable the integration of optomechanical devices fabricated by two-photon polymerization into practical applications. To improve the precision of the system, the integration of a magnetic position sensing mechanism could enable real-time position determination for closed-loop control. This approach, using a three-dimensional Hall sensor, enables accurate position tracking by mapping the magnetic field vector to the spatial position of the actuator through a one-time calibration process.12 Such a feedback system could mitigate aging, hysteresis, and self-heating effects. In addition, the MEMS scanner could dynamically adapt to operational changes, such as fluctuations in ambient temperature, improving its performance in applications that require high precision and reliability.

Acknowledgment. This work is part of BrainLinks-BrainTools which is funded by the Federal Ministry of Economics, Science and Arts of Baden-Württemberg within the sustainability program for projects of the excellence initiative II. The European Union’s Horizon 2020 research and innovation program provided funding for Aybuke Calikoglu’s involvement in this study. We thank Yanis Tage for the introduction to iterative shape compensation and for providing the beam profiler. ChatGPT (OpenAI) was used for language and grammar clean-up in the preparation of this paper.

Florian Lux received his bachelor’s and master’s degrees in microsystem engineering with a focus on photonics and biomedical engineering from University of Freiburg, Germany, in 2020 and 2022, respectively. He is currently part of the Microsystems for Biomedical Imaging Group where his research focuses on microscopes.

Aybuke Calikoglu received her bachelor’s degree in electrical and electronics engineering from Bogaziçi University, Turkey, in 2016, followed by her master’s degree in the same field in 2019. She is currently pursuing her doctorate degree in the Laboratory for Micro-Optics at the University of Freiburg. Her research focuses on utilizing 3D nanoprinting techniques to fabricate optics and novel optical-MEMS devices.

Çağlar Ataman received his PhD in electrical engineering from Koç University, Turkey, in 2008, and worked as a postdoctoral researcher at the École Polytechnique Fédérale de Lausanne, Switzerland, between 2008 and 2012. From 2012 to 2021, he was a senior scientist in the Department of Microsystems Engineering at the University of Freiburg, where he has been an assistant professor since 2021, leading the Microsystems for Biomedical Imaging Group.