Closed-loop control of a monolithically 3D nano-printed electromagnetic lens scanner with an integrated Hall sensor

Abstract

3D nano-printing through two-photon polymerization enables monolithic manufacturing of mechanical and freeform micro-optical elements with high inherent alignment accuracy. However, viscoelasticity and temperature-dependent stiffness of the photopolymer lead to hysteresis and drift, which significantly degrade open-loop position accuracy and long-term stability in quasi-static operation. Therefore, closed-loop control with integrated displacement sensing is essential for 3D nano-printed optical microsystems in practical precision positioning applications. Here, we present a closed-loop control system for a such a lens actuator that uses a commercial 3-axis Hall sensor for position tracking. A NdFeB micromagnet encircling the integrated microlens provides both the actuation force and a position-dependent sensing signal. The Hall sensor, located between an anti-Helmholtz-like coil pair that drives the scanner bidirectionally, measures the combined field due to the micro-magnet and the coil pair. Calibration-based subtraction separates the coil field and sensor offset contributions to recover the magnet field and thus the axial magnet displacement. Closed-loop operation yields a mean absolute accuracy of 0.86 um and a precision of 0.49 um over a displacement range of 150 um while eliminating viscoelastic creep, suppressing hysteresis, and minimizing temperature-induced displacement drift under coil self-heating. This sensing approach requires no additional microfabrication steps and provides a practical path toward stable and repeatable positioning for monolithically 3D nano-printed optical microsystems.

Figures (8)

• Figure 1: Working principle and photographs of the microlens scanner.a Four ortho-planar linear-motion springs connect the shuttle, consisting of a magnet and an aspherical microlens, to the outer support structure. b To measure the displacement of the shuttle, the magnetic field created by the moving magnet is used. This field is measured using a Hall sensor sandwiched between the two coils. c Two coils in an anti-Helmholtz-like configuration create the magnetic field gradient required to displace the shuttle. The magnetic field of the micro-magnet becomes distorted ($I_\textit{coil}$ = 75mA). d Close-up photograph of the shuttle and the springs. e Fully assembled device, showing the Hall sensor mounted to a flex-PCB.
• Figure 2: Sensor calibration.a Magnetic field as a function of coil current while the shuttle is fixed (n=100). b Magnetic field as a function of displacement without correcting for the magnetic field of the coil (n> 100). c Magnetic field as a function of displacement with correcting for the magnetic field of the coil (n> 100). $B_y$ is used for sensing, as it shows the highest sensitivity and linearity. d The shuttle is mechanically blocked to isolate the coil contribution to the magnetic field from the contribution of the displaced magnet while calibrating the contribution of the coil to the magnetic field. e Characterization of the magnetic field contribution of the magnet as a function of displacement. Drawings not to scale.
• Figure 3: Accuracy and precision characterization data.a The actuator was displaced in steps of 5µm in positive and negative direction. b For each level, the accuracy and precision (errorbars) were calculated (n=2500). The accuracy shows a systematic trend with a mean absolute accuracy of 0.86µm. The mean precision (std) is: 0.49µm without showing a systematic trend.
• Figure 4: Open and closed-loop step response of the lens scanner.a In open-loop operation, viscoelastic creep is present. In closed-loop operation, this creep is eliminated by the control-loop. b Following the step input, an overshoot of 44.3% ± 2.8% and ringing at the damped natural frequency can be observed for open-loop operation. In closed-loop operation, no ringing can be observed. The overshoot is reduced to 18.8% ± 0.3%. c Mismatch between setpoint and displacement, showing the viscoelastic drift in open-loop operation.
• Figure 5: Hysteresis characterization of the actuator.a-c Displacement as function of normalized target displacement for setpoints of ±25µm, ±50µm, and ±75µm, showing hysteretic behavior due to combined elastic and viscoelastic contributions at an actuation frequency of 0.25mHz. The blue lines correspond to increasing displacement, orange lines to decreasing displacement d Hysteresis in open-loop operation as a function of peak-to-peak displacement (n=5). e-g Corresponding closed-loop measurements for the same setpoints, where forward and backward trajectories largely overlap, indicating effective hysteresis compensation. h Hysteresis in closed-loop operation as function of peak-to-peak displacement (n=5).