Transcript of Coded Apertures in Mass Spectrometry
Coded Apertures in Mass SpectrometryAC10CH07-Glass ARI 9 May 2017
10:26
Coded Apertures in Mass Spectrometry Jason J. Amsden,1 Michael E.
Gehm,1
Zachary E. Russell,2 Evan X. Chen,1
Shane T. Di Dona,1 Scott D. Wolter,3
Ryan M. Danell,4 Gottfried Kibelka,5
Charles B. Parker,1 Brian R. Stoner,1,6
David J. Brady,1 and Jeffrey T. Glass1
1Department of Electrical and Computer Engineering, Duke
University, Durham, North Carolina 27708; email:
jeff.glass@duke.edu 2Ion Innovations, Roswell, Georgia 30075
3Department of Physics, Elon University, Elon, North Carolina 27278
4Danell Consulting, Winterville, North Carolina 28590 5CMS Field
Products, OI Analytical, Pelham, Alabama 35124 6Discovery Science
and Technology, RTI International, Research Triangle Park, North
Carolina 27709
Annu. Rev. Anal. Chem. 2017. 10:141–56
First published as a Review in Advance on March 6, 2017
The Annual Review of Analytical Chemistry is online at
anchem.annualreviews.org
https://doi.org/10.1146/annurev-anchem- 061516-045256
Keywords
Abstract
The use of coded apertures in mass spectrometry can break the
trade-off be- tween 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 magni- tude, with no loss in resolution
in a simple 90-degree magnetic sector. This enhanced throughput can
increase the signal level with respect to the under- lying noise,
thereby significantly improving sensitivity to low concentrations
of analyte. Simultaneous resolution can be maintained, preventing
any de- crease 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 re- constructed from the coded signal.
This review discusses the state of develop- ment, the applications
where coding is expected to provide added value, and the various
instrument modifications necessary to implement coded aper- tures
in mass spectrometers.
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1. INTRODUCTION
Advances in the performance of computing hardware have transformed
the field of sensors and an- alytical instrumentation design.
Semiconductor processing [i.e., Moore’s Law (1, 2)] and materials
chemistry innovations (3, 4) have permitted dramatic increases in
transistor speed. The resulting increases in computing power have
enabled a paradigm shift in how sensors and analytical in-
struments are designed and operated. This new approach is referred
to as computational sensing and integrates hardware and software
design to optimize application-specific sensor performance. This is
in direct contrast to the more familiar historical approach to
sensing that attempts to adapt existing technology from a
traditional application to a new area (e.g., adapting mass
spectrom- eters in analytical chemistry labs to allow trace
explosive detection in the field). Computational sensing includes a
“front-end” rethinking of sensor design utilizing a mathematical
representa- tion of the sensing process as well as “back-end”
signal processing that more efficiently achieves desired
performance from limited data. As such, computational sensing
includes enhancements to a broad array of sensing modalities,
technologies, and environments. For example, compressive sensing
theory (5–9, 10) is the realization that natural signals contain
correlations that render full sampling redundant and allow signal
recovery from undersampled measurement; adaptive sensing theory
(11–15) is the concept that the optimal approach to measurement is
adjusting the physical measurement being made as the instrument
learns about the sample. Numerous instantiations of these and
related techniques and tools have been demonstrated, including the
single-pixel camera (16), the coded aperture snapshot spectral
imager (17, 18), the coded aperture compressive tempo- ral imager
(19), compressive magnetic resonance imaging (20), compressive
holography (21, 22), compressive X-ray tomography (23, 24), ion
trap multiresonant frequency excitation (25), pseu- dorandom mass
spectrometers or monochromators (26), and coded aperture mass
spectrometry (MS) (27–30); the last technique is the topic of this
review.
This review focuses on recent progress in the theory and
experimental demonstration of spatial coding (i.e., coded
apertures) in MS. To provide the most timely and informative
review, we do not attempt to cover temporal coding in MS and
instead refer the reader to several relevant publications (25,
31–33). This limitation in scope further implies that the review
focuses on sector- based mass spectrometers, as such instruments
are the most appropriate for the implementation of spatial coding.
We begin with a general introduction of aperture coding, discuss
where coding is useful, and provide some historical context. We
then discuss the mathematical basis for spatial coding and the
reconstruction of spectra from the coded signals. Next, recent
simulations and experimental results in three geometries are
reviewed: a simple 90-degree magnetic sector, a Mattauch-Herzog
mass spectrometer, and a cycloidal mass analyzer. The review also
examines the subsystem requirements when coding is utilized, and in
particular, the geometric constraints that coding places on the
system. Finally, we discuss the conditions under which spatial
coding can be expected to significantly improve mass spectrometer
performance, and thus, by implication, this also covers the
limitations of coding.
1.1. What Is Aperture Coding?
Conventional instruments, such as optical spectrometers and mass
spectrometers, essentially act as sorters. Inputs such as ions or
photons are sorted spatially, temporally, or both via a system
architecture that uses relevant physics. Examples of spatially
sorting system architectures include diffraction gratings in optics
and sector and distance-of-flight mass analyzers in MS. Examples of
temporally sorting system architectures include time-of-flight and
ion trap mass analyzers. Figure 1 compares three different system
architectures that, using relevant physics, implement no sorting
(Figure 1a), near-perfect sorting (Figure 1b), and coded sorting
(Figure 1c). In the
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absence of sorting, the system throughput is large. However, no
information can be inferred about the system input (Figure 1d ). In
perfect sorting, the system architecture is designed using relevant
physics to implement near-perfect sorting. The spectrum can be
directly inferred through a simple calibration of the sorting
parameter (Figure 1e). However, the architecture choices necessary
to achieve near-perfect sorting limit the system performance
because the majority of the system input is lost in the sorting
process. In the coded sorting case, the system architecture still
sorts but under the realization that near-perfect sorting is not
necessary. There is a vast continuum between no sorting and
near-perfect sorting. With appropriately structured sorting, the
ability to infer the spectrum is maintained through a computational
inference but without the performance-crippling architectural
choices required for near-perfect sorting (Figure 1f ).
Figure 1g–i show examples of a simple magnetic sector mass analyzer
with a multichannel position-sensitive imaging array detector with
architecture choices to implement various degrees of sorting. In
the sector with no sorting, the ions are introduced into a region
of uniform magnetic field and travel along curved trajectories to
the detector. However, their position at the detector plane is
random and unsorted (Figure 1g). As such, it is not possible to
extract a spectrum from the detector response. In the sector
implementing near-perfect sorting, a narrow slit is used to
localize where the ions enter the magnetic field region, and an
acceleration grid constrains the energy of the ions. The position
on the detector now depends primarily on the mass-to-charge ratio
(m/z), and a spectrum can be directly inferred from the spatial
distribution of the detector response (Figure 1h). The resolution
is inversely proportional to the slit size, whereas the throughput
is directly proportional to the slit size, thereby introducing a
performance-limiting throughput versus resolution trade-off. In the
coded sector, the slit is replaced with an array of slits of
different sizes called a coded aperture. The position in the
detector plane now jointly depends on the m/z and the specific
pattern of slits (Figure 1i ). The spectrum can be computationally
inferred from the spatial distribution of the detector response.
The resolution depends on the smallest feature size, and the
throughput depends on the open area, thus breaking the throughput
versus resolution trade-off and enhancing performance. In this
example, the throughput increases threefold, as shown by three
times as many circles of each color in the coded sorting (for the
same acquisition time) leading to a threefold increase in signal
intensity and associated signal-to-background ratio (SBR) after
spectral reconstruction.
1.2. How Does Coding Improve Performance?
Several potential gains can accrue from coded aperture MS, arising
primarily from two factors: the Jacquinot (or open area) advantage
(34) and the Fellgett (or multiplex) advantage (35). The Jacquinot
advantage occurs because coding allows for maximizing spectrometer
throughput with- out sacrificing spectral resolution. The potential
benefit to the system designer depends on the specific application
but can include the following: system size reduction without a
concomitant performance decrease, system performance increase
without concomitant system size increase, relaxed ion-source design
complexity, and operation in situations with extremely limited
analyte quantity. The Fellgett advantage occurs because coded
instruments combine multiple signal el- ements together upon
transduction. For the case of additive noise, this increases the
signal level with respect to the underlying noise (i.e., increases
the signal-to-noise ratio, SNR) and therefore reduces the error of
the estimated spectrum.
If the system is shot-noise limited, however, the situation is more
complicated. Speaking gen- erally, multiplexing has no impact on
the mean error level of the estimated spectrum. However, there is
an interesting interplay with the concept of transform noise
discussed below. When the signal of interest is sparse (it occupies
only a small fraction of the total spectral channels) and
also
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stronger than the background, then multiplexing concentrates error
in the channels outside the channels of interest. As the mean level
of error is unchanged, this implies that the error in the channels
of interest must necessarily have subshot-noise–level error.
1.3. History and Progress
The first efforts in coded aperture spectroscopy arose in infrared
spectroscopy, specifically in the work of Golay in the 1950s (36,
37), and it developed rapidly (38). Eventually, the mathemati- cal
benefits of Hadamard matrix (39)-based codings were understood, and
most coded aperture spectroscopy became based upon these methods
(40–44), with development continuing over the years (45–48). Many
of the early approaches had only a single detector element [or
limited one- dimensional (1D) arrays of detectors], and as such,
required coding apertures on the input and output planes to operate
(they frequently required physical motion of one or both
apertures). An
Sorting parameter (time, position, etc.)
Co un
Co un
Co un
System input
System input
System input
a b c
d e f
g h i
Physics and system architecturePhysics and system architecture
Physics and system architecturePhysics and system
architecture
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additional impact of this limitation was that most of the systems
only achieved either the Jacquinot or Fellgett advantage but not
both. Roughly a decade ago, the availability of large detector
arrays led to the development of a fully static, single-mask
aperture coding approach that achieved both the Jacquinot and
Fellgett advantages (49).
These developments did not go unobserved in the MS community (50),
but the need for dynamic actuation of the aperture codes reduced
interest and limited the application of coding ideas to
time-of-flight spectroscopy (31, 51, 52) until recently (27–30).
These recent demonstrations of spatial coding covered in this
review are based on the static coding described in the paper by
Gehm et al. (49).
2. THE MATHEMATICS OF CODING IN MASS SPECTROMETRY
The mathematical treatment of aperture coding in MS involves the
development of a matrix equation that relates the vector of
acquired measurements, g, to the vector representing the input mass
spectrum, S:
g = HS+ n. 1.
Here, H is the system matrix or measurement matrix that
incorporates a forward model of the physics and architecture of the
measurement system (including the coded aperture), and n is a
vector representing any additive noise acquired during the
measurement process. Reconstruction or inversion is then the
process of recovering an estimate, S, of the input spectrum, S,
given a set of acquired measurements, g (the recovery will not
generally be exact due to the presence of noise). A schematic of
the general situation is shown in Figure 2, and the various aspects
are expanded upon in the subsections below.
2.1. Measurement Matrix and Forward Model
For any specific architecture, determining the measurement matrix H
begins by developing a forward model that describes the specific
architectural and physical details of the system. These details are
captured in the propagator h(x, y , x′, y ′, m/z) that maps an ion
m/z at a location (x′, y ′)
←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
Figure 1 The aperture coding concept. System input with system
architecture that, given the relevant physics, (a) does not sort,
(b) implements near-perfect sorting, and (c) implements coded
sorting. (d ) Spectral information cannot be inferred from a system
architecture with no sorting. (e) Spectral information can be
directly inferred via simple calibration of the sorting parameter
from a system architecture designed for near-perfect sorting. ( f )
Spectral information can be obtained via a computational inference
between the sorting parameter and system architecture for coded
sorting. The signal to background is increased, while the
resolution remains the same. ( g) An example of a magnetic sector
physics architecture with no sorting capability. Ions pass into a
region of uniform magnetic field (gray) directed out of the page.
No information can be obtained from the signal at the detector. (h)
An example of a magnetic sector designed to implement perfect
sorting. An acceleration grid is added to localize the ion energy,
and a narrow slit aperture is added to constrain the ion position
before entering the region of magnetic field. Spectral information
can be directly inferred via calibration of the position on the
array detector. (i ) An example of a magnetic sector designed for
coded sorting. The acceleration grid constrains the ion energy,
while the slit in h is replaced with a coded aperture of multiple
slits of various widths. In this example, the coded aperture has
two slits, one of which is two times the width of the other
separated by the width of the smaller slit. The spectral
information can be computationally inferred from the spatial
distribution of the signal at the detector. The resulting spectrum
has the same resolution due to the same minimum slit size but
higher intensity due to the increased throughput.
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Input mass spectrum
Approximate model
Figure 2 Schematic of the spectral reconstruction process. The
input mass spectrum, S, interacts with the physical architecture of
the system and is corrupted by noise, n (both shot and additive),
to yield a set of measurements, g. Knowledge of the system
architecture, including the aperture code t, yields a system-
forward model (measurement matrix), H, that describes the
measurement process. A reconstruction algorithm then takes the
acquired measurements, g, and the system-forward model, H, and
calculates S, an estimate of the input mass spectrum.
in the input plane of the system to a location (x, y) in the
detector plane of the system (this treatment assumes that all ions
have encountered an acceleration potential and, as a result, all
velocity-dependent effects can be written in terms of the ion m/z).
The details of the propagator, of course, depend on the system
specifics. For a system with an input aperture function, t(x′, y
′), the ion distribution, f (x, y), in the detector plane is
then
f (x, y) = ∫∫∫
d x′d y ′d (m/z) t (x′, y ′) h(x, x′, y , y ′, m/z)S (x′, y ′,
m/z), 2.
with S(x′, y ′, m/z) being the input mass spectral density. In a
conventional instrument, t(x, y) describes the open area of the
input slit, but in a coded system it describes the structured
pattern of openings in the coded aperture.
The ion distribution is then transduced into a set of digital
measurements via a 1D or two- dimensional (2D) array of detector
elements. We let pi (x, y) represent the pixel function of the i-th
detector element in the array. The pixel function is defined to
take a value of 1 within the spatial extent of the ion-sensitive
region of the detector element and 0 outside. With this definition,
the measurement on the i-th detector element is then given by
gi = ∫∫
d xd ypi (x, y) ∫∫∫
d x′d y ′d (m/z) t (x′, y ′) h(x, x′, y , y ′, m/z)S (x′, y ′,
m/z)+ ni , 3.
with ni the additive noise contribution at the i-th detector
element. If we assume that the input mass spectral density is
spatially uniform (treating the nonuniform case leads to a theory
of coded aperture mass spectral imaging), and we discretize the
spectrum such that Sj is the j-th m/z bin, then we can write this
as gi =
∑ j H i , j Sj +ni . We then interpret the indexed quantities as
vectors
and matrices to yield g = HS + n, as previously mentioned. Note
that for a conventional, slit- based instrument, H takes the form
of an identity matrix—there is a one-to-one correspondence between
ion m/z and a specific detector element. In a coded system, H has a
complicated, off- diagonal structure representative of
multiplexing. For a broad class of scenarios, H takes the
form
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of a discrete convolution of the discretized input spectrum S and
discretized aperture code, t. Practically, the aperture code t is
then chosen to maximize the invertibility of H given a desired open
aperture.
2.2. Reconstruction Algorithm
Reconstruction is then the process of generating an estimate S of
the input spectrum S, given the measurements, g. Conceptually, we
can view this as forming S = H−1g = H−1(H S+ n) = S+H−1n, which
clarifies why the presence of noise precludes perfect
reconstruction. Practically, numerical issues generally restrict
reconstruction via direct application of the inverse matrix, H−1.
Various techniques, including ordinary least squares (53),
non-negative least squares (54), Richardson-Lucy deconvolution
(55), or more advanced inverse solver with regularization (56), are
used in practice depending on the specific details of the
problem.
2.3. Potential Issues with Reconstruction
There are a number of important caveats regarding reconstruction,
the first being the numerical sensitivity of inversion and wide
array of potential methods mentioned above. More importantly,
successful inversion depends crucially on the accuracy of the
forward model. Mismatch can occur either because specific physical
or architectural details have been omitted in the development of
the physical model (e.g., for analytic simplicity) or because the
as-built system does not perfectly represent the intended design.
In either case, some form of calibration is generally required to
refine the forward model to the point where high-quality
reconstructions are possible. The final caveat regarding
reconstruction is the issue of transform noise. When forming the
reconstruction, noise on a given m/z channel will be distributed
across many channels upon inversion, potentially adding noise even
in channels where there is no signal. In the case of additive
noise, as described above, this has little effect, as nominally
every channel has a similar noise level; for shot-noise– limited
situations, however, channels associated with strong spectral lines
contain greater amounts of noise than the others. In this case,
transform noise can appear as weak spectral features (or occlude
actual weak spectral features that are present). This is an
unavoidable issue with shot noise in a multiplexed measurement, and
care must be taken to understand the intended system application
and whether the transform noise issue will be problematic.
3. PROOF-OF-CONCEPT DEMONSTRATIONS
In this section, we describe several proof-of-concept
demonstrations showing how aperture coding as applied to sector
mass spectrometers can increase the throughput and SBR without
adversely affecting the instrument resolution. We begin with the
initial demonstrations of 1D and 2D aperture coding using a simple
90-degree magnetic sector instrument and then show how aperture
coding is compatible with two other sector mass analyzers, the
Mattauch-Herzog and cycloidal mass analyzers.
Although a signal multiplexing technique similar to a coded
aperture approach was mentioned in a paper by C.J. Eckhardt and
Michael L. Gross in 1970 (50), the first demonstrations of aperture
coding using 1D and 2D codes in sector MS was accomplished using a
simple 90-degree magnetic sector (28, 29). Figure 3a shows a
diagram of the experimental apparatus. The apparatus comprises an
electron ionization source built from Kimball Physics eV parts, two
25× 25× 100-mm bar magnets connected via a stainless steel yoke
producing a field of 0.45 T, and a 40-mm diameter 10-µm pitch
multichannel plate (MCP) detector with a phosphor screen and camera
(camera not
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Slit Slit
S-7 S-11 S-15 S-23
15 20 25 30 35 40 45 50 55 60 0
2
4
6
8
10
12
14
Slit Cyclic S-23
FWHM 0.3 m/z
a
b
c
d
e
0
0.2
0.4
0.6
0.8
1
m/z
Slit Ethanol spectrum at 1.0 µtorr NIST Ethanol EI spectrum NIST
Water EI spectrum
15 20 25 30 35 40 45 50 55 60
0
2
4
6
8
10 S-23 Ethanol spectrum at 1.0 µtorr NIST Ethanol EI spectrum NIST
Water EI spectrum
Cyclic S-23 ethanol
y
m/z
Figure 3 One-dimensional coding proof of concept. (a) Schematic of
the 90-degree magnetic sector mass analyzer used in the
proof-of-concept experiments. (b) Diagram of the cyclic S
matrix–coded apertures used. (c) Image of the phosphor screen for
ethanol using a slit and order S-23–coded aperture. (d ) Comparison
of reconstructed spectra using slit and cyclic S-23–coded
apertures. The inset shows the full width at half maximum for both
the slit and reconstructed cyclic S-23 spectrum, indicating that
the resolution remains the same. (e) Comparison of reconstructed
spectra of slit and coded apertures for a small quantity of
analyte. The coded aperture allows detection of peaks buried in the
noise in the slit spectrum. Panels b–e adapted with permission from
Reference 28 and Springer. Copyright 2015, American Society for
Mass Spectrometry.
shown in figure). The electron ionization source was designed to
have minimal dispersion in the ion energy and angle, as this
apparatus lacked double-focusing properties. Further details on the
apparatus and ion source design can be found in the supplementary
information of Chen et al. (28). A forward model for this apparatus
was developed and calibrated using argon and then tested using
coded apertures based on cyclic S matrices (44) up to order S-23
using 1D codes (Figure 3b) and up to order S-15 using 2D codes (see
Figure 4a and Section 3.2) with a minimum feature size of 125 µm.
Acetone and ethanol were utilized as the test analytes.
148 Amsden et al.
20 30
40 50
1 3 5 7 9 11 13 15 17 1
2
3
4
5
6
7
8
Th ro
ug hp
ut g
ai n
Aperture order
Aperture order
a b
56
m/z
1
2
3
S-11
Slit-3
S-15
4
5
6
Figure 4 Two-dimensional coding proof of concept. (a) Diagram of
the two-dimensional (2D) S-matrix codes and the corresponding slit
for comparison. (b–g) Images of the phosphor screen for the slit
and corresponding 2D-coded aperture using ethanol as the analyte.
(h) Reconstructed ethanol spectra from panels b–g. (i ) Comparison
of throughput gain versus aperture order. Panels a–h adapted with
permission from Reference 29 and Springer. Copyright 2015, American
Society for Mass Spectrometry.
As described in Section 2.1, developing a forward model requires
deriving the propagator of the system that maps a point on the
aperture plane to a point on the detector plane. For this 90-degree
system, using the Lorentz force law and the radius of curvature of
the ion path, the propagator for the 90-degree system is
h(x, x′, y , y ′, m/z) = δ
x − x′, y −
. 4.
Where the primed coordinates are measured in the aperture plane,
the unprimed coordinates are measured on the detector plane, y is
the mass dispersive direction, m/z represents the mass-to- charge
ratio, B is the magnetic field, U is the ion energy, δ is the Dirac
delta function, and u/e is the ratio of an amu to the elementary
charge in the desired set of units. A full derivation of Equation 4
can be found in the supplementary material of Chen et al. (28).
Upon calibrating the forward model with singly and doubly charged
argon, the forward model was modified to include a path
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length–dependent magnification in the nonmass dispersive direction
due to the angular spread of the ion source:
h(x, x′, y , y ′, m/z) = δ
x − [1+ M x(m/z)1/4]x′, y −
√√ 8U (m/z)(u/e)
. 5.
This continuous propagator is then converted into a discretized
forward model by the action of the finite detector pixels [see
supplementary material in Chen et al. (28)]. To finalize
calibration, we take an ion energy of 2 keV and adjust the
parameters B, Mx, and δ (pixel size) to achieve the best fit with
the experimentally observed measurements of singly and doubly
charged argon.
3.1. One-Dimensional Coding in a 90-Degree Magnetic Sector
Figure 3c shows images of the MCP phosphor screen of the slit and
S-23–coded aperture with ethanol as the analyte. The images on the
MCP for both the slit and coded aperture were recorded using the
same exposure time. Figure 3d shows reconstructed mass spectra from
the images in Figure 3c. The reconstructed spectrum using the S-23
aperture shows a greater than tenfold increase in throughput over
the spectrum using the slit. In addition, as shown in the inset to
Figure 3d, the full width at half maximum of the peaks in the slit
and S-23 reconstructed spectra are the same, indicating that the
coded aperture increases throughput without degrading the
resolution.
Figure 3e demonstrates one key advantage of coding. The top shows a
spectrum of ethanol measured at 1.0 µtorr using a slit, whereas the
bottom shows a spectrum of ethanol at the same pressure but with an
S-23–coded aperture. In the spectrum reconstructed from the
S-23–coded aperture, the SBR is significantly higher, enabling
detection of peaks due to ethanol fragments that are lower
intensity than the noise in the spectrum acquired using the
slit.
3.2. Two-Dimensional Coding in a 90-Degree Magnetic Sector
In the optical domain, 2D spatially coded patterns are preferred
over 1D codes. The 2D codes provide increased measurement diversity
and therefore improved numerical conditioning of the
reconstruction. Using the same 90-degree sector instrument
described above with the same for- ward model, the 1D slits were
replaced with 2D S-matrix codes (Figure 4a) (29). For better
comparison, the length of the slit was allowed to vary to match the
overall linear dimension of the coded aperture. Figure 4b–g show
the image on the detector for the slit and corresponding coded
aperture using ethanol as the analyte. Figure 4h shows the
reconstructed spectra from the images in Figure 4b–g. Similar to
the 1D-coded apertures, the 2D apertures show an increasing
through- put with aperture order. However, due to the necessity of
incorporating support structures into the fabricated apertures, the
enabled throughput gain is actually less than with a 1D aperture of
the same order. Furthermore, a slight loss in resolution was
observed in the reconstructed spectra using the coded aperture.
This is likely a result of the relatively poor imaging properties
(such as nonfocusing in the z-direction) of this 90-degree sector
when compared to optical spectrometers using similar codes that do
not exhibit a loss in resolution.
3.3. Double-Focusing Sector Instruments
The simple 90-degree magnetic sector mass spectrometer is used to
demonstrate the ability of aperture coding to increase instrument
SBR without adversely affecting resolution or changing the
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0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.5
1.0
1.5
2.0
0.5
1.0
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–400 –200 0 200 400 0.0 0.2 0.4 0.6 0.8 1.0
Particle trajectories
50 mm
10 mm
Matrix method: S-7 code on detector plane
COMSOL/C#: S-7 code on detector plane
Experimental method: S-7 code on detector plane
Figure 5 Coding with the Mattauch-Herzog mass spectrometer. (a)
Characteristic trajectories from the COMSOL and particle tracing
simulation. (b) S-7 aperture code at the aperture plane. (c) Image
of the S-7 aperture code on the detector plane calculated using
transfer matrices. (d ) Image of the S-7 aperture code at the
detector plane simulated using COMSOL and particle tracing. (e)
Image of the S-7 coded aperture on the detector of the OI
Analytical/Xylem IonCam transportable mass spectrometer. Panels a–e
adapted with permission from Reference 27 and Springer. Copyright
2016, American Society for Mass Spectrometry.
measurement time required to achieve a given level of performance.
However, it has limited mass range and resolution due to the
inability to correct for the dispersion in the ion source. In
contrast, double-focusing mass analyzers, such as the
Mattauch-Herzog (57), Bainbridge-Jordan (58), and
Hinterberger-Konig (59), offer a first-order correction to the
energy and angular dispersion of the ions emerging from the ion
source. The cycloidal mass analyzer developed by Bleakney &
Hipple (60) produces perfect focusing for sufficiently uniform
fields. The following sections describe work proving the
compatibility of aperture coding with the Mattauch-Herzog and
cycloidal mass analyzers.
3.3.1. One-dimensional coding in a double-focusing Mattauch-Herzog
mass analyzer. To evaluate the compatibility of aperture coding
with the Mattauch-Herzog mass analyzer, Russell et al. (27)
compared simulated results using a first-order transfer matrix
formalism, a finite element field solver, and a particle tracing
algorithm; they compared the simulated results with those obtained
by replacing the slit in an OI Analytical miniature Mattauch-Herzog
instrument with an S-7–coded aperture. Figure 5a shows some
characteristic particle trajectories emanating from the central
optic axis and ±1,150 µm from it for different masses that were
calculated using the finite element field solver and particle
tracing algorithm.
Using the transfer matrix formalism for the Mattauch-Herzog
geometry described in detail in Burgoyne et al. (61), the simulated
image of the S-7 aperture pattern at the detector was compressed
but well preserved (Figure 5c). As the transfer matrix formalism
does not allow for fringing fields and incorporates the paraxial
approximation that is valid only for distributions of ions close to
the optic axis, the compatibility of the Mattauch-Herzog mass
analyzer was investigated using finite element field solvers for
the electric and magnetic fields. A custom particle tracing program
based on the velocity Verlet algorithm and bilinear field
interpolation was used to determine the simulated image quality of
an S-7–coded aperture on the detector plane (Figure 5d ). Similar
to the transfer matrix calculation, the aperture pattern was also
compressed but well preserved. Unlike
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AC10CH07-Glass ARI 9 May 2017 10:26
the transfer matrix, the finite element simulations showed a
nonuniform intensity distribution that is likely a result of
fringing fields near the entrance and exit of the electric
sector.
To verify the compatibility of aperture coding with the
Mattauch-Herzog mass analyzer, the slit in an OI Analytical/Xylem
IonCam transportable mass spectrometer (http://www.oico.
com/documentlibrary/3390spec.pdf ) was replaced with an S-7–coded
aperture. Higher-order apertures were not possible due to the width
of the electric sector gap. The experimental results showed a
similar compression of the coded aperture with poorer than expected
resolution of the aperture and an intensity falloff at the edges of
the pattern (Figure 5e). These effects are likely a result of the
nonuniform illumination of the aperture by the ion source, fringing
fields from the narrow electric sector gap, and nonuniform
attenuation of the pattern by the circular Herzog shunts at the
entrance and exit of the electric sector. Results showed that the
Mattauch-Herzog is compatible with aperture coding, but
modifications are needed to optimize the compatibility. Work is
underway to develop electric sectors capable of imaging
higher-order codes with the Mattauch-Herzog mass analyzer.
3.3.2. One-dimensional coding in a cycloidal mass analyzer. Whereas
most double-focusing mass analyzers correct for energy and angular
dispersion to first order, the cycloidal mass analyzer described by
Bleakney & Hipple (60) is unique among sector mass analyzers in
that it exhibits double focusing to all orders. Using
perpendicularly oriented uniform magnetic and electric fields, ions
emanating from the ion source travel cycloidal trajectories. The
position a measured from the ion source at which an ion crosses the
detector plane after traversing a 360-degree cycloidal path is
described by the following equation,
a = m Z
E + d , 6.
where m/z is the ion mass to charge, B is the magnitude of the
magnetic field, E is the magnitude of the electric field, and d
represents the distance between where the ion was generated and the
origin of the coordinate system at the center of the ion source.
The position does not depend on the energy or angle of ion emission
from the ion source. From this equation it is also evident that the
cycloidal mass analyzer will be inherently compatible with aperture
coding, provided that the electric and magnetic fields are of
sufficient uniformity. A prototype instrument is currently under
development to verify this hypothesis.
4. FUTURE DIRECTIONS
4.1. System Requirements
As discussed in Section 3.3, some technical challenges are
associated with adapting traditional mass analyzer geometries such
as the Mattauch-Herzog and cycloid instruments with aperture
coding. Both the cycloid and Mattauch-Herzog mass analyzers require
ion sources that can produce ions over an extended region along the
axis of the coded aperture. In addition, both require use of a
focal- plane ion array detector. In recent years, a number of ion
array detectors have been developed that can meet this requirement,
including one based on a charge transimpedance amplifier array (62,
63) and charge-coupled device (CCD) technology called the IonCCD
(64). The Mattauch-Herzog instrument, which is used in a variety of
applications ranging from miniature systems (65–67) to inductively
coupled plasma mass spectrometers for elemental analysis (68) and
secondary ion mass spectrometers (69), was shown to be compatible
with coding via simulation and experiment. However, fringing fields
at the entrance and exit of the electric sector limit the ability
to resolve
152 Amsden et al.
AC10CH07-Glass ARI 9 May 2017 10:26
complex codes. Novel electric sector geometries are needed that
limit the effects of fringing fields to fully realize the
throughput enhancement enabled by aperture coding in the Mattauch-
Herzog mass analyzer. The cycloid mass analyzer is inherently
compatible with aperture coding and is particularly well suited to
miniaturization for environmental applications (70–73) due to the
overlapping nature of the electric and magnetic sectors. However,
the imaging quality of the cycloid instrument depends on the
uniformity of the electric and magnetic field. It is relatively
easy to produce a uniform electric field using an array of
regularly spaced electrodes. However, novel permanent magnet
geometries that are lightweight and provide high field uniformity
analogous to the Halbach (74) and Stelter (75) arrays are necessary
to fully realize the potential of a miniature cycloidal mass
analyzer coupled with aperture coding.
4.2. Applications
Coded aperture techniques should find wide application in areas
that are highly sample constrained or that require simultaneous
detection or miniaturization. Instruments that collect spectra in
se- ries, such as ion traps or quadrupoles, are not good candidates
for coded aperture technique, but temporal coding is applicable
(25). Instruments that detect ions in parallel will benefit from
these techniques, as described in three examples. First, secondary
ion mass spectrometry (SIMS) uses a beam of ions to ionize solid
surfaces (76). In sector-based SIMS, these ions are detected using
an array of detectors, which are frequently electron multipliers.
Increasing throughput would allow a lower concentration limit to be
detected or more samples to be processed. This is a limiting factor
in the widespread adoption of SIMS-based diagnostic techniques
(77). Second, isotope ratio mass spectrometry is frequently
performed with magnetic sector-based instruments, as it requires
high-precision and high-quality peak shapes (78). Increasing
sensitivity and improving sample uti- lization through coding would
allow smaller samples to be processed. Finally, miniature magnetic
sector instruments would benefit from the throughput increase while
maintaining resolution that aperture coding provides. The smaller
size of the instrument limits the SNR because of both a reduction
in the total number of ions generated and the reduced capability of
smaller pumps, requiring the efficient use of samples.
4.3. Direct Detection
A promising research avenue for future consideration is direct
detection. Here, the aperture code is chosen not to maximize the
invertibility of H, but rather to produce a set of distinct,
distinguishable signatures that individually correspond to any one
of a finite set of compounds or mixtures of interest. In this
model, spectral estimation is not required, and direct detection of
the compounds of interest is determined by the presence of the
corresponding signature(s). The primary advantage of direct
detection is system resource efficiency; such an approach would
typically require fewer detector elements than a corresponding
general instrument designed for full spectral estimation. A further
enhancement would be to consider methods for adaptively adjusting
the aperture code t in response to prior measurements to maximize
discrimination between compounds of interest that may be present. A
version of this approach was recently demonstrated in optical
spectroscopy by one of the authors (35).
DISCLOSURE STATEMENT
S.T.D. and Z.E.R. are establishing a new venture based on
technology covered in this review. The following patents related to
the technology discussed here have been filed: US 7399957 B2
www.annualreviews.org • Coded Apertures in Mass Spectrometry
153
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(C.B.P., D.J.B., J.T.G., and M.E.G.) and PCT/US16/59496 ( J.J.A.,
D.J.B., E.X.C., S.T.D., J.T.G., M.E.G., C.B.P., and Z.E.R.).
ACKNOWLEDGMENTS
J.J.A., D.J.B., S.T.D., J.T.G., M.E.G., C.B.P., and Z.E.R.
acknowledge financial support from the Advanced Research Projects
Agency-Energy (ARPA-E), US Department of Energy (under award number
DE-AR0000546), and US Department of Homeland Security (under award
HSHQDC- 11-C-00082). D.J.B., S.T.D., J.T.G., C.B.P., and Z.E.R.
received funding from the National Science Foundation (under grant
0801942). The views and opinions of the authors expressed do not
necessarily state or reflect those of the United States Government
or any agency thereof.
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and Michael T. Bowers 365
Applications of Surface Second Harmonic Generation in Biological
Sensing Renee J. Tran, Krystal L. Sly, and John C. Conboy 387
Bioanalytical Measurements Enabled by Surface-Enhanced Raman
Scattering (SERS) Probes Lauren E. Jamieson, Steven M. Asiala,
Kirsten Gracie, Karen Faulds,
and Duncan Graham 415
Single-Cell Transcriptional Analysis Angela R. Wu, Jianbin Wang,
Aaron M. Streets, and Yanyi Huang 439
Errata
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All Articles in the Annual Review of Analytical Chemistry,
Vol.10
Chemical and Biological Dynamics Using Droplet-Based
Microfluidics
Sizing Up Protein–Ligand Complexes: The Rise of Structural Mass
Spectrometry Approaches in the Pharmaceutical Sciences
Applications of the New Family of Coherent Multidimensional
Spectroscopies for Analytical Chemistry
Coupling Front-End Separations, Ion Mobility Spectrometry, and Mass
Spectrometry for Enhanced Multidimensional Biological and
Environmental Analyses
Multianalyte Physiological Microanalytical Devices
Coded Apertures in Mass Spectrometry
Magnetic Resonance Spectroscopy as a Tool for Assessing
Macromolecular Structure and Function in Living Cells
Plasmonic Imaging of Electrochemical Impedance
Tailored Surfaces/Assemblies for Molecular Plasmonics and Plasmonic
Molecular Electronics
Light-Addressable Potentiometric Sensors for Quantitative Spatial
Imaging of Chemical Species
Analyzing the Heterogeneous Hierarchy of Cultural Heritage
Materials: Analytical Imaging
Raman Imaging in Cell Membranes, Lipid-Rich Organelles, and Lipid
Bilayers
Beyond Antibodies as Binding Partners: The Role of Antibody
Mimetics in Bioanalysis
Identification and Quantitation of Circulating Tumor Cells
Single-Molecule Arrays for Protein and Nucleic Acid Analysis
The Solution Assembly of Biological Molecules Using Ion Mobility
Methods: From Amino Acids to Amyloid β-Protein
Applications of Surface Second Harmonic Generationin Biological
Sensing
Bioanalytical Measurements Enabled by Surface-Enhanced Raman
Scattering (SERS) Probes
Single-Cell Transcriptional Analysis