Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annual Meeting Optical Society of America

Focusing of cold neutral atoms: a Fresnel zone plate

N. P. Bigelow, Mara Goff Prentiss, D. M. Tennant, John E. Bjorkholm, M. O'Malley

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We have fabricated a free-standing transmission Fresnel zone plate for the focusing of long-thermal-wavelength neutral atoms. The zone plate was fabricated from a 0.7μm thick boron-doped silicon membrane. The pattern was formed by means of electron-beam lithography, and the final grating was generated by reactive ion etching. The zone plate is composed of 100 zones, the diameter of the outermost zone is approximately 80 μm. The zone plate is designed to focus incident atoms having a thermal wavelength of 17 Å into a 2000 Å spot at a focal length of about 1 cm. A maximum of 8% of the incident flux will be transmitted and focused into the primary spot with this design. The use of diffraction optics for the focusing of an atomic beam is novel in that it does not rely on any electromagnetic forces for achieving focusing. As a result, this approach can be used to focus any particle with a long thermal de Broglie wavelength.

DOI
10.1364/oam.1990.fh5

Related papers

Focusing of a neutral helium beam with a photon-sieve structure

Sabrina D. Eder, X. Guo, T. Kaltenbacher +4 more

The manipulation of low-energy beams of neutral atoms and molecules via their de Broglie wavelength is a branch of atom optics often referred to as de Broglie matter wave optics. The application areas include fundamental quantum mechanics, atom interferometry, and the development of new microscopy instrumentation. The focusing of de Broglie matter waves with a Fresnel zone plate was used to demonstrate the first neutral helium microscopy imaging. The ultimate resolution of such a microscope is limited by the width of the outermost zone. Because a Fresnel zone plate for atoms cannot be fabricated on a substrate (the low-energy atom beams would not be able to penetrate the substrate material), this gives a fabrication determined limit for the first-order focus of around 30--50 nm. Therefore, it is important to search for alternative optical elements that enable higher resolution. Photon sieves consist of a large number of pinholes, arranged suitably relative to the Fresnel zones. The great advantages are that the width of the pinholes can be larger than the respective Fresnel zones and a free-standing pinhole is much easier to fabricate than a free-standing zone. Thus, with a photon-sieve structure applied for de Broglie matter wave manipulation, the fabrication limit for focusing is reduced to potentially around 3--5 nm. Here we present a realization of such an ``atom sieve,'' which we fabricated out of a silicon nitride (SiN) membrane, using electron-beam lithography and reactive ion etching. Our atom sieve is 178 $\ensuremath{\mu}\mathrm{m}$ in diameter and has 31 991 holes. The diameter of the holes varies from 1840 to 150 nm. Using a beam of neutral, ground-state helium atoms with an average wavelength of 0.055 nm, we demonstrate helium atom focusing down to a spot size of less than 4 $\ensuremath{\mu}\mathrm{m}$. The focus size is limited by the intrinsic velocity spread of the helium beam.

Physical Review A•Apr 8, 2015•22 citations

Imaging and focusing of atoms by a fresnel zone plate

O. Carnal, M. Sigel, Tycho Sleator +2 more

Focusing of and imaging with atoms by means of a spherical Fresnel zone plate has been observed for the first time. An intense beam of metastable helium atoms with atomic de Broglie wavelength ${\ensuremath{\lambda}}_{\mathrm{dB}}$=0.5--2.5 \AA{} is passed through either a single or a double slip with dimensions in the 10-\ensuremath{\mu}m range. This transverse intensity distribution is imaged by a Fresnel zone plate, 210 \ensuremath{\mu}m in diameter and with an innermost zone diameter of 18.76 \ensuremath{\mu}m. For ${\ensuremath{\lambda}}_{\mathrm{dB}}$=1.96 \AA{} the focal length is 0.45 m. The imaging properties of the zone plate are presented and compared with numerical calculations.

Physical Review Letters•Dec 2, 1991•167 citations

Fabrication of large free-standing nanostructured zone plates for focusing a Bose-Einstein condensate

Espen Werdal Selfors

Matter wave optics is a fascinating area of physics touching many scientific disciplines ranging from microscopy to high precision gravity measurements. One of the major recent breakthroughs was the realization in 1995 of a Bose-Einstein condensate of atoms - a perfectly coherent atom source. Bose-Einstein condensates have been studied intensely over the last couple of decades, but surprisingly little work has been done on manipulation of the condensates using their de Broglie wavelength. The original aim of this thesis was to create a Fresnel zone plate for the first focusing of a Bose-Einstein condensate via the de Broglie wavelength. The zone plate design parameters were chosen to fit the experimental setup of Prof. Zeilinger in Vienna, currently one of the only setups in the world where this experiment can be carried out. The original aim of the thesis has been fulfilled. A free-standing silicon nitride zone plate with a diameter of 5 mm, and a focal length of 60 cm for a wavelength of 100 nm has been successfully created, tested with laser light and is now ready for experiments in Vienna. The zone plate has 44 zones, a 2 mm central stop and the width of the outermost zone is 12 µm. To the best of our knowledge this zone plate has a diameter more than an order of magnitude larger than any zone plates previously created for the focusing of matter waves. The much larger wavelength of the Bose-Einstein condensate compared to previous experiments meant that previously used fabrication methods could not be applied and new methods had to be developed as part of this thesis. Aluminium wet etching, dry-etching of SiO2 and silicon nitride using only a PMMA mask and quantified wet-etching of silicon were all established for the first time at the UiB NanoStructures laboratory as part of this thesis.

•Sep 20, 2017•0 citations

Focusing of a neutral helium beam below one micron

Sabrina D. Eder, Thomas J.G. Reisinger, Martin Greve +2 more

In 2008 we presented the first images obtained with a new type of matter wave microscope: NEutral Helium Atom MIcroscopy (NEMI). The main features in NEMI are the low energy of the atoms (<0.1 eV) and the fact that they are neutral. This means that fragile and/or insulating samples can be imaged without surface damage and charging effects. The ultimate resolution limit is given by the de Broglie wavelength (about 0.06 nm for a room-temperature beam), but reaching a small focus spot is still a major challenge. The best result previously was about 2 μ m. The main result of this paper is the focusing of a helium atom beam to a diameter below 1 μ m. A particular challenge for neutral helium microscopy is the optical element for focusing. The most promising option is to manipulate neutral helium via its de Broglie wavelength, which requires optical elements structured to nanometre precision. Here we present an investigation of the helium focusing properties of nanostructured Fresnel zone-plates. Experiments were performed by varying the illuminated area and measuring the corresponding focused spot sizes and focused beam intensities. The results were fitted to a theoretical model. There is a deviation in the efficiency of the larger zone plate, which indicates a distortion in the zone-plate pattern, but nevertheless there is good agreement between model and experiments for the focus size. This together with the demonstration of focusing to below 1 μ m is an important step towards nanometre resolution neutral helium microscopy.

New Journal of Physics•Jul 6, 2012•45 citations

Towards Realization of an Atomic de Broglie Microscope: Helium Atom Focusing Using Fresnel Zone Plates

R. Bruce Doak, R. E. Grisenti, Stefan Rehbein +3 more

A neutral, ground-state, ${}^{4}\mathrm{He}$ atom beam has been focused using Fresnel zone plates. At only moderate demagnification $(0.40\ifmmode\times\else\texttimes\fi{})$, a focused spot diameter of $\ensuremath{\le}2.0\ensuremath{\mu}\mathrm{m}$ is achieved at a signal intensity of 500 counts/s. This is an improvement over previous work by a factor of 10 in resolution, ${10}^{3}$ in signal intensity, and ${10}^{8}$ in focused beam density, and allows the full intrinsic intensity profile of a focused atomic Fresnel spot to be measured for the first time. Raster scans of 15 and $25\ensuremath{\mu}\mathrm{m}$ wide slits across the focused spot demonstrate transmission scanning helium de Broglie microscopy of micron resolution.

Physical Review Letters•Nov 22, 1999•125 citations

Free-standing, axially-symmetric diffraction gratings for neutral matter-waves: experiments and fabrication

Thomas J.G. Reisinger

Since de Broglie’s famous postulation of the wave-nature of material particles and its subsequent experimental verification, it is known that atoms and molecules behave like waves on a small scale. The investigation of matter waves is a fundamental topic in quantum mechanics. Furthermore, matter waves have many applications in a number of scientific fields. For example they are used to investigate materials by studying the diffraction of atoms (Helium Atom Scattering) or electrons (Low-energy electron-diffraction) from the material’s surface. The topic of this thesis has been to make nano-structured optical elements for matter-waves and use them in a number of experiments. A major result of this thesis is the performance of the classical Poisson-spot experiment with neutral matter-waves. The Poisson-spot refers to the bright interference spot observed in the shadow of a circular obstacle. The experiment gave convincing evidence of the wave nature of light at the beginning of the 19th century. The first two articles (A&B) in this thesis are concerned with the Poisson-spot experiment for matter waves and its applications. The experiment was performed using low-energy deuterium molecules (normal D2, 23.5 meV), which is described in the first article. In the second article the feasibility of using the Poisson-spot experiment to demonstrate the wave-nature of large molecules is studied. The wave properties of large molecules are an important topic in current research. The remaining three articles are concerned with Fresnel zone-plates. Fresnel zoneplates are axially symmetric diffraction gratings that can be used to focus waves. Loosely formulated the relationship between Fresnel zone-plates and the circular object in the Poissonspot experiment is the same as the relationship between multiple-slit gratings and a single straight edge. Paper C studies the application of microscopy with neutral atoms and molecules and the limitations of focusing matter waves with zone plates. The fabrication of the nanostructured free-standing zone-plates using electron-beam lithography is the topic of paper D. A second, new application of Fresnel zone-plates is introduced in paper E: There a zone plate is used for a direct size measurement of the so-called virtual source in a supersonic expansion. The main-result from the Poisson-spot experiment was the observation of the Poisson spot with a molecular-deuterium beam and the successful comparison of the collected experimental data with Fresnel-diffraction theory. The wave-length independence of the on-axis interferencecondition in the Poisson-spot experiment and the weak constraints on angular alignment and position of the circular object led us to conclude that the Poisson spot is a good candidate for demonstrating the wave nature of larger molecules. This idea is studied further in paper B, where among other things the feasibility of a Poissonspot experiment with the fullerene molecule C70 is examined. The main conclusion from this article was that the wave-nature of a molecular-beam can be demonstrated in diffraction experiments with circular discs that have varying amount of intended edge-corrugation. This is because the dependence of the bright spot on the edge-corrugation in the particle-model is different than in the wave-model. The result for the C70 Poisson-spot was that the experiment would be very challenging with count rates as low as 10−4 s−1. However, one possibility would be, due to the simplicity of the setup, to parallelize the experiment and measure the diffraction pattern behind many circular discs at once. This could be realized using the fabrication techniques discussed in chapter 4. Other applications of the Poisson spot could include the study of the Casmir-Polder potential, molecule-lithography and diffraction experiments with atom-lasers from Bose-Einstein condensates. While Fresnel zone-plates can be used to focus any type of wave they suffer from strong chromatic aberration since their focal length is inversely proportional to wavelength. In the case of neutral atom and molecule focusing this is what limits resolution. Paper C presents the highest resolution helium transmission-images hitherto and results from the first focusing of molecular deuterium with a zone plate. In addition the paper discusses the resolution-limit and finds that with presently available techniques a minimal spot size of 300 nm full-width-athalf- maximum is feasible using a zone plate of 200 μm diameter and a beam with speed ratio of about 500. The Fresnel zone-plates used to focus the supersonic-expansion beams need to be freestanding, since the low-energy atoms and molecules do not penetrate any material. In paper D an electron-beam lithography fabrication-process for free-standing zone-plates is presented. The process uses a 200-nm-thin layer of low-stress silicon-nitride for the material of the zone plates. The fabricated zone plates were tested in the supersonic-expansion beam apparatus. The transmission and first-order diffraction-efficiency are close to the theoretical prediction for the smaller 190 μm-diameter zone plates patterned with a single electron-beam write-field. A reduction to 70 % for the 388-μm-diameter zone-plate was observed which was attributed to stitching errors since it was stitched together from four write-fields. In chapter 4 additional unpublished results are presented on spatial-phase-locked electron-beam lithography, which aims at the reduction of stitching errors and other pattern-placement errors in electron-beam lithography. Finally in paper E one of the fabricated zone plates in addition to a previously existing one is used to measure the virtual source-width of a molecular deuterium supersonic-expansion beam. The virtual source-width is a measure of the beam’s temperature perpendicular to the beam axis. The beam’s energy distribution along the beam axis is measured using the timeof- flight method. Data sets for source temperatures T0=310 K and T0=106 K were collected in the stagnation pressure ranges p0=3-171 bar and p0=3-131 bar, respectively. The measured parameters were compared to a simple model of the expansion which explicitly includes the coupling between translational and rotational degrees of freedom. The data generally corresponded very well to the model, except for the virtual source size which was systematically about 2/3 of the model’s prediction. For the cold source-conditions the beam is increasingly heated due to condensation effects at increasing pressures, which results in a clear deviation from the model. This could be used to estimate the fraction of condensed molecules in the beam.

•Oct 4, 2011•1 citation
We have fabricated a free-standing transmission Fresnel zone plate for the focusing of long-thermal-wavelength neutral atoms. The zone plate was fabricated from a 0.7μm thick boron-doped silicon membrane. The pattern was formed by means of electron-beam lithography, and the final grating was generated by reactive ion etching. The zone plate is composed of 100 zones, the diameter of the outermost zone is approximately 80 μm. The zone plate is designed to focus incident atoms having a thermal wavelength of 17 Å into a 2000 Å spot at a focal length of about 1 cm. A maximum of 8% of the incident flux will be transmitted and focused into the primary spot with this design. The use of diffraction optics for the focusing of an atomic beam is novel in that it does not rely on any electromagnetic forces for achieving focusing. As a result, this approach can be used to focus any particle with a long thermal de Broglie wavelength.
The manipulation of low-energy beams of neutral atoms and molecules via their de Broglie wavelength is a branch of atom optics often referred to as de Broglie matter wave optics. The application areas include fundamental quantum mechanics, atom interferometry, and the development of new microscopy instrumentation. The focusing of de Broglie matter waves with a Fresnel zone plate was used to demonstrate the first neutral helium microscopy imaging. The ultimate resolution of such a microscope is limited by the width of the outermost zone. Because a Fresnel zone plate for atoms cannot be fabricated on a substrate (the low-energy atom beams would not be able to penetrate the substrate material), this gives a fabrication determined limit for the first-order focus of around 30--50 nm. Therefore, it is important to search for alternative optical elements that enable higher resolution. Photon sieves consist of a large number of pinholes, arranged suitably relative to the Fresnel zones. The great advantages are that the width of the pinholes can be larger than the respective Fresnel zones and a free-standing pinhole is much easier to fabricate than a free-standing zone. Thus, with a photon-sieve structure applied for de Broglie matter wave manipulation, the fabrication limit for focusing is reduced to potentially around 3--5 nm. Here we present a realization of such an ``atom sieve,'' which we fabricated out of a silicon nitride (SiN) membrane, using electron-beam lithography and reactive ion etching. Our atom sieve is 178 $\ensuremath{\mu}\mathrm{m}$ in diameter and has 31 991 holes. The diameter of the holes varies from 1840 to 150 nm. Using a beam of neutral, ground-state helium atoms with an average wavelength of 0.055 nm, we demonstrate helium atom focusing down to a spot size of less than 4 $\ensuremath{\mu}\mathrm{m}$. The focus size is limited by the intrinsic velocity spread of the helium beam.
Focusing of and imaging with atoms by means of a spherical Fresnel zone plate has been observed for the first time. An intense beam of metastable helium atoms with atomic de Broglie wavelength ${\ensuremath{\lambda}}_{\mathrm{dB}}$=0.5--2.5 \AA{} is passed through either a single or a double slip with dimensions in the 10-\ensuremath{\mu}m range. This transverse intensity distribution is imaged by a Fresnel zone plate, 210 \ensuremath{\mu}m in diameter and with an innermost zone diameter of 18.76 \ensuremath{\mu}m. For ${\ensuremath{\lambda}}_{\mathrm{dB}}$=1.96 \AA{} the focal length is 0.45 m. The imaging properties of the zone plate are presented and compared with numerical calculations.
Matter wave optics is a fascinating area of physics touching many scientific disciplines ranging from microscopy to high precision gravity measurements. One of the major recent breakthroughs was the realization in 1995 of a Bose-Einstein condensate of atoms - a perfectly coherent atom source. Bose-Einstein condensates have been studied intensely over the last couple of decades, but surprisingly little work has been done on manipulation of the condensates using their de Broglie wavelength. The original aim of this thesis was to create a Fresnel zone plate for the first focusing of a Bose-Einstein condensate via the de Broglie wavelength. The zone plate design parameters were chosen to fit the experimental setup of Prof. Zeilinger in Vienna, currently one of the only setups in the world where this experiment can be carried out. The original aim of the thesis has been fulfilled. A free-standing silicon nitride zone plate with a diameter of 5 mm, and a focal length of 60 cm for a wavelength of 100 nm has been successfully created, tested with laser light and is now ready for experiments in Vienna. The zone plate has 44 zones, a 2 mm central stop and the width of the outermost zone is 12 µm. To the best of our knowledge this zone plate has a diameter more than an order of magnitude larger than any zone plates previously created for the focusing of matter waves. The much larger wavelength of the Bose-Einstein condensate compared to previous experiments meant that previously used fabrication methods could not be applied and new methods had to be developed as part of this thesis. Aluminium wet etching, dry-etching of SiO2 and silicon nitride using only a PMMA mask and quantified wet-etching of silicon were all established for the first time at the UiB NanoStructures laboratory as part of this thesis.
In 2008 we presented the first images obtained with a new type of matter wave microscope: NEutral Helium Atom MIcroscopy (NEMI). The main features in NEMI are the low energy of the atoms (<0.1 eV) and the fact that they are neutral. This means that fragile and/or insulating samples can be imaged without surface damage and charging effects. The ultimate resolution limit is given by the de Broglie wavelength (about 0.06 nm for a room-temperature beam), but reaching a small focus spot is still a major challenge. The best result previously was about 2 μ m. The main result of this paper is the focusing of a helium atom beam to a diameter below 1 μ m. A particular challenge for neutral helium microscopy is the optical element for focusing. The most promising option is to manipulate neutral helium via its de Broglie wavelength, which requires optical elements structured to nanometre precision. Here we present an investigation of the helium focusing properties of nanostructured Fresnel zone-plates. Experiments were performed by varying the illuminated area and measuring the corresponding focused spot sizes and focused beam intensities. The results were fitted to a theoretical model. There is a deviation in the efficiency of the larger zone plate, which indicates a distortion in the zone-plate pattern, but nevertheless there is good agreement between model and experiments for the focus size. This together with the demonstration of focusing to below 1 μ m is an important step towards nanometre resolution neutral helium microscopy.
A neutral, ground-state, 4He{}^{4}\mathrm{He}4He atom beam has been focused using Fresnel zone plates. At only moderate demagnification $(0.40\ifmmode\times\else\texttimes\fi{})$, a focused spot diameter of $\ensuremath{\le}2.0\ensuremath{\mu}\mathrm{m}$ is achieved at a signal intensity of 500 counts/s. This is an improvement over previous work by a factor of 10 in resolution, 103{10}^{3}103 in signal intensity, and 108{10}^{8}108 in focused beam density, and allows the full intrinsic intensity profile of a focused atomic Fresnel spot to be measured for the first time. Raster scans of 15 and $25\ensuremath{\mu}\mathrm{m}$ wide slits across the focused spot demonstrate transmission scanning helium de Broglie microscopy of micron resolution.
Since de Broglie’s famous postulation of the wave-nature of material particles and its subsequent experimental verification, it is known that atoms and molecules behave like waves on a small scale. The investigation of matter waves is a fundamental topic in quantum mechanics. Furthermore, matter waves have many applications in a number of scientific fields. For example they are used to investigate materials by studying the diffraction of atoms (Helium Atom Scattering) or electrons (Low-energy electron-diffraction) from the material’s surface. The topic of this thesis has been to make nano-structured optical elements for matter-waves and use them in a number of experiments. A major result of this thesis is the performance of the classical Poisson-spot experiment with neutral matter-waves. The Poisson-spot refers to the bright interference spot observed in the shadow of a circular obstacle. The experiment gave convincing evidence of the wave nature of light at the beginning of the 19th century. The first two articles (A&B) in this thesis are concerned with the Poisson-spot experiment for matter waves and its applications. The experiment was performed using low-energy deuterium molecules (normal D2, 23.5 meV), which is described in the first article. In the second article the feasibility of using the Poisson-spot experiment to demonstrate the wave-nature of large molecules is studied. The wave properties of large molecules are an important topic in current research. The remaining three articles are concerned with Fresnel zone-plates. Fresnel zoneplates are axially symmetric diffraction gratings that can be used to focus waves. Loosely formulated the relationship between Fresnel zone-plates and the circular object in the Poissonspot experiment is the same as the relationship between multiple-slit gratings and a single straight edge. Paper C studies the application of microscopy with neutral atoms and molecules and the limitations of focusing matter waves with zone plates. The fabrication of the nanostructured free-standing zone-plates using electron-beam lithography is the topic of paper D. A second, new application of Fresnel zone-plates is introduced in paper E: There a zone plate is used for a direct size measurement of the so-called virtual source in a supersonic expansion. The main-result from the Poisson-spot experiment was the observation of the Poisson spot with a molecular-deuterium beam and the successful comparison of the collected experimental data with Fresnel-diffraction theory. The wave-length independence of the on-axis interferencecondition in the Poisson-spot experiment and the weak constraints on angular alignment and position of the circular object led us to conclude that the Poisson spot is a good candidate for demonstrating the wave nature of larger molecules. This idea is studied further in paper B, where among other things the feasibility of a Poissonspot experiment with the fullerene molecule C70 is examined. The main conclusion from this article was that the wave-nature of a molecular-beam can be demonstrated in diffraction experiments with circular discs that have varying amount of intended edge-corrugation. This is because the dependence of the bright spot on the edge-corrugation in the particle-model is different than in the wave-model. The result for the C70 Poisson-spot was that the experiment would be very challenging with count rates as low as 10−4 s−1. However, one possibility would be, due to the simplicity of the setup, to parallelize the experiment and measure the diffraction pattern behind many circular discs at once. This could be realized using the fabrication techniques discussed in chapter 4. Other applications of the Poisson spot could include the study of the Casmir-Polder potential, molecule-lithography and diffraction experiments with atom-lasers from Bose-Einstein condensates. While Fresnel zone-plates can be used to focus any type of wave they suffer from strong chromatic aberration since their focal length is inversely proportional to wavelength. In the case of neutral atom and molecule focusing this is what limits resolution. Paper C presents the highest resolution helium transmission-images hitherto and results from the first focusing of molecular deuterium with a zone plate. In addition the paper discusses the resolution-limit and finds that with presently available techniques a minimal spot size of 300 nm full-width-athalf- maximum is feasible using a zone plate of 200 μm diameter and a beam with speed ratio of about 500. The Fresnel zone-plates used to focus the supersonic-expansion beams need to be freestanding, since the low-energy atoms and molecules do not penetrate any material. In paper D an electron-beam lithography fabrication-process for free-standing zone-plates is presented. The process uses a 200-nm-thin layer of low-stress silicon-nitride for the material of the zone plates. The fabricated zone plates were tested in the supersonic-expansion beam apparatus. The transmission and first-order diffraction-efficiency are close to the theoretical prediction for the smaller 190 μm-diameter zone plates patterned with a single electron-beam write-field. A reduction to 70 % for the 388-μm-diameter zone-plate was observed which was attributed to stitching errors since it was stitched together from four write-fields. In chapter 4 additional unpublished results are presented on spatial-phase-locked electron-beam lithography, which aims at the reduction of stitching errors and other pattern-placement errors in electron-beam lithography. Finally in paper E one of the fabricated zone plates in addition to a previously existing one is used to measure the virtual source-width of a molecular deuterium supersonic-expansion beam. The virtual source-width is a measure of the beam’s temperature perpendicular to the beam axis. The beam’s energy distribution along the beam axis is measured using the timeof- flight method. Data sets for source temperatures T0=310 K and T0=106 K were collected in the stagnation pressure ranges p0=3-171 bar and p0=3-131 bar, respectively. The measured parameters were compared to a simple model of the expansion which explicitly includes the coupling between translational and rotational degrees of freedom. The data generally corresponded very well to the model, except for the virtual source size which was systematically about 2/3 of the model’s prediction. For the cold source-conditions the beam is increasingly heated due to condensation effects at increasing pressures, which results in a clear deviation from the model. This could be used to estimate the fraction of condensed molecules in the beam.