Biomedical Engineering Reference
In-Depth Information
Figure 1.7: Geometrical variables used for the calculations of the pressure
distributions
P
(
r
,θ,
t
) for a planar circular transducer of radius
a
.
Again,
ρ
is the density of the medium and
c
is the speed of sound. The impulse
function
ζ
(
t
,δ
) is generally approximated [15] by a Gaussian (Fig. 1.9(a)), which
envelopes the intensity distribution, and is given by:
ζ
(
t
,δ
)
=
I
(
r
,θ,
t
) exp
(
t
−
δ
)
2
2
σ
−
(1.4)
2
where
σ
is the pulse standard deviation. We consider that the beam is colli-
mated by
θ
=
θ
a
. In our model only the corresponding interval
d
θ
≈
0
.
1
◦
is used
that corresponds to the transducer lateral resolution zone (Fig. 1.9(b)). Hence
Figure 1.8:
Transducer pressure distribution.