High-resolution [JH1] soft
x-ray digital in-line holographic microscopy
Abstract: A scheme of sHigh-spatial-resolution
soft x-ray digital in-line holographic microscopy was
developed. to achieve high spatial
resolution. ItThe scheme
usesd
partially coherent and highly divergenting[JH2] lights, which were generated by a combination
of a Fresnel zone plate (FZP) and a pinhole with a radius of
200 nm radius, when
thewith incidence incoherent lights were tightly
focused on the pinhole. At a wavelength of 2.38 nm, objectives such as a two
objects, a carbon powder particle
and a a gold -pattern,
were imaged withto a spatial
resolution of ~150 nm. The scheme overcamesuperseded
the achievable resolution, (i.e. the
pinhole’s radius), of typical
pinhole-based holographic microscopy.
OCIS codes: (090.0090) Hh[JH3] olography; (090.1995) digital holography;
(110.2960) image analysis; (110.7440) x-ray imaging; (340.6720) synchrotron radiation; (340.7460) x-ray
microscopy
1. Introduction
Lensless x-ray holography has been ofattracted
interest for the pastin
recent years for its utility toin
obtaining complex field information withat
a high spatial resolution. Since Gabor’s invention in 1948 innovation [1],
holography has been proved asto be
a powerful technique that offerings
3D sample
information of a sample from a single 2D hologram.
Soft x-ray holography with aof sub-100
nm resolution, has been demonstrated
throughin the forms of both Fourier transform
holography (FTH) [2, 4] and Gabor holography (or in-line
holography) [3]., has been demonstrated.
In the reported FTH, [2, 4], a delicate
pinhole was fabricated inon the
sample plane in order to generate a coherent and divergenting
reference wave. High-resolution imaging withto
50 nm resolution was reported withfor a scheme
that
usedthat uses a Fresnel zone plate (FZP)
to generate a reference wave and a mask-sample structure [2]. In the setup, the
pinhole size limited the resolution and the CCD detector’s dimensions
limited the magnification. The inherent problem ofwith
the
FTH is theits limited
brightness due to athe
nanoscale pinhole size. Recently, more intense holograms have been acquiredachieved
by replacing
the pinhole withsubstituting multiple pinholes [5]
for
the single one orand by
means of binary uniformly redundant arrays (URAs) [6]. The main drawback
of those
reportedthese FTH schemes, however, is
that
one hasthe need to fabricatedrill
a pinhole(s) or fabricate URAs near the sample atin or on
the same substrate, which limits practical applications forto
diverse samples and/or in-situ experiments.
In a[JH4] typical x-ray digital in-line holography setup
[7-10] which uses a
spherical reference wave, a pinhole, an object, and a CCD are positioned in series
inon
different planes. in series. If
the magnification is sufficiently large, enough,
then[JH5] the resolution is determined by the radius
of the pinhole. The highest spatial resolution by the pinhole-based
digital in-line holography reported to date[JH6] is ~400 nm [7]. One may obtain aA
high-NA (numerical
aperture) (NA) coherent
light also can be obtained without a pinhole,
by using spherical mirrors with extreme ultraviolet (EUV) radiation [11-12]. However,
the
resolution is limited by the longer wavelength of the EUV.
limited
the resolution. One may also overcome theThis limitation
of NA can be overcome by recording holograms
with a high-resolution photoresist nearby a sample [3]. AlthoughDespite
the high- resolution was achieved,
the
method required a post-process tohologram
digitizatione the hologram by use of
an atomic force microscopy is required,
limiting the capability
[JH7] of in-situ investigation.
Fully coherent reference waves, specifically low-NA undulator
radiation or long-wavelength
EUV radiation, have been used forwith
the above described methods to illuminate the entire CCD or resist;.
undulator
radiation of low NA or a EUV radiation of long wavelength. A Ffew
researchesstudies
werehave
reported on the resolution of the in-line holography using a partially
coherent light. OneTwo of them
showed through calculations that,
although
the highly coherent light produces a high-resolution
image, there is no need to pursue very high, coherence
more than abeyond-the-criterion
coherence [13, 14]. In fact, Iit
was provedn that a
partially coherent source doeshas not
significantly lowerdeleterious effect on[JH8] the resolution [15]. TheThis
result has stimulatedmotivated ourthe
present studyinvestigation
withof
a rather incoherent x-ray source.
In this study, we presentreport
a
high-resolution soft x-ray digital in-line
holographic microscopy by usemeans of a
spatial filter composed of an FZP and pinhole. The pinhole with a
radius of 200 nm radius generates highly divergenting
and partially coherent lights [JH9] when incidence incoherent lights are tightly
focused by the FZP on the pinhole. TheThis
combination results in a relatively high NA reference wave, even with
a short wavelength of 2.38 nm. AA ccarbon
powder particle and a gold- pattern
were imaged withto a spatial
resolution of ~150 nm. This is the highest resolution ever reported withfor
digital in-line holographic microscopy. The scheme overcamesuperseded
the achievable resolution, (i.e. the
pinhole’s radius),
of typical pinhole-based in-line holographic microscopy.
2. Experiment
The
experiments were carried out with a modified TXM of ~50 nm spatial resolution [16] that
was newly developed aton the 7B1
beamline at Pohang Light Source (PLS). The spatial
resolution of the TXM was ~50 nm. Figure
1 showsis
a thumbnail view of the experimental setup. In the
experiment, 2.38 nm sSoft x-rays
(520 eV) of 2.38 nm wavelength withand a 1000X resolving
power (E/ΔE) of 1000 were used. The rays’
have
a temporal coherence length (l2/Δl) of ~2 mm, which
limits the observable region of interference in in-line holography. The spatial filter is composed of an FZP and a pinhole.
It
has 4600 zones and is made out of 140 nm
thick gold on a silicon nitride membrane. The focal length (f) of the 1st-order
diffraction of the FZP is 92 mm, and the range of the NA is 0.005 ~– 0.01 at the wavelength of 2.38 nm
wavelength. The
expected
efficiency of the 1st-order
diffraction’s expected efficiency is ~10 %.
Because the FZP has the central beam stop, the beam’s profile on any
plane excepting on the focal
plane, the beam’s profile on any plane is of an annular
shape. The minimum size of the
focused beam, which isas
determined by the beamline geometry, is ~1 μm in the vertical
direction and more than 10 μm in the horizontal
direction. The ZP’s depth of focus (DOF) is ~20 μm. The pinhole, withof
radius R=200 nm, was
drilled on a 3 mm-thick nickel plate by focused ion beam (FIB) milling.
Fig. 1. Schematic layout of the experiment
and conceptual enlargement of the illumination angle.
If we assume that the
illumination beam is a highly collimated plane wave and that the
FZP is a combination of an annular pupil and a thin
lens, then the field distribution at the
focal plane is proportional to the Fourier transform of the annular flattop
beam. The Fourier transform provides a 2D spatial spectrum of the beam. The pinhole
functions as a low-pass filter, which passes smaller allowing
spatial frequencies smaller than the cutoff frequency to pass
and blockings higher frequencies
ofon
the spectrum. Thus the pinhole effectively excludes the edge[JH10] of the annular disk and
passestakes
in the global distribution of the beam. Figure 1’s Cconceptual
figuresdepictions
of a line’s intensity profiles beforein
front of[JH11] and afterbehind[JH12] the pinhole,
as
is shown in Fig. 1, show that the width (from minima to minima[JH13] ) of the latter became
much wider than that of the former, effectively increasing the NA. In this
experiment,[JH14] forAs
regards the converging
incidence beam, with an angle of 0.005 rad., the diverging[JH15] angle
of
the beam afterbehind[JH16] the 200
nm-radius pinhole became ~0.018 rad. ian[JH17] . The
pinhole, Iin addition
to its
spatial filtering function, the pinhole defines
athe
spatial coherence. Even though the pinhole size does not satisfy the condition
for coherent light, R=λ/4πθ, the transmitted lights have[JH18] a partial
coherence. As a result, the spatial filter generates partially coherent and highly
divergenting soft x-rays.
It should be noted that the wavelength is the shortest and the corresponding NA
is rather high, as everalways[JH19]
reported inof the digital
in-line x-ray holography. The sample is placed at ~3 mm
from the pinhole. As is described in Ref. 16, the pinhole and the sample are located
in an atmospheric pressure,
helium-ambient
environment. with helium-ambient. The holographic image is recorded on an in-vacuum
back-illuminated 16-bits
CCD detector (1024 x 1024 pixels, 13 μm pixel size) placedpositioned
at
1040 mm downstream of the sample. In order to characterize the
imaging performance of the in-line holography, two samples were imaged..
The
samples, each of which was placed on a 100 nm-thick
silicon nitride membrane, One is a included
a random-shaped
carbon powder particle withof
a few microns sizesdiameter. The other is and a gold pattern
‘160’, made of gold with of
160 nm thickness. The samples were on a silicon nitride membrane of
100 nm thickness.
The nNumerical reconstruction
of the hologram, back-propagation of the hologram to
the object plane with illumination of the reference wave, was doneperformed
by a convolution approach [17]: 
where 
is a complex object
field aton the
object plane, 
is a hologram aton
the CCD plane, 
is a reference wave aton
the hologram plane, 
is the impulse response function:
, r is the distance between a point in the hologram and a point inon
the reconstruction plane, 
is the wave number:
, and 
is a 2D Fourier
transform of the . The reference wave aton the
hologram plane isis assumed asas
a plane wave, which is simply a constant. Because
the hologram is produced by a spherical wave, the magnified object field is
obtained at a reconstruction distance 
, where A is the pinhole-sample distance, B is the sample-CCD distance, and M is the magnification of the system.
3. Results
Fig. 2. Holograms of a carbon powder
particle with respect to various
pinhole
sizes, with a radiius
of (a) 700, (b) 500, (c) 400, and (d) 200 nm.
Holograms of a a carbon
powder particle with different pinhole sizes were
obtained with different pinhole sizes to verify
the enhancement of the spatial coherence and the numerical apertureNA
of the spatial filter. Figures 2(a) ~[JH20] – (d) show the holograms
by
use ofand the pertinent pinholes withof
radiius R=700 nm, 500 nm, 400 nm and 200 nm, respectively. The hHolograms
2(a)-–2(c) were acquired
for 180 s, and 2(d), for 300 s. Because of the limited detector size, we used a
part of the annular ring of the FZP’s 1st-order
diffraction, which is more clearly noticeable in 2(a). As the pinhole’s size
decreased, the visibility of the fringes increased and the high spatial frequencies
of the object field were revealed. In spite of the intensity’s decrease, the
interference region expanded as the pinhole size decreased. When using the
pinhole withof R=200 nm, the interference fringes
extended to almost the full area of the CCD.
Figure 3 shows images of the fishlike carbon powder
particle. To compare the reconstructed holographic image with the
real object,, as shown in Fig. 3(a), we
imaged the powder[JH21] with the TXM that is described
in Ref. 16 (Fig. 3(a))[JH22] . The
figureimage
was obtained at the same photon energy (520 eV) with an exposure time of 60 s. Figure
3(b) shows the hologram of the powder by use offor
the R=200 nm pinhole,
with
an exposure time of 300 s and with a338X
magnification. of 338. The
reconstructed amplitude image 3(c) shows particle detailsed
image such as a bump, of the
particle that is indicated by the red arrow. In this image, the
reconstructed distance lies at the focus of the bump[JH23] , and some parts of the
edges awayoutside from the
field
of focus are blurred. Figure 3(d) showsis a
reconstructed phase image.
Fig.
3. Images
of a
fishlike carbon powder particle.
(a) TXM’s absorption contrast image. (b) Image of hologram.
(c)
Reconstructed amplitude image. (d) Reconstructed phase image. The Rreconstructed
images werewere enlarged..
To accurately quantify the spatial resolution
of the reconstructed image, a gold pattern ‘160’ made of gold withof
160 nm thickness was imaged. The pattern hashad
morea
sharper edge than the carbon powder
particle. The Hhologram
image and the reconstructed amplitude image are shown in Figs. 4(a) and
4(b). A line profile of the magnified image 4(c) was obtained,
and is plotted in Fig. 4(d). The 10% to 90% contrast change (knife-edge-criterion)
in the line profile hads a width of
150 nm. This is the highest resolution so far reported inof
digital in-line holographic microscopy; andit
overcomessupersedes
the criterion that the best resolution is defined by the pinhole radius size. In
our geometry, assuming coherent illumination, the CCD size limits the resolution.
The estimated resolution is ~160 nm (considering the CCD diagonal length: 18.8
mm), which matches to our measured resolution within the experimental
error. This therefore implies that partially coherent light also resulted
in the same theoretically expected resolution based on coherent illumination,
and that the resolution depends only on the effective NA when the coherencey
of the illumination is moregreater than
athe
criterion.
Fig. 4. Images
of 160
nm-thick gold pattern ‘160’. made of
gold with 160 nm thickness. (a) Hologram image.
(b) Reconstructed amplitude image. (c) Magnified image of (b). (d) A lLine
profile of the line indicated in (c).
4.
Conclusions
We
presented a high-resolution
soft x-ray digital in-line holographic microscopy usingthat
uses highly divergenting short
wavelength lights that were generated by a spatial
filter composed of an FZP and a pinhole. At a 2.38 nm
wavelength of 2.38 nm provided by incoherent
synchrotron radiation, samples were imaged withto
a spatial resolution of ~150 nm. ItThis overcamesuperseded
the resolution limit of typical pinhole-illuminated in-line holography. The method
described here hasallows more rooms
to
enhance thefor further resolution
enhancement. For example, the CCD’s area and the FZP’s NA,
are
rather small in thisthe
present experimentation, were rather small and
low. Thus, uUsing a high-NA’s
FZP to enlarge the illumination angle, and using a
large-area CCD to detect more lights, one could
enhance the resolution could be enhanced.
Moreover,
Tthe exposure
time ofin our case iswas
rather long, due to the limited
flux of the source. Thus, using a brighter
source maymight[JH24] decrease the exposure time and may reduce
blurring of the finest fringes, resulting in higher resolution images.
An effective method withfor a
limited-flux source is to replace the gold-patterned
FZP towith a nickel-patterned
FZP. ItThis substitution
giveswould
provide moreapproximately double
the photon flux about a factor of 2 at a
wavelength of 2.8 nm. We expect that, using this
method, one can obtain a highresolution
holographic images down toof
sub-100 nm resolution and better,
sooner or later, will be achieved. sooner
or later. This scheme maycould
also be effectively applied forto hard
x-rays toin
investigationse of
low-Z comprising materials,
which
showing relatively low absorption contrasts.
Acknowledgements
We acknowledge the
financial support of the Basic Science Research Program administered by the
National Research Foundation of Korea (NRF) and funded by the
Ministry of eEducation,
Science and Technology (Ggrant
Nno.
R15-2008-006-03002-0).