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

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 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 a noise floor of 5 pm/sqrt{hbox {Hz}} (lambda /160,000) above 30 Hz in a facile implementation, which we use to measure oscillations of 17 pm amplitude (lambda /50,000) with a signal to noise ratio of 3.