Statistical Aspects of Image Handling in Low-Dose Electron Microscopy of Biological Material

In low-dose circumstances the image intensity distribution recorded on the micrograph is a realization of a stochastic process. This noise process that is directly related to the way in which images are recorded has been investigated in this chapter. The stochastic nature of the recorded image has a consequence that the results of image processing also become stochastic quantities, for example, the results obtained with an algorithm for phase retrieval. The chapter discusses the properties of the various methods and algorithms that are proposed in the literature for solving the phase problem when they are applied to low-dose imaging conditions. It mentions the basic integral equation that relates the object wave function to a recorded intensity distribution in the image plane. In order to keep the equations as simple as possible, one lateral dimension of the images only is treated in the chapter. For electron microscopes with square diaphragms (if there are any), the extension to two lateral dimensions is straightforward. The chapter discusses the contrast between imaging of the substructure of biological specimens by means of an electron microscope and low-dose imaging. The imaging of the substructure of biological specimens by means of an electron microscope is greatly limited by the radiation sensitivity of these objects. In low-dose imaging, however, the contrast is very noisy. Because of this poor signal-to-noise ratio, the evaluation in particular of nonperiodic object structures is very cumbersome.