SPARK, a kernel of software programs for spatial reconstruction in electron microscopy

Abstract

Summary SPARK, an acronym for ‘SPAtial Reconstruction Kernel’, is the nucleus of a software library being developed for the three‐dimensional (3‐D) reconstruction of objects observed by the electron microscope. A unifying concept is used: the Fourier transform, known in several central sections, is resampled to obtain a 3‐D Cartesian grid, which is inverted by a fast Fourier transform. This technique is used for both single‐axis tilting (of 2‐D periodic layers or of isolated objects) and for the random conical‐tilt technique. The principles that make it possible to recover Cartesian grids in the two different geometries are illustrated and some preliminary results are reported. SPARK resamples the Cartesian grids with the use of a fast and efficient algorithm of Shannon interpolation developed by the authors. Compared to back‐projection techniques the method shows a considerable improvement in execution time with no sacrifice in accuracy; it therefore allows the effects of a variety of parameters in a given reconstruction to be scrutinized in a reasonable time. Some new possibilities and future extensions of the library are briefly outlined.