IEEE_Photonics_Journal_Paper

IEEE Photonics Journal Volume Extreme Ultraviolet Holographic Imaging
Volume Extreme Ultraviolet Holographic Imaging
With Numerical Optical Sectioning
VICTOR MAESTRE RAMIREZ, Member, IEEE, M. C. Marconi, Senior Member, IEEE,
R. A. Bartels,
C. S. Menoni, Fellow, IEEE, J. J. Rocca
NSF ERC for Extreme Ultraviolet Science & Technology and Department of Electrical and Computer
Engineering, Colorado State University, Fort Collins 80521 USA
DOI: 10.1109/JPHOT.2009.XXXXXXX
1943-0655/$25.00 ©2009 IEEE
Manuscript received March 3, 2008; revised November 10, 2008. First published December 10, 2008. Current
version published February 25, 2009. This research was sponsored by the National Science Foundation through
the NSF ERC Center for Extreme Ultraviolet Science and Technology, NSF Award No. EEC-0310717. This paper
was presented in part at the National Science Foundation.
Abstract: Three dimensional images were obtained using a single high numerical aperture hologram
recorded in a high resolution photoresist with a table top α = 46.9 nm laser. Gabor holograms
numerically reconstructed over a range of image planes by sweeping the propagation distance allow
numerical optical sectioning that results in a robust three dimension image of a test object with a
resolution in depth of approximately and a lateral resolution of 164 nm.
Index Terms: Holography, image analysis.
1. Introduction
Holographic imaging in the soft X-ray (SXR) and extreme ultraviolet (EUV) have been demon-
strated in several experiments realized using EUV/SXR lasers and synchrotron sources. These
include the first realization of soft X-ray laser holography at Lawrence Livermore National Labora-
tory using a large laser facility, and the holographic recording of biological samples and sub-micron
structures using soft X-ray radiation from synchrotrons, among other experiments [?], [?]. A key
idea in these experiments is to use coherent short wavelength illumination to achieve a spatial
resolution beyond the reach of visible light.
Using synchrotron radiation Gabor and Fourier holograms have been demonstrated [?] with
spatial resolution below 100 nm at SXR wavelengths. Compact EUV sources based on high
harmonic generation (HHG) were also used to demonstrate table-top in-line EUV holography with
a spatial resolution of 7.9 m and 0.8 m. Time resolved holographic imaging, that exploits the
short pulsewidth of the HHG sources, was also implemented to study the ultrafast dynamics
of surface deformation with a lateral resolution of the order of 100 nm [?], [?]. The recent
development of compact coherent EUV laser sources, [?] has opened new opportunities for the
implementation of novel imaging schemes with nanometer-scale resolution that fit on a table-top
[?], [?]. In this paper, we present a proof of principle experiment in which we demonstrate that
three dimensional imaging in a volume may be obtained from a single high numerical aperture
(NA) hologram obtained with a table top EUV laser. Gabor holograms were numerically recon-
Vol. 23, No. 11, November 2022 Page 1

structed over a range of image planes by sweeping the propagation distance. This numerical
sectioning technique for holography is verified to produce a robust three dimension image of a test
object.
Holographic imaging in the soft X-ray (SXR) and extreme ultraviolet (EUV) have [?] been
demonstrated in several experiments realized using EUV/SXR lasers and synchrotron sources.
These include the first realization of soft X-ray laser holography at Lawrence Livermore National
Laboratory using a large laser facility, and the holographic recording of biological samples and
sub-micron structures using soft X-ray radiation from synchrotrons, among other experiments [?],
[?]. A key idea in these experiments is to use coherent short wavelength illumination to achieve
a spatial resolution beyond the reach of visible light [?].
Using synchrotron radiation Gabor and Fourier holograms have been demonstrated with spatial
resolution below 100 nm at SXR wavelengths. Compact EUV sources based on high harmonic
generation (HHG) were also used to demonstrate table-top in-line EUV holography with a spa-
tial resolution of 7.9 m and 0.8 m. Time resolved holographic imaging, that exploits the short
pulsewidth of the HHG sources, was also implemented to study the ultrafast dynamics of surface
deformation with a lateral resolution of the order of 100 nm. The recent development of compact
coherent EUV laser sources has opened new opportunities for the implementation of novel imaging
schemes with nanometer-scale resolution that fit on a table-top. In this paper, we present a proof
of principle experiment in which we demonstrate that three dimensional imaging in a volume
may be obtained from a single high numerical aperture (NA) hologram obtained with a table top
EUV laser. Gabor holograms were numerically reconstructed over a range of image planes by
sweeping the propagation distance. This numerical sectioning technique for holography is verified
to produce a robust three dimension image of a test object.
structures using soft X-ray radiation from synchrotrons, among other experiments. A key idea in
these experiments is to use coherent short wavelength illumination to achieve a spatial resolution
beyond the reach of visible light.
resolution below 100 nm at SXR wavelength. Compact EUV sources based on high harmonic
of principle experiment in which we demonstrate that three dimensional imaging in a volume
may be obtained from a single high numerical aperture (NA) hologram obtained with a table top
EUV laser. Gabor holograms were numerically reconstructed over a range of image planes by
sweeping the propagation distance. This numerical sectioning technique for holography is verified
to produce a robust three dimension image of a test object.
Using synchrotron radiation Gabor and Fourier holograms have been demonstrated with spa-
tial resolution below 100 nm at SXR wavelength. Compact EUV sources based on high har-

monic generation (HHG) were also used to demonstrate table-top in-line EUV holography with
a spatial resolution of 7.9 m and 0.8 m. Time resolved holographic imaging, that exploits the
short pulsewidth of the HHG sources, was also implemented to study the ultrafast dynamics of
surface deformation with a lateral resolution of the order of 100 nm. The recent development of
compact coherent EUV laser sources has opened new opportunities for the implementation of
novel imaging schemes with nanometer-scale resolution that fit on a table-top. In this paper, we
present a proof of principle experiment in which we demonstrate that three dimensional imaging
in a volume may be obtained from a single high numerical aperture (NA) hologram obtained with
a table top EUV laser. Gabor holograms were numerically reconstructed over a range of image
planes by sweeping the propagation distance. This numerical sectioning technique for holography
is verified to produce a robust three dimension image of a test object.
resolution below 100 nm at SXR wavelength. Compact EUV sources based on high harmonic
of principle experiment in which we demonstrate that three dimensional imaging in a volume may
be obtained from a single high numerical aperture (NA) hologram obtained with a table top EUV
laser. Gabor holograms were numerically reconstructed over a range of image planes by sweeping
the propagation distance.
2. Experimental Details
The experimental set up is schematically illustrated in Fig. 1. A compact α = 46.9 nm table top
discharge-pumped capillary Ne-like Ar laser occupying only a 1 ? 0.5 m2 footprint on an optical
table was used for the recording of the hologram.
2.1. Some Extra Details
Lasing was obtained in the 46.9 nm 3s 1P1 ? 3p 1S0 transition of neon-like Ar by exciting Ar
filled alumina capillaries 3.2 mm in diameter with a current pulse having an amplitude of 10% to
90% rise time of first half-cycle duration.
2.1.1. Even more details
The pulse generator consists of a 4 stages Marx generator charged at voltages around 45 kV. The
fast current pulse was produced by discharging a water dielectric cylindrical capacitor through a
spark gap switch connected in series with the capillary load. The current pulse rapidly compresses
the plasma column to achieve a dense and hot filamentary plasma channel where a population
inversion is created by strong monopole electron impact excitation of the laser upper level and
rapid radiative relaxation of the laser lower level. The water serves as a liquid dielectric for the
capacitor and also cools the capillary.

Fig. 1. (a) Diagram of the experimental set up. (b) Detail of the test object used.
2.1.1.a. A continuous
Flow of Ar is injected in the front of the capillary and an optimum Ar gas pressure of 490 mTorr is
maintained in the capillary channel. The EUV laser and the vacuum chamber where the hologram
was exposed, are connected via a vacuum manifold that provides differential pumping of the
chamber that is maintained at 10-5 Torr. The laser, operated with 18.4 cm long capillaries,
produces 0.1J pulses at a repetition rate of 1 Hz 15. The high temporal and spatial
x =
z
X
1=0
21
Q (1)
coherence of the EUV table top laser permits the recording of large NA holograms for high resolu-
tion holographic imaging 18. The test object used in the holographic volume imaging experiment
consisted of a tilted metallic surface covered with opaque spherical objects as can be seen in (1).
This test object was fabricated placing a 100 nm thick aluminum foil covering a hole 1.5 mm in
diameter made in a 80 m thick mylar sheet. The hole was partially covered with a second mylar
sheet 80 m thick, as schematically indicated in Fig. 2.
Humanoid robots have received much attention recently. Although they are able to walk without
falling, their movements are not natural looking. In order for these robots to move more like
humans, two technological obstacles need to be addressed: Firstly, there is a lack of flexibility
in their body torsos. In all human activities, movements from the spine are involved. Yet, this
important factor has been neglected by the majority of humanoid robotic researchers. One of the
main reasons is that the added degrees of freedom (DOF) make it more costly and difficult to

Fig. 2. Lasing was obtained in the 46.9 nm 3s 1P1 ? 3p 1S0 transition of neon-like Ar by exciting
Ar filled alumina capillaries 3.2 mm in diameter with a current pulse having an amplitude Lasing was
obtained in the 46.9 nm 3s 1P1 ? 3p 1S0 transition of neon-like Ar by exciting Ar filled alumina
capillaries 3.2 mm in diameter with a current pulse having an amplitude
build a robot. Another key issue is that it is very difficult to program these types of robots so
that they can maintain balance. This numerical sectioning technique for holography is verified to
produce a robust three dimension image of a test object. This numerical sectioning technique for
holography is verified to produce a robust three dimension image of a test object. This numerical
sectioning technique for holography is verified to produce a robust three dimension image of a
test object.
Z = x1 + x2 + x3 + x4 + x5 + x6
+a + b (2)
+a + b (3)
+ a + b (4)
+ a + b (5)
In order to address the above technological challenges, we need to develop flexible spine
humanoid robots as experimental platforms. Recently, a few researchers have developed several
spinal robots based on the anatomy of the human skeleton, Mizuuchi built a tendon-driven robot
called “Kenta” [?], [?]. Although the robot has a spine, there has been no data to show that it
can move in a flexible way. Also, the robot cannot stand up without external support because the
upper body is too heavy [?]. Mizuuchi later improved his prototype. However, it is also unable to
stand up without external support [?], [?].
At the German Space Agency (DLR), Hirzinger and his group developed a spine robot called
“Justin”. The robot has a 3-DOF movable upper-torso, two arms and dexterous hands. Unlike the
tendon-based robots developed by Mizuuchi and his colleagues, each controllable spinal joint of
Justin is directly actuated by a DC Motor via a Harmonic Drive Gear. In order to prevent the robot
from falling, the designers fixed the robot to a large platform [?]. In November, 2007, researchers
from Sugano Lab of Waseda University announced a new humanoid robot for household work and
home care. The robot is called “Twendy-One”. It has a 4-DOF spine but it is fixed on a wheeled
mobile platform. Thus, balancing is not an issue for this robot. It has a 4-DOF spine but it is fixed

TABLE I
MATH SPACINGS USED BY L
ATEX
Size Width Cmd. Used for Example
small 1/6 em , symbols ab
medium 2/9 em : binary operators a + b
large 5/18 em ; relational operators a = b
negative small −1/6 em ! misc. uses ab
on a wheeled mobile platform. Thus, balancing is not an issue for this robot.
Inspired by the flexibility of belly dancers, Or conducted the first scientific study on belly dancing
[?]. He developed a database of belly dancing movements using computer animations. Later, Or
recorded the movements of a professional belly dancer using a 12-camera VICON [?] motion
capture system. By analyzing the movements of the dancer, he developed a spinal mechanism
which allows a full-body humanoid robot to exhibit all the human spine motions in 3D although
with less degree of freedom [?]. Moreover, the robot is able to stand up while performing dynamic
torso motions without external support. In terms of controlling the mechanical spine, Or used
a model of the lamprey central pattern generator. Experimental results showed that by using
such neural networks, only three control parameters are needed to generate all human spinal
motions. In order to conduct research on human-robot interactions, Or developed a new, full-body
flexible spine humanoid robot [?], [?]. Experimental results showed that it is possible for humans to
perceive emotions expressed by a flexible spine humanoid robot. Later, Or developed the world’s
first humanoid robot that can walk more naturally, like a human, with flexible spinal motions.
The aluminum foil contours over the semicircular aperture to produce a variable height surface
with the desirable characteristics for this test in Table I. The 100 nm aluminum foil has a transmis-
sion of approximately 35% at α = 46.9 nm considering the layer of native oxide 19 and effectively
cuts the lower photon energy plasma emission from the Ar discharge in the laser source. The
sample was immersed in a solution of MIBK-methyl isobutyl ketone (4-Methyl-2- Pentanone) with
IPA (isopropyl alcohol) 1:3 for 30 seconds, rinsed with IPA for 30 seconds, and was finally dried
using compressed nitrogen x =
z
P
1=0
21
Q.
3. Results
We adjusted the1
exposure so that the photoresist operated in a linear response regime. With
exposure by the EUV laser, the holographic interference pattern generated by the reference and
the object beams was recorded in the photoresist and converted to a surface modulation after the
development. Thus, the holograms were recorded as a relief pattern in the surface of a photoresist
deposited on a Si wafer.
• Weight parameters for the simulated robot.
• Length of each body link.
• Specifications of body joints. Upper Torso means the spine. Due to symmetry, body parts
from the right are not shown.
• Neuron parameters. Θ is the threshold, Γ is the gain. τD and τA are respectively the time
constant of the dendritic sums and that of the frequency adaptation. µ is the coefficient of
frequency adaptation.
Holograms recorded in such a fashion can not be reconstructed in the conventional way with
1The aluminum foil contours over the semicircular aperture to produce a variable height surface with the desirable
characteristics for this test. The 100 nm aluminum foil has a transmission of approximately 35% at α = 46.9 nm considering
the layer of native oxide 19 and effectively cuts the lower photon energy plasma emission from the Ar discharge in the
laser source.

TABLE II
POSSIBLE Ω FUNCTIONS
Range Ω(m)
x < 0 Ω(m) =
m
X
i=0
K−i
x ≥ 0 Ω(m) =
√
m
TABLE III
NETWORK DELAY AS A FUNCTION OF LOAD
Average Delay
β
λmin λmax
1 0.057 0.172
10 0.124 0.536
100 0.830 0.905*
*
limited usability
an optical reconstruction beam. In order to numerically reconstruct the holograms, the surface
modulation was digitized with a Novascan atomic force microscope (AFM) operated in tapping
mode. Holograms recorded in such a fashion can not be reconstructed in the conventional way
with an optical reconstruction beam. In order to numerically reconstruct the holograms, the surface
modulation was digitized with a Novascan atomic force microscope (AFM) operated in tapping
mode.
1) Screenshot of the Webots simulation environment.
2) Schematic diagram of the simulated robot.
3) Schematic of the model lamprey CPG. Connections with a dot ending represent inhibitory
connections while those with an arrow ending represent excitatory connections.
4) Sample output of a segmental oscillator (the 20th segment from the CPG). MNl and MNr
respectively represents the output from the left and right motoneurons. Note the regularity
of the neural pulses.
Two holograms digitized in this manner are displayed in Fig. 2. The digital reconstruction of the
hologram digitized by the AFM is based on a numerical Fresnel propagator in Table II and III. To
obtain the amplitude and the phase distribution of the field in the image plane, the field emerging
from the hologram illuminated by a plane wave is back propagated with the Fresnel-Kirchhoff
integral. The integral was evaluated by the product of the spatial frequency representation of the
hologram obtained through a two dimensional fast Fourier transformation and the quadratic phase
free space Fresnel propagator in the spatial frequency domain.
Theorem 1 (Einstein-Podolsky-Rosenberg):
The back-propagation distance is determined by calculating the Fresnel zone plate (FZP) focal dis-
tance for the specific hologram geometry. For the specific geometry employed in this experiment,
the FZP focal length is approximately the distance between the object and the recording medium.
The digital images of the holograms processed with the Fresnel propagation code generated the
reconstructed images shown in Fig. 2.
an optical reconstruction beam. In order to numerically reconstruct the holograms, the surface
modulation was digitized with a Novascan atomic force microscope operated in tapping mode.

Lemma 1:
The back-propagation distance is determined by calculating the Fresnel zone plate (FZP) focal
distance for the specific hologram geometry For the specific geometry employed in this experiment,
an optical reconstruction beam. In order to numerically reconstruct the holograms.
Proof:
The back-propagation distance is determined by calculating the Fresnel zone plate (FZP) focal dis-
tance for the specific hologram geometry. For the specific geometry employed in this experiment,
4. Conclusions
We have demonstrated that through detailed processing of the reconstructed holographic images,
performed by changing the object-hologram distance in the reconstruction code, it is possible to
discriminate depth in the object. Using a specially fabricated object composed of spherical markers
465 nm in diameter spread on a tilted transparent surface, the reconstruction and analysis of
the hologram allowed to map the surface topography with a resolution close to 2 m, with such
resolution depending on the particular NA of the exposure.
The lateral resolution of the image obtained by numerical reconstruction was assessed utilizing
a wavelet image decomposition and image correlation. The best lateral resolution obtained with
a high NA recording, 164 nm, represents an improvement of more than a factor two relative to
previously published results.
Acknowledgements
The authors wish to thank the anonymous reviewers for their valuable suggestions.

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