Achieving 5 Picometer Resolution: The Rasnik Alignment System

When we set out to develop the Rasnik 3-point alignment system, the goal was audacious: achieve spatial resolution at the picometer scale. For context, a picometer is one trillionth of a meter—roughly the diameter of a hydrogen atom.

The Challenge

Next-generation physics experiments demand unprecedented precision. Whether for:

• The LISA space mission detecting gravitational waves from supermassive black hole mergers
• The VATIGrav experimental setup testing fundamental physics
• The Cool Copper Collider requiring alignment of 2000 accelerator modules over 2.3 km

Traditional alignment methods simply couldn't meet these requirements.

The Rasnik Principle

The Rasnik system uses an elegant optical approach. Light from a point-like monochromatic source passes through a zone lens, creating a Fraunhofer diffraction pattern on an image sensor. By analyzing this pattern, we can determine the three-dimensional position of objects with extraordinary precision.

The beauty of this method is its simplicity and robustness. No complex electronics at the measurement point—just optics and geometry.

Algorithm Development

Developing the control algorithms was the intellectual heart of this project. We needed to:

1. Real-time processing: Analyze diffraction patterns at high frequency
2. Error correction: Account for environmental factors like temperature variations
3. Multi-point coordination: Align thousands of reference points simultaneously

The mathematics involved Fourier analysis, statistical filtering, and iterative optimization—all running in real-time.

Applications

LISA Space Mission

For LISA, the requirements are extreme. Three spacecraft separated by millions of kilometers must maintain picometer-level knowledge of their relative positions. Our ground-based Rasnik system provides crucial validation of the optical metrology concepts.

Cool Copper Collider

The C³ accelerator represents perhaps the most demanding terrestrial application. Aligning 2000 modules within 10 µm transversally over 2.3 km requires a robust, scalable system. Rasnik provides the solution.

Lessons Learned

This project taught me invaluable lessons:

• Precision engineering is an art: Every component, every reflection, every thermal expansion matters
• Collaboration is essential: Working with teams at CERN, DESY, and universities worldwide
• Patience pays off: Achieving 5 pm/√Hz took years of incremental improvements

Future Prospects

The technology we've developed has applications far beyond our initial scope. Semiconductor manufacturing, quantum computing, and even biological imaging could benefit from this level of precision.

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This work is published in arXiv:2510.03539 and presented at LCWS 2024