APPLIED PHYSICS LETTERS
VOLUME 79, NUMBER 15
8 OCTOBER 2001
Single sharp spot in fluorescence microscopy of two opposing lenses
C. M. Blanca,a) J. Bewersdorf, and S. W. Hellb)
High Resolution Optical Microscopy Group, Max Planck Institute for Biophysical Chemistry,
Göttingen, Germany
共Received 13 June 2001; accepted for publication 27 July 2001兲
We demonstrate theoretically, experimentally, and in an imaging application the possibility to
generate a single predominant sharp diffraction maximum in the effective point-spread function of
a fluorescence microscope that coherently uses two opposing lenses. This is achieved through binary
pupil filters that preclude the origination of the unfavorable strong interference side maxima that are
otherwise present in these systems. Mathematical postprocessing, which has so far been a
prerequisite to gain artifact-free images, is now optional or obsolete. © 2001 American Institute of
Physics. 关DOI: 10.1063/1.1407303兴
In scanning confocal and multiphoton microscopes, imaging is performed with a spatially confined, threedimensional 共3D兲 effective point-spread function 共EPSF兲, the
extent of which determines the spatial resolution. Therefore,
the most direct way of improving the resolution is to define
methods reducing the EPSF spatial extent. Due to the laws of
diffraction, the minimal full width at half maximum
共FWHM兲 of the main maximum of the EPSF is of the order
of 200 nm in the transverse direction, but only 500– 600 nm
along the optic axis.1 This discrepancy clearly calls for methods rendering an axially narrower EPSF.
If we leave aside the concept of stimulated emission
depletion microscopy, which requires two trains of ultrafast
light pulses, the only way to axially sharpen the FWHM
three- to sevenfold is by interfering wave fronts of two opposing lenses, as it is utilized in scanning 4Pi-confocal
microscopy,2 as well as in the nonscanning standing-wave3
共SWM兲 and I5M microscopy.4 Unfortunately, this approach is
challenged by the fact that the resulting narrower main maximum is accompanied by interference sidelobes causing periodic artifacts in the image. A remedy for the lobes is data
deconvolution; however, this is applicable only if the optical
transfer function 共OTF兲 is contiguous at the given noise
level.5 In spite of reported advancements, the ultimate goal
of creating a single clear-cut spot that is much sharper than
in standard microscopy has not been achieved with these
systems.
We now report that by applying amplitude filters in a
4Pi-confocal microscope employing coherent illumination
for two-photon excitation 共type A兲, a solitary maximum can
be produced, that is 4 –5 times sharper than its confocal
counterpart. This solitary maximum is accompanied by only
minimal lobes. As a result, the need for computational postprocessing of the acquired data, which up to now has been
critical, is virtually eliminated. The structure of most objects
can now be inferred from the raw image data. Equally important is the fact that through the absence of computation,
lower signals can be tolerated in the image.
Consisting of a single dark ring 共DR兲, the amplitude filter is very simple 共Fig. 1兲. Since we insert it only in the
illumination path no fluorescence light is wasted. Similar filters were proposed for axial super-resolution in confocal
microscopy,6 but the predicted axial narrowing is only of the
order of 15%, and hence, only had little impact in practice.
This is not so if two opposing lenses are used since any small
reduction of the axial width of the main maximum leads to a
sharp decline in the height of the interference sidelobes.
In the way it works, the filter can be perceived as a
minimal Toraldo filter;7 however, in our case it is not devised
for reducing the FWHM of the central peak, but for canceling the energy in the interference sidelobes. The filter simply
divides the illumination wave front of the two lenses into an
inner part and an outer ring, each producing a standing wave.
While the standing wave from the inner part has a high spatial frequency, the one produced by the outer ring features a
frequency reduced by the cosine of the angle between the
marginal rays of the aperture and the optic axis, which is of
the order of 0.4. Upon coherent overlap the main maximum
is strengthened, but the field of the first side maxima, having
opposing signs, is reduced. As a result, the energy of the first
side maxima is spread across their higher-order counterparts,
which can now be suppressed by multiphoton excitation and
confocalization.
This reasoning is fully supported by the results shown in
a兲
On leave from National Institute of Physics, University of the Philippines,
Diliman, Quezon City 1101, The Philippines.
b兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
FIG. 1. Scheme of the dark ring 共DR兲 filter inserted into the two arms of a
4 Pi-confocal microscope of type A with coherent illumination.
0003-6951/2001/79(15)/2321/3/$18.00
2321
© 2001 American Institute of Physics
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2322
Appl. Phys. Lett., Vol. 79, No. 15, 8 October 2001
Blanca, Bewersdorf, and Hell
FIG. 2. Z responses of the DR-4 Pi microscope feature a pronounced main
maximum and low sidelobes, found in the calculation 共solid兲 and in the
measurement 共boxes兲. The broad curve 共diamonds兲 exhibits the standard
confocal z response, whereas the crosses the 4 Pi z response without DR.
The inset shows the computed z response for three-photon excitation. Note
the excellent agreement between theory and experiment and the marked
improvement of axial resolution.
Fig. 2, displaying the measured and calculated z responses of
a 4Pi-confocal microscope, that is, the curve obtained
through scanning an infinitely thin fluorescence plane along
the optic axis:
I 共 z 兲 ⫽C
冕冕
⬁
0
2␲
0
兩 E1 共 z,r, ␾ 兲 ⫹E2 共 ⫺z,r,⫺ ␾ 兲 兩 2n
⫻ 关 h det共 z,r 兲 丢 d 共 r 兲兴 rdrd ␾ .
共1兲
The field of the two lenses is calculated through
E i 共 u, v , ␾ 兲 ⫽ 关 ⫺iA 共 I 0 ⫹I 2 cos 2 ␾ 兲 ,⫺iAI 2 sin 2 ␾ ,
⫺2AI 1 cos ␾ 兴 ,
共2兲
with I 0,1,2 being numerically calculated integrals over the
aperture angle ␪ 苸 关 0,␣ max兴 as defined in Ref. 8, but for a
pupil function taking into account the ring filter:
F共 ␪ 兲⫽
再
1
0
␪ ⭐ ␣ 1 ; ␣ 2 ⭐ ␪ ⭐ ␣ max
.
␣ 1⭐ ␪ ⭐ ␣ 2
共3兲
The angles ␣ 1 and ␣ 2 are defined by the inner and outer radii
of the ring, r 1 and r 2 , respectively. The detection PSF
h det(z,r) is calculated for a single lens field, using the appropriate fluorescence wavelength and convolved with the image function d(r) of the confocal detector pinhole in the
focalplane, which is 1 for r⬍D and 0 elsewhere. The parameter n defines the mode of excitation, with n⫽2 denoting
two-photon absorption.
The solid line in Fig. 2 shows the calculated z response
I(z) for ␣ 1 ⫽0.25, ␣ 2 ⫽0.82, and ␣ max⫽1.1, corresponding
to a numerical aperture of 1.35 oil immersion, a refractive
index of 1.518, D⫽167 nm, ␭ exc⫽760 nm, ␭ det⫽580 nm,
and n⫽2. As intuitively anticipated, the z response is characterized by a strong main maximum with a FWHM of 120
nm, i.e., ⬃4 times narrower than its confocal counterpart.
Importantly, the lobes are suppressed to values of 14%,
which in many applications should be close to the noise
level.
To examine whether this solitary maximum can be realized, we measured the corresponding z response in a 4Pi
setup 共Fig. 1兲. For this purpose, the beam of a mode-locked
FIG. 3. Measured optical transfer function along the reciprocal optic axis of
the confocal 共light solid兲 and the DR-4 Pi-microscope 共solid兲 featuring a
fundamentally enlarged bandwidth.
Ti–Sapphire laser was divided into two partial wave fronts,
each of which passed a fused silica plate of ␭/10 planarity.
An aluminum ring was glued onto each plate, serving as the
binary dark ring filter. The wave fronts propagated to the
lenses 共PL APO Leica, 100⫻, 1.4 NA oil兲 to interfere at the
common focal point. The radii of the rings were r 1
⫽0.8 mm and r 2 ⫽2.35 mm, yielding the ␣ 1,2 elected above.
The fluorescence light was collected through one of the
lenses without obstruction. After passing through a dichroic
mirror and a Schott BG39 color glass filter, it was focused
onto a detector pinhole of diameter 0.65 times the Airy disk.
The z response is obtained by scanning a monomolecular,
fluorescent Langmuir–Blodgett film along the optic axis.
The theory is impressively confirmed by the measurement 共Fig. 2兲. Similarly to the calculation, the FWHM of the
main maximum of the experimental z response is 120 nm
and the interference sidelobes are down to 14% of the central
peak, which is 2.5 times lower than the lobe height obtained
without amplitude filter. Comparison with the standard 共twophoton兲 confocal z response with FWHM 550 nm demonstrates that the DR-4 Pi-confocal microscope provides right
away with a fundamentally sharper effective PSF, testifying
to a higher axial resolution.
In the optical transfer functions of two-lens systems, the
presence of lobes is manifested as dents (4 Pi), strong depressions (I 5 M ), or even zeros 共SWM兲 within the enlarged
bandwidth of the OTF.5,9 Depending on the noise level, the
weak regions of the OTF render the required data processing
challenging (I 5 M ) or even impossible 共SWM兲. The sharp
focal peak of Fig. 2, however, yields an enlarged axial OTF
without periodic dents. This is demonstrated in Fig. 3, which
depicts the Fourier transform of the z response for the confocal and the DR-4 Pi-confocal microscope. The comparison
shows that our scheme not only enlarges the axial bandwidth
but also strongly transfers spatial frequencies throughout the
region of support of the OTF. This greatly facilitates image
postprocessing, which, however, is not always mandatory in
this system.
To prove this, we recorded Escherichia coli bacteria both
with the standard confocal setting and with its
DR-4 Pi-confocal counterpart. For this purpose the bacterial
membranes were labeled with the dye DH-5␣ and mounted
in Aquatex 共Merck, Inc.兲. The membrane basically forms a
hollow ‘‘bag,’’ which is too small to be resolved by the
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Appl. Phys. Lett., Vol. 79, No. 15, 8 October 2001
FIG. 4. XZ images of a membrane-labeled E. coli bacterium recorded with
the confocal 共a兲 and the DR-4 Pi-confocal 共b兲 microscope. The superior
resolution of the latter enables the resolution of the membrane structure of
the bacterium, without any data deconvolution. The line confocal 共dashed兲
and the DR-4 Pi-confocal 共solid兲 profiles in 共c兲 are extracted from the lines
indicated in 共a兲 and 共b兲, respectively. The two distinguished peaks allow the
separation of the membranes in 共b兲, but not in 共a兲. The raw data are pixelated
with subresolution pixels of 60 nm (x) and 19 nm (z). For display the data
were smoothed at the subresolution scale with a linear 3⫻3 filter.
⬃220⫻550 nm resolution of the confocal microscope. Indeed, Fig. 4共a兲 shows that the confocal image is entirely
smeared out, so that no indication for the membrane can
be found. By contrast the consequently recorded
DR-4 Pi-confocal microscope depicts the membrane and reveals its bag-shaped structure. Also within the sample, the
typical sidelobe height is brought down to a residual 14%.
The superior axial resolution is also evident in the raw data
line profiles through the center of the bacterium. The peaks
in the profiles clearly locate and separate the two membranes
without any mathematical deconvolution.
Blanca, Bewersdorf, and Hell
2323
As can be noticed from the theoretical and experimental
data, as well as in the images, the reshuffling of the intensity
to the outer lobes leaves a small haze in the raw data. By
applying a three-photon excitation process in a
DR-4 Pi-confocal microscope, say at ␭ exc⫽1000 nm, the
haze would be reduced since in this case the sidelobes are
readily reduced to 3.3%, as shown in the inset of Fig. 2.
However, as a three-photon process leads to restrictions as
far as the mode of excitation is concerned, we think that two
other approaches will be more successful. First, one could
apply a mathematical deconvolution, which because of the
favorable OTF should be very effective; in many cases, it is
a simple linear mathematical filter. Second, one could refine
the dark ring filter. As is the case also in the Toraldo concept,
one could devise filters with more than just one ring and
filters featuring smooth amplitude and also phase transitions.
Clearly, such filters will also be helpful in the single-photon
excitation mode.
We have calculated the radial structure of the EPSF of
the DR-4 Pi microscope and found that the lateral side
maxima are increased only slightly, and that the overall lateral resolution is not decreased. The reason for the first is the
strong confocal suppression, whereas for the second it is the
annular structure of the DR filter, which is even known to
lead to lateral super-resolution.
In summary, we have demonstrated theoretically and experimentally a predominant focal peak in a fluorescence microscope using two opposing lenses that is 4.6 times sharper
than that of confocal microscopy. Our approach uses simple
aperture filters in the illumination path of the objective lenses
and leaves a solitary main focal maximum. As demonstrated
in the images, fundamentally superior axial resolution in 3D
microscopy can be achieved without mathematical postprocessing.
Two of the authors 共C.M.B. and S.W.H.兲 acknowledge a
postdoctoral grant by the University of the Philippines 共0074兲 and a project grant by the DFG 共He-1977兲, respectively.
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