4.1 Correlation and Spectral Characteristics of Dynamic Speckle-Field …
323
Statistical characteristics of dynamic speckle-field, which are studied for a model
of diffusely reflecting disk, can be applied for a model of deep phase screen, which
was examined by the authors of work [16].
In this case, rotating matt diffusely scattering disk can serve as a phase screen.
Obtaining for the rotating disk (4.17) can be reduced to the view which corresponds
to an object moving at a constant velocity [16]. In this case, temporal correlation
function of speckles intensity fluctuation will be
γ I (0, τ ) = exp
−τ
2
/τ
2
c
,
(4.20)
where τ c is the time correlation determined as
τ c =
1
|
υ|
1
W 2 +
σ
2
x 2
−
1
2
,
(4.21)
where |
υ| = ωd is the value of linear velocity of diffusers shift.
The parameter σ, which determines diffraction conditions, is calculated according
to formula
σ =
R
μ
+ 1,
(4.22)
where R is the distance between the object and the observation plane; μ is the radius
of wave front curvature.
For this scheme, geometry schemes in (4.17) can be written as
P −
z
μ
d = P +
z
μ
d = ρ 0
1 +
R
μ
= ρ o σ,
(4.23)
as z = R, d is the distance between the center of the illuminated zone to the center
of disc; P is the transverse distance;
k =
2π
λ
is the wave number;
(4.24)
x = λR/π W is the average speckle size.
(4.25)
The beam width W in the object plane at a distance R = z from waist is calculated
according to formula
W = W 0
1 +
z
2
d 2
1
2
,
(4.26)
μ = z
1 +
a
2
z 2
,
(4.27)
323
Statistical characteristics of dynamic speckle-field, which are studied for a model
of diffusely reflecting disk, can be applied for a model of deep phase screen, which
was examined by the authors of work [16].
In this case, rotating matt diffusely scattering disk can serve as a phase screen.
Obtaining for the rotating disk (4.17) can be reduced to the view which corresponds
to an object moving at a constant velocity [16]. In this case, temporal correlation
function of speckles intensity fluctuation will be
γ I (0, τ ) = exp
−τ
2
/τ
2
c
,
(4.20)
where τ c is the time correlation determined as
τ c =
1
|
υ|
1
W 2 +
σ
2
x 2
−
1
2
,
(4.21)
where |
υ| = ωd is the value of linear velocity of diffusers shift.
The parameter σ, which determines diffraction conditions, is calculated according
to formula
σ =
R
μ
+ 1,
(4.22)
where R is the distance between the object and the observation plane; μ is the radius
of wave front curvature.
For this scheme, geometry schemes in (4.17) can be written as
P −
z
μ
d = P +
z
μ
d = ρ 0
1 +
R
μ
= ρ o σ,
(4.23)
as z = R, d is the distance between the center of the illuminated zone to the center
of disc; P is the transverse distance;
k =
2π
λ
is the wave number;
(4.24)
x = λR/π W is the average speckle size.
(4.25)
The beam width W in the object plane at a distance R = z from waist is calculated
according to formula
W = W 0
1 +
z
2
d 2
1
2
,
(4.26)
μ = z
1 +
a
2
z 2
,
(4.27)