Defocusing error

When the specimen is rotated out of the vertical position (a < 90°) in the sense shown in Fig. 9-16, the top part moves behind, and the bottom in front of, the focusing circle. The diffracted beam therefore widens at the counter slit, and the measured diffracted intensity from a random specimen may decrease as a departs from 90°. This effect is called the defocusing error. It may be minimized by slit adjustment (widening the counter slit and decreasing the vertical opening in slit D) or corrected by calculation [9.14, 9.15]. 

In real curvature sensors, a vibrating membrane mirror is placed at the telescope focus, followed by a collimating lens, and a lens array. At the extremes of the membrane throw, the lens array is conjugate to the required planes. The defocus distance can be chosen by adjusting the vibration amplitude. The advantage of the collimated beam is that the beam size does not depend on the defocus distance. Optical fibers are attached to the individual lenses of the lens array, and each fiber leads to an avalanche photodiode (APD). These detectors are employed because they have zero readout noise. This wavefront sensor is practically insensitive to errors in the wavefront amplitude (by virtue of normahzing the intensity difference). 

The defocus values for electron micrographs can be readily estimated on the basis of the CTF rings visible in the incoherently averaged Fourier transforms of individual particle images (Zhou et at., 1994, 1996). This method has become a routine practice universally adapted for the initial evaluation and determination of CTF parameters as defined in Eqs. (2) and (3). So far, the determination of the cumulative B factors for 3-D reconstruction has been somewhat ad hoc. The cumulative B factor used in these studies is determined either by trial and error with the initial value derived from previous results, or from the incoherently averaged Fourier transforms of particle images. Different approaches have been adopted to make corrections for the CTF and the function of the micrographs. They differ in the steps where these corrections are made and in whether or how the E function is corrected. 

Identification of a structure or of a defect in a structure proceeds by trial and error . A model is proposed, and a matrix of images that varies the two main independent variables (foil thickness and defocus) is computed. 

The circle of confusion is taken as the lens focal length divided by 1000 [15]. This formula is valid only for normal lenses. The depth of focus Af is the amount of defocus that introduces a wavefront error, and can be calculated using... 

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