Performance Testing of a Trillium-based 21-Positioner Module for Stage-5 Telescopes

Technical Summary: Performance Testing of a Trillium-based 21-Positioner Module for Stage-5 Telescopes

Problem Statement
Next-generation astronomical surveys, such as the Chinese MUST, American Spec-S5, and European WST (Stage-5 telescopes), require highly multiplexed spectroscopic instruments capable of placing thousands of robotic fiber positioners on a focal plane with millimeter-scale pitches. These systems demand extreme precision to simultaneously acquire spectra from faint, high-redshift galaxy populations while avoiding mechanical interference between overlapping patrol regions. This paper addresses the need to evaluate the performance metrics of a specific modular prototype: a 21-positioner unit based on the Trillium open design (originally developed by Lawrence Berkeley National Laboratory) and manufactured by Orbray Co., Ltd. The goal is to determine if this 6.2-mm-pitch architecture meets the rigorous reliability and accuracy requirements for Stage-5 instrumentation.

Methodology
The study employed a comprehensive testing protocol adapted from previous iterations of these prototypes, utilizing a custom test bench equipped with high-resolution cameras (Basler acA3800) and Gaussian fitting algorithms to track fiber tip centroids.

• XY Positioning Tests: To measure repeatability, datum repeatability, backlash, and non-linearity, the authors addressed the challenge of testing 21 coupled positioners without collision. They formulated the workspace geometry as a graph coloring problem, grouping the 21 positioners into four non-interfering sets (Red, Green, Blue, Purple) based on adjacency constraints. This allowed for near-parallelized testing where positioners in the same group could be actuated simultaneously.
• Angular Tilt Tests: Tilt was characterized by mounting optical fibers on precision cylinders and rotating the alpha and beta arms. A bi-convex lens and diffuser screen setup isolated tilt-induced displacement from XY translation. Centroids were tracked as arms rotated to fit circles, from which tilt angles and radii were derived.
• Physical Verification: To validate optical measurements, additional beta arm samples were physically measured using a Hauser P320 microscope to assess manufacturing tolerances regarding arm length and ferrule hole diameters.

Key Results
The evaluation covered 19 functional positioners (two units, 33 and 43, were excluded due to mechanical failures during testing).

• Repeatability: The beta arm demonstrated strong performance, with an average combined repeatability of 2.41 µm RMS, well within the ≤6 µm target. However, the alpha arm showed significant variance; while the average was 18.23 µm RMS, five units exhibited exceptionally high errors (up to 77.87 µm). Excluding these outliers, the alpha arm average dropped to 5.65 µm, meeting the target.
• Datum Repeatability: The beta arm met the ≤50 µm RMS requirement across all units. The alpha arm generally met the target, though anomalies were noted, including a hardstop malfunction in Positioner 33 that caused physical damage.
• Backlash: Alpha arm backlash was generally acceptable (average 3.30°), with only Positioner 23 exceeding the ≤5° limit. Conversely, the beta arm exhibited significantly higher backlash (average 11.32°), with all units exceeding the 5° threshold. The authors suggest this may be calibrated via software rather than requiring hardware changes.
• Angular Tilt: This metric proved the most challenging. The desired threshold was ≤0.4°. Only 3 of the 19 tested units achieved this. The average Root Sum Square (RSS) tilt was 0.46°, with over one-third of the units exceeding the threshold by at least 0.1°.
• Motion Range and Arm Length: Most positioners approached but did not fully achieve the desired motion ranges (370° for alpha, 190° for beta). Measured arm lengths deviated from the expected 1.8 mm, a discrepancy the authors attribute more to non-smooth mechanical motion than to manufacturing errors in the arm length itself.

Significance and Claims
The paper claims that the Trillium-based Orbray prototype demonstrates "promising performance" suitable for Stage-5 telescope instrumentation, provided specific mechanical and software issues are resolved. The study successfully identifies that while the beta arm design is robust, the alpha arm requires refinement in actuation and hardstop reliability.

The authors emphasize that the observed high backlash in the beta arm and the angular tilt issues likely stem from mechanical flexibility and design constraints inherent to the coupled gear system. They propose that future iterations should focus on:

1. Mechanical Reinforcement: Increasing the stiffness of the positioner structure to reduce tilt.
2. Software Compensation: Implementing calibration for non-linearities and backlash, particularly for the beta arm.
3. Design Modifications: Addressing the alpha arm actuation anomalies and hardstop failures.

The paper concludes that while the prototype is not yet fully compliant with all Stage-5 metrics, the characterization provides a clear roadmap for optimization. The results indicate that with the successful mitigation of the identified anomalies, the design holds potential for high-density fiber positioning in next-generation astronomical systems.