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Step 7 |

Our basic explanation is split into several steps

Page 3

More information on how it works

The spatial resolution is determined by the maximum cyclotron

radius of the electrons as they leave the sample surface. The

radius depends on the energy of the electrons and the strength of

the magnetic field at the surface.

radius of the electrons as they leave the sample surface. The

radius depends on the energy of the electrons and the strength of

the magnetic field at the surface.

A disk of confusion is created by electrons being emitted at all

angles up to 90o from the magnetic axis.

The maximum off-axis distance is twice the maximum radius. The

helical trajectories have a maximum radius that depend on the

energy of the electrons E, and the magnetic field B, in the following

relationship:

angles up to 90o from the magnetic axis.

The maximum off-axis distance is twice the maximum radius. The

helical trajectories have a maximum radius that depend on the

energy of the electrons E, and the magnetic field B, in the following

relationship:

The probability of being at a distance x from the point of emission

can be calculated using this geometry:

can be calculated using this geometry:

The cyclotron orbit is illustrated by the circle of radius r. The

point the electron crosses the image plane will be a distance x

from the point of emission where x is given by the cosine law:

point the electron crosses the image plane will be a distance x

from the point of emission where x is given by the cosine law:

For a uniform distribution of radii from 0 to xmax, t:he probability

of an electron crossing the image plane between x and x+dx is:

of an electron crossing the image plane between x and x+dx is:

This equation can be integrated numerically. This gives the one

dimensional PSF. Dividing the result by 2πr, the area of the PSF

at a radius r, gives the cross section of the 2 dimensional PSF as

shown on the right.

While the one dimensional PSF is sharply peaked at the center,

nearly 50% of the integrated intensity is at a radius greater than 1

rmax.

dimensional PSF. Dividing the result by 2πr, the area of the PSF

at a radius r, gives the cross section of the 2 dimensional PSF as

shown on the right.

While the one dimensional PSF is sharply peaked at the center,

nearly 50% of the integrated intensity is at a radius greater than 1

rmax.

VPPEM Point Spread Function (PSF)

edge resolution in microns approximately equals:

with E in electron volts and B in Tesla.

While the energy of the electrons can be changed within the field

by biasing the sample, but this does not change the spatial

resolution. The angle of deflection due to terminating the vector

potential field is inversely proportional to the square root of the

energy of the electrons when they exit the field. However, the

angles of the cyclotron orbits also change in the same way as

the electrons are accelerated or decelerated.

with E in electron volts and B in Tesla.

While the energy of the electrons can be changed within the field

by biasing the sample, but this does not change the spatial

resolution. The angle of deflection due to terminating the vector

potential field is inversely proportional to the square root of the

energy of the electrons when they exit the field. However, the

angles of the cyclotron orbits also change in the same way as

the electrons are accelerated or decelerated.

How it works |