  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 $\lambda/10^{7}$.
