Toru
Aonishi
*a,
Takafumi
Hirata
b,
Tatsu
Kuwatani
cd,
Masuto
Fujimoto
e,
Qing
Chang
c and
Jun-Ichi
Kimura
c
aSchool of Computing, Tokyo Institute of Technology, Nagatsuda 4259, Yokohama 226-8502, Japan. E-mail: aonishi@c.titech.ac.jp; Tel: +81-45-924-5546
bGeochemical Research Center, The University of Tokyo, Hongo, 7-3-1, Tokyo 113-0033, Japan. E-mail: hrt1@eqchem.s.u-tokyo.ac.jp; Tel: +81-3-5841-4621
cDepartment of Solid Earth Geochemistry, Japan Agency for Marine-Earth Science and Technology, Natsushima-cho 2-15, 237-0061, Yokosuka, Japan. Tel: +81-46-867-9765
dPRESTO, Japan Science and Technology Agency (JST), Honcho 4-1-8, Kawaguchi, 332-0012, Japan
eDepartment of Geoscience, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
First published on 10th August 2018
To improve the spatial resolution of the two-dimensional elemental images of solid organic and inorganic materials, a novel numerical correction method was developed for laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). Diffusion and dilution of LA aerosol particles in the carrier gas during transportation from the LA cell to the ICP are the major cause of image diffusion along the axis of a one-dimensional line scan. The correction calculations use (1) numerical forward modelling of the diffused elemental signals and (2) a non-negative signal deconvolution inversion calculation technique to retrieve the original signal profiles. This method improves spatial resolution with a semi-quantitative determination of the ablated masses. We used this method to sharpen the spatial distribution images of rhodium particles contained within a meteorite sample.
Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) can generate both macro and microscopic images with extremely high sensitivity, and it has a high throughput capability (Fig. 1a and b).3,10,11 Recently, LA-ICP-MS imaging systems with submicron- to micron-scale resolution have been developed.12 Reportedly, the spatial resolution of these systems can be improved to about 1 μm when they are equipped with a time-of-flight (TOF)-ICP-MS13,14 or even with conventional quadrupole ICP-MS instruments using a rapid sample aerosol transfer ablation cell and tubing.15 However, improving the spatial resolution of the LA-incorporated method requires more effort. The cause of deterioration in these images is twofold. One is the practical limit of the laser beam size, usually a few to a few dozen micrometres in diameter. This is partly because of the physical diffraction limit of the focusing objective lens of the laser and largely because of the trade-off between elemental sensitivity in the ICP-mass spectrometer and elemental abundances in samples. The second major cause of image deterioration is the aerodynamic diffusion–dilution of LA aerosols during transport from the sampling cell to the ICP ion source15–17 particularly for a normal LA system using a large-volume sample cell and a transfer tubing that is ca. 4 mm in diameter (Fig. 1c).
Examination of the fluid dynamics in the sample cell and transfer tubing has led to improvements in the geometric design of the LA-ICP-MS hardware (Fig. 1a and c). Recent hardware developments have improved sample transport with minimal stagnation and enabled fast washout of the sample cell to minimize the dilution–diffusion effects.16–18 Nevertheless, the limited laser beam size and shape and the dilution–diffusion effect remain significant hurdles for nano- to micrometre-scale analyses in elemental imaging. This is particularly true when rapid imaging over a wide area is required, although this is one of the advantages of LA-ICP-MS over other micro-analytical techniques. To cope with this problem, numerical signal deconvolution approaches have been developed to improve the spatial resolution of elemental imaging. These approaches include the deconvolution of LA signals from overlapping ablation pits in grid ablation or line scanning using a circular laser beam16,19–22 and the deconvolution of the diffusion–dilution effect in LA aerosol transport using continuous line scan ablation.23,24
Data science has contributed significantly to these numerical approaches. In particular, recent interdisciplinary studies have focused on inverse problems such as deconvolution for extracting pertinent information from large sets of experimental data by using statistics, machine learning, and other forms of artificial intelligence.25,26 Such approaches have been used to improve magnetic resonance imaging (MRI),27 seismic tomography,28 geodesic inversion,29etc. Following similar data-science methods, we developed a novel non-negative deconvolution (ND) calculation algorithm to increase the spatial resolution of LA-ICP-MS. We focused on two-dimensional elemental imaging of micrometre-sized metal particles using line scans where the acquired data were heavily distorted because of dilution–diffusion effects during aerosol transport. The metal particles of interest are sufficiently smaller than the laser beam size and are occasionally sampled by the LA. The ND method proposed here improves the spatial resolution from ∼50 to ∼30 μm in a 10% valley definition23 used for roughly estimate of resolution with a semi-quantitative estimation of the individual particle signals in rapid line-scan mode (laser scan velocity of 25 μm s−1). Herein, we describe the ND algorithm and demonstrate improved imaging of rhodium metal nuggets in an approximately 2.5 × 2.5 mm area of a calcium–aluminium-rich inclusion (CAI)30 in a meteorite from northwest Africa.
The meteorite sample used for the Rh imaging analysis was a NWA (Northwest Africa) 7678 carbonaceous chondrite (CV3). The dark weathered exterior of the saw-cut sample revealed many chondrules smaller than 1 mm, with a few as large as 5 mm, and scattered CAIs larger than 1 cm that were set in a dark grey groundmass. Nearly all of the Fe–Ni was oxidized by weathering.31 The meteorite was cut into pieces using a low-speed diamond cutter (Isomet 1000, Buehler, Lake Bluff, Illinois). Prior to the image analysis using LA-ICP-MS, the surface of the sample was polished using diamond paste (#8000). Neither coatings of conductive materials nor additional matrix components were prepared in this study. Information and access to the NWA7678 meteorite sample are available from one of the authors TH (E-mail: hrt1@eqchem.s.u-tokyo.ac.jp).
ICP-mass spectrometer | |
Instrument | Nu AttoM SF-ICP-MS |
ICP incident power | 1350 W |
He carrier gas | 740 mL min−1 |
Ar makeup gas | 850 mL min−1 |
Scan mode | Deflector scan |
Monitored isotopes | 53Cr |
Data acquisition | Time resolved analysis (TRA) |
Dwell time | 100 ms per isotope |
Instrument | iCAP Qc (Thermo Fisher Scientific) |
ICP incident power | 1550 W |
He carrier gas | 736 mL min−1 |
Ar makeup gas | 850 mL min−1 |
Scan mode | Standard mode |
Monitored isotopes | 19F, 23Na, 24Mg, 27Al, 29Si, 31P, 32S, 35Cl, 44Ca, 57Fe, 59Co, 60Ni, 103Rh, 139La |
140Ce, 146Nd, 147Sm, 175Lu, 178Hf, 182W, 193Ir, 204Pb, 206Pb, 208Pb, 232Th, 238U | |
Data acquisition | Time resolved analysis (TRA) |
Dwell time | 10 ms per isotope |
Laser ablation system | |
Instrument | CyberProbe UV Ti:S femtosecond laser THG |
Wavelength | 266 nm |
Pulse duration | 230 fs |
Fluence | 2.4 J cm−2 |
Repetition rate | 2 Hz |
Ablation pit size | 5 μm |
Scan speed | 10 μm s−1 |
Instrument | NWR193 (ESI), ArF excimer laser |
Wavelength | 193 nm |
Pulse duration | 5–10 ns |
Fluence | 2.4 J cm−2 |
Repetition rate | 20 Hz |
Ablation pit size | 10 μm |
Scan speed | 25 μm s−1 |
An ArF excimer-based laser ablation system (NWR193, ESI New Wave Research, Montana, USA) was used for two-dimensional (imaging) Rh mapping of the CAI meteorite sample. The ICP-MS instrument was quadrupole based (iCAP Qc, Thermo Fisher Scientific, Bremen, Germany). The LA-ICP-MS experimental parameters were optimized to obtain the maximum signal intensities of 63Cu and 64Zn by ablating an SRM 610 synthetic glass standard from the National Institute of Standard and Technology (NIST). Single line profiles were obtained by moving a circular laser spot 10 μm in diameter with a scanning velocity of 25 μm s−1. The repetition rate of the laser pulse was set at 20 Hz. A two-dimensional map was obtained by repeated line-profiling analyses across the sample. The distance between two adjacent analysis lines was 10 μm. The dwell time of the data acquisition was 10 ms for all analytes (in total 26 elements/isotopes, covering 19F to 238U: Table 1), and the total time for a single mass scan was 0.287 s (∼287 ms), corresponding to the time intervals of the analysis cycles on 103Rh.
A simple linear dynamic model mathematically consists of a dead-time lag and a higher-order lag representing the aerosol transport through the tubing in the laminar flow regime.33 The element signal y(t) evoked by a single pulse is modeled as follows:
y(t) = xg(t), | (1) |
(2) |
The LA-ICP-MS technique uses multiple line scans to generate images like those shown in Fig. 1b. Under linear conditions, the element signal evoked by N laser pulses can be given by a linear summation of single-pulse response functions (eqn (1)), as follows:
(3) |
y = Gx + s, | (4) |
In the measurement of the Cr patterns printed on a glass substrate, the fs laser pulse irradiation interval was set to 0.5 s and the signal acquisition period was 0.10 s, while in the measurement of Rh in the CAI inclusions, the ns laser pulse irradiation interval was set to 0.05 s and the signal acquisition period was 0.287 s (Table 1). Thus, the discrete intervals of ti and ξk in the M × N Green's function matrix G were set to the individual interval values in each of the two cases. The values of the single-pulse-evoked g(t) parameters were determined to be τ1 = 0.3401 s, τ2 = 0.0730 s, and Δ = 0.1107 s for Cr patterns sampled by fs LA and τ1 = 0.3886 s, τ2 = 0.3665 s and Δ = 0.2072 s for CAI sampled by ns LA. The numbers below decimals indicate significant digit figures not for measurement accuracy but for the numerical calculation of the inversion analysis. Note that the dead time Δ calculated in this model does not correspond to the actual delay time of the equipment, as t = 0 in the abscissa does not correlate to the time of the LA shot. This discrepancy does not affect following discussions.
J = ‖y − Gx‖2 + λ‖Lx‖2 | (5) |
Here, the first term of J is the square error that measures the residual between the generative model and observed signal. The second term in eqn (5) is an L2-norm regularisation term to overcome the ill-posed problem, where λ is a regularisation parameter. L in the regularisation term is an N × N matrix given by
We were able to determine a suitable value for the regularisation parameter by using the cross-validation method. This optimization problem can be solved using the quadratic programming method. The estimate of obtained with this method is constrained to have a non-negative value, which reflects the physical constraint that the ion signal intensity must be non-negative. It should be noted that if the objective function J is minimized without non-negative constraints, the conventional Wiener filter (WF) with the smooth constraint: = (GTG + λLTL)−1GTy can be obtained. To determine the efficacy of the non-negative constraint, we compared the performance of the ND algorithm with that of the WF with the smooth constraint.
We performed a leave-one-out cross-validation to determine the value of the regularisation parameter λ in the objective function J.25 The kth observation was retained as validation data, and the remaining observations were used as training data for estimating x denoted as \k. Then, we quantified the prediction error by calculating the mean-squared error between the kth validation observation and the corresponding prediction based on the estimate of \k. By repeating the calculation of the prediction error with each of the observations and averaging them, we obtained the generalization error (GE). We then determined the value of the regularisation parameter λ by searching for the minimum GE for each LA line profile.
To quantitatively evaluate the proposed method, we used the following synthetic data. First, we synthesized the original aerosol mass x that accurately reflects the typically measured distributions. The positions of the particles were randomly generated using a Bernoulli process, and the spatial elemental distribution of each of the particles was represented by a Gaussian distribution with a resolution of 30 μm in a 10% valley definition. The peak value of each of the elemental distributions was randomly generated from a Gamma distribution. Next, using the generative model described by eqn (4), we synthesized the observed signal y with Gaussian noise.
The time scale of the synthetic data was adapted to mirror that of the real data. In the actual equipment, the interval of the laser pulse was 0.05 s, and the signal acquisition period was 0.287 s for the CAI. The discrete intervals of ti and ξk in the generative model (eqn (4)) were set to 0.05 s and 0.287 s for ns LA. The parameter values of g(t) were set as τ1 = 0.3886 s, τ2 = 0.3665 s, and Δ = 0.2072 s, as noted above. Furthermore, 1 s corresponded to 25 μm because the stage velocity was 25 μm s−1 in the actual equipment for CAI. The artificial data used in the numerical experiments were composed of an 80 s time sequence (Fig. 2a and b).
To determine the effect of the non-negative constraint on the model performance of particle detection in CAI, we compared the performance of the ND with that of the WF. The experiments confirmed that the cross-validation method could select a nearly optimal λ value (Fig. 2a and c). The ND algorithm with the chosen λ could retrieve the original aerosol mass x accurately reflecting the particles with a resolution of 30 μm in a 10% valley definition (Fig. 2b), and the ND algorithm outperformed the WF method in terms of accuracy (Fig. 2d). The experiments with synthetic data confirmed that the ND algorithm worked well (Fig. 2a and c). Furthermore, the experiments using synthetic data with Poisson noise confirmed that the ND algorithm could work better than the WF when counting rates are low at small signal sizes or small laser spot sizes used (data not shown).
In practice, measurements on LA signals tend to include high-frequency noise; such noise originates from irregular ablation of the sample surface due to LA–sample surface coupling,37 the particle size distribution of the LA aerosols that arises from heterogeneous diffusion during aerosol transfer (see Fig. 1), flicker noise from the ICP,38 and quantisation noise at the analogue–digital converter. The last two sources are known to affect analytical precision when the LA signals are close to the limit of detection,38 but the first two affect even strong LA signals. To simulate their effects, we added both Gaussian (Fig. 3a) and Gamma noise (Fig. 3b) to the synthetic LA profiles.
When the Gaussian noise was applied, the profile obtained by the synthetic experiment reproduced well the onset and offset of the ablation of a hypothetical Cr pattern having very sharp edges (Fig. 3a). The synthetic LA signal with Gaussian noise (Fig. 3a, red) strictly followed the profile in response to the τ-factors and showed rounded rectangular shapes after the onset/offset of the sample ablation. The intensity curve calculated with the ND model (Fig. 3a, blue) reproduced quite well the original rectangular signal profile with almost vertical edges at the onset and offset of Cr ablation. When gamma noise was applied (Fig. 3b, red), the calculated ND slopes were slanted during rise/fall at the onset/offset of ablation (Fig. 3b, blue). Time intervals during the rise and fall of the synthetic signal were ca. 1.5 s between the base level to the first peak and between the last peak to the base level (red), whereas they were reduced to ca. 1 s by the ND model (blue).
The measured LA signals from the 1951 USAF test target (Fig. 3c) were more irregular than the synthetic signals with Poisson noise. In Fig. 3d, the horizontal scale of 1 s correlates with a 10 μm length scale, which includes two non-overlapping 5 μm LA craters (Fig. 3c). The time intervals between the base level to the first peak were ca. 2.5 s (25 μm) in contrast to 1.5 s (15 μm) in the ND model results, indicating an improvement in spatial resolution. Although the ND model offset did not significantly reduce tailing during the fall of the signal after the ablation, it eliminated spiky noise signals on the falling slopes that were above the resolution in a 10% valley definition threshold (Fig. 3d). Overall, the ND model improved the resolution of the edges of Cr patterns from 25 to 15 μm measured based on the average length between the first contact of LA to the Cr patterns and the first peaks of the Cr signal. It should be noted that no resolution improvement can be expected from the model when the signal-to-noise ratio is close to the lower limit of detection.
The spatial resolution of the individual peaks is better than 30 μm in a 10% valley definition, so that each identifiable peak may originate from a single Rh nugget with a diameter <30 μm or singular to aggregated Rh particles of submicron size dispersed within a region <30 μm in diameter. Measurements using a scanning electron microscope did not find any large Rh particles of micrometre size (not shown); the appropriate interpretation is thus sub-micrometre-scale Rh-rich particles. Given that the normalized single-pulse response function conserves the total ion count and the non-negative constraint maintains the non-negativity of the estimated mass (Fig. 4d), the aerial integral of the signal intensity profile closely reproduces the sub- to tens of micrometre-scale particle mass volume when the LA-ICP-MS sensitivity factor is provided for various matrices and 100% transfer of the ablated sample to the ICP and the fluctuations in ionization efficiency are minor based on the instantaneous mass load if the ablated mass is small assumed. A semi-quantitative treatment can be applied using the areas of the deconvolution peaks, even without the sensitivity factor. Therefore, the area of each peak corresponds to the integrated signal intensity from the aggregated particles. This indicates that smaller amounts of Rh metal particles result in smaller peak areas and they are spatially resolvable when they are separated by >30 μm (Fig. 4d). Note that peak deconvolution using a Wiener filter is not appropriate for such a quantitative approach (Fig. 4e).
The line profile analysis was followed by Rh imaging analysis of a 2.5 × 2.5 mm square area (Fig. 4a–c). Typical sizes of metal grains in refractory siderophile elements, including Rh, Ir, and Os, can vary significantly, ranging from <1 to 5 μm in CAI.7,30,39 This suggests that the size of the metal grains examined in this study is significantly smaller than 30 μm and the grains are dispersed as single or aggregated metal particles within the regions of bright spots of Rh concentrations scattered over the 2.5 × 2.5 mm measured area in the CAI (Fig. 4a). The resulting Rh distribution images with and without ND corrections are compared in Fig. 4b and c. These images demonstrate the considerable sharpening of peaks corresponding to the Rh nuggets.
Under the ablation conditions used in this study, a spatial resolution better than 10 μm was not achieved. This is simply because of the large LA beam with a diameter of 10 μm scanned at a velocity of 25 μm s−1 with a 20 Hz laser pulse repetition rate. The use of a smaller crater (e.g. 2 μm) with a lower repetition rate (e.g. 2 Hz) and a slower scanning velocity (e.g. 2 μm s−1) in combination with a rapid aerosol transfer cell and tubing can further improve the spatial resolution. The improvement can only be realized when the transient sampling of the circular laser ablation pits is properly decomposed19 in tandem with the ND method for diffusion–dilution in aerosol transport, as proposed in this study. This double deconvolution can deal with the two major causes of deterioration of spatial resolution in LA imaging (see the Introduction). As such, the model calculations will be the ultimate challenge in the numerical modelling approach for LA-ICP-MS imaging. For this purpose, further hardware development for high-speed signal integration and data processing in the ICP-MS will be required to minimize the quantization problem of the acquired LA signals.40 Addressing these issues will be the goal for future development of the method described herein.
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