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.

随着光学显微镜、半导体技术和基础科学领域越来越追求纳米级或以下的精度，对亚纳米级位移和位置传感的需求不断增长。我们表明，积分球内光的多次反射产生的散斑图案提供了异常灵敏的位移探针。我们使用分成两个独立半球的积分球，其中一个半球可以在任何给定方向上自由移动。两个半球的相对运动产生散斑图案的变化，从中我们可以分析地推断出位移的幅度。该方法在简单的实现中允许 5 pm/ \(\sqrt{\hbox {Hz}}\) ( \(\lambda /160,000\) ) 的本底噪声高于 30 Hz，我们用它来测量 17 pm 的振荡幅度 ( \(\lambda /50,000\) )，信噪比为 3。