Inspired by recent developments in localization microscopy that applied averaging of identical particles in 2D for increasing the resolution even further, we discuss considerations for alignment (registration) methods for particles in general and for 3D in particular. We detail that traditional techniques for particle registration from cryo electron microscopy based on cross-correlation are not suitable, as the underlying image formation process is fundamentally different. We argue that only localizations, i.e. a set of coordinates with associated uncertainties, are recorded and not a continuous intensity distribution. We present a method that owes to this fact and that is inspired by the field of statistical pattern recognition. In particular we suggest to use an adapted version of the Bhattacharyya distance as a merit function for registration. We evaluate the method in simulations and demonstrate it on three-dimensional super-resolution data of Alexa 647 labelled to the Nup133 protein in the nuclear pore complex of Hela cells. From the simulations we find suggestions that for successful registration the localization uncertainty must be smaller than the distance between labeling sites on a particle. These suggestions are supported by theoretical considerations concerning the attainable resolution in localization microscopy and its scaling behavior as a function of labeling density and localization precision.

We propose a method for simultaneously measuring the position and emission color of single fluorescent emitters based on the use of a large pitch diffraction grating in the emission light path. The grating produces satellite spots adjacent to the main spot; the relative distance between the spots is a measure for the emission wavelength. We present proof-of-principle experiments on beads and mixtures of quantum dots using a spatial light modulator for making a programmable diffraction grating. A wavelength precision of around 10 nm can be achieved for 1000 signal photons and practical background levels, while maintaining a localization precision of around 10 nm. Super-resolution microscopy based on the localization of stochastically activated single fluorescent molecules is a powerful technique for studying biological structure on the nanoscale [1][2][3]. The study of biological function on this scale requires imaging two or more interacting molecular species. These species are usually differentiated by labeling with fluorescent molecules that have different emission colors. The different species can be imaged subsequently by changing illumination and filter sets [4] or simultaneously by using multibandpass filters and a dichroic beamsplitter in the emission path for imaging two color channels simultaneously [5,6]. The latter approach allows for multiplexing three and, in some cases, four different fluorescent species. An alternative is the use of activator-reporter labeling techniques in which different activator molecules can couple to the same reporter molecule, thereby allowing for subsequent imaging of the different channels by switching the illumination wavelength only [7]. Multicolor localization approaches are also applied in single particle tracking, broadening the scope to emitters such as quantum dots (QDs) [8].A different approach to color measurement is enabled by placing a blazed diffraction grating with a fine pitch in the emission path [9,10]. In this way two subimages, corresponding to the zeroth and first diffraction orders, are imaged side by side on two camera halves. The 0th order image gives the positions of the emitters; the 1st order image is smeared out in proportion to the emission spectral width over many pixels, thus enabling spectroscopic measurements. The resulting low signal-to-background ratio (SBR), however, compromises spectral and localization precision. Moreover, differentiation between species does not necessarily require measuring the full emission spectrum. Here, we propose a new method for measuring both the position and the color of single emitters based on the use of a grating with a relatively large pitch. The grating produces a set of satellite diffraction orders directly adjacent to the 0th order, the main spot. Now the satellite order(s) are projected just a handful of pixels away instead of to the other half of the camera. A consequence is that spot broadening due to the emission spectral width is at the subpixel level. The distance between the diffraction spots Δx ...