Measuring picometre-level displacements using speckle patterns produced by an integrating sphere

TL;DR

This paper introduces a highly sensitive method for measuring picometre-level displacements using speckle patterns generated inside an integrating sphere, achieving unprecedented precision suitable for nanoscale applications.

Contribution

The authors demonstrate a novel speckle-based displacement sensing technique utilizing an integrating sphere, achieving sub-50 picometre accuracy with potential for further improvement.

Findings

Displacement can be measured with as little as 40 pm uncertainty.

The method can potentially reach tens of femtometres in precision.

Speckle pattern analysis enables high-sensitivity displacement detection.

Abstract

As the fields of optical microscopy, semiconductor technology and fundamental science increasingly aim for precision at or below the nanoscale, there is a burgeoning demand for sub-nanometric displacement and position sensing. We show that the speckle patterns produced by multiple reflections of light inside an integrating sphere provide an exceptionally sensitive probe of displacement. We use an integrating sphere split into two equal and independent hemispheres, one of which is free to move in any given direction. The relative motion of the two hemispheres produces a change in the speckle pattern from which we can analytically infer the amplitude of the displacement. The method allows displacement measurement with uncertainty as small as 40 pm ($\lambda/20,000$) in a facile implementation. We show how, under realistic experimental parameters, the uncertainty in displacement could be improved to tens of femtometres, or $\lambda/10^{7}$.