76
2 Holographic Microscopy of Phase and Diffuse Objects …
heterogeneity size in comparison with λ, more light is reflected. So, for high A in
(2.11), it is necessary to use the correlation function ρ 1 ( x 0 )ρ 1
x
0
different from
delta function and dependent on surface particular properties.
Thus, the above-mentioned results confirm the limits of possible shift in holographic microinterferometry schemes. The increase of the object longitudinal shift
range can be reached by the decrease of the objective aperture and by the loose of
the resolution. During interference studies of the objects, which change light beam
amplitude distribution, it is necessary to consider the fact that defocusing distorts the
image itself as well as phase difference between the images. It is also obvious that the
use of microobjective in the schemes of holographic interference microscopy does
not allow considerable increasing sensitivity to longitudinal shift measurements, but
it improves spatial resolution. It is shown that the use of 10×–40× magnification
objectives allows measuring shifts to tens of micron. This fact along with the simple
identification of interferograms, observed in real time, makes the methods of holographic interference microscopy with high spatial resolution quite useful for the
studies of diffusive objects [59, 68].
2.1.4 Interference Pattern Localization at Homogeneous
Radial Change of Cylinder Object
Some biological objects (nerve, nerve fiber and others) have cylindrical symmetry.
Under the influence of different physical agents (for example, magnetic field, pressure), the changes corresponding to three-dimensional compression or object broadening can be observed. In the series of experiments under the influence of pulsed
magnetic field on isolated nerve, it is impossible to observe any interference fringes.
One of the reasons for this could be the disagreement of the observing plane and
localization plane. In connection with this, there was made a preliminary theoretical
analysis of double-exposed interferograms under homogeneous radial broadening of
the cylinder object in the scheme shown in Fig. 2.6a.
The interference pattern localization plane is assumed as a maximal contrast
plane. Let us consider that the object has R 0 radius and is under homogeneous radial
deformation R, β = R/R 0 . Reflection index for all object points is equal to 1,
out of it—it is equal to zero. The object is projected by the lens 4 with the focal
distance f and the aperture q which is at a distance d from the object, on the plane
P, the defocusing parameter (see Fig. 2.6a)
ε =
1
d
+
1
p
−
1
f
.
(2.20)
Localization plane can be detected by the search of maximum value of module of
a complex number:
2 Holographic Microscopy of Phase and Diffuse Objects …
heterogeneity size in comparison with λ, more light is reflected. So, for high A in
(2.11), it is necessary to use the correlation function ρ 1 ( x 0 )ρ 1
x
0
different from
delta function and dependent on surface particular properties.
Thus, the above-mentioned results confirm the limits of possible shift in holographic microinterferometry schemes. The increase of the object longitudinal shift
range can be reached by the decrease of the objective aperture and by the loose of
the resolution. During interference studies of the objects, which change light beam
amplitude distribution, it is necessary to consider the fact that defocusing distorts the
image itself as well as phase difference between the images. It is also obvious that the
use of microobjective in the schemes of holographic interference microscopy does
not allow considerable increasing sensitivity to longitudinal shift measurements, but
it improves spatial resolution. It is shown that the use of 10×–40× magnification
objectives allows measuring shifts to tens of micron. This fact along with the simple
identification of interferograms, observed in real time, makes the methods of holographic interference microscopy with high spatial resolution quite useful for the
studies of diffusive objects [59, 68].
2.1.4 Interference Pattern Localization at Homogeneous
Radial Change of Cylinder Object
Some biological objects (nerve, nerve fiber and others) have cylindrical symmetry.
Under the influence of different physical agents (for example, magnetic field, pressure), the changes corresponding to three-dimensional compression or object broadening can be observed. In the series of experiments under the influence of pulsed
magnetic field on isolated nerve, it is impossible to observe any interference fringes.
One of the reasons for this could be the disagreement of the observing plane and
localization plane. In connection with this, there was made a preliminary theoretical
analysis of double-exposed interferograms under homogeneous radial broadening of
the cylinder object in the scheme shown in Fig. 2.6a.
The interference pattern localization plane is assumed as a maximal contrast
plane. Let us consider that the object has R 0 radius and is under homogeneous radial
deformation R, β = R/R 0 . Reflection index for all object points is equal to 1,
out of it—it is equal to zero. The object is projected by the lens 4 with the focal
distance f and the aperture q which is at a distance d from the object, on the plane
P, the defocusing parameter (see Fig. 2.6a)
ε =
1
d
+
1
p
−
1
f
.
(2.20)
Localization plane can be detected by the search of maximum value of module of
a complex number: