(4.57), from which the intensity Iσ passing the analyser follows as
(4.62)
with γ in Equation (4.56). This leads to
with a in Equation (4.55).
This reduced intensity is plotted versus a in Figure 4.4. The values are considerably larger than in the normally black mode in Figure 4.3. If the cell is fully addressed, the LC molecules orient themselves parallel to the field, and hence the incoming light, linearly polarized along the x-axis, reaches the crossed analyser unchanged, and is hence blocked independent of the wavelength. This generates an excellent black state if a field is applied. Therefore, the normally white cell is the preferred LCD.
The black state is independent of the thickness d. In the white state in Equation (4.63) and in Figure 4.4, the first maximum of the intensity lies in the vicinity of the first maximum of the cos term occurring at
Figure 4.4 The intensity of light passing through a non-addressed normally white TN-LCD with twist angle β = π/2 and with a = 2dΔn/λ according to Equation (4.63)
4.2.2 The supertwisted nematic LC cell (STN-LCD)
Linear polarized light is fed into the STN cell (Scheffer and Nehring, 1998) again with α = 0 in Figure 4.1. The twist angle β at z = d is, however, β > π/2, with values typically between π and 3(π/2). With the twist angle β in Equation (4.49) and a in Equation (4.48), we rewrite γ in Equation (4.47) with p from Equation (4.49) as
With γ in Equation (4.64), and β0 in Equation (4.50), Equation (4.52) governing the field-free state provides for the coordinates x′ and y′ with the angle ψ in Figure 4.1, and again, drawn in Figure 4.5
(4.65)
leading to
Figure 4.5 Angles and coordinates for an STN display
and
For
Equations (4.66) and (4.67) yield
(4.69)
and
Osx′ reaches its maximum
(4.71)
for
If the axis x′ of the analyser is at an angle ψ = −α to the x-axis, the maximum intensity
