Page 120 - Fundamentals of Light Microscopy and Electronic Imaging

PHASE CONTRAST MICROSCOPY 103

the resultant P wave, and vice versa. A complete description of this form of wave analy-
sis is given by Hecht (1998), Pluta (1989), and Slayter (1976), but for our purposes, a
brief definition will be sufficient to explain the diagram. The phase shift of D relative to
S on the graph is shown as , where 90° /2, and is the relative phase shift
(related to the optical path difference) between the S and P vectors. For objects with
negligible optical path differences (phase shifts ), is 90°. As shown in the figure,
a D wave of low amplitude and small phase shift results in a P wave with an amplitude
that is nearly equal to that of the S wave. With similar amplitudes for S and P, there is no
contrast, and the object remains invisible.

The Role of Differences in Optical Path Lengths

We encountered the concept of optical path length previously when we discussed the
action of a lens in preserving the constancy of optical path length between object and
image for coherent waves emerging from an object and passing through different
regions of the lens (Fig. 5-6). For phase contrast microscopy, we are concerned with the
role of the object in altering the optical path length (relative phase shift ) of waves
passing through a phase object.
Since the velocity of light in a medium is v c/n, where c is the speed of light in a
vacuum, rays of light passing through a phase object with thickness t and refractive
index n greater than the surrounding medium travel slower through the object and
emerge from it retarded in phase relative to the background rays. The difference in the
location of an emergent wavefront between object and background is called the phase
shift δ (same as φ above), where δ in radians is

δ 2
/λ,

and
is the optical path difference, which was defined in Chapter 5 as

(n n )t.
2
1

The Optical Design of the Phase Contrast Microscope

The key element of the optical design is to (1) isolate the surround and diffracted rays
emerging from the specimen so that they occupy different locations in the diffraction
plane at the back aperture of the objective lens, and (2) advance the phase and reduce the
amplitude of the surround light, in order to maximize differences in amplitude between
the object and background in the image plane. As we will see, the mechanism for gen-
erating relative phase retardation is a two-step process: D waves are retarded in phase by
/4 at the object, while S waves are advanced in phase by a phase plate positioned in
or near the diffraction plane in the back aperture of the objective lens. Two special
pieces of equipment are required: a condenser annulus and an objective lens bearing a
phase plate for phase contrast optics.
The condenser annulus, an opaque black plate with a transparent annulus, is posi-
tioned in the front aperture of the condenser so that the specimen is illuminated by
beams of light emanating from a ring (Fig. 7-6). (In some texts, the illuminating beam
emergent from the condenser is described as a hollow cone of light with a dark center—