Biomedical Engineering Reference
In-Depth Information
and spatial characteristics of sample and reference beam matches, and it can be
defined as
SR
. /
p
I
S
I
R
:
SR
. /
D
(5.9)
Then the irradiance equation Eq.
5.8
can be expressed as follows:
I
D
D
I
S
C
I
R
C
2
p
I
S
I
R
ReŒ
SR
. /:
(5.10)
The normalized correction function
SR
. / is a complex periodic function of ,
and the interference pattern results if
j
SR
. /
j
has a nonzero value. Depending upon
the value of
j
SR
. /
j
, the following type of coherence occurs:
0<
j
SR
. /
j D
1; Complete coherence
j
SR
. /
j
<1; Partial coherence
j
SR
. /
j D
0; Complete incoherence
In an interference pattern, the fringe intensity varies between two limits I
max
and
I
min
.FromEq.
5.10
, this can be written as
I
max
D
I
S
C
I
R
C
2
p
I
S
I
R
j
SR
j
;
(5.11)
I
min
D
I
S
C
I
R
2
p
I
S
I
R
j
SR
j
:
(5.12)
Thus, the visibility of fringe V is defined as the ratio
2
p
I
S
I
R
j
SR
j
I
max
C
I
min
I
max
I
min
I
max
C
I
min
D
V
D
:
(5.13)
If I
max
D
I
min
,thenV
Dj
SR
j
, that is, the fringe visibility is equal to the
modulus of degree of partial coherence. Thus, depending upon the different cases of
degree of partial coherence, the interference fringe visibility varies from maximum
contrast of unity (in case of complete coherence,
j
SR
. /
jD
1) to zero contrast
(complete incoherence,
j
SR
. /
jD
0); there are no interference fringes at all.
Depending upon the source, the light will have frequencies within a certain
frequency spectrum. According to Fourier analysis, this can be written as
2
0
!
D
:
(5.14)
where ! is the spectral linewidth of the source and
0
is the coherence time, which
is the time interval in which the phase of the wave can be predictable. The coherence
length, l
c
D
c
0
, is the propagation path difference where the beam can maintain
a specified degree of coherence. Using Eq.
5.14
, the coherence length can be
written as
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