256
3 Holographic Interferometry for Studying …
remoteness of points of the deformed surface and the shift directions. For example, if
there are annular structures in the interference pattern, then for this case, contraction
of the rings to the center will prove the presence of convexity, and their recession
from the center—the concavity of the surface.
3.3.6 Ways of Estimating the Shift Points of the Object Under
Study with the Interference Holographic Method
It is known that registration and reconstruction of a double-exposure hologram, one
exposure of which corresponds to the initial state of the object under study P and the
other one—to the altered one P 1 (for example a deformed one), give the possibility
to form a holographic interferogram containing the information about shifts of this
object in the period of time between the exposures (Fig. 3.35).
And the phase difference of the obtained interferogram is estimated by the
expression
ϕ =
K 1 ·
L,
(3.74)
where
K 1 =
K 2 −
K 1 is the vector of sensitivity;
L is the shift vector;
K 1 is the
wave vector of the illuminating wave;
K 2 is the wave vector of the object wave.
As it follows from (3.74), it is only possible to determine the projection of the
shift vector
L to the bisectrix of the angle between the directions of illumination
and observation for these fixed directions of illumination and observation. To find
the space vector
L of shift points of the object, it is necessary to have at least three
equations like (3.74) and solve the system of equations.
To do this, either the illumination direction should be altered or the interference
pattern should be observed from different directions.
The average speed of shifts of this object point can be estimated by the formula
V =
L//t
(3.75)
where t is the time interval between pulses of the laser radiation.
It is suggested that holograms are recorded and reconstructed with two spatially
separated reference beams to determine the direction of relative shifts of points on
the surface under study. If the optical path length of one of the reconstructed beams
is gradually changed through the known method at the reconstruction stage, then it is
possible to determine the direction of the shift vector of points on the surface under
study according to the shift direction of interference fringes (Fig. 3.41).
For example, let the phase difference ϕ = ϕ 2 − ϕ 1 > 0, and the gradual phase
shift δ be inserted into the wave ϕ 2 . It is necessary to determine the shift direction
of the analyzed point 2 relative to the initial point 1.
The intensity quantity will be in these points
3 Holographic Interferometry for Studying …
remoteness of points of the deformed surface and the shift directions. For example, if
there are annular structures in the interference pattern, then for this case, contraction
of the rings to the center will prove the presence of convexity, and their recession
from the center—the concavity of the surface.
3.3.6 Ways of Estimating the Shift Points of the Object Under
Study with the Interference Holographic Method
It is known that registration and reconstruction of a double-exposure hologram, one
exposure of which corresponds to the initial state of the object under study P and the
other one—to the altered one P 1 (for example a deformed one), give the possibility
to form a holographic interferogram containing the information about shifts of this
object in the period of time between the exposures (Fig. 3.35).
And the phase difference of the obtained interferogram is estimated by the
expression
ϕ =
K 1 ·
L,
(3.74)
where
K 1 =
K 2 −
K 1 is the vector of sensitivity;
L is the shift vector;
K 1 is the
wave vector of the illuminating wave;
K 2 is the wave vector of the object wave.
As it follows from (3.74), it is only possible to determine the projection of the
shift vector
L to the bisectrix of the angle between the directions of illumination
and observation for these fixed directions of illumination and observation. To find
the space vector
L of shift points of the object, it is necessary to have at least three
equations like (3.74) and solve the system of equations.
To do this, either the illumination direction should be altered or the interference
pattern should be observed from different directions.
The average speed of shifts of this object point can be estimated by the formula
V =
L//t
(3.75)
where t is the time interval between pulses of the laser radiation.
It is suggested that holograms are recorded and reconstructed with two spatially
separated reference beams to determine the direction of relative shifts of points on
the surface under study. If the optical path length of one of the reconstructed beams
is gradually changed through the known method at the reconstruction stage, then it is
possible to determine the direction of the shift vector of points on the surface under
study according to the shift direction of interference fringes (Fig. 3.41).
For example, let the phase difference ϕ = ϕ 2 − ϕ 1 > 0, and the gradual phase
shift δ be inserted into the wave ϕ 2 . It is necessary to determine the shift direction
of the analyzed point 2 relative to the initial point 1.
The intensity quantity will be in these points