Biomedical Engineering Reference
In-Depth Information
The appropriate moments of the third order are written in the following forms:
0
@
1
A
x
1
x
1
x
2
x
1
x
3
x
1
x
4
x
2
x
2
x
3
x
2
x
4
x
3
x
3
x
4
x
4
0
@
1
A
x
2
x
2
x
3
x
2
x
4
x
3
x
2
x
3
x
4
0
@
1
A
x
1
x
2
.1/
x
2
x
2
.2/
x
3
x
2
.3/
x
4
x
2
.4/
x
3
.1/
x
2
.1/
x
2
.2/
D
D
D
;
;
;
0
1
x
3
x
3
x
4
x
4
@
A
;
x
2
.3/
x
2
.4/
D
D
x
4
0
1
0
1
x
1
x
1
x
2
x
1
x
2
x
2
x
1
x
x
.1/
x
2
x
x
.2/
;
x
1
x
1
x
2
x
2
@
A
@
A
;
x
x
.1/
x
x
.1/
x
x
.2/
x
2
;
x
x
.1/
D
D
D
D
;
1
0
@
y
1
y
1
y
2
y
1
y
2
y
2
A
x
y
.1/
D
:
If the motion of the monochromatic beam is described by the equation of the
third order approximation, we have two phase moments of the third order:
˚
x
1
;x
2
;x
1
;x
1
x
2
;x
1
x
2
;x
2
;x
1
y
1
;x
1
y
1
y
2
;x
1
y
2
;x
2
y
1
;x
2
y
1
y
2
;x
2
y
2
x
x
Œ3
Q
and
˚
y
1
;y
2
;y
1
;y
1
y
2
;y
1
y
2
;y
2
;y
1
x
1
;y
1
x
1
x
2
;y
1
x
2
;y
2
x
1
;y
2
x
1
x
2
;y
2
x
2
:
Q
y
x
Œ3
To the linear equation of the first approximation we associate a linear equation for
the phase moments of the first order:
P
1
x
.
z
/xŒ1;
D
dxŒ1=d
z
where
:
0
1
P
1
x
.
z
/
D
ˇ
2
f.
z
/0
