Polarization Microscopy - Biomedical Optical Phase Microscopy and Nanoscopy - page 325

As a practical example, consider a mitotic spindle observed in a microscope that is
equipped with low NA lenses (NA # 0.5). When the spindle axis is contained in the focal
plane, the illuminating and imaging beams run nearly perpendicular to the spindle axis.
Under those conditions, the retardance measured in the center of the spindle is proportional
to the average birefringence induced by the dense array of aligned spindle MTs. To
determine Δn , it is possible to estimate the thickness, l , either by focusing on spindle fibers

located on top and bottom of the spindle and noting the distance between the two focus
positions, or by measuring the lateral extent of the spindle when focusing through its center.
The latter approach assumes a rotationally symmetric shape of the spindle. Typical values
for the spindle retardance of crane fly spermatocytes ( Figure 15.4B ) and of other cells is
3 m, leading to an average birefringence

of around 10 2 4 . It has been found that the retardance value of the spindle is largely
independent of the NA for imaging systems using NA # 0.5 [3] .

5 nm and the spindle diameter is about 30 40 μ

On the other hand, when using an imaging setup that employs high NA optics (NA . 0.5)
for illuminating and imaging the sample, the measured retardance takes on a somewhat
different context. For example, the retardance measured in the center of an MT image
recorded with an LC-PolScope equipped with a high NA objective and condenser lens is
0.07 nm. A detailed study showed that the peak retardance decreased inversely with the NA
of the lenses. However, the retardance integrated over the cross-section of the MT image
was independent of the NA [40] . While a conceptual understanding of the measured
retardance of submicroscopic filaments has been worked out in the aforementioned
publication, a detailed theory of these and other findings about the retardance measured
with high NA optics has yet to materialize.

15.7.15 Retarder

A retarder, or waveplate, is an optical device that is typically made of a birefringent
plate. The retardance of the plate is the product of the birefringence of the material
and the thickness of the plate. Fixed retarder plates are either cut from crystalline
materials such as quartz, calcite, or mica, or they are made of aligned polymeric
material. If the retardance of the plate is λ /4, for example, the retarder is called a

quarter waveplate.

A variable retarder can be made from a liquid crystal device. A thin layer of highly
birefringent liquid crystal material is sandwiched between two glass windows, each bearing
a transparent electrode. A voltage applied between the electrodes produces an electric field
across the liquid crystal layer that reorients the liquid crystal molecules. This reorientation
changes the birefringence of the layer without affecting its thickness or the direction of its
slow axis.