Rasnik 3-point alignment system: algorithm, control framework, and its applications

TL;DR

Rasnik delivers drift-free, absolute-position sensing across four degrees of freedom using a coded ChessField mask and 2D FFT-based spectral analysis, enabling sub-nanometer precision over working distances from $50\ \mathrm{mm}$ to $15\ \mathrm{m}$. The RasCal software provides near real-time processing on commodity hardware, achieving up to $274.5\ \mathrm{Hz}$ during live capture (and $>300\ \mathrm{Hz}$ in maximum throughput) with a displacement sensitivity of about $5\ \mathrm{pm}/\sqrt{\mathrm{Hz}}$ in controlled conditions. The approach is demonstrated in Watt's linkage dynamics (RasWatt) and LISA Quadrant Photoreceiver testing, underscoring its applicability to gravitational-wave detectors and space instrumentation. However, velocity-dependent linearity errors and a fundamental periodic component from discrete Fourier peak estimation remain, though mitigable via small differential rotation and post-processing; future work will pursue higher-fidelity peak estimation and closed-loop integration. Overall, RasCal constitutes a robust, cost-effective precision metrology solution for demanding alignment tasks in physics experiments and space hardware qualification.

Abstract

Rasnik is a three-point optical displacement sensor originally developed for particle detector alignment in high-energy physics experiments, including the muon chambers of L3 at LEP and ATLAS at the LHC. The system has evolved from four-quadrant photodiodes to CMOS pixel sensors with custom ChessField coded masks, enabling absolute position measurement with no cumulative drift due to absolute value coded. Key advantages include electromagnetic immunity through purely optical measurement principles, working distances from 50 mm to 15 m, and multi-degree-of-freedom sensitivity perpendicular to the optical axis. RasCal, a comprehensive control and analysis software, is presented in this paper and its real-time image processing shows 5 pm/$\sqrt{\text{Hz}}$ spatial resolution. With GPU acceleration, 274.5 Hz is achieved during live camera acquisition and 109 Hz on CPU. In maximum-throughput configurations, the processing rates exceed 300 Hz on simple consumer hardware. System performance is demonstrated across diverse applications: 5 pm/$\sqrt{\text{Hz}}$ displacement sensitivity is achieved in the VATIGrav setup, dynamic behavior is characterized with a Watt's linkage. In addition, the lack of cumulative drift due to absolute coding with minimal thermal sensitivity under controlled conditions is used for vibration and thermal characterization of photodiode mounts for the LISA space mission. Millisecond-level command latency and thread-safe multi-camera support are provided by the RasCal software, establishing it as a robust and cost-effective precision measurement solution for demanding alignment applications in gravitational-wave detectors and space instrumentation.

Figures (17)

• Figure 1: Rasnik: an LED back-illuminates a coded mask and this object is projected onto a pixel sensor using a lens. If any of these three elements move in four degrees of freedom ($x$, $y$, $z$ and roll) the image shifts or rotates and this can be determined using image processing software. The roll (rotation around the $z$-axis) of the lens is not determined. The span of the systems have varied between 50mm and 15m. Adapted from ref. 3point.
• Figure 2: A Rasnik image from a coded mask. The ninth row and ninth column of each $9 \times 9$ block are encoded with 8-bit binary value which corresponds to the coarse position on the mask. 6th row and 7th column in this image counting from top left corner's white square as 1.
• Figure 3: Spectral analysis workflow for Rasnik position measurement. The process begins with image preprocessing (cropping, binning, windowing) followed by 2D FFT analysis to extract spatial frequencies. Peak fitting in the frequency domain determines pattern parameters (period, phase, rotation), which are combined with code square identification to calculate absolute position.
• Figure 4: Phase spectrum from the 2D FFT analysis of the ChessField pattern. The zero-shifted representation shows phase values color-coded at each spatial frequency, with peaks at positions $(2i-1)f_x, (2j-1)f_y$ for integers $i,j$. These phase values encode the spatial position of the pattern, enabling sub-pixel measurement precision.
• Figure 5: System resource utilization during Rasnik image processing. (a) CPU utilization showing 235% usage for CPU-only implementation (blue) versus 115% for GPU-accelerated implementation (red). (b) GPU utilization showing 25% usage for GPU implementation and zero for CPU-only. The vertical dotted line at 154 seconds marks GPU processing completion. Both implementations processed 43,000 images, achieving 9.2ms/image (CPU) and 3.6ms/image (GPU) respectively.