Digital Optical and Scanning Probe Microscopy for Inspection and Manipulation of Biocells - Bioanalysis Advanced Materials Methods and Devices - page 95

displacement. For the second type of speckle motion, speckles deform, disappear,
and reappear without appreciable displacement of their positions. This type of
speckle motion is called speckle “boiling.” In both cases, the speckle behavior
depends not only on the motion of the scatterers but also on the parameters of the
optical scheme used for the observation of the speckle. In most cases, the mode of
dynamic biospeckle is mixed and speckles both translate and gradually change their
structure. One of the main factors characterizing the dynamic behavior of speckle
patterns is the shape of the illuminating wavefront. For Gaussian beam illumina-
tion, the radius of the beam spot in the object plane, o , and the radius of the
wavefront curvature, r, are expressed as functions of the distance z from a position
on the beam waist:

" # 1 = 2 " # 1 = 2

2 2

z
z 0

z
z 0

o ¼ o 0 1 þ ; r ¼ z 1 þ ; (7.2)

where z 0 ¼ po 0 2 / l and o 0 is the spot radius at the beam waist. Two parameters, the
correlation time, t c , and the lapse time, t d , have been introduced by Asakura and
Takai [ 8 ] to describe the dynamic behavior of speckles composed of both boiling
and translation:

" #

;

2 r c 2

rj

ðt t d Þ gD I ð r ; tÞ¼ exp Þ exp (7.3)

t

c

r 2

where r T 1 , and the lapse time t d depends on ( r ). Let us

consider probing light scattered by a single erythrocyte moving with a constant
velocity v. Parameters t c , and, t d are expressed via parameters of the optical
imaging scheme. Thus, for a simple single lens arrangement, they are

¼ vecr 1, t ¼ T 2

" # 1 = 2

2 vr

1
v

s i
D 2 þ

d i
r c

1
d 0

t

c d i
r c

1
d 0

t c ¼ es i ; t d ¼ es i ; (7.4)

jj

where d 0 is the distance from the object plane to the imaging lens, d i is the distance
from the lens to the observation plane,

e ¼ 1/ d 0 +1/ d i 1/ r is a defocusing

parameter, D is the imaging lens diameter, and s ¼ 1+ d 0 / r . The dynamic speckle

size, r 0 c , is related to a static speckle size parameter rc ¼ pl d i / D , and the

translation distance, rT :

r c þ r T d i D

s i

1
d 0

r 0 c ¼

r c Þ ;

r T ¼ es i (7.5)

1 þ sin Yð r T = j

being the angle between the vectors of v and r . Equation 7.5 shows that the
correlation time of the intensity fluctuations in speckle pattern is inversely

Y

with