5.4 Theoretical Study of Biomechanical Characteristics of Skeletal …
393
Fig. 5.12 To the question of optimization of the optical scheme of the laser specklometer. Reprinted
from [87] with permission
where is the element of the solid angle, at which the illuminated area P is seen
(Fig. 5.12); A is the amplitude of the incident wave; λ is the wavelength of the incident
light.
Let (x, y, z) be coordinates of (.) P, and (ξ, η, β) are coordinates of (.) Q. Suppose
that ξ = S sin θ, η = S cos θ, x = ρ sin ψ, y = ρ cos ψ.
As (.) Q lies on the spherical wave front, then
β = −
d 2 − S 2 ρ 2 = −d
1 −
1
2
S
2
ρ
2
d 2 + · · ·
that is why
q
R =
xξ + yη + zβ
d
=
Sρ cos(θ − )
d
− z
1 −
1
2
S
2
ρ
2
d 2 + · · ·
(5.9)
We will introduce dimensionless variables:
u =
2π
λ
S
d
2
z, v =
2π
λ
S
d
ρ =
2π
λ
S
d
x 2 + y 2
Let terms with ρ/d in the degree exceeding the second one be negligibly small.
Then,
k
q
R = vρ cos(θ − ) −
d
S
2
u +
1
2
uρ
2
, d =
S
2
ρdρdθ
d 2
Taking into account the previously mentioned information, we obtain
U (P) = −
i
λ
S
d
A exp
i
d
S
2
u
1
0
2π
0
exp
−i
vρ cos(θ − ψ) +
1
2
uρ 2
ρdρdθ