Saturated Reconstruction of a Volume of Neocortex.

We describe automated technologies to probe the structure of neural tissue at nanometer resolution and use them to generate a saturated reconstruction of a sub-volume of mouse neocortex in which all cellular objects (axons, dendrites, and glia) and many sub-cellular components (synapses, synaptic vesicles, spines, spine apparati, postsynaptic densities, and mitochondria) are rendered and itemized in a database. We explore these data to study physical properties of brain tissue. For example, by tracing the trajectories of all excitatory axons and noting their juxtapositions, both synaptic and non-synaptic, with every dendritic spine we refute the idea that physical proximity is sufficient to predict synaptic connectivity (the so-called Peters' rule).

Super-resolution laser scanning microscopy through spatiotemporal modulation.

Super-resolution optical microscopy has attracted great interest among researchers in many fields, especially in biology where the scale of physical structures and molecular processes fall below the diffraction limit of resolution for light. As one of the emerging techniques, structured illumination microscopy can double the resolution by shifting unresolvable spatial frequencies into the pass-band of the microscope through spatial frequency mixing with a wide-field structured illumination pattern. However, such a wide-field scheme typically can only image optically thin samples and is incompatible with multiphoton processes such as two-photon fluorescence, which require point scanning with a focused laser beam.

Extended depth-of-focus microscopy via constrained deconvolution.

We derive a method for extended depth-of-focus imaging, i.e., a method to render a 2-D image of a thick specimen, such that all the structures within the specimen appear in focus and with greatly increased contrast.

Optical sectioning microscopy.

Confocal scanning microscopy, a form of optical sectioning microscopy, has radically transformed optical imaging in biology. These devices provide a powerful means to eliminate from images the background caused by out-of-focus light and scatter. Confocal techniques can also improve the resolution of a light microscope image beyond what is achievable with widefield fluorescence microscopy.

Fluorescence microscopy.

Although fluorescence microscopy permeates all of cell and molecular biology, most biologists have little experience with the underlying photophysical phenomena. Understanding the principles underlying fluorescence microscopy is useful when attempting to solve imaging problems. Additionally, fluorescence microscopy is in a state of rapid evolution, with new techniques, probes and equipment appearing almost daily.

Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy.

We derive an algorithm for maximum-likelihood image estimation on the basis of the expectation-maximization (EM) formalism by using a new approximate model for depth-varying image formation for optical sectioning microscopy. This new strata-based model incorporates spherical aberration that worsens as the microscope is focused deeper under the cover slip and is the result of the refractive-index mismatch between the immersion medium and the mounting medium of the specimen. Images of a specimen with known geometry and refractive index show that the model captures the main features of the image.

Numerical evaluation of Hankel transforms for oscillating functions.

Six methods for the numerical calculation of zero-order Hankel transforms of oscillating functions were evaluated. One method based on Filon quadrature philosophy, two published projection-slice methods, and a third projection-slice method based on a new approach to computation of the Abel transform were implemented; alternative versions of two of the projection-slice methods were derived for more accurate approximations in the projection step. These six algorithms were tested with an oscillating sweep signal and with the calculation of a three-dimensional diffraction-limited point-spread function of a fluorescence microscope.