ABERRATION CORRECTION USING OFF-AXIS HOLOGRAPHY .1. ABERRATION ASSESSMENT

In order to carry out aberration correction, the aberration working on each hologram must be estimated. Since it is rather difficult to prec isely control aberration coefficients in the experimental stage, we de veloped a procedure to estimate the working aberration from the hologr am itself. In this procedure, the specimen is assumed to be an approxi mate phase object. Therefore, the amplitude variation of the restored wave should be minimized when the aberration is corrected. We assume a symmetrical aberration function parametrized only by a spherical aber ration coefficient and a defocus value. A normalized standard deviatio n is then calculated from the restored wave for each combination of th ese parameters. The working aberration is determined from the combinat ion of the parameters giving the smallest standard deviation. This pro cedure is applied to holograms taken of an amorphous carbon film which can be considered as an approximate phase object. The side-bands of t he hologram have information of up to 3.3 nm(-1), and the aberration c orrection is carried out over this range. The same procedure can be ap plied in order to correct aberration beyond the Scherzer limit when us ing crystal specimens.