Back Focal Plane Research Articles

Dark-field (Diffrimoscopic) Images of Periodic Objects (Coherent Illumination)

The intensity distributions have been computed in the dark-field images of coherently illuminated objects with periodically varying transmission. To get this dark field an obstacle is placed centrally in the back focal plane of the imaging system and the image so formed is called the diffrimoscopic image. The image is characterized by the appearance of a dark fringe at the geometric image of the edges of the object. The effect of the width of the obstacle and the aperture of the imaging system on image intensity distribution have been studied. It has been shown that the dark fringes appear exactly at the geometric image of the edges separating the light and dark regions of a rectangular wave object. The width of the dark fringe is inversely proportional to the aperture width. The position and the width of the dark fringe are independent of the width of the obstacle which affects mainly the intensity away from the dark fringe.

Optical Simulation of the Origin of Contrast in the Electron Microscope

A simple setup is described that simulates an electron microscope imaging a two-dimensional lattice. The diffraction pattern in the back focal plane is large enough to be easily observed and manipulated. The origin of contrast can be demonstrated by filtering out the image contributions of the individual Fourier components. The experiment can be used to demonstrate Abbe's theory of the microscope, origin of phase contrast, and two-dimensional Fourier transforms.

High Resolution Electron Microscopy Using Phase Plates

The phase contrast transfer properties of objective lenses used in electron microscopy are not at all satisfactory and therefore the interpretation of phase contrast images is quite limited in the high resolution field. Phase contrast, however, is the dominant factor in creating contrast in high resolution electron microscopy. This is why methods which promise to improve the transfer conditions are of great importance.A series of experiments has been reported to improve the contrast transfer conditions by zonal or semicircular filtering in the back focal plane of the objective lens or in subsequent light optical reconstruction. By these methods the transfer properties can be improved only to a certain degree.For ideal imaging a transfer function would be desirable that is of constant value for the whole spatial frequency spectrum relevant to high resolution microscopy. This should in principle be attainable by inserting a phase shifting foil of varying thickness into the back focal plane.

Dark Field Procedures in Electron Microscopy of Particulate Biological Material

The dark field image of a specimen is obtained by allowing elastically scattered electrons to pass along the optic axis of the objective lens. Most of the inelastically scattered and the undeflected electrons are eliminated by various procedures, three of which have been found practical in conventional transmission electron microscopes. These three procedures are based on the use of: i) “beam stop” dark field apertures positioned in the back focal plane of the objective lens, as described by Thon; ii) electron beam tilted mechanically, or by a deflecting magnetic coil system between the condenser lens and the object; iii) a “cone mantle” illumination of the object obtained by an annular condenser aperture of appropriate dimension. Our observations have been made with Siemens Elmiskop 1A and 101 electron microscopes, equipped with pointed cathodes (single crystal or lancet-shaped). All samples were supported by ultrathin (2 to 3 nm) carbon films. They included: (a) various viral DNA-cytochrome c monolayers, (b) horse spleen ferritin, (c) B. Subtilis SP 50 bacteriophages, and (d) 50 S E. Coli ribosomal particles. Samples (c) and (d) were stained with uranyl ions.

A Calibration Method Usable in the Production of Phase Plates for High Resolution Electron Microscopy

It is well known that phase contrast in electron microscopy is normally due to the phase shift γ introduced by defocusing and spherical aberration of the objective lens. It is given by Scherzer's formula (2) :(1)where γ is the electron wavelength, Csthe spherical aberration coefficient, θ the diffraction angle and Δz the defocus value.However, in this way, only sections out of the spatial frequency spectrum contained in the abject are transferred to the image. In order to transmit the whole frequency spectrum, it has been proposed that a phase shifting plate is inserted into the back focal plane of the objective lens.

Applications of a Micro-Recording Device

As described earlier the ELMISKOP 101 can be used as a very versatile micro-recorder. For this the cross-over of the electron gun is demagnified by the condensor system and the objective lens of the microscope (maximum demagnification 5000 x) Using the magnetic deflection system the minute probe can be shifted within the back focal plane of the objective lens. In this way contamination traces may be produced on a thin carbon foil.It is possible to drive the probe by an external electronic control unit with different programs. The control unit consists of a scanning generator to write gratings, point patterns and concentric circles to be used as calibration objects for the electron microscope, a flying spot scanner for the production of arbitrary halftone pictures and a unit with attached paper tape recorder.

Experiments with Optical Image Reconstruction of High Resolution Electron Micrographs

AbstractA light optical image reconstruction apparatus, especially designed for optical filtering of high resolution phase contrast electron micrographs, is described. According to theory, in the case of pure weak phase objects such a subsequent light optical filtering of the micrographs using coherent light is equivalent to filtering in the back focal plane of the electron microscope objective lens. The effectiveness and the reliability of the apparatus was tested by reconstruction experiments using several types of filters including zone correction plates.

A simple quantitative experiment on Fourier methods in optical systems

A stage micrometer is illuminated from below through an almost closed substage iris diaphragm and brought to focus with a * 10 objective. When the eyepiece of the microscope is removed the light distribution in the back focal plane of the objective is seen to be a diffraction pattern of light spots. Selected orders of this pattern are then obscured by placing suitable masks in the back of the objective and the effects on the final images are examined photographically. The nature of these images is then observed qualitatively and by inference one is led to an analysis in terms of the Fourier component gratings.

Enhanced contrast in electron microscopy of unstained biological material. I. Strioscopy (dark-field microscopy).

SUMMARYElectron‐optical methods of enhancing contrast are being investigated in order to eliminate the artifacts associated with heavy‐metal contrasting procedures. This report gives a quantitative discussion of the application of the strioscopic dark‐field method to model biological objects. Beam‐stopping apertures were constructed by microwelding fine platinum wires on to platinum objective apertures. These were precisely located and centred in the back focal plane of the objective lens. Contrast was evaluated by a sensitive micro‐Faraday cage system. Bright‐field and strioscopic contrast of organic layers up to 557 nm thickness were investigated and related to the transition from single to plural scattering. The spherical‐aberration phase‐contrast contribution could be separated from the amplitude contrast in bright‐field microscopy by extrapolation to zero object thickness. Strioscopic contrast of thin layers was found to be much greater than bright field aperture contrast and shown to be non‐linear with respect to thickness in the region 0·7–10 nm. For diffraction patterns made up of a few discrete beams the resolution is high, but is considerably less for diffusely scattering and thick objects. Strioscopy may be the method of choice for obtaining contrast of unstained or weakly‐stained objects at high acceleration voltage.

Informational Analysis of Performance for a High Resolution Electron Microscore

Conventional performance criteria for transmission electron microscopes generally involve statements of the spatial resolution permitted by the aberrations of the system and the contrast level permitted by the nature of the object under study. An attempt has been made to formulate a more meaningful set of criteria, which take into account all the essential phenomena encountered in the study by transmission electron microscopy of biologically important macromoleeules. These phenomena include beam coherence and energy spread, interaction of beam with sample, defocus and primary and secondary spherical aberration, diffraction by the objective aperture and retardation by a possible phase shift film in the back focal plane, multiple scattering of electrons in the detecting emulsion, and noise arising from electron and silver grain statistics.

Strioscopic Electron Microscopy

The dark field technique of strioscopy has provided high contrast with reasonable resolution at the organelle level for diffusely scattering, biological-type specimens and information concerning scattering processes in electron microscopy. It has involved the removal of the direct beam from the diffraction pattern by a central wire and subsequent image formation by diffracted beams, limited by a central back focal plane aperture. Strioscopic apertures (Fig. 1) have been constructed by microwelding 10µ platinum wire onto conventional platinum objective apertures. These strioscopic apertures were carried in the normal objective lens aperture holder. The focal length of a Siemens Elmiskop IA E/M was shortened to achieve coincidence of aperture and diffraction planes (Fig. 2).

Development of Electron Mirror Microscope

Our electron mirror microscope has been improved by adopting magnetic lenses, which enable a wide range of magnification to be obtained. This improved version, known as the JEM-M1 (35kV acceleration) uses the straight design and shadow projection method.The construction of the newly designed instrument is illustrated in Fig. 1 and Fig. 2 shows a sectional view of its electron optical column. The electron gun assembly is located under the console table. Incident beam alignment is carried out by means of the deflection coil knob, the electron gun horizontal movement knob and the condenser lens knob located on the table. The zircaloy crystal located above the screen and on the optical axis enables the alignment procedure to be carried out easily and simply because it radiates light when impinged by the electron beam. The projector lens, having a short focal length, combined with the condenser lens, forms a small source for the shadow projection image on its back focal plane. The intermediate lens, acting on the reflected beam, produces image magnification by changing the excitation current. Magnification in the range x200 – x1500 is possible without any appreciable distortion.

Four Stage E.M. for Phase Contrast and Strioscopic Microscopy

Phase contrast electron microscopy should allow visualization of unstained biological structures. In an attempt to achieve this, we have modified a Siemens Elmiskop la microscope, in a way similar to that described by Faget, et al. (Proc. Fifth Int. Congr. Electron Microscopy, Philad., 1962, Abstract A-7). A number of phase contrast and strioscopic arrangements can be tested. A section consisting of phase plate chamber and additional intermediate lens (I2) was added to the column between the standard intermediate lens (I1) and the projector lens (Fig. 1). I1 was set, so as to project the back focal plane of the objective to the level of the phase plate holder (Fig. 2). I2 supplied final magnifications from 1,000 x to 80,000 x. Resolution was better than 15 Å. Two stigmators were used, one in the objective back focal plane and one in the plane of the phase plate. The source consisted of either a hairpin- or point- filament to allow variable coherence of illumination.

A Slotted Electrode Stigmator for Correction of Short Focal Length Objectives

One of the difficulties which must be overcome in the design of objective lens stigmators is that they necessarily take up space where it is most precious, in the vicinity of the specimen. The space following the specimen is needed for the contrast aperture while the space between magnetic poles in the gap is required for stage mechanism. To go appreciably below the objective back focal plane to position stigmators subjects the image to possible image distortion when correction is large. A further problem is caused by the trend to shorter objective focal lengths, e.g., 1.5 mm, thus further reducing the space available for the stigmator.To adapt the electrostatic stigmator to these physical restraints, a design has been completed which is only 0.75 mm thick and has a free bore diameter of the same size. Its sensitivity is 0.1 micron/volt with 100 kV electrons. The overall diameter is uncritical and may be adapted to the physical requirements of the system. It should be possible to make stigmators of 3 mm thickness with a simple reduction of critical dimensions (thickness and slot width).

Detection of Differences in Real Distributions

If two coherently illuminated distributions are spatially separated at the front focal plane of a spherical lens and the resulting diffraction pattern is square-law recorded in the back focal plane, the Fourier transform of the record contains comparative data about the two input distributions. The transform of the record presents data in a reference frame that simplifies the problem of identifying and locating differences between the two input distributions. The process of transforming, detecting, and retransforming is a method of convolving the two input distributions. If the inputs are identical, the autocorrelation function is derived. If only real functions are evaluated, the autocorrelation function is symmetrical about the correlation peak. An asymmetry indicates a difference between the inputs, i.e., a cross-correlation function. The value of the technique is that it reduces the procedure for comparing spatial distributions to a search for asymmetry about an easily defined point. The same process may be used to identify spatial distributions by heterodyning a reference distribution with the field of view to be searched. The cross correlation function derived contains a sharp correlation peak for each target within the field of view.

Interference Microtopography with Incoherent Light

Conventional coherent illumination provides the interference at high orders necessary for microtopography. However, the resulting interferogram is not a true, undistorted contour map of the specimen, nor is there any direct method of assessing the distortion. In addition, coherent illumination gives poor resolution, and when vertical illumination is used reflections in the objective reduce the contrast. These problems are all ameliorated by using incoherent illumination limited to a small range in angle relative to the plane of the reference reflector but unconfined in azimuth, i.e., the illumination produced by an annular source in the back focal plane of the illuminating lens.

Numerical Evaluation of Electron Image Phase Contrast

This paper is concerned with phase contrast in electron images with emphasis on a periodic scattering object. The Kirchoff diffraction or imaging integral over the back focal plane is formulated in terms of the amplitude and phases of the scattered wave, using coordinates adapted to numerical methods. The integral was programmed for evaluation on the IBM 7090 and the image plane amplitude displayed on a microfilm plotter. The effects of spherical aberration, aperture size, defocus and thermal motion of the scattering atoms on image contrast of atom positions for chains of nickel and of gold atoms were investigated for separations of 2 Å and 8 Å. In the range of atomic separations, spherical aberration is the most destructive single factor in the loss of phase contrast. It appears that an objective lens with a spherical aberration coefficient less than 0.2 mm will be necessary if phase contrast images of atom locations are to be attained. In addition, a practical quarter-wave phase plate is essential for the objective lens system and will be much more effective than defocus contrast. Even so the contrast is marginal for photographic recording except for the case of a thin perfect crystal. Amplitude contrast is very small for atom positions and should be minimized by the use of a large objective aperture. Phase contrast should improve with increasing accelerating potentials due to reduced inelastic cross sections compensating the loss in elastic contrast near 2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> volts.

Zonenplatten zur �ffnungsfehlerkorrektur und zur Kontrasterh�hung

A new type of zone plate is proposed whose purpose is to increase the contrast in electron micrographs. It consists of a circular aperture and a number of concentric rings, and it is arranged in the back focal plane of an electron objective lens with spherical aberration. The diameters of the outer rings are chosen such as to leave through only such parts of the wave surface which reach the image point with a phase delay of (2n+1)π relative to its paraxial part. The intensity distribution in the image plane is calculated for this zone plate and for a similar type of zone plate suggested byHoppe whose purpose is to reduce the resolution limit. Numerical calculations are made for the special case that the intensity is constant over the plane of the zone plate. The results show that an increase of resolving power may be expected if Hoppe's plate is used, and that the image contrast may be considerably increased by the new contrast plate without any serious reduction of resolving power.

The Abbe Theory of Microscopic Vision and the Gibbs Phenomenon

An elementary discussion of the Abbe theory of microscopic vision is given, suitable for teaching purposes. The effect of the phases in the back focal plane of the objective is briefly outlined. The consequence of limiting the aperture of the system in this plane is shown to be an image marred by diffraction. The relationship to Fourier's theorem having been indicated, the Gibbs phenomenon is next described. A standard formula for the finite sum of a Fourier series is taken and adapted to the case of imaging a suitable grating with a microscope objective limited by a slit aperture. If the grating slits are very narrow compared with the opaque region separating them, the image of each is shown to be marred by a set of fringes, due to the Gibbs phenomenon, exactly equivalent to the diffraction fringes from the single slit in the microscope objective.

An improved phase-contrast microscope with variable amplitude and phase difference.

SYNOPSISAn instrument is described in which the back focal plane of the objective is re‐imaged into a more accessible position by the aid of a concave mirror without the introduction of any additional air‐glass interfaces. As a result, interchange of phase plates is greatly facilitated and amplitude and phase variation can be achieved efficiently at all powers.