Journal of Microscopy, Vol. 191, Pt 3, September 1998, pp. 266–274.
Received 5 January 1998; accepted 18 May 1998
3D microscopy of transparent objects using third-harmonic
generation
M. MÜLLER,* J. SQUIER,† K. R. WILSON§ & G. J. BRAKENHOFF*
*BioCentrum Amsterdam, Institute for Molecular Cell Biology, Kruislaan 316, 1098 SM
Amsterdam, The Netherlands
†Department of Electrical and Computer Engineering, and §Department of Chemistry, University of
California San Diego, Urey Hall Addition, Mail Code 0339, La Jolla, CA 92093–0339, U.S.A.
Key words. Confocal microscopy, multiphoton excitation, third-harmonic
generation.
Summary
It is demonstrated that third-harmonic generation (THG)
near interfaces in the refractive index or the third-order
nonlinear susceptibility (x(3)) permits three-dimensional
imaging of transparent objects. The nonlinear dependence
of THG on the excitation power provides inherent optical
sectioning. At the same time, the nonresonant nature of
THG, in combination with the near-IR excitation wavelengths used (1–2 mm), render this technique potentially
(biologically) nondamaging and nonbleaching. A specific
property of THG imaging is its sensitivity to – and potential
use for imaging of – the relative orientation of interfaces
with respect to the axis of propagation of the excitation
radiation.
Introduction
A number of nonlinear optical techniques, including twophoton absorption (Webb, 1990; Denk et al., 1990; Piston &
Webb, 1991), three-photon absorption (Gryczynski et al.,
1996; Hell et al., 1996), multifrequency excitation (Hell
& Wichmann, 1994) and surface second harmonic
generation (Hellwarth & Christensen, 1974; Campagnola
et al., 1997) have been introduced to (laser scanning)
microscopy over the past few years. Made possible by the
continuing advances in ultrashort pulse laser technology,
these techniques have opened new fields in microscopical
research. A general characteristic, and potential advantage,
of these techniques is their ‘self-sectioning’ property. Owing
to the nonlinear dependence of the detected signal on
the input field(s), the signal is generated only near
the focal point of the focusing microscope objective.
This permits imaging of optical slices and subsequent
Correspondence to: M. Müller. Tel: (þ31) 20 525 6221; fax: (þ31) 20 5256271;
e-mail: muller@mc.bio.uva.nl
266
reconstruction of the three-dimensional structure of the
specimen.
Recently a new member has been introduced to the
family of nonlinear optical microscopic techniques (Barad
et al., 1997). This technique is based on third-harmonic
generation (THG) off interfaces in the refractive index or the
third-order nonlinear susceptibility x(3). In this paper we
extend the technique to the realization – for what we
believe is the first time – of three-dimensional THG volume
imaging of both biological and nonbiological specimens. It
is important to note that these results represent a
demonstration of the basic THG imaging principle. Further
research is required for a complete interpretation of the
contrast-providing features in THG imaging. In addition, for
the first time we report on the k-vector dependence of the
THG signal – which is a crucial element to enable highresolution imaging based on this technique, discuss the
implications of the THG process on regular two-photon
absorption imaging and show that a line cursor geometry
can be used in THG imaging providing the possibility for
video rate imaging.
THG imaging is especially suited for the three-dimensional imaging of transparent specimens. It is generated
near gradients in the refractive index or in the third-order
nonlinear susceptibility x(3). Since it has a third-order
dependence on the excitation intensity it is generated
primarily in the focal region, automatically resulting in
sectioned imaging. It is a background-free imaging technique which does not require additional staining. The long
excitation wavelength (> 1 mm) in combination with the
nonresonant nature of the THG process makes the
technique potentially nonbleaching and further minimizes
possible biological damage.
The THG process is depicted schematically in Fig. 1.
Three photons at the fundamental frequency, q, interact
nonresonantly with the medium to produce one photon at
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Since the efficiency of THG scales with the third power of
the excitation power, it is, for a given input power, inversely
proportional to the square of the input pulse duration.
Hence, there is a clear advantage in using ultrashort pulses
for THG imaging. We have recently shown that pulses as
short as 15 fs can be produced at the focus of a highnumerical-aperture (NA) microscope objective when proper
dispersion precompensation schemes are used (Müller et al.,
1995, 1998).
Fig. 1. Schematic energy diagram for THG. The straight line
denotes the ground state of the system and dotted lines represent
so-called virtual states. In the processes three photons at the fundamental wavelength, q, are converted into one photon at the
third-harmonic frequency, 3q.
the third-harmonic frequency, 3q. This process has been
described in detail by various groups for the case of THG
through-focusing in gases (Ward & New, 1969; Largo et al.,
1987; Eramo & Matera, 1994) and we summarize only the
main features here. In the process, the optical field at the
fundamental wavelength (Eq) induces a macroscopic
polarization (P3q) of the form
P3q ~ xð3Þ E3q
ð1Þ
which in turn generates a field at the third harmonic
frequency (E3q). It follows that the THG power, P3q, has a
third-order dependence on the incident power, Pq,
P3q ~ ½xð3Þ ÿ2 P3q :
ð2Þ
Following Barad et al. (1997) and Boyd (1992), the THG
power in the case of strong focusing of a Gaussian beam can
be expressed as
ð3aÞ
P3q ~ P3q jJj2
where
∞ ð3Þ
x ðzÞ eiDkbz dz
:
ð3bÞ
J¼
2
¹ ∞ ð1 þ 2izÞ
In Eq. (3b), the integration extends over the volume of the
medium, z denotes the axial position, b ¼ kqw02 is the
confocal parameter (i.e. the axial width of the focal field
distribution), with kq the wave vector at the fundamental
wavelength and w0 the beam waist radius and Dk ¼ 3kq ¹
k3q the phase mismatch. Calculation of this integral shows
that efficient THG in a uniform medium with a focused laser
beam is possible only for Dk > 0. Hence in normally
dispersive materials, where Dk # 0, no THG is possible.
However, when the medium is not uniform, i.e. when there
is an interface either in refractive index or in the third-order
nonlinear susceptibility x(3), significant THG can be
observed. Note that the above treatment relies solely on a
breakage in axial symmetry for bulk third-harmonic
generation, rather than on a surface enhancement as
proposed by Tsang (1995).
q 1998 The Royal Microscopical Society, Journal of Microscopy, 191, 266–274
Experimental
The experimental set-up is shown in Fig. 2. The excitation
source consists of a 1-kHz optical parametric amplifier
(OPA) (Wilson & Yakovlev, 1996), operating at 1·2 mm with
a pulse duration of < 50 fs. The pulse energy of 70 mJ per
pulse is reduced, using neutral density filters, to < 1 mJ per
pulse at the output of the focusing objective. A long-wave
pass RG1000 filter blocks any residual white light or
800 nm pump light from the OPA. The single-axis scanning
mirror is positioned in a plane conjugate to that of the
objective’s entrance pupil. To permit high-speed image
acquisition and efficient use of the available OPA power, a
100-mm cylindrical lens is used for line cursor mode
excitation. The excitation light is focused onto the specimen
with a Nikon PlanApo 10/0·45 microscope objective and
the THG emission is collected in the forward direction with
an Edmund Scientific 10/0·25 microscope objective, which
images it directly onto a Hamamatsu C5985 video CCD
camera. Any residual excitation light is blocked by a 400nm interference filter (Andover 400FS20, FWHM
20 6 4 nm) in front of the camera. The effective length of
the line cursor in the focal plane is < 530 mm. With a width
of the line cursor of < 2 mm, this results in a maximum
intensity at the specimen of the order of 1012 W cm –2.
To ascertain the proper characteristics of the signal, the
Fig. 2. Experimental set-up for THG imaging. OPA: optical parametric amplifier; F1: RG1000 long-wave pass filter; Ms: singleaxis scan mirror; L: 100-mm cylindrical lens; O1: Nikon PlanApo
10/0·45 microscope objective; S: specimen; O2: Edmund Scientific
10/0·25 microscope objective; F2: 400-nm interference band-pass
filter; V: video CCD camera.
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M . M Ü L L E R E T A L .
third-order dependence of the THG on the excitation power
was checked routinely. A typical result is shown in Fig. 3(a).
The straight line represents a linear fit to the data – plotted
on a log–log scale – yielding a slope of 3·0 (6 0·07),
demonstrating the third-order dependence. Care was taken
to operate at power levels below optical breakdown, limiting
the range over which the power dependence was measured.
The axial resolution of the system is determined by a
measurement of the THG intensity as a function of the
(axial) position of the glass/air interface of a coverslip,
scanned through the focus of the focusing objective (see
Fig. 2). Figure 3(b) shows the result for objective O1
(NA ¼ 0·45), giving a full width at half-maximum (FWHM)
of the axial THG response of 11·6 (6 0·5) mm. It has been
shown (Barad et al. 1997) that the THG axial response is
approximately equal to the confocal parameter, b, of the
fundamental beam. In other words, the axial response is
Fig. 3. (a) Third-order power dependence
function of the input power. The slope of
(6 0·01). (b) Axial response of the THG
interface of a coverslip. The FWHM of
(6 0·5) mm.
of the THG signal as a
the log–log plot is 3·0
signal to the air–glass
this response is 11·6
expected to be approximately equal to the FWHM of the
axial point spread function (PSF), which for this case
(l0 ¼ 1·2 mm, NA ¼ 0·45) is < 12 mm. The generality of this
behaviour has been confirmed (data not shown) at high NA,
where an axial response of < 1 (6 0·2) mm was observed for
l0 ¼ 0·8 mm and NA ¼ 1·25 (oil).
As a first example of the imaging potential of the THG
technique a series of optical sections has been taken from a
fibre (Thorlabs FS-SN-4224) immersed in immersion oil.
The fibre (Fig. 4) consists of three layers: the jacket
(n1 ¼ 1·540) with an outer diameter of 250 mm, the
cladding (n2 ¼ 1·453) with an outer diameter of 125 mm
and the core (n3 ¼ 1·458) with a diameter of 5·5 mm. The
imaging set-up in these pilot experiments is limited both in
signal-to-noise (S/N) – the effective dynamic range is given
by a maximum signal count of < 220 against < 1·5 counts
additive noise from the detection system – and in axial
resolution (NA ¼ 0·45). The result of this is that both the
immersion-oil/jacket interface (due to insufficient S/N) and
cladding/core (due to insufficient axial resolution) are not
resolved in the optical sections shown in Fig. 5. (Note that
with an improved S/N the immersion-oil/jacket interface
would be resolved readily, as demonstrated by the measured
THG signal from an immersion-oil/coverslip interface – see
Discussion.) The scanning direction of the line cursor is
along the horizontal axis in all images shown. Figure 5
clearly shows the sectioning capability of THG imaging and
some imperfections on the cladding’s surface. Another
interesting feature is the absence of signal from interfaces
orientated parallel to the optical axis. This characteristic
can be understood from the requirement of symmetry
breakage with respect to the focal plane in bulk THG (see
above). Since the generation of the third-harmonic signal
depends on the breakage of the axial symmetry with respect
Fig. 4. Schematic of the jacket/cladding/core dimensions of the
fibre used in the THG imaging experiments.
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Fig. 5. THG imaging optical sections of a fibre immersed in immersion oil. The signal is generated at the jacket/cladding interface. The sections are separated axially by 10 (6 1) mm (the original data set was taken at 5 (6 1)-mm intervals).
to the focal plane, it may be expected that the sensitivity of
the technique with respect to surfaces orientated parallel to
the optical axis increases with increasing NA. Figure 6
shows a three-dimensional reconstruction (based on the
simulated fluorescence process method (SFP) (van der Voort
et al., 1993). The thickness of the layer shown is determined
by the limited axial resolution of the THG imaging set-up.
To demonstrate that the THG method is capable of
imaging both jacket and core, Fig. 7 shows a number of the
optical sections of the top half of the same fibre, this time
not immersed in immersion oil. In this case, the refractive
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index change at the air/jacket interface is large enough to
overcome the limited S/N, permitting detection of signal
generation at both the air/jacket and the jacket/cladding
interfaces. Note that no signal is generated in between the
interfaces, i.e. in the bulk material. Note also that the signal
from the jacket/cladding interface is weaker than that from
the air/jacket interface because of the reduced refractive
index change. Close inspection of panels 8 and 9 in Fig. 7
shows that the core is visible as a transmission feature,
illuminated by third-harmonic radiation generated at the
air/jacket interface.
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M . M Ü L L E R E T A L .
Discussion
Fig. 6. Three-dimensional reconstruction – based on the SFP
method – of the optical sections shown in Fig. 5.
The practical applicability of THG imaging and its
potential for three-dimensional imaging of biological specimens is demonstrated in Fig. 8. This figure shows several
sections of plant leaf cells. The specimen is prepared by
cutting a thin slice of the leaf – including the upper
epidermis and first layer in the mesophyll – and mounting it
with a drop of water. No staining is applied. The bright
granular features are probably the chloroplasts on top of the
upper epidermis layer of the leaf, the cell walls of which are
clearly visible. The three-dimensional structure and the
organization of the chloroplasts in ring-shaped structures is
evident in the THG images, but can only be guessed in the
regular transmission image. It should be re-emphasized at
this point that the contrast-generating mechanism in THG
imaging is fundamentally different from, for instance,
confocal fluorescence or phase contrast microscopy. In
THG imaging the contrast results from (local) interfaces in
refractive index and/or x(3), whereas confocal fluorescence
microscopy measures local fluorescence intensity and
phase contrast microscopy is sensitive to accumulated
phase differences. Note also that there are several arguments which exclude ‘autofluorescence’ as a potential
source for artefacts in the THG-imaging signal. First, the
detection is limited to the exact third-harmonic frequency at
400 (6 20) nm. Thus, even for a three-photon absorption
process there would have to be a negligible Stokes shift for
an autofluorescence signal to occur. Second, no fluorescence signal has been observed in the backscattering
direction. Third, the autofluorescence of chloroplasts is
primarily at longer wavelength (> 600 nm). Finally, the
collection efficiency of the set-up for fluorescence (< 1·5%
for the NA ¼ 0·25 objective O2 – see Fig. 2) is extremely
small.
A number of general observations can be made with respect
to THG imaging. First, the third-harmonic radiation is
generated predominantly in the forward direction. In fact,
we have not observed any THG in the backscattering
direction. Second, as may be expected from the IR
wavelength of excitation and the nonresonant property of
the THG process, there is no apparent bleaching. We have
monitored images of the leaf (as shown in Fig. 8) – while
the leaf was continuously exposed to the laser radiation –
for over an hour without observing any significant change
in detected THG intensity. Third, there is an upper limit both
in power and in intensity that can be used in THG imaging
in particular and nonlinear optical imaging with ultrashort
pulses in general. This limit is set by the onset of processes
like white light generation, self-focusing and cavitation. In
our experiments we observed both white light generation
and cavitation on the cladding/jacket interface of the fibre
when working above this power limit. A dramatic example
of this phenomenon is shown in Fig. 9. The breakdown of
the medium is a threshold phenomenon. Care was taken to
apply a laser power well below this threshold in all images
taken other than in Fig. 9.
The potential advantages of the THG imaging technique
are obvious. It is a background-free imaging technique
which requires no additional staining of the specimen and
provides inherent optical sectioning. At the same time it is a
nondamaging microscopical technique since it relies on
nonresonant excitation at near-IR wavelengths where most
specimens are nonabsorbing, but still refractive. This
nondamaging characteristic is especially important for
applications involving live specimens. The technique is
sensitive to changes in both refractive index and x(3). For
example, we could easily resolve the immersion-oil/coverslip
interface in THG, although the two are refractive index
matched. This means that materials which have almost
identical refractive index but significant differences in x(3)
will produce substantial THG. An additional significant
difference with conventional ‘phase contrast’ techniques is
that the THG imaging technique is sensitive to local
changes in refractive index, rather than in an accumulated
phase difference.
A specific aspect of the technique is its sensitivity to the
orientation of the direction of propagation of the excitation
light, relative to the plane of the interfaces. This sensitivity
could be exploited, for instance by making – in a high-NA
system – multiple images at various orientations of the
specimen with respect to the optical axis, or vice versa by
using different regions of the high-NA illumination cone.
An interesting opportunity presents itself in combining
THG imaging with three-photon absorption (3PA) imaging.
In this case the former is detected in the forward direction,
whereas the latter can be detected in the backscattering
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Fig. 7. THG imaging optical sections of a fibre in air. The THG signal is generated both at the air/jacket interface and at the jacket/cladding
interface. The sections are from the top half of the fibre and are separated axially by 10 (6 1) mm (the original data set was taken at
5 (6 1)-mm intervals).
direction. Such a set-up would provide the opportunity for
relative localization of fluorescence labelling dyes with
respect to interfaces in refractive index and/or x(3). Both
THG and 3PA provide inherent three-dimensional imaging
potential and can be done simultaneously. Since the
sectioning in both techniques is determined by the
excitation process, co-localizing the THG and 3PA images
is straightforward. We have already observed substantial
3PA in Rhodamine 6G at 1·2 mm.
An important observation is the general presence of THG
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when using ultrashort pulses. A significant THG signal is
always produced near the interface of the coverslip. This is
especially relevant for two-photon absorption (TPA) imaging, where the excitation energies generally used (0·01–
1 nJ per pulse) are more than sufficient to produce
substantial amounts of THG. Similarly, THG will be
produced at existing interfaces while imaging the specimen.
Since TPA imaging is commonly done near 800 nm, this
implies that significant amounts of 265-nm radiation may
routinely be generated. Although much of this UV light will
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M . M Ü L L E R E T A L .
Fig. 8. Several THG imaging optical sections
of plant leaf cells. The leaf is used as found
and prepared by cutting a thin slice – including the upper epidermis and part of the mesophyll – and mounting it with a drop of water.
The upper epidermis is at the bottom of the
specimen. The sections are a selection of
a complete stack, taken at 5 (6 1) mm axial
spacing, at axial positions as indicated in
the figure. Panel 5 shows the regular widefield transmission image.
be absorbed by water, the radiation damage induced in TPA
imaging through THG requires careful examination. The
occurrence of THG in TPA imaging will generally pass
unnoticed since the radiation produced is absorbed by either
the specimen or the glass and thus remains confined to the
specimen. There are multiple ways to diminish this possible
harmful side-effect of THG in TPA imaging. For instance,
since the integrated TPA fluorescence signal scales linearly
with the pulse duration (for constant pulse energy),
whereas the integrated THG signal has a quadratic
dependence, increasing the pulse width by a factor of 10
would require a 10 times longer integration time in TPA
imaging, while reducing the THG by an order of magnitude.
Alternatively one could change to a longer wavelength and
use a three-photon absorption process instead, hence
shifting the THG to longer wavelength as well, where they
are potentially less damaging.
Given sufficient excitation power levels, the THG process
generally provides a signal, which is readily recorded on a
standard video CCD camera. Combined with the fact that
the repetition rate of the excitation laser source can be
maximized owing to the instantaneous nonresonant nature
of THG, this points to real-time THG imaging potential. In
fact, we have already observed THG imaging of the coverslip
surface at semi video rates, using only a 1-kHz OPA system.
Several new laser systems – especially fibre lasers – are now
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Fig. 9. Several THG imaging exposures – taken 1 min apart – of a single optical section of the fibre of Fig. 5. The excitation power level is
above damage threshold, resulting in cavitation at the jacket/cladding interface.
becoming available commercially (Sucha, 1998); these
combine sufficient power, pulse duration, operating wavelength and repetition rate to make them suitable for THG
imaging at an affordable price level.
In summary, we have presented three-dimensional THG
imaging near x(3) and/or refractive index interfaces in both
biological specimens and nonbiological samples, using a line
cursor mode laser scanning transmission microscope. The
technique permits potentially nondamaging and nonbleaching optical sectioning of transparent specimens. The general
features of the technique suggest that it may find
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application in fields ranging from biology to the materials
sciences. We are currently investigating the fundamental
properties of the technique and the extension to high-NA
imaging.
Acknowledgments
This research was financially supported in part by the
Stichting voor Fundamenteel Onderzoek der Materie, Utrecht,
The Netherlands, under grant no. 94RG02. This work was
performed at the University of California at San Diego.
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M . M Ü L L E R E T A L .
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