Non-diffracting optical quasi-Bessel beams provide an opportunity to construct optical fields of complex architecture. The constructed beams may have a bright central peak or zero intensity on the beam axis and have the beam size of only a few microns propagating over a long-defined distance, which is not possible with conventional Gaussian or high-order Laguerre- Gaussian beams. In this work we demonstrate the possibility of constructing a needle-like diverging optical funnel with zero intensity on the axis. The primary aim is to numerically construct and optimize the optical field, which could transversely compress and focus a stream of µm- and sub-µm size particles injected into vacuum or gaseous environment by applying light pressure and photophoretic forces pushing particles into the area with lower intensity. We present the results of numerical modelling of an “optical funnel” based on re-imaging a non-zero-order quasi-Bessel beam, formed by an axicon and a phase plate or using an SLM, with a collimator. The funnel geometry, namely, the μm-size of the beam cross-section, several-mm long propagation length and its divergence, all is controlled and optimized by changing the topological charge at a fixed collimation of the re-imaging optics, or/and by varying the collimation with fixed topological charge of the beam. The simulated profiles will have an application for optical guiding and focusing of aerosolised beam of particles, large biomolecules and viruses to the micron-size focus of x-ray Free Electron Lasers in order to increase the delivery efficiency of isolated single particles in coherent diffractive imaging experiments.
Optical trapping of light-absorbing particles in a gas environment is usually dominated by laser-induced thermal or photophoretic forces, which can be orders of magnitude higher than the force due to radiation pressure. Particle guiding with photophoretic forces over large distances in open air was recently realised by an optical pipeline, formed by a vortex laser beam of doughnut-like intensity profile, with a high-intensity ring of light that surrounds a dark core. We are adapting the optical pipeline concept for the purpose of guiding aerosolized particles into the intense focus of a x-ray free-electron laser (XFEL), in order to enable high-efficiency femtosecond x-ray coherent diffractive imaging (CDI). XFEL-based CDI allows single-shot nanometer-resolution imaging, and multi-shot Angstrom-resolution tomography in the case of reproducible nanoparticles, at a time resolution better than 10 femtoseconds. Remarkably, by imaging at timescales shorter than atomic motion, the crucial resolution-limiting effects of radiation damage may be overcome for radiation-sensitive targets such as viruses and biomolecules. Following on our previous work, we are developing an optical first-order Bessel-like beam with a variable-diameter hollow core and an axial-to-lateral aspect ratio up to ~2000, that can be used to guide particles with a spatial precision of less than a few µm over centimetre-long distances. We present the ways to control the beam divergence aiming to focus the stream of particles by thermal forces and forces of radiation pressure, analyse the forces acting on the particle in the beam, and uncover the beam structure and intensity to apply for a real-time experiment with XFEL.
Optical trapping of light-absorbing particles in a gaseous environment is governed by a laser-induced photophoretic force, which can be orders of magnitude stronger than the force of radiation pressure induced by the same light intensity. In spite of many experimental studies, the exact theoretical background underlying the photophoretic force and the prediction of its influence on the particle motion is still in its infancy. Here, we report the results of a quantitative analysis of the photophoretic force and the stiffness of trapping achieved by levitating graphite and carbon-coated glass shells of calibrated sizes in an upright diverging hollow-core vortex beam, which we refer to as an ‘optical funnel’. The measurements of forces were conducted in air at various gas pressures in the range from 5 mbar to 2 bar. The results of these measurements lay the foundation for developing a touch-free optical system for precisely positioning sub-micrometer bioparticles at the focal spot of an x-ray free electron laser, which would significantly enhance the efficiency of studying nanoscale morphology of proteins and biomolecules in femtosecond coherent diffractive imaging experiments.
We have developed a high-aspect ratio optical pipeline aiming to produce a highly collimated stream of micron-size
particles in either gaseous or vacuum environments. A hollow, first-order quasi-Bessel beam with variable divergence
was generated with a phase-only spatial light modulator (SLM), by superimposing the quadratic phase of a lens and an
axicon with a 0.5° base angle. The beam was further re-imaged to form a centimetre-long funnel beam with ~5μm
diameter and up to 2000 length-to-diameter aspect ratio. The divergence of the central core of the Bessel beam was
controlled by varying the effective lens in the hologram. The SLM-based optical beam was compared to a similar
beam composed using a physical axicon. The experimental tests were conducted with 2-μm size polystyrene spherical
particles to evaluate the optical force. We present estimated optical forces exerted on the particles in the transverse
plane, both depending on the particle size, laser power, and background-gas pressure.
Femtosecond (fs) laser pulses focused and confined inside the bulk of a material can deposit a volume energy density up to several MJ/cm3 in a sub-micron volume. This creates highly non-equilibrium, hot, dense and short-lived plasmas with conditions favorable for arrangement of atoms into unusual material phases. Singlecrystal silicon was exposed to strong shock waves induced by laser micro-explosion in confined geometry. The conditions of confinement were realized by focusing 170-fs pulses, with the energy up to 2.5 μJ, on a Si surface buried under a 10-μm thick SiO2-layer formed by oxidation of a Si-wafer. The generated intensity was 1015 W/cm2, well above the threshold for optical breakdown and plasma formation. The shock wave modified areas of the Si crystal were sectioned using a focused-ion beam and characterized with scanning electron microscopy. A void surrounded by a shock-wave-modified Si was observed at the Si/SiO2 boundary. The results demonstrate that confined micro-explosion opens up new perspectives for studies of high-pressure materials at the laboratory table-top expanding the laser-induced micro-explosion capabilities into the domain of non-transparent materials.
We describe synthesis of a new super-dense phase of aluminum under extreme pressure and temperature conditions
created by laser-induced microexplosions in sapphire. Micro explosions in sub-micrometer sized regions
of sapphire were induced by tightly-focused femtosecond laser pulses with a temporal length of ~ 100 fs and
an energy of ~ 100 nJ. Fast, explosive expansion of photogenerated high-density plasma created strong heating
and pressure transients with peak temperature and pressure of ~ 105 K and 10 TPa, respectively. Partial
decomposition of sapphire in the shock-compressed sapphire led to formation of nanocrystalline bcc-Al phase,
which is different from ambient fcc-Al phase, and was permanently preserved by fast quenching. The existence
of super-dense bcc-Al phase was confirmed using X-ray diffraction technique. This is the first observation of
bcc-Al phase, which so far has been only predicted theoretically, and a demonstration that laser-induced micro
explosions technique enables simple, safe and cost-efficient access to extreme pressures and temperatures
without the tediousness typical to traditional techniques that use diamond anvil cells, gas guns, explosives, or
megajoule-class lasers.
We demonstrate that a speckle pattern in the spatially coherent laser field transmitted by a diffuser forms a multitude of
three-dimensional bottle-shaped micro-traps. These multiple traps serve as a means for an effective trapping of large
number of air-born absorbing particles. Confinement of up to a few thousand particles in air with a single beam has been
achieved. The ability to capture light-absorbing particles suspended in gases by optical means opens up rich and diverse
practical opportunities, including development of photonic shielding/fencing for environmental protection in
nanotechnology industry and new methods of touch-free air transport of particles and small containers, which may hold
dangerous substances, or viruses and living cells.
Singular optical beams have been studied for many years after the pioneering work where the wave function of the laser radiation is presented as a steady-state solution of the wave equation for a harmonic oscillator. A major step in understanding the nature of singular beams has been made by introducing the concept of the angular momentum of light and analyzing local energy transfer in a vortex beam. It is now well accepted that the orbital angular momentum of light is an intrinsic feature of the optical vortex. However, the orbital angular momentum was always analyzed for travelling modes and the important issue of the orbital angular momentum associated with standing waves still remains open. The main motivation of our work is to reveal the structure of the orbital angular momentum in a standing wave formed by the counter-propagating optical vortices and study its suitability for an optical trapping and guiding. In this work we show that a superposition of two (or more) vortex beams generates a field structure which has a form of a standing wave in both the radial and longitudinal directions, but it is rotating simultaneously along the tangential direction. We demonstrate that then field of this optical vortex structure could be used as an optical trap and simultaneously transfer the angular momentum of the electromagnetic wave to an object inside the area of vortex localisation. We believe this study provides a basis for developing a novel concept of three-dimensional optical traps where vortices could be created in a local volume by a direct transfer of the angular orbital momentum of the electromagnetic wave to trapped objects.
We present experimental and theoretical study of refractive index modification induced by femtosecond laser
pulses in photorefractive crystals. The single pulses with central wavelength of 800 nm, pulse duration of 150 fs,
and energy in the range of 6-130 nJ, tightly focused into the bulk of Fe-doped LiNbO3 and stoichiometric LiTaO3
crystals induce refractive index change of up to about 10-3 within the volume of about (2.0 x 2.0 x 8.0) μm3.
The photomodification is independent of the polarization orientation with respect to the crystalline c-axis. The
recorded region can be erased optically by a defocused low-intensity single pulse of the same laser. Recording
and erasure can be repeated at the same position many times without loss of quality. These findings demonstrate
the basic functionality of the ultrafast three-dimensional all-optical rewritable memory. Theoretically they are
interpreted by taking into account electron photogeneration and recombination as well as formation of a space-charge
field. The presented analysis indicates dominant role of photovoltaic effect for our experimental conditions,
and suggests methods for controlling various parameters of the photomodified regions.
We present the experimental and theoretical studies of the optical response from the single-crystal of bismuth to the excitation by the femtosecond laser pulse. The experimental results revealed a complex, first - positive and a few picoseconds later - negative, change in time-dependent reflectivity, which could not be explained in the light of the existing theories. It is shown that reflectivity oscillations are related to the excitation of coherent phonons by the pulse with duration shorter of all relaxation times. We demonstrate that swiftly heated electrons are responsible for the phonon excitation due to the fast modification of the attractive (electronic) part of inter-atomic potential. The electronic perturbation of potential is also responsible for the red shift of phonon frequency and for the increase in the amplitude of phonons. The coherent phonon excitation process as well as the change in the reflectivity is related mainly to the modification of the electron-phonon momentum exchange frequency. The comparison between the theory and experiments shows an excellent agreement. Moreover, the reflectivity measurements allow direct recovery of the electron-phonon coupling rate in bismuth crystal, which has not been measured before.
We study the formation of carbon nanoclusters created by MHz repetition rate - picosecond laser pulses. We show that the average size of a nanocluster is determined exclusively by single laser pulse parameters and is largely independent of the gas fill (He, Ar, Kr, Xe) and pressure, in a range from 20 mTorr up to 200 Torr. We provide evidence of the formation of large clusters at higher pressures in excess of 400 Torr, where the gas fill density is comparable or higher to the density of carbons in the ablated plume, and use simple kinetic theory to estimate cluster sizes, which are in qualitative agreement with the experimental data. We conclude that at pressures well below 400 Torr, the role of the buffer gas is to induce a transition between thin solid film formation on the substrate and nanofoam formation by diffusing the clusters through the gas, with no significant effect upon the average cluster size. At the higher pressure the buffer gas serves as a confiner for the carbon plume, increasing the collision frequency between the carbon atoms and resulting in cluster size growth. We also introduce preliminary ICCD imaging results investigating the temporal evolution of the laser plume.
The non-equilibrium transformations induced by sub-picosecond lasers on space scale of nanometers and time
scale of less than picosecond are considered in this presentation. We demonstrate that the fast (during the pulse
time) change in the inter-atomic potential due to the electrons excitation is responsible for the swift coherent
atomic displacement. We calculate the coherent displacement of atoms in non-equilibrium and compare it to
that following from the familiar Lindemann approach to the melting in thermodynamic equilibrium.
We compare our analysis with the experiments on non-equilibrium phase transformation of Gallium by 150 fs
pulses at intensity well below the ablation threshold. The presented analysis and direct measurements indicate
that the melting in its conventional sense either is not completed, or that, most probably, some transient state of
matter has been created during the interaction even when the deposited energy exceeds three times the equilibrium
enthalpy of melting.
In conclusion we address some unresolved problems in understanding of ultra-fast phase transformations induced
by ultra-short laser pulses in non-equilibrium conditions.
We report here experimental results on laser ablation of metals in air and in vacuum in similar irradiation conditions. The experiments revealed that the ablation thresholds in air are less than half those measured in vacuum. Our analysis shows that this difference is caused by the existence of a long-lived transient non-equilibrium surface state at the solid-vacuum interface. The energy distribution of atoms at the surface is Maxwellian-like but with its high-energy tail truncated at the binding energy. We find that in vacuum the time needed for energy transfer from the bulk to the surface layer to build the high-energy tail, exceeds other characteristic timescales such as the electron-ion temperature equilibration time and surface cooling time. This prohibits thermal evaporation in vacuum for which the high-energy tail is essential. In air, however, collisions between the gas atoms and the surface markedly reduce the lifetime of this non-equilibrium surface state allowing thermal evaporation to proceed before the surface cools. We found that ablation threshold in vacuum corresponds to non-equilibrium ablation during the pulse, while thermal evaporation after the pulse is responsible for the lower ablation threshold observed in air. This paper provides direct experimental evidence of how the transient surface effects may strongly affect the onset and rate of a solid-gas phase transition.
We report experiments on the ablation of arsenic trisulphide and silicon using high-repetition-rate (megahertz) trains of picosecond pulses. In the case of arsenic trisulphide, the average single pulse fluence at ablation threshold is found to be >100 times lower when pulses are delivered as a 76-MHz train compared with the case of a solitary pulse. For silicon, however, the threshold for a 4.1-MHz train equals the value for a solitary pulse. A model of irradiation by high-repetition-rate pulse trains demonstrates that for arsenic trisulphide energy accumulates in the target surface from several hundred successive pulses, lowering the ablation threshold and causing a change from the laser-solid to laser-plasma mode as the surface temperature increases.
We report on three-dimensional (3D) holographic recording in As2S3 glass using 800 nm wavelength, 150 fs duration pulses. Diffractive beam splitter was used to generate 2 - 5 beams which were then focused for recording by objective lens of numerical aperture NA = 0.75. The recorded 3D hologram was read out by diffraction of 632 nm HeNe laser beam confirming the expected pattern of holograms. The mechanism of photo-darkening and optical damaging of As2S3 glass and dielectrics in general is discussed. Two-photon absorption cross-section, σ2 = 74.6 x 10-50 cm4/s, was determined by transmission for pulses of 150 fs and 800 nm wavelength. Also, it is demonstrated that the optical damage threshold scales as the bandgap energy for the fluorides. Nano-/micro-structuring of As2S3 glass by ablation in air will be also demonstrated. High fluence (> 5 J/cm2) irradiation of the 800 nm wavelength, 150 fs duration pulses was used to ablate As2S3 glass. Self-organized growth of the fibers, rods, and microsphere-type structures was observed. Composition of the nano-/micro-structured material was close to that of the source As2S3 glass (with up to 20% surplus of sulphur in nano-rods). Straight rods as thin as 20 nm in diameter and over 1 μm-long were obtained. Application potential of nano-/micro-structured As2S3 glass is discussed.
High average power (10-50W) slow mode-locked lasers operating with repetition rates of a few MHz provide a unique combination of high peak power, short pulse duration, and high brightness that makes them ideal for applications in pulsed laser ablation and nonlinear optics. With peak powers in the MW range and near diffraction-limited output beams, focussed intensities can exceed 1012W/cm2: sufficient for ablation of most solid materials or to saturate nonlinear optical interactions.
We report the use of sub-picosecond near-IR and ps UV pulsed lasers for precision ablation of freshly extracted human teeth. The sub-picosecond laser wavelength was ~800nm, with pulsewidth 150 fs and pulse repetition rate of 1kHz; the UV laser produced 10 ps pulses at 266 nm with pulse rate of ~1.2x105 pulses/s; both lasers produced ~1 W of output energy, and the laser fluence was kept at the same level of 10-25 J/cm2. Laser radiation from both laser were effectively absorbed in the teeth enamel, but the mechanisms of absorption were radically different: the near-IR laser energy was absorbed in a plasma layer formed through the optical breakdown mechanism initiated by multiphoton absorption, while the UV-radiation was absorbed due to molecular photodissociation of the enamel and conventional thermal deposition. The rise in the intrapulpal temperature was monitored by embedded thermocouples, and was shown to remain low with subpicosecond laser pulses, but risen up to 30°C, well above the 5°C pain level with the UV-laser. This study demonstrates the potential for ultra-short-pulsed lasers to precision and painless ablation of dental enamel, and indicated the optimal combination of laser parameters in terms of pulse energy, duration, intensity, and repetition rate, required for the laser ablation rates comparable to that of mechanical drill.
The reflectivity of Gallium films excited by femtosecond laser can be raised from ~55% to up to ~85% on a picosecond time-scale. Temporal behavior of the reflectivity exhibits three clearly distinguished stages: an initial 2 - 4 ps sharp rise, a relatively slow increase to a maximum value in a few 100 ps, and afterwards a long slope in ~ (0.1 - 1) μs to the original value. In this paper we present reflectivity measurements in a pump-probe scheme with one pump and two identical simultaneous femtosecond probes set at two different angles, which completely determines the real and imaginary parts of the dielectric function with time resolution ~ 200 fs. The analysis of the experimental data uncovered a number of new phenomena: (1) the energy density threshold to initiate phase transition is several times lower than the equilibrium enthalpy of melting; (2) the initial 2 - 4 ps rise of reflectivity relates to the transformation to a new phase in the absence of energy loss due to cooling. The second, slower stage (~100 ps) relates to a heat conduction dominated process; (3) the rate of the reflectivity change strongly increases with the increase of the pump laser intensity; (4) the volume fraction of the new phase reaches only 60% even with the deposited energy exceeds more than two times the equilibrium enthalpy of melting; (5) the electron-to-lattice coupling rate is a transient non-linear function of temperature that is drastically different from the equilibrium conditions. The results suggest a mechanism to control of the reflectivity switching, and thus the duty cycle of the reversible phase transition (crystal-metal-crystal), through an optimal combination of the laser parameters, target and substrate material. As a result, new all-optical switching devices with ps-range switching time could be designed utilizing the nonlinear dielectric properties of the non-equilibrium solid-state plasma.
Despite a lot of researches on Pulsed Laser Deposition (PLD) for film production over the years, it has largely been an unsuccessful technology because of the poor quality of laser deposited films, generally due to particle contamination. A way of improving the quality of thin films was recently developed at LPC by using MHz-repetition-rate IR laser pulses of ps-range pulse duration. As a result, Ultrafast PLD outperforms other methods in terms of surface quality, deposition rate and energy efficiency by up to three orders of magnitude. In addition, it is desirable to use short laser wavelength to more easily atomize the materials and also favor the material ablation through photochemical processes during the laser-matter interaction. An optical two-crystal tripling system has then been developed to produce high energy UV photons from a mode locked Nd:YVO4 laser (1.064 μm, 5.7 MHz, 12 ps, up to 1.5 W). A large number of UV photons can be obtained with this optical scheme providing optimum laser characteristics for efficient PLD. This is further applied to the synthesis of various high quality thin films, including polymer films and nonlinear optical films for photonic applications.
The regime of skin-effect interaction was proposed as the mechanism of ion acceleration, and the range of validity of the skin-effect mode was established. The results are illustrated on laser evaporation of graphite with Nd:YAG laser (1.064 micrometers ), KrF laser (248 nm) and ArF laser (193 nm). The UV lasers the interaction has a bi-modal nature: the interaction may proceed initially in the skin effect regime resulting in a few high-energy ions, until the hydrodynamics expansion begins at the later stage. The skin- effect interaction at the initial stage of UV laser pulse gives the first, to our knowledge, explanation for acceleration of ions up to approximately 100 eV at the low laser intensities 108 - 109 W/cm2 and ns-range pulse duration.
The novel technique of ultrafast pulsed laser deposition has been experimentally demonstrated by depositing high quality diamond-like carbon films using high repetition rate Nd:YAG lasers. A very effective evaporation regime was achieved by keeping the laser intensity on the target surface close to the optimum values determined in Part 1 of this paper. Evaporation of the target by low energy laser pulses at an intensity of 109 W/cm2 allows the elimination of particles from the vapor and results in films with very high surface quality, while the very high repetition rate increases the overall deposition rate. Results are presented on the evaporation of carbon using either a 10 kHz, 120 ns Q-switched Nd:YAG laser, or a 76 MHz 60 ps mode-locked Nd:YAG laser. The number of particles visible in optical microscope on the DLC film deposited using the mode-locked laser was less than one particle per mm2. SEM images demonstrated that the deposited film had a very fine surface texture of with nanoscale irregularities on the surface. AFM surface microroughness measurements revealed a saturation-like behavior of the RMS roughness at the level 12 nm over the whole deposited surface area for 10 kHz Q-switched laser evaporation and almost an atomic level (less than 1 nm) roughness for the 76 MHz mode-locked laser evaporation. Raman spectroscopy of the deposited films indicated that they were a mixture of sp3 and sp2 bonded amorphous carbon. The thickness of the diamond-like carbon film deposited simultaneously on two 4 inch silicon wafers varied by only plus or minus 5% over an area of approximately 250 cm2 and the deposition rate was approximately 2 - 6 angstrom/s at a distance of approximately 150 mm from the target.
The novel technique for deposition of a high quality thin films of different materials by the use of picosecond laser pulses delivered on a target with the repetition rate of several tens of megahertz is proposed. The differences of the proposed method from the conventional pulse laser deposition is due to shorter laser pulses (picosecond instead of nanosecond) and higher repetition rate which is tens of megahertz (MHz) instead of tens of hertz (Hz). The method allow us to significantly improve the quality of a film due to a decrease by nine orders of magnitude in a number of particles evaporating during a single laser pulse in comparison to that produced by nanosecond, 30 Hz lasers, thus removing a major disadvantage of laser deposition method which is the formation of particulates on the film. The use of a very high repetition rate laser also leads to a qualitatively new mode of vapor-substrate interaction. Due to the short time (10-7 - 10-8 sec) between the laser pulses a quasi-continuous laser plume is formed. The particles evaporated by the previous laser pulse and just deposited on the substrate do not cool down significantly by the time when the particles from the following laser pulse arrive, and therefore their chemical bonds are still reactive. As a result, the high repetition rate regime of evaporation allows for formation of structures on the substrate such as, for example, carbon nanotubes, polymer chains, etc. Another advantage is the opportunity of scanning the laser focal spot over different targets of different materials which allows for a deposition of multilayered films containing mono-atomic layers of different atoms. The results on ultrafast laser ablation and deposition are presented in two joint papers. In this paper (Part I) we present the theoretical justification of the ultrafast laser deposition method, calculating the vapor characteristics, evaporation and deposition rates for the optimal evaporation regime for different modes of laser- target interaction. In the second paper (Part II) the experimental results on evaporation of a graphite target, deposition of high quality diamond-like (DLC) films and the comparison of the laser plume characteristics to theory are presented.
We report investigations of the x-ray focusing of a square channel capillary array. We use x rays with an energy of about 1.5 keV from a laser produced plasma. We find the focal structure to be consistent with theoretical expectations. The images were recorded using x-ray film and, to within the precision with which we were able to analyze the results, the data is consistent with an array with negligible channel tilt and a surface roughness of 1.5 nm rms. This is the best performance yet reported for lobster-eye x-ray optics.
We present results of the experimental tests of various arrays of reflectors acting as X-ray optical elements. Planar reflectors were aligned with a common center of curvature to create a 1D focusing array. The experiments were carried out using X-ray radiation in the spectral range 3.5 keV to 7 keV produced at beamline X-27C of the National Synchrotron Light Source at the Brookhaven National Laboratory. The initial beam had width of 90 mm, a focal distribution had a width of 8 mm and a maximum intensity gain of 7.3, as measured with a 0.4 mm diameter pinhole. An X-ray beamsplitter consisting of arrays of reflectors has also been designed and tested. The separation of X-ray beams is 40 mrad and intensity of each of two beams is about 0.32 of the original X-ray beam.
We present an analysis of the geometric optics of spherically curved arrays of reflective surfaces. In particular, we consider optical devices in which reflective surfaces are arranged on a spherical interface and every ray reflects once from a reflector. The orientation of the reflective surfaces is not necessarily related in any way to the orientation of the interface. The analysis can be applied to any radiation that may specularly reflect from the reflectors. This may be reflection from stacks of mirrors or diffraction from the atomic planes. In this paper the principles are applied to x-ray optical systems such as capillary arrays and curved crystals. The calculations are used to find optimum configurations of reflective arrays for applications such as x-ray condensers and telescopes, to find the tolerances to which reflective arrays must be constructed, and to find the conditions where primary aberrations are eliminated.
X-ray optical devices based on arrays of capillaries and single tapered capillaries can focus and concentrate x rays by the reflection of near-grazing-incidence rays at the interior walls of the channels. Capillary arrays are true imaging devices and can be used as focusing, condensing,and collimating optics, suitable for x-ray microcopy and astronomy. Rays which enter channels and are reflected once or twice, via total external reflection, may be redirected towards the image. Theoretical calculations of the focusing performance of arrays consisting of capillaries of square and circular cross-section are given. Experimental investigations have been made using microchannel plate (MCP) detector blanks and various x-ray sources.
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