The Evolving History of Interferometric Methods in Precision Positioning

Since the earliest developments 150 years ago, advancements in light sources, optics, and data processing have solidified interferometry as an essential tool for measuring distances, displacement, and angle.¹

While it can be argued that growing demands for increasing precision have driven advances in interferometric positioning, this study follows the path to the current state of the art with a different focus: the presence of air in the beam paths and the innovations required to address refractive index changes as well as air turbulence.

Figure 1. Free-space precision stage motion measurement system. Image Credit: Zygo Corporation

Free-space, laser-based interferometers have advanced from simple Michelson geometry with fringe counting to sophisticated multi-axis instruments that reach sub-nanometer noise levels, enabling the monitoring of stage motions at several meters per second (see Figure 1).

These systems effectively comply with the Abbe principle, are directly traceable to the unit of length, and exhibit exceptional performance when placed in a vacuum.² However, among applications where the measurement beams travel through the atmosphere, variations in refractive index and turbulence become significant sources of uncertainty.

In the 1990s, considerable effort was focused on dispersion interferometry to address problems with air turbulence. In this method, the variation in the air's refractive index is employed to directly measure air density along the line of sight, utilizing laser-based interferometry that operates at two wavelengths simultaneously.

Experiments using a doubled He-Ne laser have shown that turbulence-induced errors can be reduced from 8 nm to 1 nm.² However, the demands of advanced lithography now exceed this performance level, requiring an alternative approach.

Figure 2. Large 2D grating for encoder-based stage motion control. Image Credit: Zygo Corporation

An alternative to line-of-sight interferometers is the use of encoders in conjunction with diffraction gratings to monitor both in-plane and out-of-plane motions of stages (Figure 2).

Encoders offer a key advantage over free-space systems: significantly shorter beam paths through air, which is essential for modern high-end semiconductor photolithography machines.

By adapting multi-axis encoder technology to meet photolithography’s performance demands, this approach integrates the high-speed electronics and low-noise characteristics of heterodyne free-space interferometry into new geometries.³

Figure 3. Passive sensor for multi-axis, fiber-based position measurement. Image Credit: Zygo Corporation

A third approach involves multi-axis precision positioning for short-range measurements utilizing multiplexed fiber optic interferometry (refer to Figure 3).

An example system features up to 64 passive sensors operating from a shared multi-wavelength source and detection system.⁴ It achieves a noise performance of 0.02 nm Hz^−1/2 over a measurement range of 3.5 mm ± 0.6 mm.

This level of precision pushes the boundaries of what is possible in the presence of air. To address this challenge, one or more measurement channels are dedicated to determining the local atmospheric refractive index using stable etalons of traceable, fixed length.

In this instance, the solution is to assign one or more measurement channels to the determination of the refractive index of the local atmosphere using stable etalons of traceable, fixed length.

Video Credit: Zygo Corporation

References

1. Peter and Badami, V.G. (2013). Revelations in the Art of Fringe Counting: The State of the Art in Distance Measuring Interferometry. Springer eBooks, pp.785–790. https://doi.org/10.1007/978-3-642-36359-7_143.
2. V. Badami and P. de Groot, "Displacement Measuring Interferometry," in Handbook of Optical Dimensional Metrology, edited by K. G. Harding, chapt.4, pp. 157-238, (Taylor & Francis, Boca Raton, 2013).
3. Badami, V.G., Liesener, J. and DE, P.J. (2019). Encoders graduating to extreme precision. [online] 59(2), p.26. Available at: https://www.researchgate.net/publication/332350171_Encoders_graduating_to_extreme_precision.
4. V. Badami and E. Abruña, "Absolutely: small sensor, big performance," Mikroniek (1), 5-9 (2018).

This information has been sourced, reviewed and adapted from materials provided by Zygo Corporation.

For more information on this source, please visit Zygo Corporation.