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(B) Defects in lens, Apertures and resolutions

Apertures and its role in refining defects and resolution of the lenses.

After going through the whole elements functions in TEM, how electron beam is generated and

an image is formed using lenses there are other factors that affect the image quality. The quality

of image is severely affected by different defects in the lenses. In the following sections we will

discuss about the defects in the lenses, their affects and apertures which are used to counter the

affects of the defects and also aide us in making certain procedures.

Aperture

Apertures are holes which generally are used in the lenses which help in limiting the amount of

electrons that pass through. Depending on the location of their placement and the lens in which

this aperture is used, they can be useful in various applications such as, illumination, resolution,

contrast and also selecting the mode of operation.

Generally aperture is a hole of the dimensions between 10 m to 300 m and these are

surrounded by a heavy metal called as diaphragm, usually 25- 50 m thick1

. There are different

types of apertures. Generally used apertures are circular discs with a hole in the middle; here the

aperture size is fixed. In some cases where one needs to change the aperture size, we use a model

where various holes of different size on the same rectangular metal strip as shown in the figure

below[1]:

The top circular disc shaped apertures are of

fixed type, while the bottom metal strip is one

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Apart from limiting the aperture angle, apertures are also useful in absorbing different x-rays,

other impurities such as hydro carbons etc.

Resolution

The quality of the microscope is measured in terms of the quality of image. There are different

factors which affect the quality of the image however; the parameter in terms of the quality of

the image is measured is resolution.

Resolution: Resolution can be defined as the ability to distinguish in an image two point sources

which are closely placed.

For example in the figure above, as we can see two point sources when placed closer than the

resolution limit overlaps each other in the image. Primarily this is caused according to Rayleigh

due to the diffraction. When electron beam passes through the lens they bend at the corners

causing series of Fresnel fringes. Due to this a simple point object will not be imaged as a point

but instead as a disc. Rayleigh concluded that the radius of this airy disc which is also the

minimum resolvable distance to be

(1) where is wavelength and is aperture angle.

As you can see the aperture angle plays a major role. Increasing the aperture angle improves the

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resolution by improving the illumination. However this is in ideal case where we consider no

defects, but in practice all the systems are affected by different defects.

Defects and factors affecting resolution:

Like all optical systems, TEM also affected by three major defects.

1. Spherical Aberration2. Chromatic Aberration3. Astigmatism

Before going further into looking at how the apertures work, or how these defects affect different

lenses in the TEM lets discuss about these defects.

Spherical Aberration:

Spherical aberration occurs when the electrons further from the axis, bend differently than the

ones close the axis, this is generally the case with electromagnetic lenses. Due to this, we can see

in the Figure below, different electrons focus at different places on the axis, which affects the

resolution of the resulting image.

( Figure from Transmission electron Microscopy by David B. Williams and C. Barry Carter)

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(Figure from: ENCYCLOPEDIA OF SCIENCE & TECHNOLOGY online Article Hubble space

telescope)

As we can see a point object appears as a disc shape and the radius of this is given by

again we see a very strong relation with the aperture angle. The value of theaberration increases with aperture angle. So in order to reduce the aberration it is desired to have

a low aperture angle.

Chromatic Aberration:

Chromatic aberration is caused due to the difference in frequency or to say difference in the

energy of the electrons flowing from the source. It is observed that different electrons with

different energies are bent differently by the electromagnetic field. This leads to an aberration

similar to spherical aberration as a result; different electrons focus at different places on the axis.

The electrons with lower energies are bent strongly when compared to the ones with higher

energies. The radius of the disc is given by

Again the aberration can be reduced by reducing the aperture.

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(Figure from Transmission electron Microscopy by David B. Williams and C. Barry Carter).

The primary ways to reduce this aberration is that all the electrons are of same energy that is the

source should be monochromatic. With the advanced electron guns available today, this is

possible. Yet, there is inevetitable aberration caused. This is due to the unequal absorption of

energy by the specimen, when the electrons pass through at different sites of the specimen. It is

advised that the specimen be made thin enough to minimize the absorption of energy by the

specimen. A very thin and homogeneous sample will help in reducing the chromatic aberration.

It was measured that for a 300KV system the ideal thickness of the sample to be 30nm [1] .

Practically the sample thickness varies between, 50 nm and 60nm.

Astigmatism:

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Astigmatism is due to the result of non uniform magnetic field in the lens along the bore. This

non uniform magnetic field causes a disruption in the spiral motion of the electrons, which

results in more an elliptic shape. Astigmatism can be a result of defects in the soft iron core, or

aligning of the aperture or even the impurities on the aperture. The aberration is given by[1]

Astigmatism can be eliminated by using stigmators which are small octupoles which cause a

magnetic field when required to compensate for the inhomogeneous field in the bore.

Effect of defects on resolution:

After discussing different defects it was attempted to find the affect of the defect on the

resolution, and it was found that, apart from different factors, aperture angle greatly affects the

resolution. When there are no defects, we see that the increase in aperture angle improves the

resolution as it improves the illumination. However, the same increase in aperture angle

increases the defects as well. Therefore we need to optimize the aperture angle to find the best

possible resolution. This was found to be

nd the minimum value of resolvable

distance as (C*3)1/4

Application of apertures:

After looking at different defects and how they affect the resolution. We can also observe that a

precise control of aperture angle is indeed very important to obtain the required resolution and

quality of the image. We use apertures at 1) Condenser lens 2) Objective Lens and 3)

Intermediate Lens.

Condenser Aperture:

This aperture primarily is used to reduce spherical aberration, and controlling the illumination.

The condenser aperture contains two apertures C3 and C2 where C2 aperture should always be

centered on the optical axis; otherwise, the image would be distorted. In TEM mode generally

this aperture remains fixed.

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Aperture C3 is used in reducing the spherical aberration. The spherical aberration is not observed

in the image of the specimen, but the probe formation. This will limit the probe diameter. And

the minimum radius obtainable is given by therefore properly controlling the

aperture angles gives the best probe diameter, and the optimum value is given by

. The aperture in condenser lens also can be a cause of astigmatism, if the limiting

aperture in C2 is misaligned or contaminated and starts charging up. However this as discussed

earlier can be countered by using stigmators.

(figure from Transmission electron Microscopy by David B. Williams and C. Barry Carter).

Image of C2 aperture from Transmission electron Microscopy by

David B. Williams and C. Barry Carter

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(Effect of aperture angle on aperture size and also the increase in aperture angle corresponds to

increase in probe current)[1]

Intermediate Aperture: The primary role of intermediate aperture is when we wish to obtain

diffraction pattern instead of image of sample. To do this we need to use selected area aperture,

which is not practical, considering the sample is already there and it is not possible to insert the

aperture in the sample plane. The solution to this is using virtual aperture. This can be achieved

by inserting a SAD aperture in the image plane which was obtained by the objective lens. This

can be done by adjusting the intermediate lens. We have to center this aperture on the optical

axis.

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It is very crucial that aperture be moved such that it selects the direct beam on the optic axis.

Formation of DP using SAD aperture.

figure from Transmission electron Microscopy by David B. Williams and C. Barry Carter

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Objective Aperture:

The objective aperture is the most important aperture as the objective lens. This aperture is

generally smaller than the condenser aperture and mostly uses a multiple size aperture. Hence it

is common to use a metal strip with multiple holes type of aperture here. The aperture is used to

control the illumination and contrast. The smaller the aperture angle the better the contrast. This

aperture is also used to correct the spherical aberration in the final image; hence an optimum

aperture angle is needed to be selected to get the best image.

The astigmatism also occurs in the image if aperture is misaligned and hence the aperture should

always be carefully aligned on the optic axis.

Apart from this there are many other applications of apertures that need careful observation and

practice to obtain a very accurate image and DP from the specimen. As important is the

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application of the apertures, is the maintenance of apertures. Apertures get contaminated so

often, they can be cleaned by heating them to extreme heats. Some apertures are made so thin

that by the high speed bombardment of electrons the metal gets heated red hot and cleans

automatically. But this also causes small changes in alignment. There is always a tradeoff.