Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs

A field emission system for our experimental ultra high vacuum electron microscope has been designed, constructed and tested. The electron optical system is based on the prototype whose performance has already been reported. A cross-sectional schematic illustrating the field emission source, preaccelerator lens and accelerator is given in Fig. 1. This field emission system is designed to be used with an electron microscope operated at 100-150kV in the conventional transmission mode. The electron optical system used to control the imaging of the field emission beam on the specimen consists of a weak condenser lens and the pre-field of a strong objective lens. The pre-accelerator lens is an einzel lens and is operated together with the accelerator in the constant angular magnification mode (CAM).

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Information and estimation in image processing

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125142 ◽

1987 ◽

Vol 45 ◽

pp. 14-17

Author(s):

B. Roy Frieden

Keyword(s):

Image Processing ◽

Optical System ◽

Large Amplitude ◽

Communication Theory ◽

Image Data ◽

Direct Approach ◽

Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

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Atomic Resolution in Crystal Aperture Stem

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179932 ◽

1990 ◽

Vol 48 (1) ◽

pp. 236-237

Author(s):

J T Fourie

Keyword(s):

Optical System ◽

Spherical Aberration ◽

Three Dimensional ◽

Transmission Function ◽

Optical Systems ◽

Bragg Angle ◽

Electron Optical System ◽

Intimate Contact ◽

Diffraction Effects ◽

Design Aspect

The attempts at improvement of electron optical systems to date, have largely been directed towards the design aspect of magnetic lenses and towards the establishment of ideal lens combinations. In the present work the emphasis has been placed on the utilization of a unique three-dimensional crystal objective aperture within a standard electron optical system with the aim to reduce the spherical aberration without introducing diffraction effects. A brief summary of this work together with a description of results obtained recently, will be given.The concept of utilizing a crystal as aperture in an electron optical system was introduced by Fourie who employed a {111} crystal foil as a collector aperture, by mounting the sample directly on top of the foil and in intimate contact with the foil. In the present work the sample was mounted on the bottom of the foil so that the crystal would function as an objective or probe forming aperture. The transmission function of such a crystal aperture depends on the thickness, t, and the orientation of the foil. The expression for calculating the transmission function was derived by Hashimoto, Howie and Whelan on the basis of the electron equivalent of the Borrmann anomalous absorption effect in crystals. In Fig. 1 the functions for a g220 diffraction vector and t = 0.53 and 1.0 μm are shown. Here n= Θ‒ΘB, where Θ is the angle between the incident ray and the (hkl) planes, and ΘB is the Bragg angle.

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