Image Processing Reference
where the integral is taken over the thickness d of the cell, usually few micrometers,
and n ( z ) varies from n || to n . The thermal fluctuation term in Eq. 8.1 is usually neg-
ligible, of the order of 1.7 × 10 7 radians, for commonly used nematic materials.
From Eq. 8.1, it can be seen that if more phase delay is required, the cell thickness
can be increased; however, this will increase the response time of the cell. Alterna-
tively, the optical anisotropy
n = n || -n ⊥ can be increased.
Of course, for most adaptive optical systems it is of interest to produce devices
that can modulate the phase of unpolarized light. This can be achieved in two ways,
both of which have been experimentally tested and used to build devices. The first
approach is to build and carefully align two devices so that the optical axes are or-
thogonal to each other. The other technique consists of putting in an optical contact
quarter-wave plate between the LC cell and a mirror.
In this scheme, when light passes through the LC cell, one polarization state is
retarded. The light then encounters the quarter-wave plate and reflects off the mir-
ror and through the quarter-wave plate, rotating the polarization of the light 90 deg.
The light then makes a second pass through the LC element, but this time the or-
thogonal polarization component is retarded.
Several thousand compounds are classified as LCs. Classification of all these
compounds is usually determined based on the physical mechanism that induces
the mesophase. The first class is called thermotropic, where thermal processes are
responsible for the mesophase. The second class is lyotropic, where the influence
of solvents is the physical mechanism. The lyotropic family is the largest and oc-
curs commonly in nature (soap, cell membranes, etc.), but is of little or no interest
for phase modulation. The thermotropic class is composed of three great families of
compounds—the nematic, cholesteric, and smectic.
This last family contains several different classes such as smectic A and C (usu-
ally indicated as SmA and SmC), and recently a few more classes have been identi-
fied—(SmB, E, G, H, J, and K). The two types of LCs of interest to us are the ne-
matic and a couple of smectic classes such as SmA and C. (Usually the smectic
compounds are collectively called ferroelectric).
In Fig. 8.3 is shown a simple diagram that compares the nematic and ferroelec-
tric materials to equivalent optical components, i.e., wave plates. The diagram also
compares the average switching times of the two kinds of LC materials.
8.3 Orthogonal Transfer Charge Coupled Devices
Correcting for image jitter in the focal plane can be accomplished using a sensor
and tip-tilt correcting device, but other approaches are available. Improvement in
low-light video imaging cameras over the last decade has made it is possible to ob-
tain a large number of images with short exposures. A long-exposure image can be