Page 140 - Fundamentals of Light Microscopy and Electronic Imaging

VECTORIAL ANALYSIS OF POLARIZED LIGHT USING A DICHROIC FILTER 123

aligned in the same direction as the organic matrix. The transmission axis of the filter is
perpendicular to the orientation of the crystals and linear polymers in the filter. Thus,
rays whose E vectors vibrate parallel to the crystal axis are absorbed. Waves with
oblique orientations are partially absorbed, depending on the azimuths of their vibra-
tional planes. Filters such as the Polaroid sheet that differentially transmit rays vibrating
in one plane while absorbing those in other planes are said to exhibit dichroism; hence
the common name, dichroic filter. As we will see in later sections, the Polaroid sheet is
a special kind of beam splitter designed to transmit rays vibrating at a certain azimuthal
angle as linearly polarized light. For H-series filters that are commonly employed in
microscopy, only about 25% of incident random light is transmitted, but the degree of
polarization of the transmitted rays is 99%.
If two polarizers are oriented so that their transmission axes are perpendicular to
each other, they are said to be crossed, and all of the light transmitted by the polarizer
(now linearly polarized) is extinguished by the analyzer (Fig. 8-3). The extent to which
incident random light is extinguished by two crossed polars is called the extinction fac-
tor and is defined as the ratio of the intensity of transmitted light observed for two polars
when positioned in parallel and in crossed orientations (I /I ). Extinction factors of

5
3
10 –10 or greater are required for polarization microscopy and can be obtained using
two dichroic filters.
The role of the analyzer in controlling the transmission of polarized light can be
understood from vector diagrams showing the angular orientation (azimuthal angle) and
magnitude of the E vectors of rays drawn from the perspective of viewing a ray end on,
down its axis of propagation. Figure 8-5 shows a vertically oriented analyzer, four inci-
dent waves of linearly polarized light that are equal in amplitude but vibrating in differ-
ent planes, and the amplitudes of those waves after transmission through the analyzer. If
each incident wave is resolved into its horizontal and vertical components, it can be seen
that the entire vertical component of each ray passes through the analyzer. Further, the
amplitudes of the vertical component and the transmitted ray rapidly decrease as the
plane of vibration of the incident ray approaches an azimuth perpendicular to the trans-
mission axis of the analyzer.

Analyzer

Excluded
Transmitted

Figure 8-5
Transmission through an analyzer of linearly polarized rays vibrating in different planes. A
linearly polarized ray vibrating at an azimuthal angle different from the transmission axis of
an analyzer can be resolved into its horizontal and vertical components using principles of
vector math. The amplitude of the transmitted ray is equal to the vertical vector component.