Mid-spatial frequency removal on aluminum free-form mirror

More and more optical elements are needed in modern industry, which is reflected by both the bigger amount of requirement, and more complicated designed surface such as asphere and even free form surface. As a result, optical polishing using small tools on CNC machines is applied widely in the whole world, which has a lot of advantages such as fast speed, high accuracy, high flexibility and so on. But the small tool polishing can also cause in some problems. For example, the middle spatial frequency errors (MSFE) may be increased during the polishing. The reasons may consist of the following aspects: 1) the positional error of the workpiece; 2) the mistake of error data input; 3) the unexpected stop of the polishing process; 4) the stabilization of the slurry density during the process; 5) the temperature change of the contact area between the tool and the workpiece and so on. As is known, pitch is usually used in traditional optical manufacture, and it can reduce the middle and high spatial frequency errors in a large extent because of the different removal rate between the high points and low points on the optical surface. Therefore, the application of the combination of pitch and small tool is described in this paper in order to solve the MSFE problem, and we have got good polishing results of reducing the error from 2.155nm to 0.267nm by using the new pitch tool on the CNC machine after two runs.

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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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Three-fold astigmatism: An important TEM aberration

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100150691 ◽

1993 ◽

Vol 51 ◽

pp. 972-973 ◽

Cited By ~ 1

Author(s):

O.L. Krivanek ◽

M.L. Leber

Keyword(s):

High Resolution ◽

Spatial Frequency ◽

Field Emission ◽

Azimuthal Angle ◽

Hollow Cone ◽

Small Probe ◽

Wide Range ◽

High Resolution Images ◽

Image Position

Three-fold astigmatism resembles regular astigmatism, but it has 3-fold rather than 2-fold symmetry. Its contribution to the aberration function χ(q) can be written as:where A3 is the coefficient of 3-fold astigmatism, λ is the electron wavelength, q is the spatial frequency, ϕ the azimuthal angle (ϕ = tan-1 (qy/qx)), and ϕ3 the direction of the astigmatism.Three-fold astigmatism is responsible for the “star of Mercedes” aberration figure that one obtains from intermediate lenses once their two-fold astigmatism has been corrected. Its effects have been observed when the beam is tilted in a hollow cone over a wide range of angles, and there is evidence for it in high resolution images of a small probe obtained in a field emission gun TEM/STEM instrument. It was also expected to be a major aberration in sextupole-based Cs correctors, and ways were being developed for dealing with it on Cs-corrected STEMs.

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