in 1
in T
out
E
E
2x2
out 1
out T
rotational rate, R, of 916 revolutions per second. The instantaneous linewidth of this laser is
2
2
matrix transposition, is given by
, where
0.09 nm, which corresponds to a coherence length of 16 mm. We also construct an OCT
E
M E
out2x2
2x2 in2x2
system that uses our laser source where we have shown that its parameters are optimized
.
0 5
j .
0 5
(1)
for this application. In the fourth section, we discuss design methods and fabrication
M
2x2
50/50
j .
0 5
.
0 5
techniques of fiber-lens-based optic probes. We compare in detail measured performance
with expected theoretical performance. Finally, we demonstrate the images of human skins,
presents the transfer matrix of a 50/50 2x2 coupler, and
animal arterial plaque and heart tissues acquired from our catheter-based complex SS-OCT,
0 9
.
j .
0 1
M
(2)
2x2
which proves our SS-OCT system with fiber catheter is most suitable for the applications of
90/10
j 0.1
0.9
biomedical imaging.
is the transfer matrix of a 90/10 2x2 coupler. Similarly, the output electric field of a 3x3
coupler could be written as E
M E
, where
out3x3
3x3 in3x3
2. Full Range (Complex) Optical Coherence Tomography System
1 1
1
2 1
1
j 2 Kcpl
j 2 K
e
cpl
e
(3)
M
3x3
1 1 1
1 2 1
2.1 Theoretical Analysis of the Complex System
3
3
An MZI utilizing a 3x3, two 2x2 fiber couplers, and two differential detectors is shown in Fig.
1 1
1
1 1 2
1. A 90/10 2x2 fiber coupler is used as a power divider of the light source: 90% power to the
and K is the coupling coefficient and equals to 0.7 for a 3x3 coupler with 1/3 power
cpl
sample and 10% power to reference arms. This is an advantage of the MZI (Rollins & Izatt,
coupling ratio (Sheem, 1981).
1999), which allows more light to the sample arm for compensating the lower reflection of a
biological sample in an OCT system. The 3x3 fiber coupler serves not only as a combiner of
The operation of a Mach-Zehnder interferometer could be represented by a cascade of the
the two signals from the sample and reference arms, but also provides three phase related
transfer matrices of the couplers and a matrix representing the phase shift between the
Full Range Swept-Source Optical Coherence
Tomography with Ultra Small Fiber Probes for Biomedical Imaging
31
Swanson et al. and Shishkov et al. proposed the fiber based optic probes design, but
output interferometric signals. To form two phase related differential detections, which are
presented the variations of probe structure instead of the characteristics of their
necessitated to obtain the real and imaginary parts of the interferometric signal, one of the
performance (Swanson et al., 2002; Shishkov et al., 2006). Reed et al. demonstrated the usage
output ports of the 3x3 coupler is split using one 50/50 2x2 fiber coupler. Two differential
of such probes with emphasis on their insertion loss only (Reed et al., 2002). Yang et. al.
detectors were constructed by combining one output of the 2x2 coupler and one of the
(Yang et al., 2005b), Jafri et. al. (Jafri et al., 2005), and Li et. al. (Li et al., 2006) reported OCT
remaining outputs of the 3x3 coupler. We note that the input signals for these differential
images without detailed characterization of the used fiber lens based probes. We recently
detectors are not balanced, but no optical power is lost. For comparison, the different
reported design, fabrication, and characterization of the fiber probes with comparison in
unbalanced differential detection methods with different input power ratios, achieved by
detail the actual optical performance of a fiber-based optic probe with modeling results
adjusting two additional fiber attenuators, are also shown in Fig. 1. When the input power
(Mao et al., 2007; Mao et al., 2008).
ratio is adjusted to achieve balanced detection (i.e. attenuation = 0.5), the DC component
of the interferometric signal could be dynamically removed, but one third of the optical
In the second section in this chapter, we present theoretical and experimental results for a
power would be lost.
3x3 Mach-Zehnder quadrature interferometer to acquire a complex interferometric signal for
SS-OCT system. We introduce a novel unbalanced differential detection method to improve
P
Att.
the overall utilization of optical power and provide simultaneous access to the
Reference arm
1
33
P 1
complementary phase components of the complex interferometric signal. No calculations by
Source
P
3x3
trigonometric relationships are needed. We compare the performance for our setup to that
2x2 10%
1
22
2x2
Unbalanced
Differential
of a similar interferometer with a commonly used balanced detection technique. We
90%
P
P
33
222
Detectors
demonstrate complex conjugate artifact suppression of 27 dB obtained in a swept-source
2
optical coherence tomography using our unbalanced differential detection. We show that
Sample arm
P
2
Att. P
our unbalanced differential detection has increased signal-to-noise ratio by at least 4 dB
333
comparing to a commonly used balanced detection technique. In the third section, we
Fig. 1. Mach-Zehnder interferometer using a 3x3 and two 2x2 fiber couplers to form two
demonstrate a Fourier-domain mode-lock (FDML) wavelength-swept laser based on a
channel unbalanced (attenuation = 1 - 0.5) and balanced (attenuation = 0.5) differential
polygon scanner filter and a high-efficiency semiconductor optical amplifier. Peak and
detections for acquiring real and imaginary parts of the interferometric signal.
average output powers of 98 mW and 71 mW, respectively, have been achieved without an
external amplifier, while the wavelength was swept continuously in a full wavelength of 113
To analyze our setup we could use transfer matrix descriptions for both 2x2 and 3x3
nm at center wavelength of 1303 nm. A unidirectional wavelength sweeping rate of 7452
couplers (Sheem, 1981; Priest, 1982). The output electric field of a 2x2 coupler,
nm/ms (65.95 kHz repetition rate) was achieved by using a 72 facet polygon with a
E
, due to an input electric field, E
, where T denotes
in
E E
2x2
in 1
in T
out
E
E
2x2
out 1
out T
rotational rate, R, of 916 revolutions per second. The instantaneous linewidth of this laser is
2
2
matrix transposition, is given by
, where
0.09 nm, which corresponds to a coherence length of 16 mm. We also construct an OCT
E
M E
out2x2
2x2 in2x2
system that uses our laser source where we have shown that its parameters are optimized
.
0 5
j .
0 5
(1)
for this application. In the fourth section, we discuss design methods and fabrication
M
2x2
50/50
j .
0 5
.
0 5
techniques of fiber-lens-based optic probes. We compare in detail measured performance
with expected theoretical performance. Finally, we demonstrate the images of human skins,
presents the transfer matrix of a 50/50 2x2 coupler, and
animal arterial plaque and heart tissues acquired from our catheter-based complex SS-OCT,
0 9
.
j .
0 1
M
(2)
2x2
which proves our SS-OCT system with fiber catheter is most suitable for the applications of
90/10
j 0.1
0.9
biomedical imaging.
is the transfer matrix of a 90/10 2x2 coupler. Similarly, the output electric field of a 3x3
coupler could be written as E
M E
, where
out3x3
3x3 in3x3
2. Full Range (Complex) Optical Coherence Tomography System
1 1
1
2 1
1
j 2 Kcpl
j 2 K
e
cpl
e
(3)
M
3x3
1 1 1
1 2 1
2.1 Theoretical Analysis of the Complex System
3
3
An MZI utilizing a 3x3, two 2x2 fiber couplers, and two differential detectors is shown in Fig.
1 1
1
1 1 2
1. A 90/10 2x2 fiber coupler is used as a power divider of the light source: 90% power to the
and K is the coupling coefficient and equals to 0.7 for a 3x3 coupler with 1/3 power
cpl
sample and 10% power to reference arms. This is an advantage of the MZI (Rollins & Izatt,
coupling ratio (Sheem, 1981).
1999), which allows more light to the sample arm for compensating the lower reflection of a
biological sample in an OCT system. The 3x3 fiber coupler serves not only as a combiner of
The operation of a Mach-Zehnder interferometer could be represented by a cascade of the
the two signals from the sample and reference arms, but also provides three phase related
transfer matrices of the couplers and a matrix representing the phase shift between the
32
Biomedical Imaging
sample and reference arms . Let the input electric field and the matrix representing the
0.8
phase shift between the sample and reference arms be given by E
and
P33_1
in
0 1 T
0
0.8
P33_1
P22_1
0 0
0
P22_1
120o 120o
0.6
P22_2
, respectively. In our setup, the splitter ratio of the first 2x2 coupler is 90/10.
M
P33_3
0.6
P22_2
φ
0 1
0
P33_3
j
0 0 e
120o 120o
0.4
er (a.u.)
0.4
Therefore, the output electric field, E
after the 3x3 coupler
er (A.U.)
33 (φ) E
33 ( )
E 33 ( )
33 ( ) T
E
1
2
3
0.2
Pow
shown in Fig. 1 is calculated by:
Pow 0.2
x2
E ( )
φ M M ()M
E .
(4)
0
33
3x3
φ
2x2
in
90/10
x1
0
0 1 2
3 4 5 6 7 8 9 10
0
1
2
3 4 5 6 7 8 9 10
Phase Pixel
In the case of the 2x2 coupler after the 3x3 coupler, if the input electric field is given by
Phase Pixel
E
, the output electric fields, E , E , are obtained by:
(a)
in
()
(b)
2
33 ( )
0 T
E
x 2
2
221
222
E
M
E
,
(5a)
0.8
22 ( )
2x2
in
()
0.8
1
50/ 50
2 x 2
0.7
0.7
E
M
E
.
(5b)
P1
0.6
80o
22 ( )
2x2
in
()
0.6
P2
2
50/ 50
2 x 2
0.5
0.5
0.4
0.4
Therefore, the related optical powers P , P , P , and P specified in Fig. 1 are
0.3
60o
r (a.u.)
0.3
33
0.2
1
221
222
333
er (a.u.) 0.2
calculated by:
0.1
0.1
ow
Powe
0
P E*
E .
(6)
P
-0.1
0
P1
-0.2
-0.1
P2
-0.3
-0.2
The interferometric signal powers P and P from the outputs of the two differential
-0.3
1
2
0 1 2 3 4 5 6 7 8 9 10
detectors v.s. the attenuation value and the phase shift between the sample and reference
Phase Pixel
0 1 2 3 4 5 6 7 8 9 10
Phase Pixel
arms are calculated by subtracting the two optical input signal powers of the detectors,
respectively, i.e.,
(c)
(d)
P P P , (7a)
0.8
1 ( )
33 ( )
22 ( )
0.8
1
1
0.7
Pre
P P P . (7b)
0.7
90o
2 ( )
33 ( )
( )
0.6
Pim
3
222
0.6
0.5
0.5
0.4
0.4
The phase differences between the two interferometric signals
90o
P and P and the
0.3
1
2
0.3
er (a.u.) 0.2
related power levels are obtained by graphing their function curves vs. .
er (a.u.) 0.2
0.1
0.1
Pow
0
Pow
0
The real ( P
-0.1
RE) and imaginary ( PIM) part signals, e.g. quadrature components (0o and 90o), are
-0.1
Pre
-0.2
formed from the interferometric signals P and P acquired at two differential detectors
-0.2
Pim
-0.3
1
2
-0.3
using the following trigonometric equations (Choma et al., 2003):
0 1 2
3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Phase Pixel
Phase Pixel
P
,
P