Two-Dimensional Aperture Coding for Magnetic Sector Mass Spectrometry
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In mass spectrometer design, there has been a historic belief that there exists a fundamental trade-off between instrument size, throughput, and resolution. When miniaturizing a traditional system, performance loss in either resolution or throughput would be expected. However, in optical spectroscopy, both one-dimensional (1D) and two-dimensional (2D) aperture coding have been used for many years to break a similar trade-off. To provide a viable path to miniaturization for harsh environment field applications, we are investigating similar concepts in sector mass spectrometry. Recently, we demonstrated the viability of 1D aperture coding and here we provide a first investigation of 2D coding. In coded optical spectroscopy, 2D coding is preferred because of increased measurement diversity for improved conditioning and robustness of the result. To investigate its viability in mass spectrometry, analytes of argon, acetone, and ethanol were detected using a custom 90-degree magnetic sector mass spectrometer incorporating 2D coded apertures. We developed a mathematical forward model and reconstruction algorithm to successfully reconstruct the mass spectra from the 2D spatially coded ion positions. This 2D coding enabled a 3.5× throughput increase with minimal decrease in resolution. Several challenges were overcome in the mass spectrometer design to enable this coding, including the need for large uniform ion flux, a wide gap magnetic sector that maintains field uniformity, and a high resolution 2D detection system for ion imaging. Furthermore, micro-fabricated 2D coded apertures incorporating support structures were developed to provide a viable design that allowed ion transmission through the open elements of the code.
Key wordsCoded aperture sector mass spectrometry Computational mass spectrometry Miniature mass spectrometry
Miniaturization of mass spectrometers, and magnetic sector instruments in particular, would enable handheld and portable instruments for in situ analysis in a variety of applications from security to harsh environmental monitoring and health care. Miniaturized instruments utilized in harsh environments previously had to accept trade-offs between size, resolution, and sensitivity, limiting the utility of such instruments for in situ chemical analysis and identification [1, 2]. We recently developed the theoretical and experimental basis for the use of one-dimensional (1D) spatially coded apertures in mass spectrometry, breaking the historic trade-off between throughput and mass resolution in sector instruments and, thus, enabling development of a new class of miniature sector mass spectrometers free of this constraint . Minimizing these trade-offs is expected to open up new portable instrument applications that have previously been considered unacceptable because of reduced instrument performance.
The primary application of spatially coded apertures has historically been in optical imaging and spectroscopy systems . In optical [5, 6] and X-ray [7, 8] imaging systems, a coded aperture is utilized to encode the object and enable extraction of substantially more information about the object than otherwise obtainable via conventional imaging systems. Coded apertures in optical spectroscopy are used to improve system throughput without sacrificing resolution [4, 9, 10]. Throughput gains of more than 10× with no loss in resolution over conventional slits have been reported in dispersive optical coded aperture spectroscopy [11, 12], and we have demonstrated similar gains in magnetic sector mass spectroscopy using 1D coding .
Two-dimensional (2D) spatially coded patterns are frequently preferred in optical coded aperture spectroscopy [11, 12, 13] and are easy to integrate due to the abundance of 2D imaging detectors for optical systems. In the optical spectroscopy domain, the primary advantage provided by the 2D coding is the simultaneous collection of diverse multiplex combinations of the underlying signal elements. The increased measurement diversity improves the numerical conditioning of the inverse problem that must be solved to reconstruct a spectral estimate from the measurements, leading to improved precision and robustness. The addition of the second coding dimension has also enabled a variety of high-performance spectral imaging architectures [5, 6]. Our near-term focus in the ion domain is on the improved signal conditioning, although ion spectral imaging is of future interest as well. 2D coding is expected to enable advantages in signal to noise limited applications requiring high resolution mass analysis such as portable isotopic analysis.
In this manuscript, we develop the theoretical and experimental basis that demonstrates, for the first time, that sector mass spectrometers are capable of imaging a 2D coded aperture. Furthermore, we show that some of the same advantages in the optical domain are available in the ion domain. Finally, we provide directions for future development to take full advantage of the unique benefits of coded apertures in mass spectrometry.
We have accomplished these goals by developing a 90-degree magnetic sector mass spectrometer with 2D coded apertures and deriving its associated mathematical forward model and reconstruction algorithm. The reconstruction algorithm was then used to convert collected ion intensity data into mass spectra, demonstrating the capability of sector instruments to support 2D coding approaches. We have also examined the performance of the system, theoretically and experimentally, as a function of code complexity and compared the results to the previously demonstrated 1D coding results as well as 2D results from the optical domain. We develop a simple argument that explains the results, based on the fundamental differences between light- and ion-optics, and begin initial discussion of modifications to the system that should lead to increased performance in the future.
90-Degree Magnetic Sector
A 90-degree magnetic sector geometry was chosen for this work because of its simplicity. It also has the advantage of a small size relative to double focusing instruments, which is beneficial for future miniaturization efforts. The magnet was purchased from Dexter Magnetics (Elk Grove Village, IL, USA) and consisted of two 25 by 25 by 100 mm NdFeB bar magnets spaced 25 mm apart and supported by a low-carbon stainless steel yoke. The maximum field in the gap was 0.45 T. The 25 mm gap between the poles was selected to allow large 2D coded aperture patterns to pass through the sector. This wide gap results in a larger fringing field region at the edges of the sector and induces image aberrations. These image aberrations can be accounted for by an accurate forward model of the system.
EI Ion Source
The EI ion source was constructed using a Kimball Physics (Wilton, NH, USA) eV Parts kit and a commercial tungsten filament assembly (Extrel EX100) from Scientific Instrument Services (Ringoes, NJ, USA). The ion source design was modified with an elongated filament to illuminate large coded aperture patterns (up to 5 mm on the diagonal). The energies of the emitted ions from the EI source were 2 keV. Owing to the use of a single 90-degree magnetic sector geometry as opposed to a double-focusing configuration, the potential gradient in the ionization region was kept as small as possible to achieve low ion energy dispersion. This was accomplished by minimizing the potential gradients between the ionization region, repelling electrode, and extraction aperture components. The energy dispersion of the source was measured experimentally to be less than 0.5% (data not shown).
2D Imaging Ion Detector
Spatially resolved, concurrent, 2D ion detection is not a common requirement for mass spectrometers, but it is necessary for 2D spatial coding applications. For this research, the detector subsystem was comprised of a single stack 40 mm diameter circular microchannel plate (MCP) array ion imaging detector with 10 μm channel pitch spacing coupled to a phosphor screen (Beam Imaging Solutions, BOS-40; Longmont, CO, USA) and a camera to record the resulting image. The MCP and phosphor were biased at 1 and 3 kV, respectively. The combination of the spread of electrons from the exit of the 10 μm MCP channels before striking the phosphor, and phosphor bloom, results in an effective spatial resolution for the detector system on the order of 50 μm. The patterns on the detector from the coded spectra were recorded using a 10-bit black and white camera (Sony XCD U100) with an 8.5–90 mm focal length manual zoom video lens (Edmund Optics part #68-679; Nether Poppleton, York, UK).
Coded Aperture Design and Fabrication
The coded apertures highlighted in this work are used in place of the traditional imaging slit found in most mass spectrometers (Figure 1a). The traditional slit is narrow in the mass-dispersive dimension of the system as this is a resolution defining parameter, and elongated in the non-mass-dispersive dimension to increase total signal. In previous work, we demonstrated that this slit aperture could be replaced in a sector spectrometer with a series of large and small apertures in a Cyclic-S 1D spatially coded pattern . In that case the resolution of the system was maintained between each configuration because of the slit and coded aperture having the same primary feature dimension, but the throughput was greatly improved with the code.
In order to provide a fair basis for comparison, the lengths of the slits in this work were allowed to vary to match the overall linear dimension of the corresponding 2D aperture, as shown in Figure 1b. An alternate approach to compare slit versus spatially coded patterns is to maintain the same throughput by having a very large slit and compare resolution between the code and the slit, but the performance of such a slit is so poor that no species can be resolved in the spectrum. In this work, we have extended our previous work by replacing the 1D coded aperture with a 2D coded aperture.
The inclusion of this support structure reduces the throughput of the physically-implemented aperture from the theoretical maximum provided by the underlying S-Matrix code. This is in contrast to, for example, optical spectroscopy, where no support structure is required. We are exploring modifications to this support structure design that should improve performance; we will include them in the future.
The coded apertures were fabricated using UV lithography patterning and deep reactive ion etching (DRIE) (SPTS Pegasus Deep Silicon Etcher; San Jose, CA, USA) of silicon. After etching, the final apertures were coated with gold to prevent charging from the ion beam. For this study, we used 250 μm thick silicon wafers and a minimum feature size of 125 μm.
Data Collection Procedure
Coded aperture image capture was controlled utilizing a custom LabVIEW program (National Instruments Software; Austin, TX, USA). All data presented in this paper used an exposure time of 200 ms. Analyte flow into the system from a gas reservoir at approximately atmospheric pressure was regulated using a bleed valve. For each aperture and each analyte, spectral images were taken across a range of pressures spanning from 2.5 to 10.0 μTorr in steps of 2.5 μTorr. System base pressures were held constant across the data series to ensure quantitative results for aperture gain could be acquired. Several of the coded patterns were tested multiple times, across multiple days and cycles of system venting/pump-down with consistent intensity results, verifying the reproducibility of the intensity data.
Forward Model Development
As our mass spectrometer is a multiplexed measurement system, accurate mathematical reconstruction is needed to estimate the mass spectrum from the spatial pattern produced at the detector. To explain the reconstruction process, we start by briefly describing the forward model development for the system. A more detailed derivation is contained in reference .
Using the above discrete forward model combined with a numerical inversion algorithm, we can estimate the desired mass spectrum f from measurements g.
Reconstruction Algorithm and Calibration
MLE Poisson Estimation
Since the coded sector system provides a multiplexed measurement, a numerical inversion algorithm is needed to convert from the measurement to the desired mass spectrum. Furthermore, we design our inversion algorithm based on the noise present in the system. The goal is to estimate the mass spectrum f based on the measurement g and the system forward matrix H.
This solution can be obtained using an iterative deconvolution method such as that described in reference .
Forward Model Calibration
describes the ion propagation in the y-direction, which is determined by the geometry of the 90-degree sector system.
Results and Discussion
The reconstructed acetone and ethanol mass spectra are shown in Figures 3g and 4g, respectively. The relative intensity for each spectrum is normalized to the height of the highest intensity peak from the spectrum obtained from the corresponding slit to demonstrate the throughput gain associated with the different orders of 2D S-Matrix coded apertures. After reconstruction, the 2D coded system provides qualitatively identical acetone and ethanol mass spectra as the slit systems (identical peak locations and widths). Furthermore, increasing aperture order is associated with significant improvement in throughput gain as seen by the increasing relative peak heights and the concomitant increased sensitivity to weak features.
As shown in Figure 5, the observed throughput gain matches well with theory, provided the throughput-reducing effect of the support structure is taken into account. As discussed previously, we are considering support structure modifications that should move system performance closer to that expected for a system with no support structure. We will incorporate these improvements in future designs.
Comparing reconstructed acetone and ethanol mass spectra with NIST library spectra, S-15 coded acetone reconstruction reveals some of the small peaks in the mass range of m/z = 37–41 and m/z = 14–18 that the Slit-3 failed to detect. However, it is worth noting that the reconstructed acetone mass spectrum has a broader feature at m/z = 58 than the corresponding slit measurements of this peak. In a coded aperture-based system, the spectral resolution is reduced at the extreme edge of the spectral range as portions of the extended aperture image begin to fall off the detector. This results in a loss of information in this spectral region relative to a slit and the reconstructions, therefore, demonstrate a corresponding loss of resolution. We believe this effect is responsible for the observed experimental performance at m/z = 58. This resolution roll-off is fundamentally present in any coded aperture approach. This current system is a simple test bed; final instrument designs will be optimized so that this roll-off occurs outside the target mass-range of the system. Similar sensitivity improvement to those shown here would be expected for isotopic analysis of elements such as neon, an important historic element  to examine noise-limited performance. This is a topic of ongoing research with double-focusing coded aperture mass spectrometry, but is beyond the scope of the current manuscript, which has concentrated on the first demonstration of 2D coding in mass spectrometry and identification of design factors important for its optimization in future instruments.
We have demonstrated the first application of 2D spatially coded apertures in sector mass spectrometry. The analytes of argon, acetone, and ethanol were detected by using a custom 90-degree magnetic sector mass spectrometer incorporating coded apertures and a 2D detector subsystem. 2D spatially coded spectra were successfully reconstructed by using a mathematical forward model and reconstruction algorithm. The coding concept breaks the trade-off between system throughput and resolution, a critical step in enabling mass spectrometer miniaturization without suffering a loss in performance. The 2D coding demonstrated in this research presents certain challenges in mass spectrometer design, such as the need for large uniform ion flux, sectors with large gaps that still provide good field uniformity, and high resolution 2D detection systems for ion imaging. Furthermore, 2D codes necessarily require some support structures to maintain physical integrity (in contrast to optical spectroscopy), reducing the upper bound on performance gains. While this work is intended as a proof of principle and first demonstration of 2D spatially coded mass spectrometry, future work will directly compare the trade-offs between 1D and 2D coding approaches as applied to mass spectrometry, and demonstrate a system that will address the aforementioned challenges in order to maximize instrument performance and approach the theoretical throughput gain.
This work was performed with partial support of the U.S. Department of Homeland Security Science and Technology Directorate (Contract HSHQDC-11 – C-00082). Initial development of the system algorithms utilized in this research was supported by the National Science Foundation (Grant ECCS-0801942). The authors thank the Shared Materials Instrumentation Facility at Duke and Dr. James (Mitch) Wells for useful discussions.
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