by Bernd Rieger and Sjoerd Stallinga (Delft University of Technology)
Standard fluorescent light microscopy is rapidly approaching resolutions of a few nanometers when computationally combining information from hundreds of identical structures. We have developed algorithms to combine this information taking into account the specifics of fluorescent imaging.
For a hundred years a key rule in microscopic imaging was that the resolution in a microscope is determined by the diffraction limit, which states that the smallest detail separable is given by the wavelength of the light divided by twice the numerical aperture, where the latter is a measure for how much light is captured by the objective lens from the sample. For typical values of visible light, which has a wavelength ~500 nm and high quality immersion objectives, this results in diffraction limits of ~ 200 nm.
With the advent of localisation based super-resolution microscopy around 10 years ago, resolutions in the order of tens of nanometres have been increasingly reported in the literature. As a consequence, in 2014 this particularly successful imaging modality was awarded a Nobel Prize in Chemistry. The basic idea is to localise single isolated fluorescent emitters [1, L1]. This can be realised by photo-chemically altering the properties of the dyes such that most of the time only a very small fraction of all molecules emit light. Many cycles of recording and switching will result in imaging most of the emitters present in the sample. Due to the prior knowledge that only a single emitter is seen, one can fit a model of the system’s response function (point spread function) to the data taking into account the different noise sources in a maximum likelihood model and localise the centre with an uncertainty that scales inversely with the square root of the number of detected photons. Typical values result in uncertainties in the tens of nanometres.
However, the overall resolution in an image is a combination of the localisation accuracy and the labelling density of the structure with fluorescent emitters [references in 1]. This problem can be mitigated if instances of the same biological structure are fused (combined) properly. This technique is similar to single particle analysis that has been applied in the field of cryo-electron microscopy for many years . Typically, these particles have arbitrary pose, are degraded by low photon count, false localisations and missing fluorescent labels.
Figure 1: Data fusion image from 456 individual super-resolution reconstruction of a TU Delft logo. The logo is constructed with DNA-Origami and images by PAINT imaging. The final image combines about one million localisations resulting in a computed resolution  of 4.0 nm. That is wavelength/140 resolution with the hardware of a conventional light microscope.
If the structure to be imaged is known a priori, one approach is to register all particles on a template. However, this introduces ‘template bias’, which can occur if too strong prior knowledge is imposed on the data . We are addressing this problem via a template-free data fusion method. Ideally one would be able to use an all-to-all registration and then globally optimise the translation and rotation parameters. However, this results in a computational complexity scaling with N2 where N is the number of particles. Many hundreds of particles are needed to improve the effective labelling density and in turn the resolution. Therefore we currently register pairs of particles in a tree structure from leaves to root. This reduces the computational effort to a practically feasible task without the need for super-computers, i.e., it enables the researcher to perform a full registration on the same time scale as the acquisition (order of 10-240 minutes). For the pair registration, we develop an algorithm, which takes into account the localisation accuracies and can handle missing labels . This is essential as algorithms from electron microscopy work on images rather than on point clouds with associated uncertainties. In Figure 1 we show the result of such a procedure on samples that represent logos of the TU Delft shaped by DNA-origami and imaged with DNA-PAINT . While the initial particles have computed resolution values  in the range of 10-30 nm, the final reconstructed particle has 4.0 nm resolution. This is about the best that can be expected, as the distance between the binding sites on the DNA blueprint are 5 nm.
This technique will no doubt have further applications in biology since it is common for many chemically identical copies of a structure to be present within one cell, making imaging an easy task.
This work is partly financially supported by European Research Council grant no. 648580 and National Institute of Health grant no. 1U01EB021238-01.
[L1] 350 years of light microscopy in Delft:
 B. Rieger, R.P.J. Nieuwenhuizen, S. Stallinga: “Image processing and analysis for single molecule localization microscopy”, IEEE Signal Processing Magazine, Special Issue on Quantitative Bioimaging: Signal Processing in Light Microscopy, 32:49-57, 2015.
 A. Löschberger, et al.: “Super-resolution imaging reveals eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution”, Journal of Cell Science, 125:570-575, 2012.
 R. Jungmann, et al.: “Multiplexed 3D cellular super-resolution imaging with DNA-PAINT and exchange-PAINT”, Nature Methods, 2014.
Bernd Rieger, Delft University of Technology, The Netherlands