Coincidence velocity map imaging using a single detector Free

Velocity map imaging (VMI),^1,2 combined with coincidence detection, has become an essential tool in the study of reaction dynamics, such as ionization, photo-excitation, and photo-dissociation.^3–10 VMI maps the transverse momentum of charged particles to position on a 2D detector. More precisely, there is a conversion factor, denoted by A such that $mvT→=Ar→$⁠, where $vT→$ and m are the particle’s transverse velocity and mass, respectively, while $r→$ is the position on the detector. This conversion factor A depends on the voltage V on the VMI electrostatic plates and the flight length L as follows: $A∝VL$⁠. This projection onto a 2D detector can be Abel inverted to recover the 3D distribution if the latter possesses cylindrical symmetry, with the symmetry axis being perpendicular to the projection axis. It is fairly common for a system to have a cylindrical symmetry. For instance, atoms or unaligned molecules with a linearly polarized laser field (polarization direction being the axis of symmetry) or with a circularly polarized laser field (propagation direction being the axis of symmetry). Access to the full kinematics of a single reaction requires the detection of photoelectron and photoion momenta in coincidence, and it allows for systematic studies of the underlying physical mechanisms. The most natural apparatus for coincidence VMI detection includes two sets of electrostatic lenses for VMI, and two sets of microchannel plate (MCP) coupled to delay line detectors, which provide excellent time and spatial resolution.^11,12 However, this comes with a relatively high cost and complexity. A simplification has been introduced by Lehmann and co-workers.¹³ They rapidly switch the voltages on the extraction plates in order to achieve coincidence detection with a single delay line based detector. Here we show a further modification, in which we replace the delay line detector with a fast CMOS camera.

The biggest advantage of this design is that it allows for easy switching between coincidence and non-coincidence operating modes, each of which has its unique applications. A coincidence measurement provides a detailed set of information of a dynamical process by detecting the momenta of both the electron and ion in coincidence and therefore is best at discriminating among several mechanisms and/or pathways which underlie the reaction dynamics. For instance, by assigning peaks in photoelectron spectra to specific ionic states, it allows for discriminating between direct ionization to an excited ionic state from indirect ionization to the same state via an intermediate ionic state.^14–16 It is also widely used in the study of double ionization.^17–20 On the other hand, non-coincidence measurements are particularly useful in exploring the parameter space consisting of variations in intensity, ellipticity, and pulse shape, due to the much higher data collection rate. In addition to allowing for both modes of data acquisition, this design is relatively low cost and easy to set up. In Sec. III, we present two experiments to show that this design is capable of coincidence VMI measurements with sufficient time and momentum resolution.

Currently, the biggest limitation in our apparatus lies in the fact that while the camera’s frame rate can accommodate operation at 1 kHz, we cannot record separate images for both electrons and ions using the same camera. Consequently, we only record the spatial distribution of the early-arriving photoelectrons while recording the time of flight (TOF) mass spectrum for ions. However, we are currently implementing a Timepix camera,^21,22 which can record electron and ion hits with about 1.5 ns time resolution. This allows us to use the same apparatus to record spatial information for both electrons and ions in coincidence for every laser shot at 1 kHz. Other novel detection schemes and new photo-sensor techniques have also been proposed to circumvent this difficulty.^23–25 

Our light source is an amplified Ti:sapphire laser system, producing 30 fs (intensity FWHM) pulses with a central wavelength of 780 nm and a pulse energy of 1 mJ, at a 1 kHz repetition rate. The focused laser pulses intersect an effusive molecular beam at the center of the VMI electrostatic plates (see Figure 1) inside a vacuum chamber with a base pressure of 10⁻⁹ Torr. The voltages on the VMI plates are switched from negative to positive using two DEI Scientific Pulse Generators (<25 ns rise/fall times), in sync with the arrival of the laser pulse. Due to the huge mass ratio of the cations to the electron, the cations do not move very much before the electrons leave the accelerating region and the voltages are switched to direct the ions to our detector. This way, all charged particles are sent onto a dual stack of microchannel plates (MCPs) in chevron configuration located about 20 cm away from the reaction region. The front side of the MCPs is kept at ground in order to collect all charged particles. Behind the MCPs is a fast phosphor screen which is illuminated by the electron showers coming from the MCPs. The fluorescence from the phosphor is collected by a fast CMOS camera (BASLER acA2000-340 km), whose shutter closes immediately after the arrival of the electrons. This camera can continuously acquire $360×360$ frames at a 1 kHz rate. Relatively light ionic fragments such as H₂O⁺ arrive $3∼4μs$ after the laser pulse, depending on the applied accelerating voltage. We capacitively couple a digitizing oscilloscope to the phosphor screen, allowing us to record time-of-flight (TOF) information for all arriving particles. The whole flight region is enclosed in a μ-metal tube in order to shield against external magnetic fields. Rather than saving camera images for each laser shot, we rapidly analyze each image on the fly to identify the coordinates for electron or ion hits. These coordinates are recorded and used to generate a final image which can be Abel inverted to recover the 3D momentum distribution if there is cylindrical symmetry as is the case for a linearly polarized laser pulse (for which there is cylindrical symmetry about the laser polarization vector). For more technical details, we refer readers to  Appendix A.

The first experiment whose measurements we present recorded the photoelectron spectra from the strong field ionization of CH₂IBr (see Figure 2). We chose the photoelectron spectra obtained in coincidence with the parent ion and the most abundant fragment ion to illustrate the power of coincidence detection. Clearly, photoelectron spectra measured in coincidence with the two photoion species are different. The key observation is that photoelectrons carry the information about the ionic state at the moment of ionization, while photoions carry the information about the final ionic state. Measuring them in coincidence shines light on the dynamics immediately following ionization, determining, for instance, whether an excited ionic state is populated via the direct removal of an inner core electron (red peak labeled $D2/3(8)$⁠) or via the initial removal of a valence electron followed by field driven excitation to an excited ionic state (red peaks labeled $D1(7)$ and $D0(7)$⁠). We refer interested readers to previous work¹⁵ for more detailed peak assignments and interpretation.

The second experiment is conducted with krypton in order to calibrate the energy resolution of the detector. It is known²⁶ that strong field excitation of krypton produces autoionizing Rydberg states, which lead to the appearance of electrons in the spectrum with well defined energies and narrow peak widths. We have carried out measurements of photoelectrons from Kr atoms exposed to a strong laser field and use these autoionization features to estimate the energy resolution of our detector. The data are collected in non-coincidence mode and the result is shown in Figure 3. Here we see the advantage of being able to readily switch between two detection modes. The CH₂IBr result shown in Figure 2 takes about 12 h of continuous data acquisition, while the krypton data shown here only requires a few minutes of integration. Assuming that the width of the peaks in our spectrum is the result of our finite detection resolution, we estimate the lower bound on the energy resolution of this setup to be about 30 meV full width at half maximum (FWHM). In our setup, at 100 meV, 30 meV difference in energy corresponds to about 5 pixels on the camera sensor, implying that the energy resolution is mostly limited by factors other than the camera, such as imperfect electrostatic fields for the VMI. The energy spread across a single pixel increases with energy. At about 180 pixels (2.6 eV) away from the center of the image, one pixel corresponds to 30 meV.

Here we discuss a modification to the apparatus which is currently being tested. In the measurements discussed above, in coincidence mode, only photoelectrons are measured with VMI technique due to the finite shutter speed of the CMOS camera. In other words, the exposure time is still too long to capture one frame for each particle species. However, the camera is an external standalone detector, which makes it easy to replace or modify. One possibility is to add a beam splitter after the phosphor screen to essentially duplicate the VMI image and use two cameras to capture two independent time windows. An even better solution is to utilize time-resolved cameras, such as Timepix cameras.^21,22 The pixels in this camera act largely independently of each other and record the time of arrival for above-threshold signals with a time resolution of about 1.5 ns. It also has certain multi-hit capability, that is, a single pixel can be triggered more than once per shutter. This camera offers a combination of spatial detection and time slicing. This way, we can realize complete (detection of all particles) VMI coincidence with a single detector.

In conclusion, we have illustrated the implementation of the single-detector VMI apparatus utilizing a fast CMOS camera which is capable of operating in both coincidence and non-coincidence detection modes. The ability to readily switch between the two modes makes a wide range of applications possible. Its initial installation cost is relatively low and can be easily upgraded with fast-advancing image sensor technology.

We gratefully acknowledge support from the Department of Energy under award number DEFG02-08ER15983 for the development of the apparatus. We gratefully acknowledge support from the National Science Foundation under award number 1205397 for carrying out the measurements with the apparatus.

Here we would like to list some technical details which may be helpful in setting up and maintaining the setup. First, since we are interested in measuring photoelectron spectra and identifying photoion species, the negative voltages for electrons are chosen for VMI, while the positive voltages are chosen to defocus ions to prolong the MCPs’ life time. Our experience shows that the central part of the second MCP (the one closer to the phosphor screen) tends to get charge-depleted and the gain becomes lower, as most ions hit near the center. So it helps to defocus them if one is not interested in their spatial distribution.

Second, both the camera and digitizer are controlled via LabVIEW and it is possible to analyze the coincidence data on the fly. The time consuming part of the analysis is the centrioding algorithm, which identifies hits on the image. To reduce the work load on the computer and maintain good synchronization, we analyze the TOF trace to pre-select potentially interesting images for centroiding. For instance, if no ion or too many ions are seen in the TOF, then there is no need to analyze the image.

Third, there is a trade-off between detection range/energy resolution and detection efficiency. While the voltages on the VMI plates determine the image magnification and energy range/resolution, they also control the longitudinal velocity of the electrons and ions, which affects their detection efficiency.^27,28 Since the energy range also depends on the length of the TOF region, we chose this length such that we could measure electrons between 0 and 10 eV while maintaining the VMI voltages at optimum values for electron detection on the MCPs.

Finally, we would like to note that a good CMOS camera can have a sufficient signal-to-noise ratio for coincidence measurement. We tested the sensitivity of our camera and found that the signal strength distribution is well above the background noise level. With an appropriate threshold and centroiding algorithms, this allows the camera to identify almost all incoming particles detected by the MCPs and phosphor detector.

Here we would like to clarify how we have prepared the 2D images and spectra from our data. There are mainly two ways of saving the VMI data: as images (an array of intensity values) or centroids (a list of coordinates of the detected hits). In either case, we start with a 2D projection (image in panel (a) of Figure 4) of the 3D momentum distribution. With cylindrical symmetry, we can Abel invert the data to reconstruct the 3D distribution (see panel (a)). There are multiple ways of showing this 3D data set. We can simply look at a cross section through the axis of symmetry, as the images shown in panel (b) of Figures 4 and 2. We can also integrate over the azimuthal angle around the axis of symmetry, as the images shown in panel (c) of Figures 4 and 3. This shows the yield as a function of polar angle and radial momentum. We can angularly integrate once more around the center of the image to construct the yield as a function of transverse momentum. After converting pixels into energy, with the constant given by VMI, we end up with the photoelectron spectrum, as shown in panel (d).