Page 96 - Fundamentals of Light Microscopy and Electronic Imaging

ABBE’S THEORY FOR IMAGE FORMATION IN THE MICROSCOPE 79

Lens
Grating

th
n order

Optic
axis
th
0 order
f
n ⋅

a b
Object Diffraction plane Image
plane (Back focal plane of lens) plane

Figure 5-14
Abbe’s theory for image formation in a light microscope. An objective lens focused on a
grating (2f a f) in the object plane produces a magnified real image of the grating in the
image plane. The diffraction plane is located at 1f in the back aperture of the lens. An
incident planar wavefront is shown. Diffracted nth-order and nondiffracted 0th-order rays are
separated in the diffraction plane, but are combined in the image plane.

lengths by exactly 1, 2, 3,... wavelengths, respectively. The waves at each spot are
exactly in phase and are diffracted at the slits in the specimen at the same unique
angle of diffraction ( ). Note that each point in the diffraction plane corresponds to
a certain angle of light leaving the specimen. The absence of light between the spots
is due to interference between waves that are in or out of phase with each other. The
0th- and higher-order diffraction spots are most clearly focused and separated from
one another in the diffraction plane (the rear focal plane of the objective lens).
• Image formation in the image plane is due to the interference of undeviated and
deviated components that are now rejoined and interfere in the image plane, caus-
ing the resultant waves in the image plane to vary in amplitude and generate con-
trast. Abbe demonstrated that at least two different orders of light must be captured
by a lens for interference to occur in the image plane (Fig. 5-15).

inventions were the Abbe achromatic condenser, compensating eyepieces for removing
residual color aberration, and many other significant items of optical testing equipment. Abbe
is perhaps most famous for his extensive research on microscope image formation and his
diffraction theory, which was published in 1873 and 1877. Using a diffraction grating, he
demonstrated that image formation requires the collection of diffracted specimen rays by the
objective lens and interference of these rays in the image plane. By manipulating the
diffraction pattern in the back aperture, he could affect the appearance of the image. Abbe’s
theory has been summarized as follows: The microscope image is the interference effect of
a diffraction phenomenon. Abbe also introduced the concept of numerical aperture (n sin )
and demonstrated the importance of angular aperture on spatial resolution. It took 50 years
for his theory to become universally accepted, and it has remained the foundation of
microscope optical theory ever since. Ernst Abbe was also a quiet but active social reformer.
At the Zeiss Optical Works, he introduced unheard-of reforms, including the 8-hour day, sick
benefits, and paid vacations. Upon his death, the company was handed over to the Carl
Zeiss Foundation, of which the workers were part owners.