Biomedical Engineering Reference
In-Depth Information
5.5.2.1
Spectral-Domain OCT (SD-OCT)
A typical implementation of a fiber optics-based SD-OCT setup is shown in
Fig.
5.13
a. The backscattered low-coherence light is mixed with a reference beam
by the 2
2 fiber optics-based Michelson interferometer; then the grating-based
spectrometer at the output of the interferometer separates each spectral component
detected using a linear array detector. The interference signal detected by the linear
detector is expressed as
I.k/
D
I
S
.k/
C
I
R
.k/
C
2
p
I
S
.k/I
R
.k/
X
n
˛
n
cos.2k
z
n
/;
(5.41)
where I
R
.k/ and I
S
.k/ are the wavelength-dependent intensities reflected from the
reference and sample arms, respectively, and k is the wavenumber. The third term on
the right-hand side of Eq.
5.41
represents the interference between the backreflected
lights from the sample and reference arm. ˛
n
is the square root of the sample
reflectivity at depth Z
n
. In order to reconstruct the depth information, the spectrum
is inverse Fourier transformed, which yields the following convolution:
˛
n
ı.
z
C
z
n
/
#
;
(5.42)
where .
z
/ represents the envelope of the coherence function. The first and second
terms in the right-hand side of Eq.
5.42
describe the autocorrelation (or self-
interference) of the reference signal and sample signal, respectively. The third and
fourth terms are due to the interference of the backreflected beam from reference
and sample surfaces and its complex conjugates. The SD-OCT detects the spectrally
resolved interference signal with a spectrometer that consists of a high-efficiency
diffraction grating and a high-speed line camera. Figure
5.13
b shows the reflectivity
profile of the different target positions in the ocular medium, and Fig.
5.13
cshows
the detected intensity spectrum by the camera. In order to suppress autocorrelation,
self-cross correlation, and camera noise artifacts, first, all the spectral interferograms
in each slice along the x-direction (B-scan) were ensemble-averaged at each
wavelength to obtain a reference spectrum; this background spectrum is then
subtracted from each A-scan. Since the Fourier transform relates the physical
distance (
z
) with the wavenumber .k
D
2=/, however, the spectra obtained with
the SD-OCT spectrometer are not necessarily evenly spaced in k-space. In order
to obtain a proper depth profile, the subtracted spectral interferograms are then
remapped from -space to k-space by the use of the spline interpolation method,
as shown in Fig.
5.13
d. Due to the Fourier relation (Wiener-Khintchine theorem
between the autocorrelation and the spectral power density), the depth-resolved
information can be immediately reconstructed by a Fourier transformation from the
remapped spectra, without movement of the reference arm, as shown in Fig.
5.13
e.
"
I
R
ı.
z
/
C
X
n
ˇ
FT
1
ŒI.k/
ˇ
I
S;n
ı.
z
/
C
X
n
˛
n
ı.
z
z
n
/
C
X
n
2
D
2
.
z
/
˝
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