chapter
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A new method for the determination of the coefficients of the wave aberration function

ABSTRACT: A new method for the accurate determination of both the symmetric and asymmetric coefficients of the wave aberration function has been developed. The relative defoci and displacements of images in a focal series can be determined from an analysis of the Phase Correlation Function (PCF) between pairs of images with an appropriate phase compensation. Subsequently, the absolute coefficients of both defocus and 2-fold astigmatism are determined with a Phase Contrast Index function. Extension of these methods to a series of tilted illumination images allows the asymmetric coefficients to be determined using numerical or analytical fitting of the apparent defocus and astigmatism present under tilted illumination conditions. Overall this method allows a very accurate automated aberration determination even for largely crystalline samples with little amorphous contamination.