Page 97 - Fundamentals of Light Microscopy and Electronic Imaging

80 DIFFRACTION AND INTERFERENCE IN IMAGE FORMATION

Appearance at
back focal
plane of
objective

Back focal
plane of
objective

Objective

Specimen plane
a b c d
Figure 5-15
Generation of an image by interference requires collection of two adjacent orders of
diffracted light by the objective lens. If diffraction at the specimen does not occur (a), or
diffracted rays are not collected by the objective (b), no image is formed. In (c), a minimum of
two adjacent diffraction orders (0th and 1st) are collected, and an image is formed. In (d),
multiple diffracted orders are collected, leading to a high degree of definition in the image.

• A periodic specimen with an interperiod spacing d gives rise to a periodic pattern
with spacing D in the diffraction plane, where D 1/d. Therefore, the smaller the
spacings in the object, the farther apart the spots are in the diffraction plane, and
vice versa. The relationship is

d fλ/D cos

where f is the focal length of the lens, λ is the wavelength, and is the acute angle at
the principal plane in the objective lens from which the focal length is measured and
which forms a right triangle together with the 0th- and 1st-order diffraction spots.

Abbe’s theory of image formation explains the following important points: If a
specimen does not diffract light or if the objective does not capture the diffracted light
from an object, no image is formed in the image plane. If portions of two adjacent orders
are captured, an image is formed, but the image may be barely resolved and indistinct.
If multiple orders of diffracted light are captured, a sharply defined image is formed.
The theory is also the basis for determining the spatial resolution of the light micro-
scope, which is the subject of the next chapter.

DIFFRACTION PATTERN FORMATION IN THE BACK APERTURE
OF THE OBJECTIVE LENS

Let us now consider the diffraction pattern in the microscope’s diffraction plane in the
back aperture (back focal plane) of the objective lens. Under conditions of Koehler illu-
mination, a diffraction image of a specimen is formed just behind the objective in the