Nanometric depth resolution from multi-focal images in microscopy

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy

A conventional microscope produces a sharp image from just a single object-plane. This is often a limitation, notably in cell biology. We present a microscope attachment which records sharp images from several object-planes simultaneously. The key concept is to introduce a distorted diffraction grating into the optical system, establishing an order-dependent focussing power in order to generate several images, each arising from a different object-plane. We exploit this multiplane imaging not just for bio-imaging but also for nano-particle tracking, achieving approximately 10 nm z position resolution by parameterising the images with an image sharpness metric.