Inverse Design Tool for Ion Optical Devices using the Adjoint Variable Method.

We present a computer-aided design tool for ion optical devices using the adjoint variable method. Numerical methods have been essential for the development of ion optical devices such as electron microscopes and mass spectrometers. Yet, the detailed computational analysis and optimization of ion optical devices is still onerous, since the governing equations of charged particle optics cannot be solved in closed form. Here, we show how to employ the adjoint variable method on the finite-element method and Störmer-Verlet method for electrostatic charged particle devices. This method allows for a full sensitivity analysis of ion optical devices, providing a quantitative measure of the effects of design parameters to device performance, at near constant computational cost with respect to the number of parameters. To demonstrate this, we perform such a sensitivity analysis for different freeform N-element Einzel lens systems including designs with over 13,000 parameters. We further show the optimization of the spot size of such lenses using a gradient-based method in combination with the adjoint variable method. The computational efficiency of the method facilitates the optimization of shapes and applied voltages of all surfaces of the device.

Effects of Magnetic and Electric Field Uniformity on Coded Aperture Imaging Quality in a Cycloidal Mass Analyzer.

Cycloidal mass analyzers are unique sector mass analyzers as they exhibit perfect double focusing, making them ideal for incorporating spatial aperture coding, which can increase the throughput of a mass analyzer without affecting the resolving power. However, the focusing properties of the cycloidal mass analyzer depend on the uniformity of the electric and magnetic fields. In this paper, finite element simulation and charged particle tracing were used to investigate the effect of field uniformity on imaging performance of a cycloidal mass analyzer. For the magnetic field, we evaluate a new permanent magnet geometry by comparing it to a traditional geometry. Results indicate that creating an aperture image in a cycloidal mass spectrometer with the same FWHM as the slit requires less than 1% variation in magnetic field strength along the ion trajectories. The new magnet design, called the opposed dipole magnet, has less than 1% field variation over an area approximately 62 × 65 mm; nearly twice the area available in a traditional design of similar size and weight. This allows ion imaging across larger detector arrays without loss of resolving power. In addition, we compare the aperture imaging quality of a traditionally used cycloidal mass spectrometer electric design with a new optimized design with improved field uniformity. Graphical abstract ᅟ.

Proof of Concept Coded Aperture Miniature Mass Spectrometer Using a Cycloidal Sector Mass Analyzer, a Carbon Nanotube (CNT) Field Emission Electron Ionization Source, and an Array Detector.

Despite many potential applications, miniature mass spectrometers have had limited adoption in the field due to the tradeoff between throughput and resolution that limits their performance relative to laboratory instruments. Recently, a solution to this tradeoff has been demonstrated by using spatially coded apertures in magnetic sector mass spectrometers, enabling throughput and signal-to-background improvements of greater than an order of magnitude with no loss of resolution. This paper describes a proof of concept demonstration of a cycloidal coded aperture miniature mass spectrometer (C-CAMMS) demonstrating use of spatially coded apertures in a cycloidal sector mass analyzer for the first time. C-CAMMS also incorporates a miniature carbon nanotube (CNT) field emission electron ionization source and a capacitive transimpedance amplifier (CTIA) ion array detector. Results confirm the cycloidal mass analyzer's compatibility with aperture coding. A >10× increase in throughput was achieved without loss of resolution compared with a single slit instrument. Several areas where additional improvement can be realized are identified. Graphical Abstract ᅟ.

Coded Apertures in Mass Spectrometry.

The use of coded apertures in mass spectrometry can break the trade-off between throughput and resolution that has historically plagued conventional instruments. Despite their very early stage of development, coded apertures have been shown to increase throughput by more than one order of magnitude, with no loss in resolution in a simple 90-degree magnetic sector. This enhanced throughput can increase the signal level with respect to the underlying noise, thereby significantly improving sensitivity to low concentrations of analyte. Simultaneous resolution can be maintained, preventing any decrease in selectivity. Both one- and two-dimensional (2D) codes have been demonstrated. A 2D code can provide increased measurement diversity and therefore improved numerical conditioning of the mass spectrum that is reconstructed from the coded signal. This review discusses the state of development, the applications where coding is expected to provide added value, and the various instrument modifications necessary to implement coded apertures in mass spectrometers.

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

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.

Order of Magnitude Signal Gain in Magnetic Sector Mass Spectrometry Via Aperture Coding.

Miniaturizing instruments for spectroscopic applications requires the designer to confront a tradeoff between instrument resolution and instrument throughput [and associated signal-to-background-ratio (SBR)]. This work demonstrates a solution to this tradeoff in sector mass spectrometry by the first application of one-dimensional (1D) spatially coded apertures, similar to those previously demonstrated in optics. This was accomplished by replacing the input slit of a simple 90° magnetic sector mass spectrometer with a specifically designed coded aperture, deriving the corresponding forward mathematical model and spectral reconstruction algorithm, and then utilizing the resulting system to measure and reconstruct the mass spectra of argon, acetone, and ethanol. We expect the application of coded apertures to sector instrument designs will lead to miniature mass spectrometers that maintain the high performance of larger instruments, enabling field detection of trace chemicals and point-of-use mass spectrometry.

Two-dimensional aperture coding for magnetic sector mass spectrometry.

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.