Optical Coherence Tomography: Technical Aspects - Biomedical Optical Imaging Technologies: Design and Applications - page 167

2c
! D

c
v :

l c D (5.15)

According to the Wiener-Khintchine theorem, the complex degree of coherence
SR . / can be expressed as the Fourier transform of the power spectral density S./
of the source, which is fully characterized by its spectral width (), its central
wavelength ( 0 ), and its shape [ 17 ]:

Z 1

S. v /e i2 v d v :

SR . / D (5.16)

0

From the above relation, it reveals that the width of emission spectrum of light
source and its shape are vital parameters which influence the sensitivity of the LCI
to the optical path difference of the sample and reference arms.

The normalized power spectral density of light source S./ is R S./ D 1;then
the complex coherence can be written as

SR . / Dj SR j . /e i2 v 0 ; (5.17)

where 0 is the center frequency of the light source. Equation 5.10 can be rewritten
by introducing Eq. 5.17 as follows:
I D D I S C I R C 2 p I S I R j SR . / j cos.2 v 0 /: (5.18)

The normalized correlation function for a quasi-monochromatic source can be
given by

1 ;

0

j SR . / jD < 0 I (5.19)

then Eq. 5.18 becomes as follows:
I D D I S C I R C 2 p I S I R 1

cos.2 v 0 /:

0

(5.20)

If the power spectrum of the light source is approximated by a Gaussian
spectrum,

2 p ln 2
v p

exp

2 ;

4 ln 2 v v 0
v

S. v / D (5.21)

substituting Eq. 5.21 into Eq. 5.16 results in
SR . / D exp " e i2 v 0 #

v
2 p ln 2

2

: (5.22)