Differential Interference Contrast Microscopy (DIC) - Biomedical Optical Phase Microscopy and Nanoscopy - page 31

X - and Y -polarization components, which depends on the applied voltage. The initial bias
can be adjusted by sliding of the wedge component of one of the DIC prisms. In principle,
the liquid crystal cell LC1 can be installed with the same orientation in any place in the
assembly. The second liquid crystal cell LC2 switches the polarization by 90 when the
plate retardation is a half wave ( λ /2), and preserves the beam polarization if the plate

retardance is 0 or full wave ( λ ).

The diagrams to the left and right in Figure 2.6 depict polarization transformations inside
the assembly and the corresponding change of shear directions of the output beams. The left
column illustrates a case when the beam polarizations between two prisms are preserved
and the shear direction is 45 after the second prism DIC2. The right column describes a
rotation of the output shear direction by 90 caused by switching the beam polarizations
after the first prism DIC1.

Let us examine in more detail how the beam-shearing assembly works. For example, the
initial ray A 0 falling on the first prism DIC1 has coordinates ( 2 1, 2 1). Here, the first
number means a coordinate along the X -axis, and the second one is the coordinate along
the Y -axis. The first DIC prism does not change the position of the ray with Y -polarization
and deflects the ray with X -polarization, which creates a shear distance of two units
between the two components. Thus, the first output ray A 1 has Y -polarization and
coordinates ( 2 1, 2 1). If the shear value equals 2 units, then the X -polarized second ray
has B 1 coordinates (1, 2 1).

The second liquid crystal cell LC2 preserves the linear polarized states of the beams A 1 and
B 1 or turns each of the states by 90 without altering the ray positions. In the first case (left
column), the output rays A 2 and B 2 are polarized along the Y - and X -axis, respectively. In
the second case (right column), the rays A 2 and B 2 are polarized along the X - and Y -axis,
respectively.

The second DIC prism is oriented orthogonal to the direction of the first prism. So, the
shear direction of the second prism lies along the Y -axis. The prism DIC2 does not change
the position of a ray with X -polarization, but it deflects a ray with Y -polarization. The shear
value for this second prism is also 2 units. First, we consider a case, which is shown on the
left side of Figure 2.6 , where the liquid crystal cell LC2 has retardance 0 , and therefore the
ray polarizations are not changed. Then, ray A 2 with Y -polarization and coordinates
( 2 1, 2 1) passes the second prism with displacement by 2 units in the Y -direction, and the
output ray A 0 3 has coordinates ( 2 1,1). Meanwhile, the coordinates of ray B 2 are not
changed, and the coordinates for output ray B 0 3 are (1, 2 1). As a result, in the first case, the
dual beam that falls on the specimen has shear direction 2 45 .

For the second case, after the liquid crystal cell LC2 rotates the polarization by 90 , the ray
A 2 is linearly polarized along the X -axis. Therefore, its coordinates are not changed by the