High-resolution Optical Coherence Tomography Over a Large Depth Range with an Axicon Lens

High-resolution Optical Coherence Tomography Over a Large Depth Range with an Axicon Lens
February 15, 2002 / Vol. 27, No. 4 / OPTICS LETTERS
243
High-resolution optical coherence tomography over a large
depth range with an axicon lens
Zhihua Ding, Hongwu Ren, Yonghua Zhao, J. Stuart Nelson, and Zhongping Chen
Beckman Laser Institute and Center for Biomedical Engineering, University of California, Irvine, Irvine, California 92612
Received August 18, 2001
In optical coherence tomography, axial and lateral resolutions are determined by the source coherence length
and the numerical aperture of the sampling lens, respectively. Whereas axial resolution can be improved
by use of a broadband light source, there is a trade-off between lateral resolution and focusing depth when
conventional optical elements are used. We report on the incorporation of an axicon lens into the sample
arm of an interferometer to overcome this limitation. Using an axicon lens with a top angle of 160±, we
maintained 10-mm or better lateral resolution over a focusing depth of at least 6 mm. In addition to having
high lateral resolution, the focusing spot has an intensity that is approximately constant over a greater depth
range than when a conventional lens is used. © 2002 Optical Society of America
OCIS codes: 170.4500, 110.0110.
Three-dimensional high-resolution optical imaging
has potential clinical applications in the emerging
field of biomedical optics. In a conventional optical
imaging system, axial and lateral resolutions are
correlated; hence one cannot obtain both in the same
system. Optical coherence tomography (OCT) is
a new modality that provides high-resolution subsurface microstructural images in a noninvasive
manner.1,2 OCT uses coherence gating to select minimum backscattered photons for image reconstruction.
Axial and lateral resolutions are determined by the
source coherence length and the numerical aperture
of the sampling lens, respectively. Whereas axial
resolution can be improved by use of a broadband light
source,3,4 there is a trade-off between lateral resolution
and focusing depth when conventional optical elements
(spherical lenses, mirrors, etc.) are used, because a
beam cannot be produced that has simultaneously a
long focal depth and a narrow lateral width. Whereas
high-lateral-resolution imaging requires a large numerical aperture, a long focal depth requires a small
numerical aperture. In high-speed OCT imaging, in
which an axial scanning mode (A mode) is used, a
tightly focused lens produces a micrometer-sized spot
at only one specif ic depth. The coherence gate quickly
moves out of the shallow depth of focus during the
scan. Although dynamic focusing compensation3 – 5
can be used to overcome this limitation, one can use
this method only at low speeds and therefore only in
low-frame-rate OCT systems. In addition, dynamic
focusing lenses are bulky and cannot be used when
physical space is limited, such as in endoscopic OCT.6,7
We incorporated an axicon lens8 into the sample arm
of an interferometer to achieve both high lateral resolution and a greater depth of focus simultaneously. The
term “axicon” was introduced by McLeod8 to describe
an optical element that produces a line image lying
along the axis from a point source of light. There are
many different kinds of axicon (rings, cylinders, etc.),
but the single refracting cone lens is the most common
form. Hence here we refer to an axicon lens as meaning specifically a refracting conical lens. Using an axi0146-9592/02/040243-03$15.00/0
con lens with a top angle of 160±, we maintained 10-mm
or better lateral resolution over a focusing depth of at
least 6 mm. In addition to having high lateral resolution, the focusing spot has an intensity that is approximately constant over a greater depth range.
A high-speed phase-resolved OCT system at 1.3 mm
is used in our experiments. A detailed system design
has already been described in the literature.9 We incorporate an axicon lens into the sample arm of the interferometer. A schematic of the interferometer with
a fused-silica axicon lens (2.54-cm diameter, top angle
of 160±; 1050–1350-nm antiref lection coating, 3-mm
edge thickness, and a diffraction index of 1.44681 at
1.3-mm wavelength) is shown in Fig. 1.
Light emitted from a single-mode fiber is collimated
with a lens to produce spatially coherent illumination
upon the axicon lens. Spatially coherent illumination
is necessary if the axicon lens is to produce a coherent
and sharply focused spot, similarly to a conventional
lens. If spatially incoherent light illumination is used,
the spot becomes wider and spatially incoherent,10 resulting in reduced transverse resolution and a low signal-to-noise ratio in OCT. The intensity distribution,
Fig. 1. Schematic of the sample arm of the OCT system
with an axicon lens to achieve simultaneous high lateral
resolution and greater depth of focus: a, angle formed
by the conical surface with the f lat surface of the axicon
lens; b, intersection angle of the geometrical rays with the
optical axis; Rz , radius of the incident beam; D, waist of
the incident beam; L, depth of focus.
© 2002 Optical Society of America
244
OPTICS LETTERS / Vol. 27, No. 4 / February 15, 2002
I 共r, z兲, behind the axicon lens illuminated by a collimated beam of diameter D is given by11
I 共r, z兲 苷 E 2 共Rz 兲Rz
2pk sin b 2
J0 共kr sin b兲,
cos2 b
R # D兾2,
z # L,
(1)
where E 2 共Rz 兲 is the energy of the incident beam at radius Rz that contributes to the intensity at axial point
z through the relationship
Rz 苷
z tan b
,
1 2 tan a tan b
(2)
where k is the wave number, J0 is a zero-order Bessel
function of the f irst kind, r is a radial coordinate on
the observation plane, and L is the depth of focus, approximated by
L苷
D共tan21 b 2 tan a兲 ,
2
at each focusing point for an axicon lens is smaller than
that for a conventional focusing lens. In Fig. 2 the
detected peak signal ratio of the conventional to the
axicon lens is ⬃16. There is a compromise between
signal intensity and focusing range. However, our
current system, which uses an over-the-counter axicon
lens, has a focusing range of more than 6 mm. If an
axicon lens designed specif ically for OCT is made with
a focusing range of 2 mm, the difference in peak intensity between the axicon and conventional lenses will be
further reduced.
The focusing range and lateral resolution of the
axicon-lens-based OCT system was calibrated with
a variable-frequency resolution target from Edmund
Scientific (Barrington, N.J.) Sequences of OCT images were made with targets located at different axial
positions. The density of the parallel bar to be imaged
was 50 line pairs兾mm, which corresponds to a spatial
(3)
where b 苷 sin21 共n sin a兲 2 a. The angle of intersection of geometrical rays with the optical axis is deduced
from Snell’s law and takes the form
n sin a 苷 sin共a 1 b兲 ,
(4)
where n is the refractive index of the axicon lens and
a is the angle formed by the conical surface with the
f lat surface of the axicon lens. According to Eq. (1),
central peak radius r0 of the beam behind the axicon
lens can be predicted by the f irst zero of the Bessel
function:
J0 共kr0 sin b兲 苷 0 ,
(5)
r0 苷 2.4048l兾2p sin b .
(6)
Fig. 2. Signal versus axial position in the sample arm of
the interferometer.
to result in
Inserting the parameters that pertain to the axicon lens (a 苷 10±, D 苷 2 mm, l 苷 1.3 mm, and
n 苷 1.44681) into Eqs. (3) and (6) yields an estimated
depth of focus L of 12.4 mm and a central peak radius
r0 of 6.32 mm.
To test our OCT system’s performance we measured
the relation of the detected signal to the mirror’s
axial position behind the axicon lens by blocking out
the reference arm and using a ref lecting mirror as
the sample (Fig. 2). For comparison, the ratio of the
signal to the axial position of a conventional lens
( f 苷 10 mm; NA, 0.35 was also measured. The result
clearly demonstrates that the axicon lens has a much
greater focusing range than the conventional lens.
The focusing range is approximately 7 mm (full width
at 1兾e2 ), which is smaller than the theoretical value
of 12 mm. The reason for the reduced focusing range
is that the spherical geometrical shape of the axicon’s
apex acts as an equivalent lens and focuses the central
part of the illuminating light to a point away from the
axicon’s apex. Because focal energy with an axicon
lens is distributed along the focusing range, the power
Fig. 3. OCT images and their cross-sectional prof iles normal to the bar direction (noise f loor, 26 dB). Images are
successive from top to bottom and show a target located
at different axial positions relative to the axicon apex at
intervals of 1.2 mm over a total observed depth of 6 mm.
February 15, 2002 / Vol. 27, No. 4 / OPTICS LETTERS
245
tenuation by the microspheres. For comparison, OCT
images with a conventional lens at different focusing
positions in the lumen are shown in Figs. 4B and 4C.
The bright regions correspond to the focusing depths of
the lens. Plots of the corresponding signals as a function of depth (Figs. 4B9 and 4C9) compared with those
in Fig. 4A9 clearly indicate that the signals strongly depend on the focusing locations of the lens. The OCT
signal decayed much faster farther away from the focusing location. Thus, in addition to having high lateral resolution over a greater depth range, the OCT
signal was more uniform over the depth range when
an axicon lens was used.
In conclusion, we have achieved 10-mm or better lateral resolution over a focusing depth of at least 6 mm
by using an axicon lens with a top angle of 160± in our
OCT system. These results demonstrate that an axicon lens can be used in an OCT system to maintain
high lateral resolution over a greater depth of field,
which is essential for high-resolution, high-speed OCT.
Fig. 4. OCT images of a capillary tube with polystyrene
microspheres and their prof iles along the center of the tube
in depth directions that correspond to different focusing
conditions in the sample arm: A, A0 axicon lens; B, B0 ;
conventional lens focusing at the top of the tube; C, C0 ,
conventional lens focusing at the center of the tube.
This research was supported by research grants
from the National Institutes of Health (HL-64218,
RR-01192, and GM-58785) and from the National Science Foundation (BES-86924). Institutional support
from the U.S. Air Force Office of Scientific Research
(grant F49620-00-1-0371), the U.S. Department of Energy (grant DE-FG03-91ER61227), and the Beckman
Laser Institute Endowment is gratefully acknowledged. Please address correspondence to Z. Chen at
zchen@bli.uci.edu.
References
resolution of 10 mm. Figure 3 shows the OCT images
and their corresponding cross-sectional profiles for the
target located at different axial positions relative to
the axicon apex with an interval of 1.2 mm over a total
observed depth of 6 mm. The OCT image size was
600 mm by 200 mm. These results conf irm a focusing
depth range of at least 6 mm with 10-mm or better
lateral resolution. In contrast, the Rayleigh range for
a TEM00 Gaussian beam with a 10-mm waist radius
at a wavelength of 1.3 mm was less than 0.25 mm.
To confirm the feasibility of the axicon-lens-based
OCT system, we took images of the same sample with
both axicon and conventional lenses. The sample comprised polystyrene microspheres (diameter, 0.356 mm)
inside a capillary tube immersed in water. The internal diameter of the tube was 1.1 mm, and the wall
thickness was 0.20 mm. The 2.7% polystyrene microsphere solution was diluted with distilled water at a
volume ratio of 1:10 (scattering coeff icient calculated
to be 4.8 cm21 ). An OCT image with an axicon lens is
shown in Fig. 4A, where both the lumen and the tube
wall can be observed; image size is 2 mm by 2 mm.
An OCT signal as a function of depth plotted across the
center of the lumen is shown in Fig. 4A9. Although
a slow decay in the signal is observed as a function
of depth, this decay is due mainly to scattering at-
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