Development of a planar cable-driven parallel robot for submillimeter and terahertz beam mapping measurements

TL;DR

This work presents a lightweight planar cable-driven parallel robot (CDPR) to automate submillimeter beam mapping for the TIME instrument, addressing the challenge of validating complex millimeter-wave optics in field-like conditions. By combining a four-cable planar mechanism, a minimal-end-effector payload of infrared emitters, inverse-kinematics-based control, and non-contact OpenCV-based pose tracking, the system achieves $xy$-plane RMSE of $2.7\ \mathrm{mm}$ and in-workspace repeatability better than a millimeter, with maximum deviations in $xy$ and $z$ within a few millimeters. Beam-map predictions using Zemax physical optics inform accuracy requirements, while real-world deployment demonstrated rapid mirror mapping (about 26 minutes per mirror) on a 20×20 grid, enabling efficient comparison with simulations and diagnostic insights. The mapper’s low cost, modularity, and open-source software make it readily reusable for beam- mapping tasks in other terahertz and submillimeter optical systems.

Abstract

The spatial sensitivity pattern of millimeter-wavelength receivers is an important diagnostic of performance and is affected by the alignment of coupling optics. Characterization can be challenging in the field, particularly in the decentered and tightly packed optical configurations that are employed for many astronomical millimeter-wave cameras. In this paper, we present the design and performance of a lightweight and reconfigurable beam mapper, consisting of a bank of thermal sources positioned by a planar cable-driven robot. We describe how the measurement requirements and mechanical constraints of the Tomographic Ionized-carbon Mapping Experiment (TIME) optical relay drive the design of the mapper. To quantify the positioning performance, we predict the beam patterns at each surface to derive requirements and use a non-contact computer-vision based method built on OpenCV to track the payload position with an accuracy better than 1.0 mm. We achieve an in-plane absolute payload position error of 2.7 mm (RMSE) over a $\sim$400 mm $\times$ 400 mm workspace and an in-plane repeatability of 0.81 mm, offering substantial improvements in accuracy and speed over traditional handheld techniques.

Figures (19)

• Figure 1: The TIME optical relay system for the Kitt Peak 12 m radio telescope. Light from the Cassegrain telescope enters from the top. It passes through a field derotator (K-mirror) comprising mirrors K1-3, before encountering the flat fold mirror F1, and two powered mirrors P1 and P2 near the cabin floor. The latter directs light upward to the cryostat window. (a) A Zemax OpticStudio ray trace of several feeds with the K-mirror displaced by 45$^{\circ}$ from the straight-ahead home position. (b) A mechanical rendering showing the notional path (red) of a beam through the optics, with the K-mirror rotated the opposite direction. Mirrors are highlighted in yellow. (c) The as-built optical system, installed in the ARO 12 m receiver cabin on Kitt Peak.
• Figure 2: (a) The mirror mapper, clamped on a 600 mm wide optical breadboard with holes located on a 1-inch (25.4 mm) grid pattern. At the top and bottom, aluminum extrusions provide mounting points for four stepper motors with encoders. Cable for each axis is wound onto helical drums directly driven by the stepper motors. Eyelets that control cable routing are integrated with the motor mounts. The end effector, a PCB raft of modulated infrared emitters, is suspended by the fine cables in the center of the workspace. The black and red wires hanging to the right are power and control wires for the infrared emitters. The blue, yellow, black and red twisted wires are the RS-485 bus carrying commands from the control computer to the motor driver boards. (b) A labeled schematic diagram of the system in (a). (c) A close-up view of the helical drum and motor mount with integrated cable eyelet.
• Figure 3: The end effector, consisting of 13 Hawkeye Technologies IR-50 pulsable emitters. The emitters are arranged in three groups: 1 center, 6 inner, and 6 outer. Each group is powered by 6.7 VDC from the blue screw terminal, and modulated by MOSFETs on the back of the board that are controlled via a Serial Peripherial Interface to the Texas Instruments SN74HC595 shift register.
• Figure 4: A schematic depiction of the mapper geometry. The mapper coordinate origin is in the lower left, corresponding to the intersection of the aluminum bar stock and side alignment tab. Motor mount eyelet locations are marked $m$, and are measured with calipers. Raft eyelet locations are marked $p$, and vary as a function of the mapper payload centroid, $c$, and the raft eyelet width $w$ and height $h$, which are measured with calipers. The crux of the control problem is to solve for the axis lengths $l$ of a given raft position, then translate the desired length into an angular shaft position.
• Figure 5: Schematic depiction of how systematic out-of-plane positioning errors may affect a beam mapping measurement. (a) Error in the position of the measured plane samples a converging or diverging Gaussian beam at a different beam size (beamwidth error). (b) For oblique angles of incidence, error in the position of the measured plane presents a position offset in the plane or the mirror being mapped (parallax error).