Spatially resolved height response of phase-shifting interferometers measured using a patterned mirror with varying spatial frequency

Electron channeling patterns (ECP) were first found by Coates (1967) while observing a large bulk, single crystal of silicon in a scanning electron microscope. The geometric pattern visible was shown to be produced as a result of the changes in the angle of incidence, between the beam and the specimen surface normal, which occur when the sample is examined at low magnification (Booker, Shaw, Whelan and Hirsch 1967).A conventional electron diffraction pattern consists of an angularly resolved intensity distribution in space which may be directly viewed on a fluorescent screen or recorded on a photographic plate. An ECP, on the other hand, is produced as the result of changes in the signal collected by a suitable electron detector as the incidence angle is varied. If an integrating detector is used, or if the beam traverses the surface at a fixed angle, then no channeling contrast will be observed. The ECP is thus a time resolved electron diffraction effect. It can therefore be related to spatially resolved diffraction phenomena by an application of the concepts of reciprocity (Cowley 1969).

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Determination of the Best Emulsion for the Microscopy of Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096886 ◽

1981 ◽

Vol 39 ◽

pp. 32-33

Author(s):

David A. Grano ◽

Kenneth H. Downing

Keyword(s):

Spatial Frequency ◽

Information Transfer ◽

Signal To Noise Ratio ◽

Experimental Situation ◽

Photographic Emulsion ◽

Modulation Transfer ◽

Signal To Noise ◽

Frequency Space ◽

Noise Ratio

The retrieval of high-resolution information from images of biological crystals depends, in part, on the use of the correct photographic emulsion. We have been investigating the information transfer properties of twelve emulsions with a view toward 1) characterizing the emulsions by a few, measurable quantities, and 2) identifying the “best” emulsion of those we have studied for use in any given experimental situation. Because our interests lie in the examination of crystalline specimens, we've chosen to evaluate an emulsion's signal-to-noise ratio (SNR) as a function of spatial frequency and use this as our critereon for determining the best emulsion.The signal-to-noise ratio in frequency space depends on several factors. First, the signal depends on the speed of the emulsion and its modulation transfer function (MTF). By procedures outlined in, MTF's have been found for all the emulsions tested and can be fit by an analytic expression 1/(1+(S/S0)2). Figure 1 shows the experimental data and fitted curve for an emulsion with a better than average MTF. A single parameter, the spatial frequency at which the transfer falls to 50% (S0), characterizes this curve.

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Density-based discrimination of protein and RNA in the ribosome

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100122721 ◽

1992 ◽

Vol 50 (1) ◽

pp. 464-465

Author(s):

Joachim Frank

Keyword(s):

Transfer Function ◽

Spatial Frequency ◽

Three Dimensional ◽

Wiener Filter ◽

Dark Field Image ◽

Dark Field ◽

Frequency Range ◽

Bright Field ◽

Contrast Transfer Function ◽

Pass Filter

Cryo-electron microscopy combined with single-particle reconstruction techniques has allowed us to form a three-dimensional image of the Escherichia coli ribosome.In the interior, we observe strong density variations which may be attributed to the difference in scattering density between ribosomal RNA (rRNA) and protein. This identification can only be tentative, and lacks quantitation at this stage, because of the nature of image formation by bright field phase contrast. Apart from limiting the resolution, the contrast transfer function acts as a high-pass filter which produces edge enhancement effects that can explain at least part of the observed variations. As a step toward a more quantitative analysis, it is necessary to correct the transfer function in the low-spatial-frequency range. Unfortunately, it is in that range where Fourier components unrelated to elastic bright-field imaging are found, and a Wiener-filter type restoration would lead to incorrect results. Depending upon the thickness of the ice layer, a varying contribution to the Fourier components in the low-spatial-frequency range originates from an “inelastic dark field” image. The only prospect to obtain quantitatively interpretable images (i.e., which would allow discrimination between rRNA and protein by application of a density threshold set to the average RNA scattering density may therefore lie in the use of energy-filtering microscopes.

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