The bending wave transfer function on a disordered plate.

The goal of imaging the finest detail possible in biological specimens leads to contradictory requirements for the choice of an electron dose. The dose should be as low as possible to minimize object damage, yet as high as possible to optimize image statistics. For specimens that are protected by low temperatures or for which the low resolution associated with negative stain is acceptable, the first condition may be partially relaxed, allowing the use of (for example) 6 to 10 e/Å2. However, this medium dose is marginal for obtaining the contrast transfer function (CTF) of the microscope, which is necessary to allow phase corrections to the image. We have explored two parameters that affect the CTF under medium dose conditions.Figure 1 displays the CTF for carbon (C, row 1) and triafol plus carbon (T+C, row 2). For any column, the images to which the CTF correspond were from a carbon covered hole (C) and the adjacent triafol plus carbon support film (T+C), both recorded on the same micrograph; therefore the imaging parameters of defocus, illumination angle, and electron statistics were identical.

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Possible applications of fraunhofer holography in high resolution electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108258 ◽

1978 ◽

Vol 36 (1) ◽

pp. 222-223 ◽

Cited By ~ 1

Author(s):

N. Bonnet ◽

M. Troyon ◽

P. Gallion

Keyword(s):

Electron Microscopy ◽

High Resolution ◽

Transfer Function ◽

Radiation Damage ◽

High Resolution Electron Microscopy ◽

Far Field ◽

Field Region ◽

Crystalline Materials ◽

Resolution Electron ◽

The Ideal

Two main problems in high resolution electron microscopy are first, the existence of gaps in the transfer function, and then the difficulty to find complex amplitude of the diffracted wawe from registered intensity. The solution of this second problem is in most cases only intended by the realization of several micrographs in different conditions (defocusing distance, illuminating angle, complementary objective apertures…) which can lead to severe problems of contamination or radiation damage for certain specimens.Fraunhofer holography can in principle solve both problems stated above (1,2). The microscope objective is strongly defocused (far-field region) so that the two diffracted beams do not interfere. The ideal transfer function after reconstruction is then unity and the twin image do not overlap on the reconstructed one.We show some applications of the method and results of preliminary tests.Possible application to the study of cavitiesSmall voids (or gas-filled bubbles) created by irradiation in crystalline materials can be observed near the Scherzer focus, but it is then difficult to extract other informations than the approximated size.

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Ultimate resolution and information in electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100086787 ◽

1991 ◽

Vol 49 ◽

pp. 496-497

Author(s):

D. Van Dyck

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Transfer Function ◽

Information Transfer ◽

Communication Channel ◽

Structural Information ◽

Information Rate ◽

Noise Power ◽

Signal Power ◽

Imaging Device

An (electron) microscope can be considered as a communication channel that transfers structural information between an object and an observer. In electron microscopy this information is carried by electrons. According to the theory of Shannon the maximal information rate (or capacity) of a communication channel is given by C = B log2 (1 + S/N) bits/sec., where B is the band width, and S and N the average signal power, respectively noise power at the output. We will now apply to study the information transfer in an electron microscope. For simplicity we will assume the object and the image to be onedimensional (the results can straightforwardly be generalized). An imaging device can be characterized by its transfer function, which describes the magnitude with which a spatial frequency g is transferred through the device, n is the noise. Usually, the resolution of the instrument ᑭ is defined from the cut-off 1/ᑭ beyond which no spadal information is transferred.

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Analytic integration of contrast transfer functions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010010617x ◽

1988 ◽

Vol 46 ◽

pp. 822-823

Author(s):

Peter Rez

Keyword(s):

Wave Function ◽

Transfer Function ◽

Transfer Functions ◽

Spherical Aberration ◽

Continuous Distribution ◽

Objective Lens ◽

Direction Parallel ◽

Scattering Angle ◽

Analytic Integration ◽

Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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Evaluation method for imaging plate resolution by means of phase contrast transfer function

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100139688 ◽

1995 ◽

Vol 53 ◽

pp. 662-663 ◽

Cited By ~ 1

Author(s):

T. Oikawa ◽

H. Kosugi ◽

F. Hosokawa ◽

D. Shindo ◽

M. Kersker

Keyword(s):

Transfer Function ◽

Phase Contrast ◽

Evaluation Method ◽

Amorphous Film ◽

Imaging Plate ◽

X Rays ◽

Special Shape ◽

Contrast Transfer Function ◽

Contrast Image ◽

Specimen Shape

Evaluation of the resolution of the Imaging Plate (IP) has been attempted by some methods. An evaluation method for IP resolution, which is not influenced by hard X-rays at higher accelerating voltages, was proposed previously by the present authors. This method, however, requires truoblesome experimental preperations partly because specially synthesized hematite was used as a specimen, and partly because a special shape of the specimen was used as a standard image. In this paper, a convenient evaluation method which is not infuenced by the specimen shape and image direction, is newly proposed. In this method, phase contrast images of thin amorphous film are used.Several diffraction rings are obtained by the Fourier transformation of a phase contrast image of thin amorphous film, taken at a large under focus. The rings show the spatial-frequency spectrum corresponding to the phase contrast transfer function (PCTF). The envelope function is obtained by connecting the peak intensities of the rings. The evelope function is offten used for evaluation of the instrument, because the function shows the performance of the electron microscope (EM).

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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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Correction of the contrast transfer function to determine the radial density distribution of frozen-hydrated tobacco mosaic virus

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100123088 ◽

1992 ◽

Vol 50 (1) ◽

pp. 536-537

Author(s):

Michael F. Smith ◽

John P. Langmore

Keyword(s):

Transfer Function ◽

Phase Contrast ◽

Heavy Atom ◽

Biological Molecules ◽

Frequency Compensation ◽

Contrast Transfer Function ◽

High Background ◽

Low Contrast ◽

Radial Density Distribution ◽

Excellent Preservation

The purpose of image reconstruction is to determine the mass densities within molecules by analysis of the intensities within images. Cryo-EM offers this possibility by virtue of the excellent preservation of internal structure without heavy atom staining. Cryo-EM images, however, have low contrast because of the similarity between the density of biological material and the density of vitreous ice. The images also contain a high background of inelastic scattering. To overcome the low signal and high background, cryo-images are typically recorded 1-3 μm underfocus to maximize phase contrast. Under those conditions the image intensities bear little resemblance to the object, due to the dependence of the contrast transfer function (CTF) upon spatial frequency. Compensation (i.e., correction) for the CTF is theoretically possible, but implementation has been rare. Despite numerous studies of molecules in ice, there has never been a quantitative evaluation of compensated images of biological molecules of known structure.

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