Physical Principles of Electron Microscopy: An Introduction to TEM ...

Electron Optics 33
We can define image magnification as the ratio of the lengths Xi and Xo,
measured perpendicular to the optic axis. Because the two triangles defined
in Fig. 2-5 are similar (both contain a right angle and the angle �), the ratios
of their horizontal and vertical dimensions must be equal. In other words,
v /u = Xi /Xo = M (2.3)
From Fig. 2-5, we see that if a single lens forms a real image (one that could
be viewed by inserting a screen at the appropriate plane), this image is
inverted, equivalent to a 180� rotation about the optic axis. If a second lens is
placed beyond this real image, the latter acts as an object for the second lens,
which produces a second real image that is upright (not inverted) relative to
the original object. The location of this second image is given by applying
Eq. (2.2) with appropriate new values of u and v, while the additional
magnification produced by the second lens is given by applying Eq. (2.3).
The total magnification (between second image and original object) is then
the
product of the magnification factors of the two lenses.
If the second lens is placed within the image distance of the first, a real
image cannot be formed but, the first lens is said to form a virtual image,
which acts as a virtual object for the second lens (having a negative object
distance u). In this situation, the first lens produces no image inversion. A
familiar example is a magnifying glass, held within its focal length of the
object; there is no inversion and the only real image is that produced on the
retina of the eye, which the brain interprets as upright.
Most glass lenses have spherical surfaces (sections of a sphere) because
these are the easiest to make by grinding and polishing. Such lenses suffer
from spherical aberration, meaning that rays arriving at the lens at larger
distances from the optic axis are focused to points that differ from the focal
point of the paraxial rays. Each image point then becomes a disk of
confusion, and the image produced on any given plane is blurred (reduced in
resolution, as discussed in Chapter 1). Aspherical lenses have their surfaces
tailored to the precise shape required for ideal focusing (for a given object
distance) but are more expensive to produce.
Chromatic aberration arises when the light being focused has more
than one wavelength present. A common example is white light that contains
a continuous range of wavelengths between its red and violet components.
Because the refractive index of glass varies with wavelength (called
dispersion, as it allows a glass prism to separate the component colors of
the white light), the focal length f and the image distance v are slightly
different for each wavelength present. Again, each object point is broadened
into a disk of confusion and image sharpness is reduced.