An operator algebra description of Fourier optics is used to examine the imaging properties of transmission electron microscopy when applied to the study of weak specimens. Effects due to the curvature of the incident beam, the finite extent of the source, beam tilt, and objective aperture shift are examined. An expression for the contrast transfer function is derived that can account for either beam tilt in conjunction with a centered aperture or a shifted aperture in conjunction with an aligned beam. It shows that high phase contrast over a broad spatial-frequency range can be achieved by laterally shifting the objective aperture rather than defocusing the specimen, as is normally done.
© 2003 Optical Society of America
(110.0180) Imaging systems : Microscopy
(110.4850) Imaging systems : Optical transfer functions
(110.4980) Imaging systems : Partial coherence in imaging
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
Ardan Patwardhan, "Transmission electron microscopy of weakly scattering objects described by operator algebra," J. Opt. Soc. Am. A 20, 1210-1222 (2003)