Digital Optical and Scanning Probe Microscopy for Inspection and Manipulation of Biocells - Bioanalysis Advanced Materials Methods and Devices - page 97

waveguide to the tissue under study. The scattered light, caused by the erythrocytes
moving in the illuminated volume, is collected by the second waveguide and
transported onto the CCD matrix where the biospeckle pattern is recorded. Due to
the movement of the erythrocytes, the speckles also move, thus forming a dynamic
speckle field. The biospeckle patterns are recorded using a high-resolution digital
CCD camera with a frame rate of 25 frames/s. The exposure time varies from 1/25 s
(for dynamic speckle contrast analysis in a single exposure mode) to 1/1,000 s (for
cross-correlation analysis of subsequent frames). Speckle patterns are recorded as a
distribution of gray values I(m, n) in digital form for each pixel (m, n) of the CCD
matrix. In real time operation the image analysis is performed during the time
interval between subsequent (two or more) frames. Three different mathematical
approaches are used for the analysis of the resultant biospeckle patterns, as
explained below.

7.7.1 Decorrelation of Speckle Patterns

For single-point measurements, the intensity fluctuations at the point are
characterized by the time-correlation length defined as the time at which the
normalized temporal autocorrelation function of intensity fluctuations falls to 1/ e .
This statistical quantity is inversely proportional to the fluctuating speed of the
speckle intensity. Its reciprocal value measures the velocity of a diffuse object, at
least for speckles scattered once.
A more general description of dynamic speckle patterns is based on the use of
multidimensional space-time cross-correlation functions.
The most simple approach is decorrelation analysis. In practice, many
parameters are introduced into measurement data to characterize the variations in
such speckle patterns quantitatively. Fujii et al. [ 45 ], in retinal blood flow
measurements, use the average rate of change of speckles termed AD, “the average
derivative,” and the reciprocal value BR, “the blur rate” of the speckle intensity
variations. Oulamara et al. [ 46 ] studying the biological activity of botanical
specimens by means of biospeckle pattern decorrelation analysis introduce a
parameter defined as the decorrelation mean speed (DMS) of the temporal speckle
signals. The parameter was computed as an averaged value of the squared differ-
ence between the speckle signals, the first being taken as a reference. This parame-
ter is equivalent to the so-called structural function introduced by A.N.
Kolmogorov, and widely used for statistical characterization of the intensity of
turbulent fluctuations in fluid mechanics [ 13 ]. The same parameter is used in our
approach [ 14 - 16 ]. The structural function is directly related to the correlation
function and defined as

D E

2

ð I k I n Þ

D kn ¼

Ihi :

(7.6)

Ihi