Digital reconstruction of bright field phase contrast images from high resolution electron micrographs

The theory of bright-field image formation of thin specimens in a conventional transmission electron microscope is presented. The recorded image contrast is shown to be predominantly linear in the electron atom scattering amplitudes which are in general complex (possessing phase and amplitude). A linearized image model describing multiple images of varying defocus (defocus series) is derived. Image degradation is characterized by an instrumental transfer function (including spherical aberration, defocus and partial coherence), a finite signal-to-noise ratio and a Debye--Waller temperature factor. Using the minimum mean square error criterion, a new method of image reconstruction to recover the real and imaginary parts of the ideal phase contrast image from a defocus series is derived. This new method of image reconstruction reduces to the well known Wiener filter in the appropriate limiting conditions. A defocus series of micrographs taken on the Kyoto 500 keV electron microscope using a radiation damage resistant specimen of chlorinated copper phthalocyanine is processed. The signal-to-noise ratio of this series is found to be approximately 10. A resolution of approximately 2 A is apparent in the unprocessed images. The complex image reconstructed from this defocus series shows increased resolution in the real part of the image (approximately 1.4 A) and increased heavy/light atom contrast in the imaginary part of the image.