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.

In-focus phase contrast electron microscopy has been investigated for the enhancement of bulk contrast (i.e. the contrast of large regions) of model biological specimens. Carbon film phase plates, of measured thickness, were introduced into the back focal plane ofthe objective lens. Image contrast was determined from Faraday-cage intensity measurements. A contrast enhancement was observed but was measured to be less than that obtained using a very small objective aperture. This was attributed to the smaller proportion of elastic scattering and the limited spatial frequency region over which the phase contrast transfer function was uniform. Electron beam interferometry established the ability of the phase plates to preserve the coherence of the beam traversing them. Carbon granularity, of specific dimensions, was significantly enhanced by the phase plate in accordance with the phase contrast transfer function and this enhanced granularity dominated the images of biological specimens. I N T R O D U C T I O NThe phase contrast technique, invented for light microscopy by Zernike (1942a, b), involved phase shifting the scattered relative to the non-scattered waves from a microscope specimen. Constructive or destructive interference was achieved when the wave components interfered in the image plane and image contrast was enhanced by rendering a specific detail brighter (negative contrast) or darker (positive contrast) than its surroundings. A phase plate in the diffraction plane (back focal plane) of the objective lens accomplished the required phase shift by providing an increased optical path (a phase delay) for one wave component relative to the other.Calculations (Bennet et al., 1946; Franqon, 1950;Barer, 1952) indicated the necessity of a 7r/2 rad phase delay of scattered waves for positive phase contrast in the case of hypothetical objects comparable to typical unstained biological specimens. Experimentally, Zernike (1942a, b) and Bennet et al. (1946, 1951) found a 57/2 rad phase plate to be the best compromise for routine biological light

A rapid and convenient method is described for the accurate determination of the thickness of carbon films from their optical density. A linear relationship was found between optical density and film thickness. The optical-density-thickness curve was calibrated by direct measurement of the thickness of transverse sections of carbon films embedded in epoxy resin. The method can probably be extended to thin films of soft metals and other inorganic films having significant optical density and capable of being sectioned with a diamond knife.

In-focus phase contrast has been demonstrated in the electron microscope using an arrangement analogous to that of the Zernike phase contrast light microscope. Thin carbon films with a central hole were placed in the back focal plane of the objective lens so that the scattered electrons were selectively phase-shifted by the film. The maximum phase contrast was obtained when the film thickness was adjusted to give a retardation of about pi/2 to the scattered electrons and appears to be due to the elastically scattered electrons. The observed contrast was about one-half that calculated taking into account the scattering of both the object and the phase plate and making the assumption that the inelastic scatter was incoherent. Improved phase contrast should be obtained if the nonscattered intensity is reduced by a beam stop and if phase-shifting can be accomplished by a small electrostatic lens rather than by a film. An objective lens ofthe smallest available spherical aberration is required. The in-focus phase contrast arrangement may provide useful contrast for thick (>2000 A) unstained objects in the l.0-MeV microscope. A combination contrast mode is recommended for conventional (100-kV, microscopes where amplitude contrast and enhancement of phase contrast are provided by filtering out the inelastic scatter.

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