# Compatibility of Spatially Coded Apertures with a Miniature Mattauch-Herzog Mass Spectrograph

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## Abstract

In order to minimize losses in signal intensity often present in mass spectrometry miniaturization efforts, we recently applied the principles of spatially coded apertures to magnetic sector mass spectrometry, thereby achieving increases in signal intensity of greater than 10× with no loss in mass resolution Chen et al. (J. Am. Soc. Mass Spectrom. **26**, 1633–1640, 2015), Russell et al. (J. Am. Soc. Mass Spectrom. **26**, 248–256, 2015). In this work, we simulate theoretical compatibility and demonstrate preliminary experimental compatibility of the Mattauch-Herzog mass spectrograph geometry with spatial coding. For the simulation-based theoretical assessment, COMSOL Multiphysics finite element solvers were used to simulate electric and magnetic fields, and a custom particle tracing routine was written in C# that allowed for calculations of more than 15 million particle trajectory time steps per second. Preliminary experimental results demonstrating compatibility of spatial coding with the Mattauch-Herzog geometry were obtained using a commercial miniature mass spectrograph from OI Analytical/Xylem.

## Keywords

Magnetic Sector Coded aperture Miniature mass spectrometer Charged particle optics Mattauch-Herzog## Introduction

Mass spectrometers are the gold standard for chemical detection and identification. Sector mass spectrometers in particular are noted for high performance in figures of merit such as mass resolution and detection limit [3, 4]. To achieve such high performance, sector instruments are historically quite large and expensive [5]. Miniaturization of these instruments is useful for the following evolving fields: (1) trace explosive detection and airport security [6, 7], (2) space exploration [8, 9, 10], (3) environmental monitoring [11, 12], and (4) point-of-care medical applications [13, 14]. Several groups have demonstrated examples of miniaturized mass spectrometers [15, 16, 17]. When miniaturized, these instruments suffer from performance loss in either resolution or signal intensity compared with their full-scale counterparts [18].

Spatially coded apertures have been studied extensively in optical spectroscopy [19] and shown to provide dramatic improvements in performance, such as increasing signal intensity. Spatial coding techniques were proposed as early as 1970 for mass spectrometry [20] but, to our knowledge, have only recently been demonstrated [1, 2]. The object slit aperture in a simple 90° magnetic sector mass spectrograph similar to Aston’s original instrument [21] was replaced with a patterned array of spatially distributed slits. The resulting patterned spectra recorded on an imaging ion detector were reconstructed into traditional mass spectra, demonstrating an increase in signal intensity of more than 10× for a 1D arrays of slits and 3.5× for a 2D array of slits, with no observable loss of resolution [1, 2]. The patterns for these codes were derived from a binary Hadamard code called an S-matrix [22]. The intensity of a spatially coded mass spectrum increases with the order of the coded aperture. Since the increase in signal intensity is proportional to the total open area of a code and the code is roughly 50% opaque, the expected gain of a coded system is (N + 1)/2, where N is the order of the coded pattern used. This relationship is described in [1]. Note that the intensity or throughput of the coded spectrum is proportional to the total open area of the pattern, but the resolution is defined by the smallest feature of the code [23].

Important Geometric Parameters for the Mattauch-Herzog Geometry. Ideal Theoretical Values are Those Inherent to the Mattauch-Herzog Geometry [24]

Symbol | Geometric dimension | Ideal theoretical value | Experimental value |
---|---|---|---|

| Aperture to E-sector distance | | 35.35 mm |

| Electric sector centerline radius | \( \sqrt{2}{L}_1 \) | 50 mm |

| E-sector to magnet distance | | 20 mm |

| Magnet to sensor distance | 0 | 1 mm |

| Ion radius in magnetic sector | \( \frac{1}{B}\sqrt{\frac{2Vm}{q}} \) | 25.75 mm |

| Geometric angle of electric sector | \( \frac{\pi }{4\sqrt{2}} \) | 31.8° |

| Angle ions travel in magnetic sector | \( \frac{\pi }{2} \) | \( \frac{\pi }{2} \) |

| Magnetic sector entrance angle | 0 | 0 |

| Magnetic sector exit angle | \( -\frac{\pi }{4} \) | \( -\frac{\pi }{4} \) |

| Magnetic field Strength | B | 1.05 T |

| Ion accelerating potential | V | 800 V |

## Simulation of Spatial Aperture Coding in the Mattauch-Herzog Geometry

In this section, we report on methods the two approaches used to simulate spatial coding in a Mattauch-Herzog mass spectrometer. Initial efforts focused on simulations to ensure no fundamental issues existed that inhibited the use of spatial codes in the Mattauch-Herzog geometry and determine potential performance improvements. Transfer matrix calculations were used to determine initial compatibility. For an ideal system, a high fidelity particle tracing simulation method was then used to obtain a more realistic compatibility simulated performance and estimate. In the following section, experimental verification of compatibility was performed using the miniature Mattauch-Herzog mass spectrograph shown in Figure 1 (OI Analytical, a Xylem brand, College Station TX).

## Geometric Optics Transfer Matrix Calculation

In order to validate compatibility of this geometry with spatially coded apertures, first order transfer matrix optics calculations were used as an initial model [27]. In the geometric optics approximation, ions are characterized by their positions relative to the optical axis, their angle relative to the optical axis, their energy, and their mass. By successive matrix multiplication (each matrix representing an optical element [19, 28, 29, 30]), ions are passed through the system.

*x*

_{ i },

*a*

_{ i }, energy dispersion ∂

*E*

_{ i }, and mass dispersion ∂

*M*

_{ i }. The [4 × 4] element representing the spectrometer can be constructed by the multiplication of each discrete lens element in the systems transfer matrix. The MHMS geometry shown in Figure 1 consists of the lens combination shown in Eq. (2), where the individual matrices’ meanings are defined in Table 2 and their content is defined in Burgoyne [27].

Meanings of the Transfer Matrix Symbols. The Content of the Transfer Matrices can be Found in [27]. Each Matrix on the Right Hand Side Represents a System Component or Feature

Matrix symbol | Meaning |
---|---|

[ | Drift length 1 |

[ | Sense matrix |

[ | Electric sector |

[ | Drift length 2 |

[ | Magnet entrance angle |

[ | Magnetic sector |

[ | Magnet exit angle |

[ | Drift length 3 |

The matrix algebra and accompanying linearization of the transfer function of the Mattauch-Herzog mass spectrograph do not take into account the fringing fields of the sectors, although there are methods for accounting for fringing fields with an additional lens element [29]. Further, the matrix method is a linear approximation that is not valid for large spatial distributions of ions that are far from the optical axis of the system. Thus, the second method using COMSOL for high fidelity field calculations and a C# program for particle tracing was used to address these limitations.

## Particle Tracing Using COMSOL and C#

^{6}time steps along each ion trajectory. This simulation fidelity is 100× higher than the best we could achieve using the COMSOL particle tracing module on the same workstation, and produced particle trajectories and resulting histogram patterns with much less discretization errors. This approach is limited in that it requires a substantial amount of random access memory to execute with appropriate fidelity, but working in 2D instead of 3D reduces that burden substantially. Note that the magnetic field model requires a 3D simulation to take into account the fringing fields and the effect of the yoke on the fields, so these field calculations were performed in 3D, and then a 2D slice along the midplane of the 3D field profile was exported to the particle trajectory solver. Values of

*E*

_{ x },

*E*

_{ y }, and

*B*

_{ z }along the midplane of the simulation were recorded with a spatial resolution of 15 μm for use in the particle tracing and are displayed in Figure 4a and b, along with some characteristic particle trajectories from the simulation platform shown in Figure 4c.

## Experimental Verification of Spatial Aperture Coding in the Mattauch-Herzog Geometry

Experimental validation of the compatibility of spatial aperture coding with the Mattauch-Herzog geometry is demonstrated here using the commercially available OI Analytical/Xylem IonCam Transportable Mass Spectrometer miniature Mattauch-Herzog mass spectrograph (OI Analytical, a Xylem brand, College Station TX, USA). The mass resolution for this spectrograph is cited as 24 at 6 *m/z* and 250 at 250 *m/z* [34]. The ion source for this system is a dual tungsten filament Nier-type [35] electron ionization source. The stock object slit in the system was replaced by a microfabricated spatially coded aperture (such as those described in [1, 2]) with minimum slit width of 100 μm. Although the simulations presented in this work show promising results for apertures up to order S-23, the dimensions of the electric sector gap in the mass spectrograph used here allowed apertures only as large as an S-7 aperture pattern (with expected improvement in signal intensity of 4×).

## Conclusions

We have demonstrated the first application of spatial aperture coding to the Mattauch-Herzog mass spectrograph through (1) first principles transfer matrix calculations, (2) high fidelity particle tracing, and (3) experimentally using a commercially available miniature Mattauch-Herzog mass spectrograph. The first principles transfer matrix approach showed exceptional pattern mapping and indicated compatibility of this instrument geometry with spatial aperture coding. The high fidelity particle tracing method verified the results of the transfer matrix method, and indicated a non-uniform distortion of larger spatially distributed patterns because of off-axis effects that can be improved upon by new sector designs in future work. The simulations of the MHMS geometry indicate that close to the theoretical throughput of coded apertures up to order S-23 would be expected with a system designed to accept the dimensions of these codes. This compares favorably with the experimental results obtained from the simple magnetic sector published previously [1, 2]. An S-7 aperture was successfully imaged experimentally on a commercially available miniature MHMS. However, spectral reconstruction was not possible because of aberrations in the image that are a result of the experimental apparatus not being optimized for coded apertures. Based on the simulation results and successful imaging of a coded aperture experimentally, the MHMS is expected to provide improved throughput and resolution compared with the magnetic sector in [1, 2] attributable to the minimization of dispersions in the ion energy and angles, but this will not be demonstrable until an experimental system with the geometric modifications are available for an MHMS geometry as described in the experimental verification section. New sector designs that improve the image transfer of the spatially coded apertures along the mass dispersive dimension of this geometry to correct for these distortions will be the subject of future work. The order of magnitude gains in signal intensity shown in the transfer matrix and high fidelity particle tracing simulations are expected to be obtainable experimentally after hardware modifications that increase the electric sector gap. This work describes the application of coded aperture mass spectrometry to a double-focusing instrument, the Mattauch-Herzog. By increasing the sensitivity for a given resolution through the use of coded apertures, the MHMS is expected to become viable for miniaturized applications.

## Notes

### Acknowledgments

The authors acknowledge that this work was sponsored in part by a contract with the Department of Homeland Security Science and Technology Directorate.

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