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Synthetic Bessel light needle for extended depth-of-field microscopy
Jiamiao Yang
, Lei Gong
, Yuecheng Shen
, and
Lihong V. Wang
Citation:
Appl. Phys. Lett.
113
, 181104 (2018); doi: 10.1063/1.5058163
View online:
https://doi.org/10.1063/1.5058163
View Table of Contents:
http://aip.scitation.org/toc/apl/113/18
Published by the
American Institute of Physics
Synthetic Bessel light needle for extended depth-of-field microscopy
Jiamiao
Yang,
1
Lei
Gong,
2
Yuecheng
Shen,
1
and Lihong V.
Wang
1,
a)
1
Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering,
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125, USA
2
Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei,
Anhui 230026, China
(Received 17 September 2018; accepted 20 October 2018; published online 2 November 2018)
An ultra-long light needle is highly desired in optical microscopy for its ability to improve the lat-
eral resolution over a large depth of field (DOF). However, its use in image acquisition usually
relies on mechanical raster scanning, which compromises between imaging speed and stability and
thereby restricts imaging performance. Here, we propose a synthetic Bessel light needle (SBLN)
that can be generated and scanned digitally by complex field modulation using a digital micromir-
ror device. In particular, the SBLN achieves a 45-fold improvement in DOF over its counterpart
Gaussian focus. Further, we apply the SBLN to perform motionless two-dimensional and three-
dimensional microscopic imaging, achieving both improved resolution and extended DOF. Our
work is expected to open up opportunities for potential biomedical applications.
Published by AIP
Publishing.
https://doi.org/10.1063/1.5058163
Conventional three-dimensional (3D) microscopy
suffers from a limited depth of field (DOF), which is
determined by the focal depth of the imaging objective lens.
High-resolution imaging can be achieved only near the focal
plane of the objective, and the lateral resolution decreases
rapidly with the distance from the focal plane. Thus,
scanning an object or an illuminating beam along the depth
direction is required to maintain the resolution at different
depths, which negatively impacts the imaging speed.
To extend the DOF of optical microscopy, various meth-
ods have been proposed, such as wavefront coding,
1
decon-
volution,
2
layer-by-layer frequency domain imaging,
3
and
light needles.
4
–
7
Among them, light needles were most
widely used in laser scanning microscopy, such as two-
photon microscopy,
8
,
9
optical coherence tomography,
10
,
11
light sheet microscopy,
12
,
13
and photoacoustic microscopy
(PAM).
14
,
15
In particular, the unique self-healing property of
a Bessel beam based light needle can enable imaging with an
improved penetration depth inside scattering media.
16
,
17
Nevertheless, their use in image acquisition usually relies on
mechanical raster scanning, which limits imaging speed and
stability.
Here, we propose a non-diffracting synthetic Bessel
light needle (SBLN) to extend the microscope’s DOF. The
SBLN is synthesized by two scanned symmetrical plane
waves generated by a single digital micromirror device
(DMD). Such a virtual light needle can be flexibly synthe-
sized at any position by digital means, paving the way for
scanning-free imaging. In particular, under the same
numerical-aperture (NA) objective, the SBLN achieves a
45-fold improvement in DOF over a focused Gaussian beam.
Furthermore, we apply the SBLN to acquire two-
dimensional (2D) or 3D microscopy images without
mechanical scanning, achieving the extended DOF.
A light needle is essentially a point light on each trans-
verse plane, and a point light can be regarded as a
superposition of sinusoidal fringes according to Fourier
optics.
18
Therefore, the light needle can be synthesized by
the superposition of a series of nondiffracting sinusoidal
fringes (NSFs), as illustrated in Fig.
1
. By fully exploiting
the diffraction-free nature of plane waves, we further pro-
pose to create the NSF by the interference of two symmetri-
cally incident plane waves [Fig.
1(a)
]. As a result, scanning
the two symmetrical plane waves in
k
-space can synthesize
the nondiffracting light needle [Figs.
1(b)
and
1(c)
], and its
intensity distribution in the Cartesian coordinates
ð
x
;
y
;
z
Þ
can be expressed as
I
needle
x
;
y
;
z
ðÞ
¼
ðð
k
2
x
þ
k
2
y
<
k
2
max
j
E
1
x
;
y
;
z
ðÞ
þ
E
2
x
;
y
;
z
ðÞ
j
2
dk
x
dk
y
;
(1)
where
E
1
¼
A
exp
½
i
ð
k
x
x
þ
k
y
y
þ
k
z
z
Þ
and
E
2
¼
A
exp
½
i
ð
k
x
x
k
y
y
þ
k
z
z
Þ
.
A
is the amplitude of the two plane
waves, and
k
x
,
k
y
,and
k
z
are the components of the wave
vector. In practice, the maximum wavenumber,
k
max
;
of the
two plane waves is limited by the NA of the illumination
objective lens:
k
max
¼
NA
2
p
=
k
;
where
k
is the wave-
length. The kernel
j
E
1
ð
x
;
y
;
z
Þþ
E
2
ð
x
;
y
;
z
Þj
2
indicates the
component interference pattern used to synthesize the light
needle.
If the constant background and scaling factors are
neglected, the intensity distribution can be mathematically
simplified using cylindrical coordinates
ð
r
;
h
;
z
Þ
to
I
needle
r
;
h
;
z
ðÞ
¼
2
p
2
NA
k
r
J
1
4
p
r
NA
k
;
(2)
where
J
1
ðÞ
is the first-order Bessel function of the first kind.
Thus, we call this nondiffracting focused beam as the syn-
thetic Bessel light needle. It can be seen from Eq.
(2)
that the
SBLN theoretically has an unlimited length in the
z
direc-
tion, an invariant diameter, and constant irradiance along the
needle. In fact, the length of the SBLN is determined by the
overlap of the two collimated beams after the objective in
a)
Author to whom correspondence should be addressed: LVW@caltech.edu.
0003-6951/2018/113(18)/181104/4/$30.00
Published by AIP Publishing.
113
, 181104-1
APPLIED PHYSICS LETTERS
113
, 181104 (2018)
the experiment. Nevertheless, the achievable length of the
SBLN is much greater than the DOF of the objective.
In particular, the SBLN can be synthesized at any spatial
position
ð
x
0
;
y
0
Þ
by adding a phase
u
¼
2
k
x
x
0
2
k
y
y
0
to
E
1
for each
k
value, whose intensity profile reads
I
0
needle
x
;
y
;
z
ðÞ
¼
ðð
k
2
x
þ
k
2
y
<
k
2
max
exp
i
2
k
x
x
0
2
k
y
y
0
ðÞ
½
E
1
x
;
y
;
z
ðÞ
þ
E
2
x
;
y
;
z
ðÞ
2
dk
x
dk
y
¼
I
needle
x
x
0
;
y
y
0
;
z
ðÞ
:
(3)
Thus, such a light needle can be flexibly scanned by digital
means, which enables the SBLN-based imaging to be real-
ized without mechanical scanning.
To form and scan two symmetrical plane waves, a single
DMD based complex field encoding method
19
,
20
was uti-
lized, as illustrated in Fig.
2(a)
. According to the desired
amplitude and phase of the interference field of two
symmetrical plane waves, the corresponding binary holo-
gram is generated using the super-pixel method, as shown in
Fig.
2(b)
. By switching the binary holograms, these two
plane waves were rapidly scanned in
k
-space, and a series of
NSFs were formed at the focal plane of the objective to syn-
thesize the light needle. Figure
2(c)
presents the intensity
profiles of a generated NSF with
k
x
¼
k
y
¼
10
p
=
L
at differ-
ent depths. The NA of the objective is 0.1, and the size
ð
L
L
Þ
of the NSF is 180
180
l
m
2
. Our complex field modula-
tion enables us to maintain its profile over a depth of 3 mm.
Conventionally, amplitude-only modulation is adopted for
the binary DMD. In this manner, the generated fringe blurs
quickly away from the focal plane.
By the superposition of a series of NSFs with different
k
values, the SBLN can be created. Here, 90
90
k
values
were scanned to synthesize the light needle. Figure
3(a)
shows the SBLN obtained at the center of the NSF. Four
en
face
cross-sections were taken from the SBLN to show the
profiles of the foci at different depths. For further analysis,
the full width at half maximum (FWHM) of the foci along
both
x
and
y
directions throughout the volume was calcu-
lated, which are illustrated in Figs.
3(b)
and
3(c)
, respec-
tively. The volume indicated by white color is the resolution
invariant area, where the FWHM reaches 1.9
l
m. The SBLN
achieves a much larger DOF over a focused Gaussian beam.
For a quantitative comparison, we define the DOF of the
SBLN as the axial range within which the lateral size
increases by up to a factor of
ffiffiffi
2
p
from the focal value. As a
result, the DOF of the SBLN at the center of the NSF is
2500
l
m, which is 45-fold longer than that of a Gaussian
focus.
For the purpose of imaging, we built an SBLN-based
microscope using a photodiode (PDA36A, Thorlabs, Inc.) as
a detector, which is sketched in Fig.
4(a)
. A continuous-
wave laser with a wavelength of 532 nm was used as the light
source. During the image acquisition, the two symmetric
beams were rapidly scanned by switching the binary holo-
grams displayed on the DMD. At the focal plane of the
objective (NA
¼
0.1), these two scanned beams interfered
FIG. 2. Generation of NSFs by a DMD. (a) Schematic illustration of the
experimental setup. L: lenses. (b) The amplitude and phase distributions of
the interference field of two symmetrical plane waves and its corresponding
binary hologram designed by the super-pixel method. (c) The intensity pro-
files of a fringe at different depths generated by our complex field (both the
amplitude and the phase) modulation and conventional (amplitude-only)
modulation, respectively.
FIG. 3. Synthetic Bessel light needle and its characteristics. (a)
Experimentally generated SBLN and four corresponding synthesized foci at
different depths of
0.5, 0.0, 1.0, and 1.5 mm. The focal plane is located at
z
¼
0.0 mm. (b) and (c) Varying spot sizes of the synthesized foci at different
positions in
x
and
y
directions, respectively.
Scale bars
,15
l
m.
FIG. 1. Principle of the SBLN. (a) The SBLN is synthesized by a series of
nondiffracting sinusoidal fringes (NSFs), which are created by the interfer-
ence of two symmetrically incident plane waves
E
1
and
E
2
. The two plane
waves
E
1
and
E
2
are produced and scanned by a DMD using complex field
modulation. (b) P
1
;
1
,P
1
;
2
,
,P
n
;
n
1
, and P
n
;
n
are the intensity distributions of
a series of NSFs with different spatial frequencies
k
x
and
k
y
. (c) The SBLN
can be synthesized at any position by adding an initial phase
u
to
E
1
.
181104-2 Yang
etal.
Appl. Phys. Lett.
113
, 181104 (2018)
and formed an SBLN to illuminate a USAF resolution target
that served as the object. The field of view (FOV) of the
microscope, determined by the size of the NSF, was
180
180
l
m
2
.
Figures
4(b)
and
4(c)
show the reconstructed images of
the resolution target placed at different depths acquired by
the SBLN and the focused Gaussian beam, respectively. The
results show that the features of element 6 in group 8 with a
resolution of 456.1 line pairs per mm can be resolved by
SBLN microscopy whenever the object is located in the
range of
0.8 mm to 0.8 mm. When the imaging depth
reaches
6
1.25 mm, a slightly decreased resolution is
observed, which coincides with the theoretically predicted
resolution degradation with a factor of
ffiffiffi
2
p
. In contrast, when
the focused Gaussian beam was adopted,
21
the features of
element 3 in group 6 (resolution of 80.6 line pairs per mm)
are hardly resolved at an imaging depth of
6
0.8 mm. When
the imaging depth reaches
6
1.25 mm, all the patterns in
groups 6 and 7 (lowest resolution of 64.0 line pairs per mm)
become blurred beyond recognition [Fig.
4(c)
]. Overall,
SBLN microscopy achieves an extended DOF.
Furthermore, the SBLN was applied to realize volumet-
ric imaging by introducing photoacoustic (PA) detection,
22
,
23
which is sketched in Fig.
5(a)
. The depth information was
resolved by the time-of-flight information carried by the PA
signals. A pulsed laser with a wavelength of 532 nm was
used as the light source. A 3D object made of spatially dis-
tributed carbon fibers with a diameter around 7
l
m was
imaged. The object was located in a tank filled with water,
and an ultrasonic transducer was fixed above the object to
detect the PA signals. The ultrasonic waves were coupled by
the water. Here, a montage strategy based on the movement
of the object in the horizontal direction was adopted to
obtain a larger image. Figure
5(b)
shows the volume-
rendered image of the object with an area of
600
600
2000
l
m
3
. As expected, we obtained high-
resolution imaging throughout the volume. Three
en face
image slices were taken at different depths to show its essen-
tially unchanged lateral resolution along the depth. The
corresponding line profiles across the carbon fibers are
shown in Figs.
5(c)–5(e)
. All the fibers can be clearly
resolved even when they are located at the ends of the depth
range (
z
¼
0.9 mm or
z
¼
0.9 mm). Compared to the
conventional PAM using a focused Gaussian beam, our
SBLN-based PAM greatly increases the DOF, achieving
motionless volumetric imaging. Combined with the contour-
scanning method,
24
the SBLN-based PAM can realize high-
speed motionless volumetric imaging for features of interest.
In summary, we have proposed and implemented an
ultra-long SBLN with a DMD. The SBLN achieves a 45-fold
improvement in DOF over the counterpart Gaussian focus.
Since the SBLN can be synthesized at any position within
the FOV, it is capable of performing direct 2D or 3D image
acquisition wit
hout mechanical scanning. We applied the
SBLN to perform 2D and 3D motionless imaging, achiev-
ing an extended DOF in microscopy. This extended
DOF and the motionless imaging method are expected to
open up opportun
ities for potential biomedical applica-
tions. Additionally, the approach proposed here could be
readily adapted for other imaging modalities, for example,
light-sheet microscopy
25
and structured-illumination
microscopy.
26
The authors acknowledge financial support from
National Institutes of Health (NIH) Grant Nos. DP1
EB016986 (NIH Director’s Pioneer Award), R01 NS102213
(PEDBRAIN), U01 NS090579 (BRAIN1 Initiative), and
U01 NS099717 (BRAIN2 Initiative).
1
S. C. Tucker, W. T. Cathey, and E. R. Dowski,
Opt. Express
4
, 467
(1999).
2
F. Aguet, D. Van De Ville, and M. Unser,
IEEE Trans. Image Process.
17
,
1144 (2008).
3
J. Yang, L. Gong, X. Xu, P. Hai, Y. Shen, Y. Suzuki, and L. V. Wang,
Nat. Commun.
8
, 780 (2017).
4
C.-C. Sun and C.-K. Liu,
Opt. Lett.
28
, 99 (2003).
5
H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong,
Nat.
Photonics
2
, 501 (2008).
6
M. Zhu, Q. Cao, and H. Gao,
JOSA A
31
, 500 (2014).
7
C. Gohn-Kreuz and A. Rohrbach,
Optica
4
, 1134 (2017).
8
G. Th
eriault, Y. De Koninck, and N. McCarthy,
Opt. Express
21
, 10095
(2013).
FIG. 4. SBLN-based imaging of a USAF resolution target with an extended
DOF. (a) Illustration of the SBLN microscope. (b) and (c) Resolution target
imaging at different depths by the SBLN beam and the focused Gaussian
beam, respectively.
FIG. 5. Volumetric imaging of spatially distributed carbon fibers by SBLN
PAM. (a) Illustration of the SBLN photoacoustic microscope. (b) Volume-
rendered imaging of the 3D object and three
en face
image slices taken at
different depths of
0.9, 0.0, and 0.9 mm. (c)–(e) Corresponding line pro-
files across the carbon fibers to show its essentially unchanged lateral resolu-
tion over the depth range.
Scale bar
, 150
l
m.
181104-3 Yang
etal.
Appl. Phys. Lett.
113
, 181104 (2018)
9
G. Th
eriault, M. Cottet, A. Castonguay, N. McCarthy, and Y. De Koninck,
Front. Cell. Neurosci.
8
, 139 (2014).
10
K.-S. Lee and J. P. Rolland,
Opt. Lett.
33
, 1696 (2008).
11
D. Lorenser, C. C. Singe, A. Curatolo, and D. D. Sampson,
Opt. Lett.
39
,
548 (2014).
12
T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C.
G. Galbraith, and E. Betzig,
Nat. Methods
8
, 417 (2011).
13
P. J. Keller, A. D. Schmidt, A. Santella, K. Khairy, Z. Bao, J. Wittbrodt,
and E. H. Stelzer,
Nat. Methods
7
, 637 (2010).
14
J. Shi, L. Wang, C. Noordam, and L. V. Wang,
J. Biomed. Opt.
20
,
116002 (2015).
15
B. Jiang, X. Yang, and Q. Luo,
Opt. Express
24
, 20167 (2016).
16
F. O. Fahrbach, P. Simon, and A. Rohrbach,
Nat. Photonics
4
, 780
(2010).
17
F. O. Fahrbach, V. Gurchenkov, K. Alessandri, P. Nassoy, and A.
Rohrbach,
Opt. Express
21
, 13824 (2013).
18
J. W. Goodman,
Introduction to Fourier Optics
(Roberts and Company
Publishers, 2005).
19
S. A. Goorden, J. Bertolotti, and A. P. Mosk,
Opt. Express
22
, 17999
(2014).
20
J. Yang, Y. Shen, Y. Liu, A. S. Hemphill, and L. V. Wang,
Appl. Phys.
Lett.
111
, 201108 (2017).
21
J. Yang, L. Qiu, W. Zhao, Y. Shen, and H. Jiang,
Opt. Lett.
39
, 830 (2014).
22
L. V. Wang,
Nat. Photonics
3
, 503 (2009).
23
L. V. Wang and S. Hu,
Science
335
, 1458 (2012).
24
C. Yeh, B. T. Soetikno, S. Hu, K. I. Maslov, and L. V. Wang,
J. Biomed.
Opt.
19
, 096011 (2014).
25
B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W.
Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, and Z. Liu,
Science
346
, 1257998 (2014).
26
P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson,
Nat. Methods
6
, 339 (2009).
181104-4 Yang
etal.
Appl. Phys. Lett.
113
, 181104 (2018)