NUMBER OF SAMPLING POINTS REQUIRED FOR ABERRATION CORRECTION USING OFF-AXIS ELECTRON HOLOGRAPHY

The number of the sampling points required for digital aberration correction using an off-axis electron hologram is studied based on the Whittaker-Shannon sampling theorem [see, e.g., J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968)]. The number of the sampling points in the case of a non-periodic sample depends on the width of the image-space inverse filter used for aberration correction. The minimum number estimated in this report is smaller than that reported previously [H. Lichte, Ultramicroscopy 38 (1991) 13]. Using an optimum sampling scheme we can reduce the required number of pixels for sampling the same area. For periodic specimens, the size of the inverse filter does not affect the required number of sampling points, when the sampled image distribution is made commensurate with the intrinsic periodicity of the specimen. The implication of a window function commonly used to suppress discontinuity at the sampled image boundary is also studied in the light of aberration correction. It is shown that the window function may restrict a sampling interval of an aberration function, and thus affect the required number of sampling points.