Electromagnetic Lens Research Articles

Modulation transfer function of image tube lenses

The modulation transfer function (MTF) of the proximity focusing biplanar lens and the sharp focusing electrostatic and electromagnetic lenses is derived and presented. It is shown that for a Maxwellian emission energy distribution, the MTF of the biplanar lens is MTF = exp(-4pi(2)epsilon/V(s)L(2)F(2)), where L is the screen to cathode separation in mm, f is the spatial frequency in lp/mm, V(s), is the screen voltage, and epsilon is the voltage equivalent of the most probable emission energy. For a cosine distribution, the MTF of the biplanar lens is MTF = exp(-7 piepsilon/V(s)L(2)f(2)). The MTF of sharp focusing image tube lenses is MTF = exp(-0.06pi(2)epsilon(2)M(2)f(2)/E(c)(2)), where E(c), is the cathode field strength in volts per mm and M is the magnification. In general, the MTF of image tube lenses is MTF = exp[-(pirhof)(2)], where rho is the focusing error coefficient of a particular lens.

Auger Electron Spectroscopy with the Scanning Electron Microscope

Various SEM-AES combinations have been described in the literature during the past six years. All these instruments, with one exception, were dry pumped and capable of operating at pressures below 10-7torr. The equipment described herein, see Fig.1, is a modified ULTRASCAN SEM with an Auger-electron analysis system from Physical Electronics Industries (PHI): it is also dry pumped to the low 10-7torr range.The electron optical column uses two electromagnetic lenses instead of the original three, and with a 200 micron objective aperture it delivers a maximum of 0.6 to 0.8 x 10-8A at the specimen. At the short working distance (1.2 cm) the spatial resolution is between 70 and 80 nm, while at the longer working distance (3.2 cm) the resolution is about 100 nm. The scintillator assembly was transposed to the right side of the specimen chamber so that a PHI small cylindrical-mirror velocity analyzer, with bellows extension could be mounted diametrically opposite the scintillator.

Focal length modulation of electromagnetic lenses with particular application to scanning electron microscopes

A very simple circuit has been developed which permits variation of the current through an electromagnetic lens under the command of an electrically isolated control signal. Control of the power of the electromagnetic lens may be determined by any external variable as long as that variable is capable of being converted into an electrical signal. It is particularly applicable to scanning electron microscopes. Initial development was carried out on a Stereoscan Mk IIA.

Contrast Effects in High Resolution, Low Voltage SEM

A scanning electron microscope using a field emission electron source and a single electromagnetic lens can produce a resolution of less than 180Å using an accelerating voltage of only 900v. High resolution, low voltage (0.1-2kV) scanning microscopy offers a number of advantages over the use of higher accelerating voltages. Specimen damage may be reduced because the power (P≃IV) which must be absorbed by the specimen for operation at a given probe current (I) is decreased in proportion to the reduction in accelerating voltage (V).

The oblique electron lens

An oblique electron lens is described that is especially applicable to image converters and camera tubes employing flat opaque photocathodes. The use of optical lenses, corrector plates, and/or mirrors (often employed in other electron lenses designed for use with opaque photocathodes) are eliminated. The oblique electron lens is well suited to ultraviolet and vacuum ultraviolet image converters, and to image converters employiug opaque negative electron affinity photocathodes. It is also possible to use this oblique electron lens for electronography. Measurements on an experimental tube show that a limiting resolution of 50 line pairs/mm is possible, but the intrinsic lens quality is believed to approach that of a conventional electromagnetic lens having uniform and colinear electric and magnetic fields.

An Early American Electron Microscope

An interest in the historical aspects of electron microscopy has been shown by several recent publications on the subject. As early as 1936 Dr. Paul Anderson and the late Mr. Kenneth Fitzsimmons were experimenting with an electron microscope in the Physics Department of Washington State University (then Washington State College). The instrument (see illustrations) was constructed somewhat on the designs of Knoll and Ruska. The electron source was a heated filament, and accelerating voltage was 30 KV. The microscope has three electromagnetic lenses; condenser, objective, and projector. External rectangular Helmholz coils (see illustration) corrected for the earth's magnetic field and permitted beam shift. The column is brass. The camera magazine held six lantern slide plates which could be successively exposed without breaking vacuum. Particularly interesting is the attempt to measure beam current at the fluorescent screen in order to determine photographic exposure.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

The Materials Analysis Company Model 700 Scanning Electron Microscope

The Model 700 scanning electron microscope is a high resolution instrument which incorporates the same basic modular concept that has proven so satisfactory in the Materials Analysis Company Model 400 x-ray microprobe and its latest development, the Model 400S. The instrument described here is the basic building block to which accessories such as additional display tubes, special specimen holders, etc., can be easily added.The electron-optical column consists of a triode electron gun, double electromagnetic condenser lens, and objective lens. A .004″ tungsten hairpin filament is used as the electron source, and the filament to grid spacing is externally adjustable during operation to optimize gun performance for all operating conditions. The double condenser system is unitized and uses a single energizing coil. An adjustable multiple aperture holder is provided between the double condenser lens system and the objective lens, which serves to define the convergence angle of the probe in the specimen plane.

Wave Theory of a Variable-Density Luneburg Lens

Previously, the author [J. Acoust. Soc. Am. 43, 709–715 (1968)] showed that the correct wave equation needed to describe the propagation of sound in an acoustic Luneburg lens is ∇2p − ∇ lnρ⋅∇p = (n2/Co2)∂2p/∂t2, where p is the acoustic pressure, ρ the density, Co a constant reference speed, and n2 = 2 − (r/a)2 is Luneburg's index of refraction. Here a is the lens's radius and r any radial point within it. A similar equation holds for the electromagnetic Luneberg lens with the dielectric coefficient ε replacing ρ. However, ε = n2 and consequently, it can be only one possible function of position. This is not so for the acoustic case, since ρ = n2/κCo2 (κ the compressibility), and κ can be a function of position. Previously, we investigated the case where ρ was approximately constant, so we could neglect the density-gradient term in the wave equation. (Strictly speaking, ρ cannot be constant if n is a function of position.) This case corresponds to W. J. Toulis' compliant-tubing lens, and we found that the theory agreed well with experimental data. In this paper, we examine a different possibility, viz., κ constant and ρ a function of position given by ρ = n2/κCo2. We then compare the two cases.

New Thermionic Emission Microscope

A new thermionic emission microscope has been designed and constructed. It is a two lens microscope having a combination electrostatic-electromagnetic objective lens and an electromagnetic projector lens. The microscope has a magnification range of 78 to 5600× and a resolution of about 500 Å which is independent of magnification. It is capable of operating at a vacuum of 10−8 Torr at 1600°C. A specimen temperature and control system has been incorporated which operates with an accuracy better than ±5°C. The microscope stage is so constructed that the specimen can be independently moved in the x, y, and z directions. The electron-optical axis is horizontal to facilitate the recording of data.

Using a rectangular model to obtain analytical expressions for spherical aberration of electromagnetic quadrupole lenses

Using a rectangular model to obtain analytical expressions for spherical aberration of electromagnetic quadrupole lenses

Using a rectangular model to obtain analytical expressions for spherical aberration of electromagnetic quadrupole lenses

Using a rectangular model to obtain analytical expressions for spherical aberration of electromagnetic quadrupole lenses

Discharge without electrodes by means of concentrated bombardment with microwaves

With the aid of modern microwave transmitters with high pulse power, for example, such as are employed in radar transmitters, it is possible to produce a free incandescent discharge without electrodes by concentrating radiated energy into the smallest possible space, if the pressure in the region of the focus is lowered 1,2. The waves can be concentrated by quasi-optical point to point image formation of the source of rays by means of metallic mirrors or electromagnetic lenses or by excitation of a suitable resonance cavity at its natural frequency.

On an analytical expression for the axial field of electromagnetic lenses

An equation is shown for relating the physical parameters of an electromagnetic lens (viz., the central bore diameter, pole-piece spacing, and number of amp-turns through the coil) to the variation of the axial magnetic field along the axis. The equation may also be used to find the maximum value of the axial field, the half-width of the field, and other field parameters. The results obtained with this formula are compared with those of other analytical expressions and with experimental data. (T.F.H.)

Analysis of a new crossed-field amplifier, the "EAL," or electromagnetic amplifying lens

A new form of crossed-field microwave and millimeter wave amplifier which combines an interaction process that results in axial gain with a quasi-optical handling of the RF input and output power is described. Because of its functional similarity to a microwave lens and the additional property of amplification, it is called the Electromagnetic Amplifying Lens. Its advantages are outlined, and its interaction mechanism considered in detail. It is shown that the voltage gain is a linear function of distance in the useful operating range. When the RF level is low, interference between forward- and backward-traveling waves on the waveguide results in loss of control of the space charge. This phenomenon limits the gain available with stable device operation; useful gain of at least 20 db is theoretically possible with a bandwidth of several per cent. The crossed-field interaction principle that is employed assures efficiencies of better than 50 per cent.

Angular Aberrations in Sector Shaped Electromagnetic Lenses for Focusing Beams of Charged Particles

The general expression for the second-order angular aberration of sector shaped electromagnetic lenses consisting of superimposed uniform magnetic and radial electric fields used for the plane focusing of diverging beams of charged particles is derived. The result is applied to the special cases of pure magnetic and pure electric field lenses. The ion optics of a mass spectrometer employing sector electric and magnetic lenses in tandem and which has first-order velocity focusing and second-order angular focusing is obtained.

Refracting Sound Waves

Structures are described which refract and focus sound waves. They are similar in principle to certain recently developed electromagnetic wave lenses in that they consist of arrays of obstacles which are small compared to the wave-length. These obstacles increase the effective density of the medium and thus effect a reduced propagation velocity of sound waves passing through the array. This reduced velocity is synonymous with refractive power so that lenses and prisms can be designed. When the obstacles approach a half wave-length in size, the refractive index varies with wave-length and prisms then cause a dispersion of the waves (sound spectrum analyzer). Path length delay type lenses for focusing sound waves are also described. A diverging lens is discussed which produces a more uniform angular distribution of high frequencies from a loud speaker.

An Optical Bench for Electron Optical Studies

An evacuated chamber containing a heavy lathe bed for supporting and aligning optical parts, and means for moving the essential internal components from the exterior, is described. The construction is explained in detail. Stabilized high voltage to thirty kilovolts and stabilized low voltage supplies for energizing electromagnetic lens coils are provided. The equipment may be used to illustrate the operation of such electronic equipment as cathode-ray tubes, electron microscope and diffraction apparatus, or to study the properties of phosphors and optical components such as lenses, guns, and deflection electrodes.