Two-Dimensional Aperture Coding for Magnetic Sector Mass Spectrometry

  • Zachary E. Russell
  • Evan X. Chen
  • Jason J. Amsden
  • Scott D. Wolter
  • Ryan M. Danell
  • Charles B. Parker
  • Brian R. Stoner
  • Michael E. Gehm
  • David J. Brady
  • Jeffrey T. GlassEmail author
Focus: Harsh Environment and Field-Portable Mass Spectrometry: Research Article


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.

Graphical Abstract

Key words

Coded 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 [3]. 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 [4]. 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 [3].

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.


To investigate the concept of 2D aperture coding for magnetic sector mass spectrometry, we developed an instrument consisting of a custom electron ionization (EI) ion source, a permanent magnet magnetic sector with a maximum field of 0.45 T, and a 40 mm diameter 10 μm pitch micro-channel plate (MCP) array imaging ion detector (Figure 1). To allow for larger 2D coded aperture patterns, special design considerations were needed in the ion source, magnetic sector, and detector, which are detailed below.
Figure 1

(a) Schematic of the 90-degree magnetic sector mass spectrometer developed and used in this research. This sector system is composed of an electron-ionization (EI) ion source, a coded aperture, a permanent magnet, and a micro channel plate (MCP) array and phosphor screen detector. The blue, green, and red traces represent ions of three different m/z and the multiple traces at each color correspond to the same m/z ions passing through different openings in the coded aperture [3]. (b) Schematic of the 2D S-Matrix coded apertures of order 7, 11, 15, and corresponding length slits used in this research. (c) Micrographs of the coded apertures used for this work produced using a deep reactive ion etching (DRIE) process

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 [3]. 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 2D coded apertures used in this research were S-Matrix codes with order of 7, 11, and 15 (S-7, S-11, S-15, as shown in Figure 1b and c). The S-Matrix codes were chosen because they are the optimal mask patterns when entries of only 0 and 1 can be used [9] in a multiplexed measurement system where the detected measurement is the mask matrix product with the spectrum. S-Matrix entries are composed of “1”s and “0”s, where “1” refers to a transparent square element that permits ions to pass through and “0” refers to an opaque square element that blocks ions. In optical spectroscopy, 2D coded aperture patterns can be created by exploiting opaque coatings on a clear support. In ion optics applications, a physical mask must consist of a combination of solid and open areas, limiting the physical viability to patterns that have no “floating” solid elements (i.e., all solid elements must have a continuous path to the frame of the aperture). To account for this requirement, we added interstitial supporting structures between the features in both dimensions. The interstitial supports were created with feature sizes identical to that of the open/closed features of the aperture code. With the addition of the interstitial supports, the effective coded aperture matrix is then the Kronecker product of the desired S-Matrix aperture code with a secondary matrix that describes how the features of the code are surrounded by the interstitial supports, as demonstrated by the transformation of an S-3 pattern below
$$ \left[\begin{array}{lll}1\hfill & 0\hfill & 1\hfill \\ {}0\hfill & 1\hfill & 1\hfill \\ {}1\hfill & 1\hfill & 0\hfill \end{array}\right]\otimes \left[\begin{array}{ll}1\hfill & 0\hfill \\ {}0\hfill & 0\hfill \end{array}\right]=\left[\begin{array}{llllll}0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill \\ {}0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 0\hfill & 0\hfill & 1\hfill & 0\hfill & 1\hfill \\ {}0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ {}0\hfill & 1\hfill & 0\hfill & 1\hfill & 0\hfill & 0\hfill \end{array}\right] $$

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 [3].

For notational simplicity, we use α to represent m/z, the ratio of the ion mass (in u) to the net number of elementary charges. The coordinate system used in this derivation defines the x and y coordinates as the non-mass-dispersive direction and the mass-dispersive direction in the detector plane, respectively. The x′ and y′ coordinates are the spatial dimensions of the coded aperture, as shown in Figure 1a. The ion intensity at a point (x,y) on the detector plane, is g(x,y):
$$ g\left(x,y\right)={\displaystyle \int f\left(\alpha \right){\displaystyle \int \kern-0.9em \int \kern-0.4em I\left(x^{\prime },y^{\prime}\right)t\left(x^{\prime },y^{\prime}\right)h\left(x,x^{\prime },y,y^{\prime },\alpha \right)\mathrm{d}x^{\prime}\mathrm{d}y^{\prime}\mathrm{d}\alpha .}} $$
where f(α) is the mass spectrum, I(x ′, y ′) is the ion beam intensity spatial profile at (x ′, y ′) in the coded aperture plane, t(x ′, y ′) ∈ {0, 1} is the coded aperture transmission function describing the shape of the aperture, and h(x, x ′, y, y ′, α) is a kernel describing propagation through the spectrometer for an ion of specific α.
This analytical forward model can then be discretized as:
$$ {g}_i={H}_{i,k}f\left({\alpha}_k\right), $$
with H given by:
$$ {H}_{i,k}={\displaystyle {\int}_{x_i-\varDelta /2}^{x_i+\varDelta /2}{\displaystyle {\int}_{y_i-\varDelta /2}^{y_i+\varDelta /2}{\displaystyle \int \kern-0.9em \int \kern-0.4em I\left(x^{\prime },y^{\prime}\right)t\left(x^{\prime },y^{\prime}\right)h\left(x,x^{\prime },y,y^{\prime },{\alpha}_k\right)\mathrm{d}x^{\prime}\mathrm{d}y^{\prime}\mathrm{d}y\mathrm{d}x,}}} $$
where ∆ is pixel sampling pitch size, i is the pixel index, and k is the mass spectrum discretization index. This allows expressing the discrete forward model as the linear system:
$$ g=Hf. $$

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.

There is always randomness or noise associated with measurements, and our actual detector measurements are approximated by the Poisson process:
$$ g\sim Poisson(Hf). $$
The conditional probability of observing a particular set of measurements g, given a specific input f, and forward matrix H, is known as the likelihood function [14], and for Equation (6) can be written as the following:
$$ P\left(\left.g\right|Hf\right)={\displaystyle \prod_{i=1}^M\frac{ \exp \left(-{e}_i^THf\right){\left({e}_i^THf\right)}^{g_i}}{g_i!}}. $$
Where e i is the i th canonical basis unit vector, e i T Hf refers to the n th index of vector Hf, and M is the dimension of g. Our inversion will find the f that maximizes the above conditional probability—that is, the most likely f given the observed measurement. This method is known as maximum likelihood estimation (MLE) [14], and the estimate can be written as:
$$ \widehat{f}\equiv \arg\;\min {}_{\tilde{f}}\left(- \log\;P\left(\left.g\right|Hf\right)\right). $$

This solution can be obtained using an iterative deconvolution method such as that described in reference [15].

Forward Model Calibration

Calibration of the forward model is needed to ensure that the forward matrix H can accurately match the experimental measurements. We followed the same calibration procedure as described in [3]. The empirical propagation kernel is
$$ h\left(x,x^{\prime },y,\mathrm{y}^{\prime },\alpha \right)\approx \delta \left(x-\left(1+{M}_x{\alpha}^{1/4}\right)x^{\prime },y-\sqrt{\frac{\sqrt{8U\alpha \left(u/e\right)}}{B}y^{\prime }-y{\prime}^2}\right), $$
where x − (1 + M x α 1/4)x ′ describes the ion propagation in the x-direction and the additional M x α 1/4 term is used to account for non-ideality of magnetic field and a small cone beam ion source, and
$$ y-\sqrt{\frac{\sqrt{8U\alpha \left(u/e\right)}}{B}y^{\prime }-y{\prime}^2} $$

describes the ion propagation in the y-direction, which is determined by the geometry of the 90-degree sector system.

Figure 2a and b show examples of the spatial pattern produced at the detector for argon gas with slit and S-Matrix codes. There are two main features in the argon data resulting from singly- and doubly ionized argon at m/z = 40 and 20, respectively. It is worth noting that the images from the 2D S-Matrix measurements exhibit a keystone shape, whereas the physical coded aperture is rectangular. As the physical aperture length increases with the increasing S-Matrix order complexity, the keystone shape feature is more obvious. We attribute this shape to the non-uniform magnetic field. Ions that pass through different parts of the coded aperture encounter slightly different B fields. Figure 2c illustrates the reconstructed mass spectra of argon for the Slit-3 and 2D S-15 apertures. We observe that all the reconstructed argon data conform to expected argon spectra, indicating that the reconstruction was successful.
Figure 2

Detected images and reconstructed mass spectra of argon used in the forward model calibration. (a) The detected image of argon for Slit-3. (b) The detected image of argon for S-Matrix coded aperture with order of 15. (c) The reconstructed argon mass spectra for the Slit-3 and 2D S-15 Matrix coded apertures, where the mass spectra are normalized such that the Slit-3 argon m/z = 40 peak has an intensity of 1 unit, and the S-15 argon spectrum is shifted up by 0.5 relative intensity units

Results and Discussion

The unprocessed measurement images of all the slits and 2D S-Matrix coded apertures are shown in Figure 3a–f for acetone and Figure 4a–f for ethanol. All the measurements in Figures 3 and 4 were taken at 10 μTorr with a system base pressure of 0.5 μTorr. From the unprocessed images, we observe that there is greater pattern distortion (more obvious curvature of the slit, more obvious curvature, and keystone effect for the 2D coded aperture) associated with the longer slit and higher order codes. We believe that the curvature and keystone shape distortions are caused by a combination of ion beam angular dispersion and spatially variant imperfections in the magnetic field. When measuring complex mass spectra gases, the coded sector system provides multiplex measurements. Figures 3b, d, f and 4b, d, f illustrate the complexity of the collected S-15 aperture data prior to reconstruction resulting from the distorted aperture pattern convoluted with the analyte mass spectrum.
Figure 3

Detected images and reconstructed mass spectra of acetone. (a), (c), and (e) are the detected images of acetone for Slit-1, Slit-2, and Slit-3. (b), (d), and (f) are the detected images of acetone for S-Matrix coded aperture with order of 7, 11, and 15. (g) The reconstructed acetone mass spectra for all the slits and 2D S-Matrix coded apertures, where the mass spectra are normalized such that for each pair the slit acetone m/z = 43 peak has an intensity of 1 unit

Figure 4

Detected images and reconstructed mass spectra of ethanol. (a), (c), and (e) are the detected images of ethanol for Slit-1, Slit-2, and Slit-3. (b), (d), and (f) are the detected images of ethanol for S-Matrix coded aperture with order of 7, 11, and 15. (g) The reconstructed ethanol mass spectra for all the slits and 2D S-Matrix coded apertures, where the mass spectra are normalized such that for each pair the slit ethanol m/z = 31 peak has an intensity of 1 unit

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.

A comparison of the experimentally realized throughput gain with expected theoretical gain is plotted in Figure 5. The expected theoretical throughput gain is calculated by computing the ratio of the fabricated 2D S-matrix coded aperture open area and the corresponding slit open area. The experimental throughput gain is computed by finding the ratio of the area under the strongest reconstructed mass peak for each analyte and aperture order to that of the area of the same peak for the corresponding slit. The throughput statistics shown in Figure 5 were obtained from five measurements from each of the three analytes at four pressures from 2.5 to 10 μTorr. For lower order 2D S-Matrix coded apertures, the experimental throughput gain follows the expected theoretical gain trend closely. However, the 2D S-15 code falls short slightly, where an experimental gain is 3.5 compared with a theoretical gain of 4. The difference is likely due to spatial non-uniformities in the ion beam profile over the larger 2D S-15 aperture plane.
Figure 5

Plot of the average throughput gain for 2D S-Matrix coded apertures over all pressures and analytes versus coded aperture order

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.

The detailed ethanol and acetone reconstructed mass spectra are shown in Figure 6a and b, respectively. A comparison between an S-15 coded aperture and a Slit-3 aperture are shown in each graph. The peak ratios illustrate a 3.5× throughput gain from the S-15 coded apertures. The coded instrument resolutions shown in the insets of each graph are much higher than would be observed for a single slit with a 3.5× increase in throughput. Increasing throughput by 3.5× in a simple slit instrument would introduce a corresponding loss in resolution of 3.5× compared with the observed 1.3× (i.e., 0.51/0.40) and 1.4× (i.e., 0.32/0.23) loss in the coded instrument from acetone and ethanol, respectively. This demonstrates that the historic trade-off between throughput and resolution has been largely, although not entirely, overcome in a 2D coded instrument. We attribute this minor resolution degradation in the coded instrument to poor stigmatic imaging properties of this particular sector instrument, compounded by the fact that the large spatial extent of the 2D coded patterns increases the likelihood that ions will interact with fringing fields and other non-uniformities. Experimental designs using sectors with better stigmatic imaging properties should reduce this discrepancy and will be a topic of future development.
Figure 6

Slit-3 and 2D S-15 mass spectra reconstruction comparison for acetone in (a) and ethanol in (b), where the Slit-3 reconstructed acetone and ethanol mass spectra are normalized such that the maximum peak has an intensity of 1 unit and the normalized S-15 reconstructed acetone and ethanol mass spectra are shifted up by 0.5 relative intensity unit. NIST standard EI spectra are also shown for reference [16]. Insets shown are of the primary peaks of the spectra, demonstrating the change in resolution corresponding to the intensity gain

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 [17] 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.


  1. 1.
    Badman, E.R., Cooks, R.G.: Miniature mass analyzers. J. Mass Spectrom. 35(6), 659–671 (2000)CrossRefGoogle Scholar
  2. 2.
    Ouyang, Z., Cooks, R.G.: Miniature Mass Spectrometers. Annu. Rev. Anal. Chem. 2(1), 187–214 (2009)CrossRefGoogle Scholar
  3. 3.
    Chen, E.X., Russell, Z.E., Amsden, J.J., Wolter, S.D., Danell, R.M., Parker, C.B., Stoner, B.R., Gehm, M.E., Glass, J.T., Brady, D.J.: Order-of-magnitude signal gain in magnetic sector mass spectrometry via aperture coding. Submitted for publication (2014)Google Scholar
  4. 4.
    Brady, D.J.: Optical imaging and spectroscopy, pp. 333–486. John Wiley and Sons, Hoboken NJ (2009)Google Scholar
  5. 5.
    Wagadarikar, A., John, R., Willett, R., Brady, D.: Single disperser design for coded aperture snapshot spectral imaging. Appl. Opt. 47(10), B44–B51 (2008)CrossRefGoogle Scholar
  6. 6.
    Gehm, M., John, R., Brady, D., Willett, R., Schulz, T.: Single-shot compressive spectral imaging with a dual-disperser architecture. Opt. Express 15(21), 14013–14027 (2007)CrossRefGoogle Scholar
  7. 7.
    MacCabe, K., Krishnamurthy, K., Chawla, A., Marks, D., Samei, E., Brady, D.: Pencil beam coded aperture X-ray scatter imaging. Opt. Express 20(15), 16310–16320 (2012)CrossRefGoogle Scholar
  8. 8.
    Greenberg, J.A., Krishnamurthy, K., Brady, D.: Snapshot molecular imaging using coded energy-sensitive detection. Opt. Express 21(21), 25480–25491 (2013)CrossRefGoogle Scholar
  9. 9.
    Harwit, M.: Hadamard transform optics. Academic Press, (1979)Google Scholar
  10. 10.
    Mende, S.B., Claflin, E.S., Rairden, R.L., Swenson, G.R.: Hadamard spectroscopy with a two-dimensional detecting array. Appl. Opt. 32(34), 7095–7105 (1993)CrossRefGoogle Scholar
  11. 11.
    McCain, S.T., Gehm, M.E., Wang, Y., Pitsianis, N.P., Brady, D.J.: Coded aperture raman spectroscopy for quantitative measurements of ethanol in a tissue phantom. Appl. Spectrosc. 60(6), 663–671 (2006)CrossRefGoogle Scholar
  12. 12.
    Gehm, M.E., McCain, S.T., Pitsianis, N.P., Brady, D.J., Potuluri, P., Sullivan, M.E.: Static two-dimensional aperture coding for multimodal, multiplex spectroscopy. Appl. Opt. 45(13), 2965–2974 (2006)CrossRefGoogle Scholar
  13. 13.
    Wagadarikar, A.A., Gehm, M.E., Brady, D.J.: Performance comparison of aperture codes for multimodal, multiplex spectroscopy. Appl. Opt. 46(22), 4932–4942 (2007)CrossRefGoogle Scholar
  14. 14.
    Kay, S.: Fundamentals of statistical signal processing : estimation theory. Prentice-Hall PTR, Upper Saddle River NJ, pp. 157–198 (2010)Google Scholar
  15. 15.
    Richardson, W.H.: Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62(1), 55–59 (1972)CrossRefGoogle Scholar
  16. 16.
    Linstrom, P.J., Mallard, W.G. (eds.): NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD, 20899. Retrieved 1 June 2014
  17. 17.
    Aston, F.W.: XLIV. The constitution of atmospheric neon. Lond. Edinb. Dublin Philos. Mag. J. Sci. 39(232), 449–455 (1920)CrossRefGoogle Scholar

Copyright information

© American Society for Mass Spectrometry 2015

Authors and Affiliations

  • Zachary E. Russell
    • 1
  • Evan X. Chen
    • 1
  • Jason J. Amsden
    • 1
  • Scott D. Wolter
    • 1
    • 2
  • Ryan M. Danell
    • 3
  • Charles B. Parker
    • 1
  • Brian R. Stoner
    • 4
  • Michael E. Gehm
    • 1
  • David J. Brady
    • 1
  • Jeffrey T. Glass
    • 1
    Email author
  1. 1.Department of Electrical and Computer EngineeringDuke UniversityDurhamUSA
  2. 2.Department of PhysicsElon UniversityElonUSA
  3. 3.Danell ConsultingGreenvilleUSA
  4. 4.Discovery-Science-Technology DivisionRTI InternationalResearch Triangle ParkUSA

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