Biomedical Engineering Reference
In-Depth Information
Hanbury-Brown
Twiss stellar interferometer that was used to measure the size of nearby stars
[5] . The size of a star is measured through the speckle spatial statistics. For instance, the nearby
star Sirius casts a speckle pattern across the face of the earth with an average speckle size of
several tens of meters. Experiments like these launched the field of statistical optics.
Speckle interferometry and holography provide a statistical approach to biological
specimens and applications. These techniques are closely related to phase-contrast imaging,
but they have a very different character. Speckle images tend to have low spatial
information content. A theorem in statistical optics states that a speckle field with unity
contrast contains no spatial information. Therefore, fully developed speckle provides no
structural information from a specimen, and hence provides no image at all. Structural
information comes from spatial variations in the speckle statistics. But what speckle images
lack in low resolution, they make up for with extremely high sensitivity to phase
disturbances. Indeed, substantial information comes from time-dependent phase changes
and how these changes affect the time development of speckle fields.
The analysis of dynamic speckle is the subject of dynamic light scattering (DLS). The basic
concept of DLS is an ensemble of scattering objects that are in motion. Light is scattered as
partial waves, and the motions of the objects produce phase changes in the scattered partial
waves. Because the objects are distributed in space, the relative phases are random, and if
the motions are uncorrelated, the changes in the phases are also random, leading to a
complex scrambled phase of dynamic speckle. However, the way that the objects move is
encoded in the frequency content of the speckle intensity fluctuations. For instance, uniform
motion of the scattering objects produces a Doppler shift with a well-characterized
frequency. Random diffusion has no discrete frequency but does have a well-defined knee
frequency that depends on the diffusion coefficient. Therefore, by analyzing the frequency
content of dynamic speckle across a wide range of frequencies, many different types of
motion can be studied as they are perturbed by outside influences.
In the case of living biological tissue, the scattering objects are mitochondria, nuclei,
organelles, and cell membrane. Each of these biological components has different types of
motion. In some cases, the motion is driven by molecular motors fed by ATP from active
metabolism. In other cases, the motion is driven by external forces, such as when a newly
divided cell jostles its neighbors to make room for itself. The different types of scattering
objects and their different types of motion determine the fluctuating temporal statistics of the
dynamic speckle. Clearly, there is a strong overlap in frequencies and in the sizes of
scattering objects, which produce essentially featureless fluctuation power spectra, and it is
difficult to distinguish the individual contributions. However, these power spectra can be
measured by applying external perturbations, such as altered physiological conditions or
application of a pharmaceutical drug, which cause changes in the power spectra and they
carry signatures specific to the changes in the internal motion of the live tissue.
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