A Velocity Map Imaging apparatus optimized for high-resolution crossed molecular beam experiments
AA Velocity Map Imaging apparatus optimized for high-resolution crossed molecularbeam experiments
Vikram Plomp, Zhi Gao, and Sebastiaan Y. T. van de Meerakker Radboud University Nijmegen, Institute for Molecules and Materials,Heijendaalseweg 135, 6525 AJ Nijmegen, the Netherlands (Dated: July 10, 2020)We present the design of a Velocity Map Imaging apparatus tailored to the demands of high-resolution crossed molecular beam experiments employing Stark or Zeeman decelerators. The keyrequirements for these experiments consist of the combination of a high relative velocity resolutionfor large ionization volumes and a broad range of relatively low lab-frame velocities. The SIMIONsoftware package was employed to systematically optimize the electrode geometries and electricalconfiguration. The final design consists of a stack of 16 tubular electrodes, electrically connectedwith resistors, which is divided into three electric field regions. The resulting apparatus allows for aninherent velocity blurring of less than 1.1 m/s for NO + ions originating from a 3x3x3 mm ionizationvolume, which is negligible in a typical crossed beam experiment. The design was recently employedin several state of the art crossed-beam experiments, allowing the observation of fine details in thevelocity distributions of the scattered molecules. I. INTRODUCTION
Over the past 30 years, the technique of ion imaginghas been acknowledged in a diverse selection of researchfields, and various implementations have allowed for amultitude of applications of this powerful technique [1].The method was first reported by Chandler and Houstonin 1987, where a relatively simple electrode configurationconsisting of a repeller plate and two extractor grids wasused [2]. By allowing the Newton sphere to expand dur-ing the flight towards a 2D-position-sensitive detector itwas possible to study the velocity distribution of pho-todissociation fragments of CH I. However, the spreadin initial ionization position severely limited the veloc-ity resolution. A major improvement to the ion imagingtechnique was introduced by Eppink and Parker in 1997,in the form of the Velocity Map Imaging (VMI) detectoremploying electrostatic lenses [3]. The replacement of theelectrode grids with apertures breaks the homogeneity ofthe electric fields at the transition between the electricfield regions. This allows for focussing of particles withthe same initial velocity vector [4], but originating fromdifferent positions in the ionization region, on a singlespot of the 2D-position-sensitive detector.The Eppink-Parker VMI-detector design is still em-ployed in its original form today. However, various mod-ifications have been reported to either improve the per-formance of the technique or extend its use to differentranges of application. Most notably, the concept of im-age slicing was introduced, which was first explored byGebhardt et al. [5]. Here, only a small part of the New-ton sphere in the axial direction (2D-slice) is selected fordetection at a time. Recording the 2D-velocity distribu-tion of different slices then allows for direct measurementson the full 3D-velocity distribution of the products [1].Image slicing also greatly reduces the negative effects ofNewton sphere crushing on the image resolution. Usingthis technique, experimental resolution down to 0.19% (FHWM) has been reported in photodissociation exper-iments with a high kinetic energy release [6].In the field of crossed molecular beam experiments twofrequently used VMI ion optics designs, on which manyothers are based, are those reported by Townsend et al.[7] and Lin et al. [8]. The first employs three electricfield regions, instead of the traditional two. Thus, theelectric field strength in the ionization region could bereduced, allowing image slicing of photofragment veloc-ity distributions while maintaining proper velocity map-ping conditions. The second design uses only two electricfield regions, but consists of a total of 29 electrode plates.The larger axial extent of the ion optics reduces the elec-tric field strength in the ionization region, again enablingimage slicing, as well as providing a softer focus whichimproves the velocity resolution.In a crossed beam imaging experiment the inherent res-olution is limited by the velocity spreads of the molecularbeams. Recently, the employment of molecular decelera-tors in crossed beam experiments has enhanced the pos-sibilities to investigate collisions between neutral species[9]. The narrow velocity and angular spreads of Starkor Zeeman decelerated beams result in scattering imageswith unprecedented resolution, that can be exploited toresolve structure in the scattering images that would havebeen washed out using conventional molecular beams[10–13]. With this high inherent resolution, the exper-iments become more susceptible to imperfections in thevelocity mapping. The sensitivity and resolution of theseexperiments thus not only depend on the control over theparticles before the collision, but also on the quality ofthe velocity mapping apparatus.Although the various optimized VMI-detector designshave improved the imaging resolution significantly, noneof them were originally developed for the conditions en-countered in controlled, high-resolution collision experi-ments employing decelerators. These experiments posespecific requirements on the mapping properties that aresubstantially different from those in e.g. photodissoci- a r X i v : . [ phy s i c s . a t o m - ph ] J u l ation experiments. In this work, we present a VMI-detector design specifically optimized for crossed molec-ular beam experiments employing decelerators, where aspecial emphasis is required on high-resolution imagingfor large detection volumes and a broad range of collisionenergies. II. REQUIREMENTS
We consider crossed beam experiments where at leastone of the beams contains polar molecules, like NO, thatcan be manipulated using a decelerator. To illustrate thekinematics of such an experiment, we consider the colli-sion of NO with Ne under typical conditions as an exam-ple system (see Fig. 1 for the velocity diagram detailingthe pre- and post-collision conditions). The velocity ofthe scattered NO molecules is projected on concentricNewton spheres around the center off mass (COM) ve-locity ( V COM ). Cylindrical symmetry of the experimentaround the relative velocity axis ( V REL ), however, en-sures that the center slices of these spheres, the Newtoncircles, contain complete information on the scatteringprocess [14]. The scattering distribution in both the ra-dial and angular directions along these circles is governedby the interaction between the molecules during the colli-sion. The narrow velocity spreads afforded by moleculardecelerators allow the resolving of fine details in thesescattering distributions [9]. However, the Newton sphereradius in these experiments is generally very small. Forthe example NO-Ne collision system the 363 m/s radiusof the Newton sphere corresponds to a kinetic energy ofjust 20.5 meV. This is significantly smaller than the typ-ical ≈ Forwarddirection
NO velocity90°
COM V COM V’ NO α V REL
Ne velocity
FIG. 1: Schematic 2D velocity diagram illustrating how the(collisionally excited) NO molecule velocity vectors are pro-jected on Newton circles around the center of mass (COM)after scattering with Ne at an angle of 90 ° . For a typical NOvelocity of 430 m/s and Ne velocity of 800 m/s, correspond-ing to a collision energy of ≈
410 cm − , the COM-velocityamounts to | V COM | ≈
411 m/s, and the NO velocity in theCOM-frame after elastic scattering is | V (cid:48) NO | ≈
363 m/s. Theangle between V COM and V (cid:48) NO is α = 67 . ° for the forwardscattering direction. amount of scattered molecules that can potentially be de-tected. Furthermore, the larger volume helps to reducevelocity blurring due to space charge effects under ex-perimental conditions that do allow for higher ion yields[1]. A large ionization volume, however, requires a betterfocussing of the ion optics, and is therefore in direct con-flict with the requirement of small velocity blurring. Themolecular beam that exits a Stark or Zeeman deceleratorhas a typical diameter of 2-3 mm [15, 16], which providesan upper limit to the practical size of the interaction vol-ume.3. Low electric field strength in the ionization region.The use of decelerators ensures high quantum statepurity of the molecular beams, which allows for nearbackground free measurement of state-to-state scatteringprocesses. However, for several relevant species thisstate purity is compromised by the electric fields presentin the detection region. While a Stark decelerator, forexample, only transmits NO molecules with f parity,an electric field mixes the close-lying Lambda-doubletstates with e and f parity. Although the mixingprobabilities are generally very small, their effects canbe observed in experimental scattering images. Forthe conditions in a typical VMI-detector, the paritymixing probability depends quadratically on the electricfield strength. Thus, reduced electric field strengthsin the ionization region strongly suppress the possibleinfluence of quantum state mixing. In this regard,the method of delayed extraction seems ideal, wherepulsed voltages are applied to the VMI-apparatus afterionization in field free conditions. However, this methodgenerally leads to increased velocity blurring due to thepractical limitations of high-voltage switching, leavingthe application of DC voltages the preferred method toobtain minimal blurring [1, 17].Further requirements to the mapping properties con-stitute of: • Simultaneous mapping of a large range of ion ve-locities with high resolution. • Minimal dependence of the velocity resolution onthe azimuthal angle ( α ) of the particle on the New-ton sphere. • Linear velocity mapping behaviour for a large rangeof ion velocities. • Sufficient total ion acceleration to ensure high de-tection efficiency of the employed Micro-ChannelPlate (MCP) detectors.Additional constraints to the dimensions of the VMI-apparatus are imposed for practical reasons: • The ion optics should fit within a cylinder with 80mm diameter. • The ion optics should not exceed a height of 300mm above the center of the detection region.It should be noted that the requirement of a low elec-tric field strength in the ionization region is closely re-lated to the capability of direct image slicing, as it deter-mines the total elongation of the Newton sphere. How-ever, accurate image slicing also requires focussing inarrival-time at the detector for particles starting at dif-ferent positions in the ionization volume, to minimize theeffective slice thickness. For the small Newton spheres en-countered in low-energy collision experiments, this time-focussing requirement is especially strict, and fundamen-tally conflicts with low blurring for a large ionization vol-ume [18]. While image slicing is greatly beneficial, it wasfound subordinate to the aforementioned requirementsfor the case of low energy crossed beam experiments em-ploying a decelerator. The need for direct image slicing isalso reduced by a continuously improving toolbox of gen-eral 3D-image reconstruction techniques [1], with recentadditions of e.g. the FINA software package [19].
III. ELECTROSTATIC LENS ABERRATIONS
As the main requirements to the VMI-setup entail asmall intrinsic velocity blurring for a large ionization vol-ume, it is insightful to discuss the origins of this veloc-ity blurring. The radial focussing of particles with thesame initial velocity vector is governed by the electro-static lenses at the borders of the (axial) electric fieldregions in a VMI-apparatus. These electrostatic lensesmainly suffer from two types of imperfections, namelychromatic aberrations and spherical (geometric) aberra-tions [4].Chromatic aberrations originate from the fact that thefocal length of the lenses is dependent on the ion kineticenergy at the lens plane, similar to the dependence of thefocal length of an optical lens on the wavelength of light. The extent of the aberrations depends on the relativedifference in kinetic energy of the ions at the lens plane,which can arise from either different initial velocity ordifferent ionization position (i.e. creation at a differentelectrostatic potential). These aberrations are generallylargest for the first lens encountered, since the relativekinetic energy difference will be largest here.Spherical aberrations are caused by a dependence ofthe focal length on the radial distance ( r ) from the lensaxis, i.e. the radial field strength is not perfectly lin-ear with respect to r . Since the Newton sphere expandswhen moving through the VMI-apparatus, the effect isgenerally largest for the last lens(es) encountered.Chromatic aberrations can be reduced by decreasingthe relative kinetic energy difference of the ions. Besidesthe use of a smaller ionization volume, this can effectivelybe achieved by moving away the first lens from the detec-tion region (i.e. to either obtain a smaller field strengthin the ionization region for similar potential at the lensplane, or obtain larger total ion acceleration before thefirst lens for similar field strengths). Also a soft (gradual)focus reduces the effect of the change in focal length ofthe first lens(es) on the image quality. These approachesare demonstrated in for example the designs of Townsendet al. [7] and Lin et al. [8].Spherical aberrations can be reduced by decreasing theexpansion of the Newton sphere (e.g. by using a largeroverall field strength or shorter acceleration region), in-creasing the lens diameter, or using gradually focussinglenses with a larger axial extent of each individual lens inthe ion optics system [4]. Also the use of a smaller ion-ization volume can help to reduce spherical aberrations,as this reduces the initial radius of the ion cloud.It is apparent that the two types of aberrations cangenerally not be minimized simultaneously, as they forexample have an opposite dependence on the length ofthe first field region. Thus, their combined minimumneeds to be found. For the conditions encountered in low-energy crossed beam experiments, the chromatic aber-rations tend to dominate as small Newton spheres andlarge ionization volumes are considered. Generally, onlyincreasing detector size (uniform scaling), reducing thesize of the ionization volume, and more gradual focusing,suppress both aberrations without having other negativeeffects on the mapping properties.The electrode shape plays an important role in themapping characteristics. Several efforts have been madeto adjust the traditional flat annular electrodes in or-der to increase the mapping accuracy [1], for instance toimprove the performance in crossed beam ion-moleculereaction studies [20]. Instead of the traditional electrodeplates, also cylindrical or tube-shaped electrodes can beused. These have the advantage of reduced sphericalaberrations due to an increased effective aperture for thesame lens diameter, as well as a larger axial extent of thelens fields [4]. Another benefit is that for small inter-tubegaps, the external electric field penetration into the tubesis negligible, effectively shielding the VMI-region fromoutside influences. The use of tube-shaped electrodeswas already suggested in the original work of Eppinkand Parker [3], and has been previously implemented[21]. However, their use in VMI-applications is seldomreported, although a combination of planar-shaped elec-trodes with shielding tubes is implemented in multipledesigns [20, 22].The freedom in the design parameters, i.e. the elec-trode geometries and applied voltages, can be used to finda combined minimum of the aberrations and simultane-ously satisfy the other mapping requirements. Addingdegrees of freedom, like additional field regions [7] ormagnifying lenses [18, 23, 24], can allow for further con-trol over the mapping properties. Due to the complex-ity of the system, the performance characteristics of aVMI-setup can in general not be readily calculated an-alytically. Instead, one can make use of numerical iontrajectory simulations as a method to predict and opti-mize the performance of a VMI-apparatus. IV. SIMULATION ROUTINE
The SIMION software package [25] (version 8.1) wasutilized to simulate ion trajectories, and predict the per-formance of a VMI-setup. To achieve the best perfor-mance regarding our design goals, many possible VMI-setups were simulated and analyzed. Employing the userprogramming features of SIMION, a systematic approachwas implemented to change and optimize both the geo-metrical and electrical configurations. The concepts toreduce lens aberrations, as well as previous ion opticsdesigns, were used as an inspiration and to provide astarting point for the optimization process.The global structure of the optimization routine con-sists of two main parts. The first part optimizes the volt-age configuration of the VMI-setup for a single given ge-ometrical configuration, which results in optimized per-formance for that geometry. To this extent the SIMIONbuilt-in implementation of a downhill Nelder-mead Sim-plex algorithm is used, in a similar fashion as in the workof Ryazanov et al. [18, 26]. It uses the applied electricpotentials as input parameters, and finds a (local) mini-mum of an objective function that takes into account thethree most important performance requirements, i.e. thevelocity blurring for a given size ionization volume andthe electric field strength in the detection area. The sec-ond part of the routine is used to optimize the geometryof the VMI-setup. It loops through a list of geometryvariations, each time building the fully parametrized ge-ometry file as well as the corresponding potential array.The best performance for each geometry is found throughoptimization of the electrode voltages, and stored forlater analysis and further characterization. In this way, areasonable part of the very high-dimensional parameterspace can be explored without the use of advanced andcomputationally heavy optimization algorithms.We used the example NO-Ne collision system (see Fig. 1) as a benchmark system in the optimization process.The requirement of a large detection volume is safe-guarded by spawning the NO + ions at 125 positions uni-formly distributed over a 3x3x3 mm cube for each veloc-ity vector considered. The intrinsic blurring of the VMI-apparatus σ ( V (cid:48) NO , V COM , α ) is characterized from the iontrajectories of all particles with the same initial velocityvector by using the maximum spreads in their hit po-sitions on the detector in both 2D-coordinates ( D y , D z )and their average mapping radius from the center of thesphere ( R ) as: σ ( V (cid:48) NO , V COM , α ) = (cid:113) D y + D z R (1)which is proportional to the intrinsic relative velocity res-olution ( D V /V (cid:48) NO ) for assumed linear velocity mapping.Here, D V indicates the maximum spread in the obtainedvelocity vector after mapping, i.e. the intrinsic absolutevelocity resolution. It is worth noting that, due to itsdefinition, σ increases for smaller Newton rings. Further-more, by taking the maximum spreads in the hit positionsand adding the two dimensions in quadrature, the effec-tive blurring is systematically overestimated. The defi-nition, however, does not take into account the size ofthe MCP pores and camera pixels, or effects of (partial)Newton sphere crushing, that could limit the practicalmapping resolution. For each starting position of the ion,several initial velocity vectors on differently sized Newtonspheres are probed around their common COM-velocityvector.While the simulations are performed for NO + ions,most results can easily be generalized to other species.This, since two ions with the same starting position, ve-locity direction and kinetic energy per unit charge, willhave identically shaped trajectories in electrostatic fields[27]. Only the time in which these trajectories are tra-versed will depend on the mass.Cylindrical symmetry of the electrodes is assumed inthe geometry optimization process to reduce the com-putation time. The surroundings of the ion optics andflight region are included in the geometry definition. Thedistance from the center of the ionization region to theMCP-detector, was fixed to the value of 892.5 mm in theexisting crossed beam setup. The total voltage drop overthe VMI-apparatus was kept at 2000 V in the simula-tions.A substantial amount of variations to the VMI-detector design was investigated which included, amongother things, the amount of electric field regions (in-dependent applied potentials), the field region lengths,number of individual electrodes and electrode shapes.Careful optimization of the VMI-detector geometry wasperformed. However, the addition of degrees of freedomthat allowed for only a marginally better performance,but result in a great increase in complexity of the design,was prevented. V. OPTIMIZED DESIGN
The optimized geometrical and electrical configura-tion, is shown in figure 2. It consists of 16 cylinderswith an inner diameter of 61 mm and outer diameter of64 mm. The rims ( (cid:31)
75 mm, thickness 5 mm) are addedfor mounting only, and have very small influence on themapping performance due to the rigorous shielding pro-vided by the cylinders. Of the cylinders, 15 are identicalwith a length of 19 mm. Only the first cylinder is differ-ent, since it is closed on one side by the repeller plate. Ithas a total length of 13 mm with a 3-mm thick repellerplate. The surface of the repeller plate is positioned 17mm away from the center of the ionization region. Allcylinders have a 1-mm spacing in between, to ensureelectrical isolation. The total distance from the centerof the ionization region to the MCP-detector is set to892.5 mm. The required beam access holes in the secondcylinder ( (cid:31) ° ) are not shown. They breakcylindrical symmetry, and their effect on the mappingaccuracy will be separately addressed at the end of thissection. Only four independent electric potentials are ap-plied to the system, namely on the first cylinder/repeller(U = 2000 V), the second cylinder (U = 1933 . = 1472 V) and the last cylinder(U = 0 V). The other electrodes are connected via highprecision 100 kΩ ( ± .
61 mm75 mm mm U U U U = 0 a b C y l V V InsidevacuumOutsidevacuum U U U U = 0 C y l C y l C y l C y l C y l C y l C y l c FIG. 2: (a) Cross-section of the optimized ion optics designand corresponding electric potential field as simulated withSIMION. The drawn equipotential lines have a 25 V spac-ing, with a total voltage drop of 2000 V over all cylinders.The center of the ionization volume is indicated by the blacksquare. (b) Photograph of the assembled ion optics design.(c) Electrical scheme used to provide the correct potential toeach cylinder (Cyl), employing two external power supplies(V , V ), a 200 kΩ potentiometer and 100 kΩ resistors. troduces a small, controllable, curvature of the electricfield in the ionization region, which can help to improvefocusing [26]. Additionally, this extra control over thefield in the detection region may allow to correct for pos-sible distortions introduced by the necessary access holesrequired for lasers and molecular beams. The transitionbetween the second and third field region was moved toaround cylinder eight, which allows for a low electric fieldstrength in the ionization region and strongly reduceschromatic aberrations.The simulated blurring ( σ , see Eq. 1) for the velocitymapping device is depicted in figure 3 for a variety ofNewton circle radii ( V (cid:48) NO ) and azimuthal angles ( α ) withrespect to a fixed COM-velocity vector. Considering theforward scattering direction of the reference NO-Ne colli-sion system, the simulated blurring for the 3x3x3 mm de-tection volume amounts to around only 3.14 µ m in bothdirections on the detector plane ( D y , D z ), which is justbelow the 6 µ m center-to-center pore distance of the typ-ically employed MCP-detector. Combined with an imageradius of 3.806 mm this results in σ = 0 .
0 1 2 3 4| V’ NO | ( x 363.3 m/s )−180−90 0 90 180 α ( deg . ) V e l o c i t y b l u rr i ng ( % ) FIG. 3: Simulated velocity blurring ( σ , see Eq. 1) of theoptimized VMI-apparatus when using a 3x3x3 mm ioniza-tion volume, for varying Newton circle radius ( | V (cid:48) NO | ), andazimuthal angle ( α ) with respect to a fixed COM-velocity( | V COM | = 411 . | V (cid:48) NO | = 363 . α = 67 . ° , see Fig. 1). It should be noted that the image radius ( R ) can beeasily increased, with but a marginal increase in veloc-ity blurring, by increasing the total flight length ( L ) orscaling down the applied voltages ( E ) as they are roughlyrelated as R ∝ L (cid:112) mE ·| V (cid:48) | , where m indicates the particlemass and | V (cid:48) | the velocity radius of the Newton sphere.Furthermore, the blurring is reduced for smaller ioniza-tion volumes. It was found to change similarly with anadjustment of the volume dimension along the axis ofthe VMI-apparatus, as with an equal adjustment in boththe perpendicular dimensions. E.g. for a 1x1x1 mm vol-ume the total blurring is reduced to σ = 0 . X Π / ) Lambda-doubletstates, that is negligible in a typical experiment. Thecorresponding total Newton sphere elongation ( τ ) forthe reference scattering system is 64.4 ns, which is in-dependent of the size of the ionization volume, and inprinciple allows for direct image slicing. As mentioned,however, the arrival-time focussing was not optimized forlarge ionization volumes, resulting in a fairly large time-blurring (maximum arrival-time spread D t ) of 47.3 nsfor the 3x3x3 mm volume. Again, this blurring is heavilysuppressed for smaller detection volumes, as it roughlyscales with the dimension of the ionization volume alongthe axis of the VMI-apparatus. If the NO + ions originatee.g. from a 0.5x3x3 mm volume it amounts to around D t = 7.9 ns. Scaling down of the applied voltages ( E ) canbe used to increase total Newton sphere elongation ( τ ),as they are approximately related as τ ∝ m | V (cid:48) | E , where m indicates the particle mass and | V (cid:48) | the velocity radiusof the Newton sphere. The time-blurring for a given sizeionization volume is almost independent of the velocityradius, and is loosely related to D t ∝∼ (cid:112) mE . Lastly, theso called center slice distortion, given by the difference inmean arrival time for the centre slices of Newton sphereswith different radii, was found to be negligible. Thus,direct image slicing can still be in reach under certainexperimental conditions.The stability of the optimized design was investigatedregarding deviations in both the geometry and appliedvoltages. These deviations are only expected to signifi-cantly affect the induced velocity blurring. Thus, to in-vestigate the voltage stability the velocity blurring wasmapped out for a range of voltages in the vicinity of theoptimized settings. As the lens properties only dependon the ratio of the electric field strengths of succeedingfield regions, only the potentials applied to the secondand eight cylinder have to be investigated. The resultsare depicted in figure 4.It can be seen that a narrow voltage band exists whereperfect mapping conditions are ensured. The accuracy ofcommercially available high voltage power supplies is suf-ficient to ensure proper settings for the potential on cylin-der 8. For the potential on cylinder 2, however, the rangeof good voltage settings is even narrower. This could beexpected as the first field region consists of only a sin-gle cylinder while it has the lowest electric field strength.This narrow voltage acceptance is especially challengingas most commercial power supplies have voltage outputripples and drifts of similar magnitude. For the powersupplies employed here (SRS P350) these amount to max- P o t en t i a l cy li nde r ( V ) V e l o c i t y b l u rr i ng ( % ) FIG. 4: Simulated velocity blurring ( σ , see Eq. 1) of the op-timized VMI-apparatus when using a 3x3x3 mm ionizationvolume, for varying voltages applied to the device. The po-tential applied to the first and last cylinder is fixed to 2000V and 0 V, respectively. The blurring was determined for theforward scattering direction of the elastic NO-Ne referencecollision system (see Fig. 1), for which the optimized voltagesetting is indicated by the black circle. imum 0.1 V and 0.6 V (over 8 hours), respectively. Theproblem is easily solved, however, with the use of a po-tentiometer to set the voltage on the first cylinder andsecond cylinder with a single power supply (see Fig. 2).In our implementation a 200 kΩ 10-turn precision poten-tiometer was used. This firstly allows for a much moreprecise setting of the voltage. Furthermore, it effectivelyfixes the ratio of the electric field strengths in the firstand second region, thus conserving the focussing powerof the first lens. Any voltage shift or ripple is spread outover the first two electric field regions, and can thus effec-tively be considered to accumulate on the set voltage ofcylinder 8. This voltage has a much broader acceptancerange, allowing stable operation with minimal velocityblurring.It should be noted, that a voltage shift in principle notonly affects the intrinsic velocity blurring ( σ ), but canalso slightly change the center position and radius of theimage on the detector plane. This can cause additionalblurring that is not incorporated in σ . However, it wasfound from the simulations that these effects are signif-icantly smaller than the change in the intrinsic velocityblurring ( σ ) for the large ionization volume and expectedvoltage shifts.Regarding the stability with respect to deviations fromthe proposed geometry, two effects were investigated.Firstly, the VMI performance was simulated for a sys-tem where a combination of geometrical defects was de-liberately added. It was found that, for reasonable errorsin machining and assembly, only minor changes in the VMI performance could be expected. Errors in the in-ner diameter of the cylinders cause the largest changes inperformance, which was accounted for during machiningof the electrodes. Secondly, the influence of the requiredbeam access holes in the second cylinder was investigatedin 3D-simulations that take into account the breakingof the cylindrical symmetry. Beam access holes with a5-mm diameter (every 45 ° ) allow sufficient room for ac-cess with both laser beams and molecular beams, whileshowing only marginal effects on the simulated mappingperformance. VI. EXPERIMENTAL
A VMI-apparatus following the design described abovewas constructed out of aluminum, and implemented intoan existing crossed beam scattering setup. This setup hasbeen discussed in detail before [11], and consists of a 2.6-m long Stark decelerator and a conventional beam at a90 ° crossing angle. A molecular beam of NO molecules isformed using a Nijmegen Pulsed Valve that expands 5%NO seeded in Krypton into vacuum. The Stark deceler-ator is used to produce packets of NO molecules in the j = 1 / v = 0 vibrational groundstate of the X Π / electronic ground state, with a nar-row spread around a selected mean velocity. Only theΛ-doublet level with f parity is selected. The NO par-ticles are state-selectively detected after scattering usinga recoil-free (1+1’) resonance-enhanced-multiphoton ion-ization scheme in combination with the new ion optics.The distance from the center of the ionization region tothe MCP-detector is around 892.5 mm. The ion opticscould be replaced with a reference design for performancecomparison. Either tightly focussed lasers were used todetect particles in a small ionization volume, or (par-tially) unfocussed lasers were used resulting in a largeionization volume (approximately 2.5 mm in all dimen-sions).Firstly, the well defined packets of NO j = 1 / , f ex-iting the Stark decelerator at different selected veloci-ties were imaged and used to optimize the voltage set-tings of the VMI-apparatus experimentally in so called“beamspot” measurements. The found optimized volt-age settings correspond to applied potentials of around2000, 1935, 1481 and 0 V for cylinders 1, 2, 8 and 16, re-spectively. The experimentally obtained settings are thusvery close to the predicted settings from the simulations.Furthermore, using a previously established calibrationprocedure [10], the velocity mapping was found to beperfectly linear, with each image pixel corresponding toa velocity of 1.14 m/s for the camera configuration usedhere. For the small and large ionization volume, identicalresults were obtained. For the large ionization volume, afew volt deviation in the applied potentials did not causea notable increase in blurring. For the smaller ioniza-tion volume, even larger voltage deviations are requiredto cause a notable increase in blurring. This indicatesa stable operation of the VMI-setup at minimal velocityblurring, for both the large and small ionization volume.To further investigate the performance of the newVMI-setup, the inelastic scattering of the Stark decel-erated NO molecules (430 m/s) and a conventional beamof pure He (around 1900 m/s) was used as a model sys-tem for molecule-atom collisions. This collision process isknown to exhibit narrowly spaced oscillatory structuresin the angular distribution of the scattered molecules,originating from the diffraction of matter waves duringthe collisions [10]. The observation of these diffractionoscillations provides a stringent test for the resolution ofa crossed beam scattering experiment, and thus also forthe resolution of the VMI-apparatus.The images recorded using the new ion optics areshown in figure 5, and compared to measurements un-der identical conditions but using a conventional Eppink-Parker type ion optics design [3] with optimized voltagesettings. The images are presented such that the rela-tive velocity vector is directed horizontally, with forwardscattering angles positioned at the right side of the im-age. At the forward scattering direction the initial beamgives a contribution to the signal. These measurementswere performed at a collision energy of 551 cm − , andwith either a small or large ionization volume. To ensureequal comparison of the resolution, the laser powers werereduced for the large ionization volume to give similar ionyields as for the small ionization volume. The image ra-dius for the new apparatus was found to be around 2.4mm on the MCP-detector plane, in good agreement withthe simulated radius of 2.39 mm.It can be seen that for the small ionization volumesharp images that show clear oscillatory structures inthe angular scattering distribution, can be obtained us-ing both the new and conventional ion optics design. Forlarge ionization volumes, however, the image is signifi-cantly blurred when using the conventional ion optics,while it remains perfectly sharp for the new design.For the new ion optics no detrimental effect on theimage resolution or beamspot size could be found for thelarge ionization volume as compared to the small volume.However, the presence of a deteriorative effect is knownfrom both theory and simulations, and is also proven toexist by the experimentally found increased voltage ac-ceptance range for the smaller ionization volume. Thisindicates that the intrinsic blurring induced by the VMI-apparatus should be well below the measured image res-olution, and amounts to at most 1 image pixel or 1.14m/s. Together with the 228 m/s ring radius, this re-sults in a value of σ < .
7% for the performed collisionexperiment, according to the definition of Eq. 1, or anintrinsic velocity resolution of D V /V (cid:48) NO (cid:46) . − were Conventional design New design S m a ll v o l u m e L a r g e v o l u m e FIG. 5: Velocity distributions of scattered NO molecules asmeasured with a conventional Eppink-Parker type ion opticsdesign [3] and with the new ion optics design, for both smalland large ionization volumes. The NO molecules that scat-tered into the j = 3 / , e level were detected after collision withHe at an energy of 551 cm − . The insets show an enlargedpart of the images near the forward scattering direction. Theimaged ring radii are equivalent to about 228 m/s. Each im-age pixel corresponds to a velocity of 0.92 m/s or 1.14 m/sfor the conventional and new design, respectively. studied, using a crossed molecular beam setup optimizedfor low energy collisions that has been discussed in de-tail before [13]. Here, a Stark decelerated beam of NOmolecules (650 m/s) was intersected at an angle of 10 ° with a beam of He (490 m/s) from a cooled Even-LavieValve. For this machine the new ion optics design wasuniformly scaled with a factor of approximately 1.4. Fur-thermore, a distance from the ionization region to MCP-detector of around 1133.5 mm was used, and the requiredpotentials were applied with three separate power sup-plies (i.e. without potentiometer). To illustrate the im-provements offered by the new ion optics design for lowcollision energy experiments, we compare the new de-sign under the least favourable conditions, i.e. using alarge ionization volume, with a reference ion optics designadapted from that of Townsend et al.[7] under the mostfavourable conditions, i.e. using a small ionization vol-ume. Apart from the differently sized ionization volume,a corresponding change in laser power to obtain similarsignal levels, and a slightly different distance from theionization region to the MCP-detector (1085 mm for thereference design), otherwise identical experimental con-ditions were employed. The obtained collision images aredepicted in figure 6, again presented such that the rela-tive velocity vector is directed horizontally with forwardscattering angles positioned at the right side of the im-age. Small segments of the images are masked aroundthe forward direction since the initial beam gives a con-tribution to the signal there. The new design gives amuch sharper image, even when a much larger ionizationvolume is used, resulting in a significantly improved con-trast between peaks and valleys in the angular scatteringdistribution extracted from the measured images. Forthe reference design the use of a large ionization volumeresulted in significant image blurring. Ref. design, small volume a New design, large volume bc I n t e n s i t y ( a r b . un i t s ) Scattering angle (deg.)
Ref. design, small volumeNew design, large volume
FIG. 6: Velocity distributions of scattered NO molecules asmeasured with a reference ion optics design adapted from thatof Townsend et al. [7] when using a small ionization volume(a) and with the new ion optics design when employing a largeionization volume (b). The NO molecules that scattered intothe j = 1 / , e level were detected after collision with He atan energy of 5.2 cm − . The imaged ring radii are equivalentto about 21 m/s. Each image pixel corresponds to a velocityof 1.08 m/s or 0.94 m/s for the reference and new design,respectively. The angular scattering distributions extractedfrom the images are depicted in (c). The new ion optics design discussed here has recentlybeen employed in several state-of-the-art scattering ex-periments in our lab, granting the possibility to observedetails in the velocity distributions of scattered moleculesthat had not been resolved before. For example, it al-lowed resolving narrowly spaced concentric rings, per-taining to product pairs, in the scattering distribution ofNO molecules that are excited to high rotational statesduring collisions with O molecules, thus providing ex-perimental data in the largely unexplored field of bi-molecular scattering [11]. More recently, the device has also been employed to image the onset of the resonanceregime in low-energy NO-He collisions [13]. Here, it al-lowed measuring the angular scattering distributions atcollision energies below 1 K, providing stringent tests forstate-of-the-art inelastic scattering calculations in previ-ously unexplored energy regimes. Furthermore, the ap-paratus has recently been used to capture the first high-resolution images of molecular collisions employing a Zee-man decelerator [12]. VII. CONCLUSION
We have presented an improved Velocity Map Imag-ing ion optics layout, optimized for use in crossed beamscattering experiments employing decelerators. It is par-ticularly designed to provide high-resolution imaging forlarge detection volumes and over a broad range of col-lision energies, down to the sub-Kelvin regime. Theradially compact setup consists of 16 tube-shaped elec-trodes, electrically connected via high precision resistorsthat require only two external power supplies to pro-vide the proper potentials to all electrodes. The exper-imentally determined operating conditions are in excel-lent agreement with the simulated ones. The apparatuswas found to provide for a negligible intrinsic velocityblurring, even for large ionization volumes of several mil-limetres in all dimensions. Furthermore, the low electricfield strength in the ionization region reduces unwantedmixing of states by the Stark-effect, and provides futureprospects for employing direct image slicing techniques.The presented VMI-apparatus design was optimized forthe conditions encountered in inelastic scattering exper-iments employing decelerators but might also find appli-cations in other research areas, for example in the fieldsof reactive scattering or photodissociation experiments.
VIII. ACKNOWLEDGMENTS
This work is part of the research program ofthe Netherlands Organization for Scientific Research(NWO). S.Y.T.v.d.M. acknowledges support from theEuropean Research Council (ERC) under the Euro-pean Union’s Seventh Framework Program (FP7/2007-2013/ERC Grant Agreement No. 335646 MOLBIL) andfrom the ERC under the European Union’s Horizon 2020Research and Innovation Program (Grant Agreement No.817947 FICOMOL). We thank Tim de Jongh and QuanShuai for their contribution to the measurement andanalysis of the low energy collision data. We thank Andr´eEppink and David Parker for useful discussions on theVMI technique. We thank Andr´e van Roij, Niek Janssenand Edwin Sweers for expert technical support.0 [1] M. N. R. Ashfold, N. H. Nahler, A. J. Orr-Ewing, O. P. J.Vieuxmaire, R. L. Toomes, T. N. Kitsopoulos, I. A. Gar-cia, D. A. Chestakov, S.-M. Wu, and D. H. Parker, Phys.Chem. Chem. Phys. , 26 (2006), ISSN 1463-9076.[2] D. W. Chandler and P. L. Houston, J. Chem. Phys. ,1445 (1987), ISSN 0021-9606.[3] A. T. J. B. Eppink and D. H. Parker, Rev. Sci. Instrum. , 3477 (1997), ISSN 0034-6748.[4] H. Liebl, Applied Charged Particle Optics (Springer,2008).[5] C. R. Gebhardt, T. P. Rakitzis, P. C. Samartzis,V. Ladopoulos, and T. N. Kitsopoulos, Rev. Sci. Instrum. , 3848 (2001), ISSN 0034-6748.[6] M. L. Lipciuc, J. B. Buijs, and M. H. M. Janssen, Phys.Chem. Chem. Phys. , 219 (2006).[7] D. Townsend, M. P. Minitti, and A. G. Suits, Rev. Sci.Instrum. , 2530 (2003), ISSN 0034-6748.[8] J. J. Lin, J. Zhou, W. Shiu, and K. Liu, Rev. Sci. Instrum. , 2495 (2003), ISSN 0034-6748.[9] J. Onvlee, S. N. Vogels, A. von Zastrow, D. H. Parker,and S. Y. T. van de Meerakker, Phys. Chem. Chem. Phys. , 15768 (2014), ISSN 1463-9076.[10] A. von Zastrow, J. Onvlee, S. N. Vogels, G. C. Groenen-boom, A. van der Avoird, and S. Y. T. van de Meerakker,Nat. Chem. , 216 (2014), ISSN 1755-4330.[11] Z. Gao, T. Karman, G. Tang, A. van der Avoird, G. C.Groenenboom, and S. Y. van de Meerakker, Phys. Chem.Chem. Phys. , 12444 (2018).[12] V. Plomp, Z. Gao, T. Cremers, M. Besemer, and S. Y. T.van de Meerakker, J. Chem. Phys. , 091103 (2020),ISSN 0021-9606.[13] T. de Jongh, M. Besemer, Q. Shuai, T. Karman,A. van der Avoird, G. C. Groenenboom, and S. Y. T.van de Meerakker, Science , 626 (2020).[14] M. Brouard, D. H. Parker, and S. Y. T. van de Meer-akker, Chem. Soc. Rev. , 7279 (2014), ISSN 0306-0012.[15] S. Y. T. van de Meerakker, H. L. Bethlem, N. Vanhaecke, and G. Meijer, Chem. Rev. , 4828 (2012).[16] T. Cremers, N. Janssen, E. Sweers, and S. Y. T. van deMeerakker, Rev. Sci. Instrum. , 013104 (2019).[17] D. A. Chestakov, S.-M. Wu, G. Wu, D. H. Parker, A. T.Eppink, and T. N. Kitsopoulos, J. Phys. Chem. A ,8100 (2004).[18] M. Ryazanov and H. Reisler, J. Chem. Phys. , 144201(2013), ISSN 0021-9606.[19] J. O. F. Thompson, C. Amarasinghe, C. D. Foley, andA. G. Suits, J. Chem. Phys. , 013913 (2017), ISSN0021-9606.[20] S. Trippel, M. Stei, R. Otto, P. Hlavenka, J. Mikosch,C. Eichhorn, U. Lourderaj, J. X. Zhang, W. L. Hase,M. Weidemller, et al., J. Phys.: Conf. Ser. , 012046(2009), ISSN 1742-6596.[21] B. van Oorschot, Master Thesis (Radboud University Ni-jmegen, 2012).[22] O. Ghafur, W. Siu, P. Johnsson, M. F. Kling,M. Drescher, and M. J. J. Vrakking, Rev. Sci. Instrum. , 033110 (2009), ISSN 0034-6748.[23] H. L. Offerhaus, C. Nicole, F. Lpine, C. Bordas, F. Rosca-Pruna, and M. J. J. Vrakking, Rev. Sci. Instrum. , 3245(2001), ISSN 0034-6748.[24] Y. Zhang, C.-H. Yang, S.-M. Wu, A. van Roij, W. J.van der Zande, D. H. Parker, and X. Yang, Rev. Sci.Instrum. , 013301 (2011), ISSN 0034-6748.[25] D. A. Dahl, Int. J. Mass Spectrom. , 3 (2000), ISSN1387-3806.[26] M. Ryazanov, Design and implementation of an ap-paratus for sliced velocity map imaging of H atoms (2012), URL http://chem.usc.edu/~reisler_group/assets/pdf/SVMI.pdf .[27] D. Manura and D. Dahl,
SIMION 8.1 User Manual [Sci-entific Instrument Services, Inc.] (2008), URL http://simion.com/manual/http://simion.com/manual/