scholarly journals Reduction of mid-spatial frequency errors on aspheric and freeform optics by circular-random path polishing

2021 ◽  
Author(s):  
Anthony Beaucamp ◽  
Ken Takizawa ◽  
Yanjun Han ◽  
Wu-Le Zhu
Keyword(s):  
Spatial Frequency ◽  
Random Path ◽  
Freeform Optics

Smoothing mid-spatial frequency (MSF) errors on freeform optics with an algorithm-based robotic platform utilizing deflectometry input

2021 ◽  
Author(s):  
Jennifer Coniglio ◽  
Nick Quattrociocchi ◽  
Matthew Eisner ◽  
Starbuck Beagley ◽  
Joshua Beck ◽  
...  
Keyword(s):  
Spatial Frequency ◽  
Robotic Platform ◽  
Freeform Optics

Determination of the Best Emulsion for the Microscopy of Crystals

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.

Density-based discrimination of protein and RNA in the ribosome

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.

Three-fold astigmatism: An important TEM aberration

1993 ◽  
Vol 51 ◽  
pp. 972-973 ◽  
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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