Laser-Induced Breakdown Spectroscopy Combined with Spatial Heterodyne Spectroscopy Igor B. Gornushkin,a,* Ben W. Smith,b Ulrich Panne,a,c Nicolo´ Omenettob a b c
Federal Institute for Materials Research and Testing (BAM), Richard Willsta¨tter Strasse 11, D-12489 Berlin, Germany University of Florida, Department of Chemistry, PO Box 117200, Gainesville, FL 32611 USA Department of Chemistry, Humboldt-Universita¨t zu Berlin, Brook-Taylor-Str. 2, 12489 Berlin, Germany
A spatial heterodyne spectrometer (SHS) is tested for the first time in combination with laser-induced breakdown spectroscopy (LIBS). The spectrometer is a modified version of the Michelson interferometer in which mirrors are replaced by diffraction gratings. The SHS contains no moving parts and the gratings are fixed at equal distances from the beam splitter. The main advantage is high throughput, about 200 times higher than that of dispersive spectrometers used in LIBS. This makes LIBS-SHS a promising technique for low-light standoff applications. The output signal of the SHS is an interferogram that is Fourier-transformed to retrieve the original plasma spectrum. In this proof-of-principle study, we investigate the potential of LIBS-SHS for material classification and quantitative analysis. Brass standards with broadly varying concentrations of Cu and Zn were tested. Classification via principal component analysis (PCA) shows distinct groupings of materials according to their origin. The quantification via partial least squares regression (PLS) shows good precision (relative standard deviation , 10%) and accuracy (within 6 5% of nominal concentrations). It is possible that LIBS-SHS can be developed into a portable, inexpensive, rugged instrument for field applications. Index Headings: Spatial heterodyne spectroscopy; Laser-induced breakdown spectroscopy; Fourier transform spectroscopy; LIBS; Laser-induced plasma; Interferometry.
INTRODUCTION Laser-induced breakdown spectroscopy (LIBS) has become a mature technique during last two decades,1–2 with a continuously expanding range of applications. It is used for planetary and deep-sea exploration,3–4 material sorting,5 isotope analysis of atoms and molecules,6–7 and remote detection of explosive, construction, and archeological materials.8–10 This has become possible, in part, because of recent developments in lasers, spectrometers, and detectors. The most demanding applications, in terms of instrumentation, are the remote versions of LIBS. The task here is to detect light from a 1 mm diameter plasma containing less than 1 lg of glowing matter from a distance of tens of meters. Despite the fact that the laserinduced plasma (LIP) is a relatively bright light source, the number of usable photons can be very low. Even in standard laboratory configurations, the technique does not enjoy a high sensitivity. Typical detectable concentrations are in the tens to hundreds parts per million range. Therefore, to collect more light for standoff Received 24 March 2014; accepted 3 June 2014. * Author to whom correspondence should be sent. Email: igor. [email protected]. DOI: 10.1366/14-07544
1076
Volume 68, Number 9, 2014
applications, complex telescopic systems are built, making remote LIBS bulky and expensive. One factor limiting the photon flux is the low throughput of the dispersive spectrometers that are currently used in LIBS. These spectrometers are designed to work with micrometer-size apertures (slits) to achieve an acceptable spectral resolution. For example, the very popular echelle spectrometers, which cover broad spectral ranges (200–900 nm) with a highresolution (. 10 000), have numerical apertures (NA) that rarely exceed 0.05 (f/10). Czerny–Turner spectrometers with similar resolutions have slightly better NAs (0.1) but achieve this at the expense of spectral coverage (typically 10–20 nm). A solution to this problem can be interference spectrometers, which offer significant advantages over dispersive spectrometers. The main advantage is the high throughput—typically 200 times higher than in dispersive spectrometers of similar resolution. Other advantages are easily achievable high resolution, compact size, sufficiently wide spectral coverage, economical design, mechanical stability and low cost. A promising approach for LIBS may be a spatial heterodyne spectrometer (SHS), first developed and described by Harlander and colleagues.11,12 The spectrometer is a modified version of the Michelson interferometer in which the mirrors are replaced by diffraction gratings. The SHS contains no moving parts; the gratings are fixed at equal distances from the beam splitter and slightly tilted with respect to the interferometer optical axis. The tilt provides a Littrow condition (back-diffraction) for a desired wavelength that defines the center of a spectral range. Spectra are recovered using Fourier transforms of recorded interferograms. The SHS was initially developed for low-light astronomical applications12 but recently was proved useful for Raman and infrared (IR) spectroscopy. Gomer et al.13 first demonstrated its ability to measure visible Raman spectra of liquid and solid materials using a 532 nm continuous-wave (CW) laser. The sensitivity, spectral resolution, and bandpass were found to be adequate to detect signals from strong Raman scatterers such as carbon tetrachloride (CCl4), S, cyclohexane, and toluene. Nathaniel and Underwood14 measured the Raman bands of celestine and strontium sulfate (SrSO4) minerals using a similar SHS instrument. Lin et al.15 observed the IR spectrum of water at 1364 nm. Englert et al.16 extended the IR range of SHS to 8–11 lm to detect chemicals in the atmosphere. Various designs of SHS instruments have been proposed: monolithic for the remote sensing of Earth’s atmosphere;17 SHS with
0003-7028/14/6809-1076/0 Q 2014 Society for Applied Spectroscopy
APPLIED SPECTROSCOPY
imaginary equivalent SHS works identically to the standard SHS shown in Fig. 1a (left). Therefore, in the original design, G1 ‘‘sees’’ the coordinate system as if it had gone through the same transformations as G1 but in the reverse order. Figure 1b shows the SHS, the coordinate system as viewed from G1, G2, and D, the incident and diffracted rays, and the relation between important angles. Let k be the wave vector of a plane wave entering the spectrometer. The diffracted waves k1 and k2 recombine at the beam splitter and travel toward the detector. We start by applying the grating equation r(sin a1,2 þ sin b1,2) = m/d to gratings G1 and G2, where r = 1/k is the wavenumber, d is the distance between grating grooves, a1,2 and b1,2 are the angles of incidence and diffraction with respect to the grating normal, and m is the diffraction order. Making use of the relations a1 = h c, a2 = h þ c, b1 = h c1, and b2 = h þ c2, the equations for G1 and G2 become 8 2r0 sinh > > sinðh cÞ sinðh c1 Þ ¼ > < rcosu ð1Þ 2r0 sinh > > sinðh þ c sinðh þ cÞ Þ ¼ > 2 : rcosu FIG. 1. (a) Equivalent representation of an interferometer. (b) Angles between k vectors, grating normal, and coordinate axes.
polarization gratings to address problems of alignment, size, and stability;18 and all-reflection SHS to broaden spectral coverage.19 The instrument has been commercialized; several versions of SHS are available on the market.20 In this proof-of-principle study, we investigate the potential of LIBS-SHS for material classification and quantitative analysis. The ultimate goal is to develop this technique into a compact, robust, and low-cost instrument that is suitable for field standoff applications.
THEORETICAL The theory of SHS was introduced by Harlander and colleagues in their pioneering studies.11,12 They applied interference and diffraction relations to the diffraction gratings, which replaced mirrors in a standard Michelson interferometer. It is instructive to briefly analyze the simplest SHS system to understand how it works. The task is to write the interference and grating equations in a suitable coordinate system that explains the formation of interference (Fizeau) fringes at the exit of the SHS system. Consider the SHS spectrometer in Fig. 1a, where the working surfaces of the optical elements are orthogonal to the figure plane. Let the origin of the coordinate system be at point O, the z-axis be aligned with the G2D optical axis, the y-axis be perpendicular to the image plane (and parallel to gratings grooves), and the x-axis be in the image plane. Consider the equivalent scheme of the SHS in Fig. 1a (right). This is obtained by rotating G1 about the y-axis by 908 and rotating it again about the z-axis by 1808. Assuming that G1 in the new position ‘‘sees’’ the same light as in the old position, this
where u is the angle between k and the x,z-plane (see the inset in Fig. 1b); c, c1, and c2 are the angles between the projection of k on the x,z-plane and the z-axis; h is the Littrow angle; and r0 is the Littrow wavenumber. In the derivation of Eq. 1, the expression for the Littrow wavenumber m = 2r0d sin h at a = b = h was used. Consider a simple example of a monochromatic light beam entering the spectrometer parallel to its axis. In this case, u = 0, c = 0, sin c1,2 c1,2, and cos c1,2 1. Using the expressions for the sine of the sum and difference of two angles, the grating equations for G1 and G2 become 0 1 8 > > r r 0 > A > c ¼ 2tanh@ > > < 1 r 0 1 ð2Þ > > r r > 0 > A > c ¼ 2tanh@ > : 2 r Further, the intensity produced by the interference of two coherent plane waves k1 and k 2 with equal intensities I0/2 and zero initial phases at point r in space is I ¼ I0 1 þ cos½ðk1 k2 Þ r ð3Þ The x, y, and z components of k1 and k2 are (jk1j sin c1, 0, jk1j cos c1) = (2prc1, 0, 2pr) and (jk2j sin c2, 0, jk2j cos c2) = (2prc2, 0, 2pr). Hence, the dot product in Eq. 3 is (k1 k2) r 2pr(c2 c1)x. Substituting this into Eq. 3 and using Eq. 2, the intensity of the monochromatic source as a function of position x on the detector (i.e., the interferogram) is calculated as ð4Þ Iðx Þ ¼ I0 1 þ cos½8pðr r0 Þtanh x
APPLIED SPECTROSCOPY
1077
FIG. 2. Experimental setup: (1–2) 150 mm1 diffraction grating and mirror, (3) beam splitter, (4) objective, (5) CCD camera, (6) entrance aperture, (7) beam expander, (8) glass plates, (9) beam dumps, (10) collection lens, (11) sample, (12) plasma, (13) focusing lens, (14) Nd : YAG laser, (15) mirror, (16) He-Ne laser, (17) 532 nm DPSS laser, (18) pierced mirror, (19) Ar-ion laser, (20) collimating lens, (21) hollow cathode lamp.
EXPERIMENTAL To describe an on-axis polychromatic beam with spectral density B(r), Eq. 4 should be integrated over the frequency domain Z ‘ Iðx Þ ¼ BðrÞ 1 þ cos½8pðr r0 Þtanh x d r ð5Þ 0
The intensity I(x) depends only on the x-coordinate; thus, the fringes are aligned perpendicular to the x-axis in the x,y-plane. With the exception of the constant term, I(x) is the Fourier transform of the input spectrum taken over the spectral frequency domain. Conversely, the input spectrum B(r) is recovered from I(x) by the Fourier transform over the spatial frequency domain. Zero spatial frequency corresponds to the Littrow wavenumber r0, which means the spectrometer is heterodyned at this frequency. Note that the cosine is an even function; therefore, Eq. 5 yields identical outputs for þ(r r0) and (r r0). This ambiguity can be avoided by tilting one of the gratings by a small angle g with respect to y-axis. This introduces a spatial modulation perpendicular to the modulation along the dispersion dimension x, and the new equation for the interferogram becomes
Z‘ Iðx ; y Þ ¼ 0
BðrÞ 1 þ cosf4p½2ðr r0 Þ 3 tanh x þ gr y g d r
ð6Þ
Now, a two-dimensional (2D) Fourier transform is needed to recover the original spectrum B(r). Note the resolution along the y direction is low because frequencies are not heterodyned. Further details on the theory of SHS are available in the literature.11,12 In particular, the resolving power of SHS, R = r/dr, has been shown to be equal to the theoretical resolving power of the grating system.
1078
Volume 68, Number 9, 2014
Setup. Figure 2 shows a block diagram of the experimental setup. The SHS consists of a 68 3 68 mm, 150 grooves (gr)/mm, 300 nm blaze grating (1); a k/10, 50 mm round flat mirror (2); and a cubic 50.8 mm, 400–700 nm bandwidth beam splitter (3). The 1392 3 1040 charge-coupled device (CCD) array (Cool Snap HQ, Roper Scientific) with a 6.45 3 6.45 lm pixel size and 10/20 MHz digitization rate (5) collects light from the SHS through the objective (4) with adjustable magnification and focal length. Alternatively, an intensified chargedcouple device (ICCD; PI-MAX2: 1003; Princeton Instruments) with a 1024 3 1024 array detector and a 12.8 3 12.8 lm pixel size can be used. The parallel beam of light enters the spectrometer through the iris (6) and is expanded, if necessary, by the beam expander (7). A number of lasers and line light sources are used to set a desirable Littrow wavelength for the grating (1) and to calibrate the spectrometer. These include a helium– neon (He–Ne) laser at 632.8 nm (16); a diode-pumped solid-state (DPSS) laser at 532 nm (MGL 150, Laser Photon Components UG, Dresden, Germany) (17); an Ar-ion laser (177-G02; Spectra Physics) generating a series of lines between 450 and 515 nm (19); and a number of different hollow cathode lamps (HCLs) (21). Light from these sources is guided into the spectrometer by a set of mirrors (15 and 18) and glass flats (8). The collimating lens (20) with a 15 cm focal length delivers light from the HCLs to the SHS over a distance of 3 m. The laser-induced breakdown system includes the neodymium-doped yttrium aluminum garnet (Nd : YAG) laser (1064 nm, 50 mJ pulse energy, 10 ns pulse duration; Big Sky,) (14) focused onto the target (11) using a 2.5 cm diameter, 2.5 cm focal length lens (13). This creates a 0.2 mm diameter spot on the target surface and an irradiance of 16 MW/cm2 . Another 2.5 cm diameter lens (10), placed one focal distance (7.5 cm) from the plasma, collects and collimates the plasma emission.
TABLE I. Brass standard reference materials from NIST. Sample 1104 1109 1110 1111 1113 1115 1116
Zn certified (%)
Zn found (%)
Recovery (%)
Cu certified (%)
Cu found (%)
Recovery (%)
36.36 17.4 15.2 12.81 4.8 11.73 9.44
30.4 17.7 15.2 13.7 6.7 11.0 11.6
86 101 100 107 139 94 122
61.34 82.2 84.59 87.14 95.03 87.96 90.37
66.9 81.2 84.5 86.0 93.2 89.0 88.0
109 99 100 99 98 101 97
Timing for the data acquisition is arranged as follows. When using CW light sources—that is, one of the lasers (16), (17), or (19) or the HCL (21)—the CCD operates in free-run mode, with an exposure time set by software (WinSpec/32, Version 2.5; Roper Scientific). When using a pulsed light source (i.e., the laser plasma (12)), the CCD operates in the external sync mode while the software still determines the exposure time. To synchronize the laser and the CCD, three pulse generators are used. The first (Tektronics PG 501) triggers the flash lamp of the ablation laser and the second pulse generator. The second (HP 8012B) provides a 180 lsdelayed pulse to the Q switch of the laser and third pulse generator. The third triggers the CCD at a variable delay time with respect to the laser pulse starting from the 200 ns delay. This unavoidable initial delay is due to the lag between the Q switch and laser output (125 ns) and the signal processing time of the CCD. In any case, early LIP does not yield good interference images because it emits mostly Bremmstruhlung/ photorecombination continuum and not much structured spectrum. The optimal delay for obtaining sharp interferograms is about 4 ls. This delay is used throughout the experiments using LIP. The exposure time is set to 100 ls and includes all of the luminous plasma lifetime.
Samples. The samples are brass certified reference materials from the National Institute of Standards and Technology (NIST). Table I provides the concentrations of the major elements, Cu and Zn that were used for quantitative LIBS-SHS analysis. Metallic foils of Cu and Zn (Goodfellow, USA) were also used to generate interferograms. The Littrow wavelength of the SHS was aligned with the center of a spectral region of interest (480–520 nm) at about 500 nm. Procedure. The spectrometer was aligned and set at the desired Littrow wavelength using the Ar-ion, Nd : YAG, or He–Ne laser. The Littrow wavelength was tuned by rotating the diffraction grating. To obtain clean interferograms, the background was subtracted from each image. The background was collected by successively blocking one of the two arms of the interferometer and summing up the images. When operating with CW light sources, the CCD camera was set to the free-run mode with the exposure time depending on the brightness of the source. For operation with LIPs, the delay generator triggered the CCD several microseconds after the laser pulse to cut off the plasma continuum radiation. The usual acquisition mode for LIPs was 4 ls for the delay time, 100 ls for the gate, and 50 accumulations on the same sample spot.
FIG. 3. The SHS with HCL filled with Ar and comparison of the resulting spectrum with the spectrum from a low-resolution Czerny–Turner spectrometer.
APPLIED SPECTROSCOPY
1079
FIG. 4. Gallery of SHS interferograms obtained using HCLs and an Ar-ion laser. Insets show spectra measured using an Ocean Optics spectrometer. The Littrow wavelengths of the SHS for each interferogram were set to approximately the middle points of the spectral fragments given in insets.
Software. The initial data were collected and background-subtracted using WinSpec software (Princeton Instruments). Further data processing was performed using homemade software written in Matlab R2013a. This includes the routines for fast Fourier transform (FFT), PCA, and PLS analyses. Yet another routine was written for processing the images resulting from FFT of the interferograms. Pixels on the images were binned along the dimension of low dispersion (vertically); thereafter, analytical lines were identified and processed.
RESULTS AND DISCUSSION Characterization of the Spatial Heterodyne Spectrometer with Continuous Wave Light Sources. To establish the spectral characteristics of the SHS and calibrate it in terms of wavelength, interferograms were collected from various CW light sources. An example is shown in Fig. 3 for the mercury HCL filled with Ar. The Ar spectrum was recorded by the SHS with a Littrow wavelength at 770 nm. The interferogram was transformed using the FFT, followed by binning the image pixels along the direction of minimal dispersion (i.e., vertically). The resulting SHS spectrum was then directly compared with the spectrum from a Czerny–Turner spectrometer with similar resolution. Based on this comparison, the spectral lines were identified. Using a set of line sources such as HCLs, the procedure of tuning the SHS to a desired spectral range took several minutes.
1080
Volume 68, Number 9, 2014
The spectral resolution and spectral range of the SHS were evaluated using simple calculations and from numerous spectra taken under different light sources. The maximum (theoretical) resolving power of the diffraction grating is given by R = mN, where m is the diffraction order and N is the number of groves illuminated by the light. For the current system, R = 150 gr/mm 8 mm = 1200, corresponding to a minimal resolved interval Dk = 0.4 nm at 500 nm. The spectral coverage is, correspondingly, L = Dk Npix/2 = 0.4 nm 696 240 nm, taking into account the Nyquist condition, with the Npix/2 limit for the number of resolved spectral elements.12 Here Npix = 1392 is the total number of pixels on the detector in the direction of maximal spectral resolution. Apart from the spectrometer itself, the resolution depends on fringe focusing conditions (i.e., the focal length and magnification of the camera objective).13 In the current case, it was about fourfold lower than the predicted theoretical resolution. This can be verified from Fig. 3. Note that high resolution was not the goal in this proof-of-principle investigation. If desired, we can easily improve the resolution by replacing the mirror by a second diffraction grating and/or using gratings with a higher number of grooves per millimeter. To give reader an impression of how the interferograms look for different spectral ranges and different line densities, a selection of SHS interferograms supplemented by reference spectra taken using a dispersive spectrometer (Ocean Optics) are presented in Fig. 4.
FIG. 5. The LIBS-SHS spectrum of brass foil with the Zn and Cu lines identified.
Obviously, light sources emitting more spectral lines produce more complex interferograms. Spatial Heterodyne Spectroscopy of Laser-Induced Plasma. We chose laser-induced breakdown on brass to study the performance of LIBS-SHS because of the relative simplicity of brass spectra. The SHS was tuned to the range 450–600 (with the Littrow wavelength at 500 nm) because this range contains several strong spectral lines of Cu and Zn. Figure 5 shows a processed LIBSSHS spectrum with the lines identified. The interferograms exhibit the best contrast when the delay time is set to 4 ls and integration time is set to 100 ls. These setting were used throughout LIBS-SHS experiments. To test the sensitivity of LIBS-SHS, the emission signal was gradually attenuated by factors of 10, 100, and 1000 using neutral-density filters. Figure 6 displays the interferograms, their FFTs, and the spectra obtained using different degrees of attenuation. In each case, the signal consists of 50 accumulations. We can see that the emission lines of Cu and Zn are distinct for 10- and 100fold attenuations, but the signal-to-noise ratio degrades insignificantly. Even at 1000-fold attenuation, when no visible pattern can be recognized in the interferogram, the FFT still yields recognizable Cu and Zn emission signals. A simple estimate shows that minimal detectable signals from Cu and Zn correspond to concentrations of about 0.05%. Note that this result is obtained without optimization of the SHS system, using a nonintensified CCD detector and relatively weak spectral lines. Classification of the Brass Samples. Laser-induced breakdown spectroscopy is often used for classification
rather than for quantitative analysis.21 To investigate the potential of LIBS-SHS for material classification, we conducted a PCA on the brass data. The PCA was applied in two ways: on the raw interferograms and on truncated 2D images after the FFT. Prior to the PCA, the corresponding matrices were rearranged into vectors and then into new matrices suitable for PCA. The columns and rows of these matrices correspond to variables (pixel-wise intensities) and observations (samples) in chemometric notation. Figures 7 (left and middle) display an interferogram and its Fourier image obtained from one of the brass samples. Similar FFT images of all interferograms were used as the input data in both the PCA (classification) and PLS (quantitative analysis). The PCA of the truncated data set is shown in Fig. 7 (right) in terms of two first principal components (PCs). The distinct grouping is observed for all but two compositionally closest samples, 1111 and 1115. Pure Cu and brass samples were also included in the analysis. Their scores form groups most distant from other groups. The PCA on the raw interferograms (not shown) yielded results similar to those in Fig. 7 but with less compact grouping. That was logical for data not filtered by FFT, which removes a significant amount of noise from the interferograms. Further improvement can be expected from better-quality (i.e., contrast) interferograms, which can be achieved by equalizing the blazing/ reflection of a grating-mirror pair at Littrow and other wavelengths. Quantitative Analysis of the Brass Samples: A Feasibility Study. Quantitative analysis of the brass
APPLIED SPECTROSCOPY
1081
FIG. 6.
Test for sensitivity using the gradual attenuation of the LIBS-SHS signal.
samples was attempted in two ways: univariate, using single lines, and multivariate, using a PLS routine. For the univariate analysis, FFT images of the initial interferograms (e.g., Figs. 7 [middle and left]) were vertically binned to yield conventional spectra in terms of intensities versus wavelength. Such spectra are shown in Fig. 8 (left). The ‘‘wavelengths’’ are, in fact, the wavelength indices, that is, the pixel numbers along the high-dispersion dimension. We still needed to relate them to wavelengths. This was done by comparing the FFT images of brass plasmas to those of Cu and Zn HCL plasmas. For the multivariate analysis, FFT images of interferograms were used as is, without binning. The Zn I 481.05 nm line was chosen for the construction of the univariate calibration plot. In addition
to the brass standards, pure Zn and Cu samples were added to the sample set to expand the concentration range to cover 0 and 100% for both Cu and Zn. All spectra were preprocessed: the background under the lines was removed, and the lines were smoothed using a gentle three-point, first-order Savitzky–Golay filter and approximated using a Lorentzian profile. The analytical signal was the line integral intensity taken within limits 61.4 FWHM (where FWHM is the full width at halfmaximum) as recommended in the literature.22 We can see that the calibration plot in Fig. 8 (right) is S-shaped, showing a plateau at both low and high concentrations. We can offer no conclusion at this point about whether this is an instrumental artifact or reflects physical processes, and therefore we made no attempt to predict
FIG. 7. Interferogram (left). Average spectra of brass samples after FFT (middle). The PCA performed on individual spectra (right).
1082
Volume 68, Number 9, 2014
FIG. 8. Average spectra of brass samples after the FFT of the interferograms (left). Plot of the integral intensity of the Zn I 481.05 nm line versus concentration (right).
unknown concentrations from this S-shaped calibration function. Note, however, that the breakdown of brass samples is notorious for nonstoichiometric ablation; this effect has been described in several papers.23 As alluded to earlier, brass was chosen as a test sample because of the simplicity of its spectrum. The reproducibility of the analytical signal was typical for LIBS, 610% relative standard deviation (RSD) over the whole concentration range. An attempt at quantitative analysis was also made based on multivariate PLS analysis. Here, three spectra out of five replicates (50 accumulations each) were randomly chosen for calibration. Two remaining spectra were used as unknowns. There was a concern that PLS could be unsuitable for quantification due to the nonlinear response that was seen in the univariate case. Therefore, prior to analysis, we performed a crossvalidation to determine which samples constituted a reliable calibration set and how many PCs should be taken. Figure 9 (left) shows the estimated mean square prediction error (MSPE) as a function of the number of PCs. We can see that the model remains imprecise; it shows a high MSPE for both Zn and Cu when pure Zn and Cu are included in the calibration set. Removing these samples brings the MSPE to an acceptable level of about 10%. The plots in Fig. 9 (left) also imply that using more than three PCs would be ill advised. Doing so
FIG. 9.
would not improve the prediction accuracy but would lead to overfitting of the calibration set. Therefore, only three PCs were chosen for the calibration model. The results of the PLS analysis are listed in Table I and shown in Fig. 9 (right) in the form of a correlation plot of certified and determined concentrations. The correlation is very high, with a slope near 458 and 0.996 coefficient of determination. The precision is also high (the error bars in Fig. 9 are concealed inside markers), under 1% RSD, but statistically insignificant because it is derived from only two measurements (two unknowns). The accuracy (‘‘Recovery’’ column in Table I) is within 6 5% of nominal values for almost all the samples except for those with minimal and maximal concentrations. This deviation is probably due to the slightly nonlinear behavior of the calibration set. Similar results (not shown) were obtained for a PLS analysis of the raw interferograms. However, the number of PCs used had to be doubled (six instead of three). Therefore, the results might not be reliable due to significant overfitting. As mentioned before, FFT filters out a significant amount of noise from the raw interferograms.
CONCLUSION This study has demonstrated that a SHS can be used in combination with a LIP to detect spectra and that it can
Cross-validation with all samples, including pure Zn and Cu (left). Correlation between the determined and certified concentrations (right).
APPLIED SPECTROSCOPY
1083
be used to tackle both quantitative analysis and classification tasks. In this pilot experiment, the LIBSSHS system was not optimized to obtain maximal sensitivity and resolution. Instead, the simplest of all possible designs was used. Nevertheless, we were able to obtain both classification and quantification results. The quantitative analysis of the brass samples provided an acceptable accuracy (6 5% of nominal concentrations) and precision (RSD , 10%). The minimal detectable concentrations of Zn and Cu in brass were estimated at around 0.05%. A further increase in performance can be expected from a better design of the SHS. This would include using matching pairs of optical elements (mirror–grating or grating–grating), a better detector (ICCD instead of CCD), and focusing optics. In addition to the obvious advantage of high throughput and resolution, LIBS-SHS is easily adaptable to any spectral range—ultraviolet, IR, or even vacuum ultraviolet. This capability stems from using diffraction gratings instead of the mirrors used in conventional interferometry. Using the gratings significantly relaxes the requirements for the quality of the optics and reduces the cost. In summary, based on the preliminary results of this study, we can conclude that LIBS-SHS has clear potential to become a technique of choice in some LIBS applications, especially those requiring standoff capability. ACKNOWLEDGMENTS The authors thank Prof. S. Michael Angel from the University of South Carolina for providing useful information. Also, the authors thank the current and former graduate students of the University of Florida, Laser Spectrochemistry laboratory, for assistance in setting up the experiment. 1. D.W. Hahn, N. Omenetto. ‘‘Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma-Particle Interactions: Still-Challenging Issues Within the Analytical Plasma Community’’. Appl. Spectrosc. 2010. 64(12): 335A-366A. 2. D.W. Hahn, N. Omenetto. ‘‘Laser-Induced Breakdown Spectroscopy (LIBS), Part II: Review of Instrumental and Methodological Approaches to Material Analysis and Applications to Different Fields’’. Appl. Spectrosc. 2012. 66(4): 347-419. 3. R.C. Wiens, S. Maurice, J. Lasue, O. Forni, R.B. Anderson, S. Clegg, S. Bender, D. Blaney, B.L. Barraclough, A. Cousin, L. Deflores, D. Delapp, M.D. Dyar, C. Fabre, O. Gasnault, N. Lanza, J. Mazoyer, N. Melikechi, P.-Y. Meslin, H. Newsom, A. Ollila, R. Perez, R.L. Tokar, D. Vaniman. ‘‘Pre-Flight Calibration and Initial Data Processing for the Chemcam Laser-Induced Breakdown Spectroscopy Instrument on the Mars Science Laboratory Rover’’. Spectrochim. Acta, Part B. 2013. 82: 1-27. 4. A.P.M. Michel, M. Lawrence-Snyder, S.M. Angel, A.D. Chave. ‘‘Laser-Induced Breakdown Spectroscopy of Bulk Aqueous Solutions at Oceanic Pressures: Evaluation of Key Measurement Parameters’’. Appl. Optics. 2007. 46(13): 2507-2515. 5. R. Noll. Laser-Induced Breakdown Spectroscopy: Fundamentals and Applications. Berlin- Heidelberg, Germany: Springler-Verlag, 2012. Pp. 484-488.
1084
Volume 68, Number 9, 2014
6. F.R. Doucet, G. Lithgow, R. Kosierb, P. Boucharda, M. Sabsabi. ‘‘Determination of Isotope Ratios Using Laser-Induced Breakdown Spectroscopy in Ambient Air at Atmospheric Pressure for Nuclear Forensics’’. J. Anal. Atom. Spectrom. 2011. 26(3): 536-541. 7. X. Mao, A.A. Bol’shakov, I. Choi, C.P. McKay, D.L. Perry, O. Sorkhabi, R.E. Russo. ‘‘Laser Ablation Molecular Isotopic Spectrometry: Strontium and Its Isotopes’’. Spectrochim. Acta, Part B. 2011. 66(11-12): 767-775. 8. J.L. Gottfried, F.C. De Lucia, Jr., C.A. Munson, A.W. Miziolek. ‘‘Laser-Induced Breakdown Spectroscopy for Detection of Explosives Residues: A Review of Recent Advances, Challenges, and Future Prospects’’. Anal. Bioanal. Chem. 2009. 395(2): 283-300. 9. K. Novotny, J. Kaiser, J. Novotny, G. Vı´ tkova´, R. Malina, D. Procha´zka, V. Kanicky, V. Otruba, M. Lisˇka. ‘‘Utilization of Remote-LIBS Technique for Comparison of Brick Samples’’. Paper presented at: NASLIBS. New Orleans, LA; July 13-15, 2009. 10. S. Tzortzakis, D. Anglos, D. Gray. ‘‘Ultraviolet Laser Filaments for Remote Laser-Induced Breakdown Spectroscopy (LIBS) Analysis: Applications in Cultural Heritage Monitoring’’. Opt. Let. 2006. 31(8): 1139-1141. 11. J. Harlander. Spatial Heterodyne Spectroscopy: Interferometric Performance at Any Wavelength Without Scanning. [Ph.D. Dissertation]. Madison, WI: University of Wisconsin, 1991. 12. J.M. Harlander, R.J. Reynolds, F.L. Roesler. ‘‘Spatial Heterodyne Spectroscopy for the Exploration of Diffuse Interstellar Emission Lines at Far-Ultraviolet Wavelength’’. Astrophys. J. 1992. 396(2): 730-740. 13. N.R. Gomer, C.M. Gordon, P. Lucey, S.K. Sharma, J.C. Carter, S.M. Angel. ‘‘Raman Spectroscopy Using a Spatial Heterodyne Spectrometer: Proof of Concept’’. Appl. Spectrosc. 2011. 65(8): 849-857. 14. T.A. Nathaniel, C.I. Underwood. ‘‘Spatial Heterodyne Raman Spectroscopy’’. Paper presented at: 42nd Lunar and Planetary Science Conference. The Woodlands, TX; March 7-11, 2011. 15. Y. Lin, G. Shepherd, B. Solheim, M. Shepherd, S. Brown, J. Harlander, J. Whiteway. ‘‘Introduction to Spatial Heterodyne Observations of Water (SHOW) Project and Its Instrument Development’’. Paper presented at: XIV International TOVS Study Conference. Beijing, China; May 25-31, 2005. 16. C.R. Englert, D.D. Babcock, J.M. Harlander. ‘‘Spatial Heterodyne Spectroscopy for Long-Wave Infrared: First Measurements of Broadband Spectra’’. Opt. Eng. 2009. 48(10): 105602. 17. J.M. Harlander, F.L. Roesler, J.G. Cardon, C.R. Englert, R.R. Conway. ‘‘Shimmer: A Spatial Heterodyne Spectrometer for Remote Sensing of Earth’s Middle Atmosphere’’. Appl. Optics. 2002. 41(7): 1343-1352. 18. M.W. Kudenov, M.N. Miskiewicz, M.J. Escuti, E.L. Dereniak. ‘‘Spatial Heterodyne Interferometry with Polarization Gratings’’. Opt. Lett. 2012. 37(21): 4413-4415. 19. J.M. Harlander, J.E. Lawler, J. Corliss, F.L. Roesler, W.M. Harris. ‘‘First Results from an All-Reflection Spatial Heterodyne Spectrometer with Broad Spectral Coverage’’. Opt. Express. 2010. 18(6): 6205-6210. 2 0 . L i g h t M a c h in e r y . ‘‘ O p t ic a l C o m p o n e n t s ’’ . h t t p : / / w w w . lightmachinery.com/optical-components.html [accessed Mar 24 2014]. 21. I.B. Gornushkin, B.W. Smith, H. Nasajpour, J.D. Winefordner. ‘‘Identification of Solid Materials by Correlation Analysis Using a Novel Microscopic Laser Induced Breakdown Spectrometer’’. Anal. Chem. 1999. 71(22): 5157-5164. 22. E. Voigtman. ‘‘Gated Peak Integration Versus Peak Detection in White Noise’’. Appl. Spectrosc. 1991. 45(2): 237-241. 23. V. Margetic, A. Pakulev, A. Stockhaus, M. Bolshov, K. Niemax, R. Hergenro¨der. ‘‘A Comparison of Nanosecond and Femtosecond Laser-Induced Plasma Spectroscopy of Brass Samples’’. Spectrochim. Acta B. 2000. 55(11): 1771-1785.
Federal Institute for Materials Research and Testing (BAM), Richard Willsta¨tter Strasse 11, D-12489 Berlin, Germany University of Florida, Department of Chemistry, PO Box 117200, Gainesville, FL 32611 USA Department of Chemistry, Humboldt-Universita¨t zu Berlin, Brook-Taylor-Str. 2, 12489 Berlin, Germany
A spatial heterodyne spectrometer (SHS) is tested for the first time in combination with laser-induced breakdown spectroscopy (LIBS). The spectrometer is a modified version of the Michelson interferometer in which mirrors are replaced by diffraction gratings. The SHS contains no moving parts and the gratings are fixed at equal distances from the beam splitter. The main advantage is high throughput, about 200 times higher than that of dispersive spectrometers used in LIBS. This makes LIBS-SHS a promising technique for low-light standoff applications. The output signal of the SHS is an interferogram that is Fourier-transformed to retrieve the original plasma spectrum. In this proof-of-principle study, we investigate the potential of LIBS-SHS for material classification and quantitative analysis. Brass standards with broadly varying concentrations of Cu and Zn were tested. Classification via principal component analysis (PCA) shows distinct groupings of materials according to their origin. The quantification via partial least squares regression (PLS) shows good precision (relative standard deviation , 10%) and accuracy (within 6 5% of nominal concentrations). It is possible that LIBS-SHS can be developed into a portable, inexpensive, rugged instrument for field applications. Index Headings: Spatial heterodyne spectroscopy; Laser-induced breakdown spectroscopy; Fourier transform spectroscopy; LIBS; Laser-induced plasma; Interferometry.
INTRODUCTION Laser-induced breakdown spectroscopy (LIBS) has become a mature technique during last two decades,1–2 with a continuously expanding range of applications. It is used for planetary and deep-sea exploration,3–4 material sorting,5 isotope analysis of atoms and molecules,6–7 and remote detection of explosive, construction, and archeological materials.8–10 This has become possible, in part, because of recent developments in lasers, spectrometers, and detectors. The most demanding applications, in terms of instrumentation, are the remote versions of LIBS. The task here is to detect light from a 1 mm diameter plasma containing less than 1 lg of glowing matter from a distance of tens of meters. Despite the fact that the laserinduced plasma (LIP) is a relatively bright light source, the number of usable photons can be very low. Even in standard laboratory configurations, the technique does not enjoy a high sensitivity. Typical detectable concentrations are in the tens to hundreds parts per million range. Therefore, to collect more light for standoff Received 24 March 2014; accepted 3 June 2014. * Author to whom correspondence should be sent. Email: igor. [email protected]. DOI: 10.1366/14-07544
1076
Volume 68, Number 9, 2014
applications, complex telescopic systems are built, making remote LIBS bulky and expensive. One factor limiting the photon flux is the low throughput of the dispersive spectrometers that are currently used in LIBS. These spectrometers are designed to work with micrometer-size apertures (slits) to achieve an acceptable spectral resolution. For example, the very popular echelle spectrometers, which cover broad spectral ranges (200–900 nm) with a highresolution (. 10 000), have numerical apertures (NA) that rarely exceed 0.05 (f/10). Czerny–Turner spectrometers with similar resolutions have slightly better NAs (0.1) but achieve this at the expense of spectral coverage (typically 10–20 nm). A solution to this problem can be interference spectrometers, which offer significant advantages over dispersive spectrometers. The main advantage is the high throughput—typically 200 times higher than in dispersive spectrometers of similar resolution. Other advantages are easily achievable high resolution, compact size, sufficiently wide spectral coverage, economical design, mechanical stability and low cost. A promising approach for LIBS may be a spatial heterodyne spectrometer (SHS), first developed and described by Harlander and colleagues.11,12 The spectrometer is a modified version of the Michelson interferometer in which the mirrors are replaced by diffraction gratings. The SHS contains no moving parts; the gratings are fixed at equal distances from the beam splitter and slightly tilted with respect to the interferometer optical axis. The tilt provides a Littrow condition (back-diffraction) for a desired wavelength that defines the center of a spectral range. Spectra are recovered using Fourier transforms of recorded interferograms. The SHS was initially developed for low-light astronomical applications12 but recently was proved useful for Raman and infrared (IR) spectroscopy. Gomer et al.13 first demonstrated its ability to measure visible Raman spectra of liquid and solid materials using a 532 nm continuous-wave (CW) laser. The sensitivity, spectral resolution, and bandpass were found to be adequate to detect signals from strong Raman scatterers such as carbon tetrachloride (CCl4), S, cyclohexane, and toluene. Nathaniel and Underwood14 measured the Raman bands of celestine and strontium sulfate (SrSO4) minerals using a similar SHS instrument. Lin et al.15 observed the IR spectrum of water at 1364 nm. Englert et al.16 extended the IR range of SHS to 8–11 lm to detect chemicals in the atmosphere. Various designs of SHS instruments have been proposed: monolithic for the remote sensing of Earth’s atmosphere;17 SHS with
0003-7028/14/6809-1076/0 Q 2014 Society for Applied Spectroscopy
APPLIED SPECTROSCOPY
imaginary equivalent SHS works identically to the standard SHS shown in Fig. 1a (left). Therefore, in the original design, G1 ‘‘sees’’ the coordinate system as if it had gone through the same transformations as G1 but in the reverse order. Figure 1b shows the SHS, the coordinate system as viewed from G1, G2, and D, the incident and diffracted rays, and the relation between important angles. Let k be the wave vector of a plane wave entering the spectrometer. The diffracted waves k1 and k2 recombine at the beam splitter and travel toward the detector. We start by applying the grating equation r(sin a1,2 þ sin b1,2) = m/d to gratings G1 and G2, where r = 1/k is the wavenumber, d is the distance between grating grooves, a1,2 and b1,2 are the angles of incidence and diffraction with respect to the grating normal, and m is the diffraction order. Making use of the relations a1 = h c, a2 = h þ c, b1 = h c1, and b2 = h þ c2, the equations for G1 and G2 become 8 2r0 sinh > > sinðh cÞ sinðh c1 Þ ¼ > < rcosu ð1Þ 2r0 sinh > > sinðh þ c sinðh þ cÞ Þ ¼ > 2 : rcosu FIG. 1. (a) Equivalent representation of an interferometer. (b) Angles between k vectors, grating normal, and coordinate axes.
polarization gratings to address problems of alignment, size, and stability;18 and all-reflection SHS to broaden spectral coverage.19 The instrument has been commercialized; several versions of SHS are available on the market.20 In this proof-of-principle study, we investigate the potential of LIBS-SHS for material classification and quantitative analysis. The ultimate goal is to develop this technique into a compact, robust, and low-cost instrument that is suitable for field standoff applications.
THEORETICAL The theory of SHS was introduced by Harlander and colleagues in their pioneering studies.11,12 They applied interference and diffraction relations to the diffraction gratings, which replaced mirrors in a standard Michelson interferometer. It is instructive to briefly analyze the simplest SHS system to understand how it works. The task is to write the interference and grating equations in a suitable coordinate system that explains the formation of interference (Fizeau) fringes at the exit of the SHS system. Consider the SHS spectrometer in Fig. 1a, where the working surfaces of the optical elements are orthogonal to the figure plane. Let the origin of the coordinate system be at point O, the z-axis be aligned with the G2D optical axis, the y-axis be perpendicular to the image plane (and parallel to gratings grooves), and the x-axis be in the image plane. Consider the equivalent scheme of the SHS in Fig. 1a (right). This is obtained by rotating G1 about the y-axis by 908 and rotating it again about the z-axis by 1808. Assuming that G1 in the new position ‘‘sees’’ the same light as in the old position, this
where u is the angle between k and the x,z-plane (see the inset in Fig. 1b); c, c1, and c2 are the angles between the projection of k on the x,z-plane and the z-axis; h is the Littrow angle; and r0 is the Littrow wavenumber. In the derivation of Eq. 1, the expression for the Littrow wavenumber m = 2r0d sin h at a = b = h was used. Consider a simple example of a monochromatic light beam entering the spectrometer parallel to its axis. In this case, u = 0, c = 0, sin c1,2 c1,2, and cos c1,2 1. Using the expressions for the sine of the sum and difference of two angles, the grating equations for G1 and G2 become 0 1 8 > > r r 0 > A > c ¼ 2tanh@ > > < 1 r 0 1 ð2Þ > > r r > 0 > A > c ¼ 2tanh@ > : 2 r Further, the intensity produced by the interference of two coherent plane waves k1 and k 2 with equal intensities I0/2 and zero initial phases at point r in space is I ¼ I0 1 þ cos½ðk1 k2 Þ r ð3Þ The x, y, and z components of k1 and k2 are (jk1j sin c1, 0, jk1j cos c1) = (2prc1, 0, 2pr) and (jk2j sin c2, 0, jk2j cos c2) = (2prc2, 0, 2pr). Hence, the dot product in Eq. 3 is (k1 k2) r 2pr(c2 c1)x. Substituting this into Eq. 3 and using Eq. 2, the intensity of the monochromatic source as a function of position x on the detector (i.e., the interferogram) is calculated as ð4Þ Iðx Þ ¼ I0 1 þ cos½8pðr r0 Þtanh x
APPLIED SPECTROSCOPY
1077
FIG. 2. Experimental setup: (1–2) 150 mm1 diffraction grating and mirror, (3) beam splitter, (4) objective, (5) CCD camera, (6) entrance aperture, (7) beam expander, (8) glass plates, (9) beam dumps, (10) collection lens, (11) sample, (12) plasma, (13) focusing lens, (14) Nd : YAG laser, (15) mirror, (16) He-Ne laser, (17) 532 nm DPSS laser, (18) pierced mirror, (19) Ar-ion laser, (20) collimating lens, (21) hollow cathode lamp.
EXPERIMENTAL To describe an on-axis polychromatic beam with spectral density B(r), Eq. 4 should be integrated over the frequency domain Z ‘ Iðx Þ ¼ BðrÞ 1 þ cos½8pðr r0 Þtanh x d r ð5Þ 0
The intensity I(x) depends only on the x-coordinate; thus, the fringes are aligned perpendicular to the x-axis in the x,y-plane. With the exception of the constant term, I(x) is the Fourier transform of the input spectrum taken over the spectral frequency domain. Conversely, the input spectrum B(r) is recovered from I(x) by the Fourier transform over the spatial frequency domain. Zero spatial frequency corresponds to the Littrow wavenumber r0, which means the spectrometer is heterodyned at this frequency. Note that the cosine is an even function; therefore, Eq. 5 yields identical outputs for þ(r r0) and (r r0). This ambiguity can be avoided by tilting one of the gratings by a small angle g with respect to y-axis. This introduces a spatial modulation perpendicular to the modulation along the dispersion dimension x, and the new equation for the interferogram becomes
Z‘ Iðx ; y Þ ¼ 0
BðrÞ 1 þ cosf4p½2ðr r0 Þ 3 tanh x þ gr y g d r
ð6Þ
Now, a two-dimensional (2D) Fourier transform is needed to recover the original spectrum B(r). Note the resolution along the y direction is low because frequencies are not heterodyned. Further details on the theory of SHS are available in the literature.11,12 In particular, the resolving power of SHS, R = r/dr, has been shown to be equal to the theoretical resolving power of the grating system.
1078
Volume 68, Number 9, 2014
Setup. Figure 2 shows a block diagram of the experimental setup. The SHS consists of a 68 3 68 mm, 150 grooves (gr)/mm, 300 nm blaze grating (1); a k/10, 50 mm round flat mirror (2); and a cubic 50.8 mm, 400–700 nm bandwidth beam splitter (3). The 1392 3 1040 charge-coupled device (CCD) array (Cool Snap HQ, Roper Scientific) with a 6.45 3 6.45 lm pixel size and 10/20 MHz digitization rate (5) collects light from the SHS through the objective (4) with adjustable magnification and focal length. Alternatively, an intensified chargedcouple device (ICCD; PI-MAX2: 1003; Princeton Instruments) with a 1024 3 1024 array detector and a 12.8 3 12.8 lm pixel size can be used. The parallel beam of light enters the spectrometer through the iris (6) and is expanded, if necessary, by the beam expander (7). A number of lasers and line light sources are used to set a desirable Littrow wavelength for the grating (1) and to calibrate the spectrometer. These include a helium– neon (He–Ne) laser at 632.8 nm (16); a diode-pumped solid-state (DPSS) laser at 532 nm (MGL 150, Laser Photon Components UG, Dresden, Germany) (17); an Ar-ion laser (177-G02; Spectra Physics) generating a series of lines between 450 and 515 nm (19); and a number of different hollow cathode lamps (HCLs) (21). Light from these sources is guided into the spectrometer by a set of mirrors (15 and 18) and glass flats (8). The collimating lens (20) with a 15 cm focal length delivers light from the HCLs to the SHS over a distance of 3 m. The laser-induced breakdown system includes the neodymium-doped yttrium aluminum garnet (Nd : YAG) laser (1064 nm, 50 mJ pulse energy, 10 ns pulse duration; Big Sky,) (14) focused onto the target (11) using a 2.5 cm diameter, 2.5 cm focal length lens (13). This creates a 0.2 mm diameter spot on the target surface and an irradiance of 16 MW/cm2 . Another 2.5 cm diameter lens (10), placed one focal distance (7.5 cm) from the plasma, collects and collimates the plasma emission.
TABLE I. Brass standard reference materials from NIST. Sample 1104 1109 1110 1111 1113 1115 1116
Zn certified (%)
Zn found (%)
Recovery (%)
Cu certified (%)
Cu found (%)
Recovery (%)
36.36 17.4 15.2 12.81 4.8 11.73 9.44
30.4 17.7 15.2 13.7 6.7 11.0 11.6
86 101 100 107 139 94 122
61.34 82.2 84.59 87.14 95.03 87.96 90.37
66.9 81.2 84.5 86.0 93.2 89.0 88.0
109 99 100 99 98 101 97
Timing for the data acquisition is arranged as follows. When using CW light sources—that is, one of the lasers (16), (17), or (19) or the HCL (21)—the CCD operates in free-run mode, with an exposure time set by software (WinSpec/32, Version 2.5; Roper Scientific). When using a pulsed light source (i.e., the laser plasma (12)), the CCD operates in the external sync mode while the software still determines the exposure time. To synchronize the laser and the CCD, three pulse generators are used. The first (Tektronics PG 501) triggers the flash lamp of the ablation laser and the second pulse generator. The second (HP 8012B) provides a 180 lsdelayed pulse to the Q switch of the laser and third pulse generator. The third triggers the CCD at a variable delay time with respect to the laser pulse starting from the 200 ns delay. This unavoidable initial delay is due to the lag between the Q switch and laser output (125 ns) and the signal processing time of the CCD. In any case, early LIP does not yield good interference images because it emits mostly Bremmstruhlung/ photorecombination continuum and not much structured spectrum. The optimal delay for obtaining sharp interferograms is about 4 ls. This delay is used throughout the experiments using LIP. The exposure time is set to 100 ls and includes all of the luminous plasma lifetime.
Samples. The samples are brass certified reference materials from the National Institute of Standards and Technology (NIST). Table I provides the concentrations of the major elements, Cu and Zn that were used for quantitative LIBS-SHS analysis. Metallic foils of Cu and Zn (Goodfellow, USA) were also used to generate interferograms. The Littrow wavelength of the SHS was aligned with the center of a spectral region of interest (480–520 nm) at about 500 nm. Procedure. The spectrometer was aligned and set at the desired Littrow wavelength using the Ar-ion, Nd : YAG, or He–Ne laser. The Littrow wavelength was tuned by rotating the diffraction grating. To obtain clean interferograms, the background was subtracted from each image. The background was collected by successively blocking one of the two arms of the interferometer and summing up the images. When operating with CW light sources, the CCD camera was set to the free-run mode with the exposure time depending on the brightness of the source. For operation with LIPs, the delay generator triggered the CCD several microseconds after the laser pulse to cut off the plasma continuum radiation. The usual acquisition mode for LIPs was 4 ls for the delay time, 100 ls for the gate, and 50 accumulations on the same sample spot.
FIG. 3. The SHS with HCL filled with Ar and comparison of the resulting spectrum with the spectrum from a low-resolution Czerny–Turner spectrometer.
APPLIED SPECTROSCOPY
1079
FIG. 4. Gallery of SHS interferograms obtained using HCLs and an Ar-ion laser. Insets show spectra measured using an Ocean Optics spectrometer. The Littrow wavelengths of the SHS for each interferogram were set to approximately the middle points of the spectral fragments given in insets.
Software. The initial data were collected and background-subtracted using WinSpec software (Princeton Instruments). Further data processing was performed using homemade software written in Matlab R2013a. This includes the routines for fast Fourier transform (FFT), PCA, and PLS analyses. Yet another routine was written for processing the images resulting from FFT of the interferograms. Pixels on the images were binned along the dimension of low dispersion (vertically); thereafter, analytical lines were identified and processed.
RESULTS AND DISCUSSION Characterization of the Spatial Heterodyne Spectrometer with Continuous Wave Light Sources. To establish the spectral characteristics of the SHS and calibrate it in terms of wavelength, interferograms were collected from various CW light sources. An example is shown in Fig. 3 for the mercury HCL filled with Ar. The Ar spectrum was recorded by the SHS with a Littrow wavelength at 770 nm. The interferogram was transformed using the FFT, followed by binning the image pixels along the direction of minimal dispersion (i.e., vertically). The resulting SHS spectrum was then directly compared with the spectrum from a Czerny–Turner spectrometer with similar resolution. Based on this comparison, the spectral lines were identified. Using a set of line sources such as HCLs, the procedure of tuning the SHS to a desired spectral range took several minutes.
1080
Volume 68, Number 9, 2014
The spectral resolution and spectral range of the SHS were evaluated using simple calculations and from numerous spectra taken under different light sources. The maximum (theoretical) resolving power of the diffraction grating is given by R = mN, where m is the diffraction order and N is the number of groves illuminated by the light. For the current system, R = 150 gr/mm 8 mm = 1200, corresponding to a minimal resolved interval Dk = 0.4 nm at 500 nm. The spectral coverage is, correspondingly, L = Dk Npix/2 = 0.4 nm 696 240 nm, taking into account the Nyquist condition, with the Npix/2 limit for the number of resolved spectral elements.12 Here Npix = 1392 is the total number of pixels on the detector in the direction of maximal spectral resolution. Apart from the spectrometer itself, the resolution depends on fringe focusing conditions (i.e., the focal length and magnification of the camera objective).13 In the current case, it was about fourfold lower than the predicted theoretical resolution. This can be verified from Fig. 3. Note that high resolution was not the goal in this proof-of-principle investigation. If desired, we can easily improve the resolution by replacing the mirror by a second diffraction grating and/or using gratings with a higher number of grooves per millimeter. To give reader an impression of how the interferograms look for different spectral ranges and different line densities, a selection of SHS interferograms supplemented by reference spectra taken using a dispersive spectrometer (Ocean Optics) are presented in Fig. 4.
FIG. 5. The LIBS-SHS spectrum of brass foil with the Zn and Cu lines identified.
Obviously, light sources emitting more spectral lines produce more complex interferograms. Spatial Heterodyne Spectroscopy of Laser-Induced Plasma. We chose laser-induced breakdown on brass to study the performance of LIBS-SHS because of the relative simplicity of brass spectra. The SHS was tuned to the range 450–600 (with the Littrow wavelength at 500 nm) because this range contains several strong spectral lines of Cu and Zn. Figure 5 shows a processed LIBSSHS spectrum with the lines identified. The interferograms exhibit the best contrast when the delay time is set to 4 ls and integration time is set to 100 ls. These setting were used throughout LIBS-SHS experiments. To test the sensitivity of LIBS-SHS, the emission signal was gradually attenuated by factors of 10, 100, and 1000 using neutral-density filters. Figure 6 displays the interferograms, their FFTs, and the spectra obtained using different degrees of attenuation. In each case, the signal consists of 50 accumulations. We can see that the emission lines of Cu and Zn are distinct for 10- and 100fold attenuations, but the signal-to-noise ratio degrades insignificantly. Even at 1000-fold attenuation, when no visible pattern can be recognized in the interferogram, the FFT still yields recognizable Cu and Zn emission signals. A simple estimate shows that minimal detectable signals from Cu and Zn correspond to concentrations of about 0.05%. Note that this result is obtained without optimization of the SHS system, using a nonintensified CCD detector and relatively weak spectral lines. Classification of the Brass Samples. Laser-induced breakdown spectroscopy is often used for classification
rather than for quantitative analysis.21 To investigate the potential of LIBS-SHS for material classification, we conducted a PCA on the brass data. The PCA was applied in two ways: on the raw interferograms and on truncated 2D images after the FFT. Prior to the PCA, the corresponding matrices were rearranged into vectors and then into new matrices suitable for PCA. The columns and rows of these matrices correspond to variables (pixel-wise intensities) and observations (samples) in chemometric notation. Figures 7 (left and middle) display an interferogram and its Fourier image obtained from one of the brass samples. Similar FFT images of all interferograms were used as the input data in both the PCA (classification) and PLS (quantitative analysis). The PCA of the truncated data set is shown in Fig. 7 (right) in terms of two first principal components (PCs). The distinct grouping is observed for all but two compositionally closest samples, 1111 and 1115. Pure Cu and brass samples were also included in the analysis. Their scores form groups most distant from other groups. The PCA on the raw interferograms (not shown) yielded results similar to those in Fig. 7 but with less compact grouping. That was logical for data not filtered by FFT, which removes a significant amount of noise from the interferograms. Further improvement can be expected from better-quality (i.e., contrast) interferograms, which can be achieved by equalizing the blazing/ reflection of a grating-mirror pair at Littrow and other wavelengths. Quantitative Analysis of the Brass Samples: A Feasibility Study. Quantitative analysis of the brass
APPLIED SPECTROSCOPY
1081
FIG. 6.
Test for sensitivity using the gradual attenuation of the LIBS-SHS signal.
samples was attempted in two ways: univariate, using single lines, and multivariate, using a PLS routine. For the univariate analysis, FFT images of the initial interferograms (e.g., Figs. 7 [middle and left]) were vertically binned to yield conventional spectra in terms of intensities versus wavelength. Such spectra are shown in Fig. 8 (left). The ‘‘wavelengths’’ are, in fact, the wavelength indices, that is, the pixel numbers along the high-dispersion dimension. We still needed to relate them to wavelengths. This was done by comparing the FFT images of brass plasmas to those of Cu and Zn HCL plasmas. For the multivariate analysis, FFT images of interferograms were used as is, without binning. The Zn I 481.05 nm line was chosen for the construction of the univariate calibration plot. In addition
to the brass standards, pure Zn and Cu samples were added to the sample set to expand the concentration range to cover 0 and 100% for both Cu and Zn. All spectra were preprocessed: the background under the lines was removed, and the lines were smoothed using a gentle three-point, first-order Savitzky–Golay filter and approximated using a Lorentzian profile. The analytical signal was the line integral intensity taken within limits 61.4 FWHM (where FWHM is the full width at halfmaximum) as recommended in the literature.22 We can see that the calibration plot in Fig. 8 (right) is S-shaped, showing a plateau at both low and high concentrations. We can offer no conclusion at this point about whether this is an instrumental artifact or reflects physical processes, and therefore we made no attempt to predict
FIG. 7. Interferogram (left). Average spectra of brass samples after FFT (middle). The PCA performed on individual spectra (right).
1082
Volume 68, Number 9, 2014
FIG. 8. Average spectra of brass samples after the FFT of the interferograms (left). Plot of the integral intensity of the Zn I 481.05 nm line versus concentration (right).
unknown concentrations from this S-shaped calibration function. Note, however, that the breakdown of brass samples is notorious for nonstoichiometric ablation; this effect has been described in several papers.23 As alluded to earlier, brass was chosen as a test sample because of the simplicity of its spectrum. The reproducibility of the analytical signal was typical for LIBS, 610% relative standard deviation (RSD) over the whole concentration range. An attempt at quantitative analysis was also made based on multivariate PLS analysis. Here, three spectra out of five replicates (50 accumulations each) were randomly chosen for calibration. Two remaining spectra were used as unknowns. There was a concern that PLS could be unsuitable for quantification due to the nonlinear response that was seen in the univariate case. Therefore, prior to analysis, we performed a crossvalidation to determine which samples constituted a reliable calibration set and how many PCs should be taken. Figure 9 (left) shows the estimated mean square prediction error (MSPE) as a function of the number of PCs. We can see that the model remains imprecise; it shows a high MSPE for both Zn and Cu when pure Zn and Cu are included in the calibration set. Removing these samples brings the MSPE to an acceptable level of about 10%. The plots in Fig. 9 (left) also imply that using more than three PCs would be ill advised. Doing so
FIG. 9.
would not improve the prediction accuracy but would lead to overfitting of the calibration set. Therefore, only three PCs were chosen for the calibration model. The results of the PLS analysis are listed in Table I and shown in Fig. 9 (right) in the form of a correlation plot of certified and determined concentrations. The correlation is very high, with a slope near 458 and 0.996 coefficient of determination. The precision is also high (the error bars in Fig. 9 are concealed inside markers), under 1% RSD, but statistically insignificant because it is derived from only two measurements (two unknowns). The accuracy (‘‘Recovery’’ column in Table I) is within 6 5% of nominal values for almost all the samples except for those with minimal and maximal concentrations. This deviation is probably due to the slightly nonlinear behavior of the calibration set. Similar results (not shown) were obtained for a PLS analysis of the raw interferograms. However, the number of PCs used had to be doubled (six instead of three). Therefore, the results might not be reliable due to significant overfitting. As mentioned before, FFT filters out a significant amount of noise from the raw interferograms.
CONCLUSION This study has demonstrated that a SHS can be used in combination with a LIP to detect spectra and that it can
Cross-validation with all samples, including pure Zn and Cu (left). Correlation between the determined and certified concentrations (right).
APPLIED SPECTROSCOPY
1083
be used to tackle both quantitative analysis and classification tasks. In this pilot experiment, the LIBSSHS system was not optimized to obtain maximal sensitivity and resolution. Instead, the simplest of all possible designs was used. Nevertheless, we were able to obtain both classification and quantification results. The quantitative analysis of the brass samples provided an acceptable accuracy (6 5% of nominal concentrations) and precision (RSD , 10%). The minimal detectable concentrations of Zn and Cu in brass were estimated at around 0.05%. A further increase in performance can be expected from a better design of the SHS. This would include using matching pairs of optical elements (mirror–grating or grating–grating), a better detector (ICCD instead of CCD), and focusing optics. In addition to the obvious advantage of high throughput and resolution, LIBS-SHS is easily adaptable to any spectral range—ultraviolet, IR, or even vacuum ultraviolet. This capability stems from using diffraction gratings instead of the mirrors used in conventional interferometry. Using the gratings significantly relaxes the requirements for the quality of the optics and reduces the cost. In summary, based on the preliminary results of this study, we can conclude that LIBS-SHS has clear potential to become a technique of choice in some LIBS applications, especially those requiring standoff capability. ACKNOWLEDGMENTS The authors thank Prof. S. Michael Angel from the University of South Carolina for providing useful information. Also, the authors thank the current and former graduate students of the University of Florida, Laser Spectrochemistry laboratory, for assistance in setting up the experiment. 1. D.W. Hahn, N. Omenetto. ‘‘Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma-Particle Interactions: Still-Challenging Issues Within the Analytical Plasma Community’’. Appl. Spectrosc. 2010. 64(12): 335A-366A. 2. D.W. Hahn, N. Omenetto. ‘‘Laser-Induced Breakdown Spectroscopy (LIBS), Part II: Review of Instrumental and Methodological Approaches to Material Analysis and Applications to Different Fields’’. Appl. Spectrosc. 2012. 66(4): 347-419. 3. R.C. Wiens, S. Maurice, J. Lasue, O. Forni, R.B. Anderson, S. Clegg, S. Bender, D. Blaney, B.L. Barraclough, A. Cousin, L. Deflores, D. Delapp, M.D. Dyar, C. Fabre, O. Gasnault, N. Lanza, J. Mazoyer, N. Melikechi, P.-Y. Meslin, H. Newsom, A. Ollila, R. Perez, R.L. Tokar, D. Vaniman. ‘‘Pre-Flight Calibration and Initial Data Processing for the Chemcam Laser-Induced Breakdown Spectroscopy Instrument on the Mars Science Laboratory Rover’’. Spectrochim. Acta, Part B. 2013. 82: 1-27. 4. A.P.M. Michel, M. Lawrence-Snyder, S.M. Angel, A.D. Chave. ‘‘Laser-Induced Breakdown Spectroscopy of Bulk Aqueous Solutions at Oceanic Pressures: Evaluation of Key Measurement Parameters’’. Appl. Optics. 2007. 46(13): 2507-2515. 5. R. Noll. Laser-Induced Breakdown Spectroscopy: Fundamentals and Applications. Berlin- Heidelberg, Germany: Springler-Verlag, 2012. Pp. 484-488.
1084
Volume 68, Number 9, 2014
6. F.R. Doucet, G. Lithgow, R. Kosierb, P. Boucharda, M. Sabsabi. ‘‘Determination of Isotope Ratios Using Laser-Induced Breakdown Spectroscopy in Ambient Air at Atmospheric Pressure for Nuclear Forensics’’. J. Anal. Atom. Spectrom. 2011. 26(3): 536-541. 7. X. Mao, A.A. Bol’shakov, I. Choi, C.P. McKay, D.L. Perry, O. Sorkhabi, R.E. Russo. ‘‘Laser Ablation Molecular Isotopic Spectrometry: Strontium and Its Isotopes’’. Spectrochim. Acta, Part B. 2011. 66(11-12): 767-775. 8. J.L. Gottfried, F.C. De Lucia, Jr., C.A. Munson, A.W. Miziolek. ‘‘Laser-Induced Breakdown Spectroscopy for Detection of Explosives Residues: A Review of Recent Advances, Challenges, and Future Prospects’’. Anal. Bioanal. Chem. 2009. 395(2): 283-300. 9. K. Novotny, J. Kaiser, J. Novotny, G. Vı´ tkova´, R. Malina, D. Procha´zka, V. Kanicky, V. Otruba, M. Lisˇka. ‘‘Utilization of Remote-LIBS Technique for Comparison of Brick Samples’’. Paper presented at: NASLIBS. New Orleans, LA; July 13-15, 2009. 10. S. Tzortzakis, D. Anglos, D. Gray. ‘‘Ultraviolet Laser Filaments for Remote Laser-Induced Breakdown Spectroscopy (LIBS) Analysis: Applications in Cultural Heritage Monitoring’’. Opt. Let. 2006. 31(8): 1139-1141. 11. J. Harlander. Spatial Heterodyne Spectroscopy: Interferometric Performance at Any Wavelength Without Scanning. [Ph.D. Dissertation]. Madison, WI: University of Wisconsin, 1991. 12. J.M. Harlander, R.J. Reynolds, F.L. Roesler. ‘‘Spatial Heterodyne Spectroscopy for the Exploration of Diffuse Interstellar Emission Lines at Far-Ultraviolet Wavelength’’. Astrophys. J. 1992. 396(2): 730-740. 13. N.R. Gomer, C.M. Gordon, P. Lucey, S.K. Sharma, J.C. Carter, S.M. Angel. ‘‘Raman Spectroscopy Using a Spatial Heterodyne Spectrometer: Proof of Concept’’. Appl. Spectrosc. 2011. 65(8): 849-857. 14. T.A. Nathaniel, C.I. Underwood. ‘‘Spatial Heterodyne Raman Spectroscopy’’. Paper presented at: 42nd Lunar and Planetary Science Conference. The Woodlands, TX; March 7-11, 2011. 15. Y. Lin, G. Shepherd, B. Solheim, M. Shepherd, S. Brown, J. Harlander, J. Whiteway. ‘‘Introduction to Spatial Heterodyne Observations of Water (SHOW) Project and Its Instrument Development’’. Paper presented at: XIV International TOVS Study Conference. Beijing, China; May 25-31, 2005. 16. C.R. Englert, D.D. Babcock, J.M. Harlander. ‘‘Spatial Heterodyne Spectroscopy for Long-Wave Infrared: First Measurements of Broadband Spectra’’. Opt. Eng. 2009. 48(10): 105602. 17. J.M. Harlander, F.L. Roesler, J.G. Cardon, C.R. Englert, R.R. Conway. ‘‘Shimmer: A Spatial Heterodyne Spectrometer for Remote Sensing of Earth’s Middle Atmosphere’’. Appl. Optics. 2002. 41(7): 1343-1352. 18. M.W. Kudenov, M.N. Miskiewicz, M.J. Escuti, E.L. Dereniak. ‘‘Spatial Heterodyne Interferometry with Polarization Gratings’’. Opt. Lett. 2012. 37(21): 4413-4415. 19. J.M. Harlander, J.E. Lawler, J. Corliss, F.L. Roesler, W.M. Harris. ‘‘First Results from an All-Reflection Spatial Heterodyne Spectrometer with Broad Spectral Coverage’’. Opt. Express. 2010. 18(6): 6205-6210. 2 0 . L i g h t M a c h in e r y . ‘‘ O p t ic a l C o m p o n e n t s ’’ . h t t p : / / w w w . lightmachinery.com/optical-components.html [accessed Mar 24 2014]. 21. I.B. Gornushkin, B.W. Smith, H. Nasajpour, J.D. Winefordner. ‘‘Identification of Solid Materials by Correlation Analysis Using a Novel Microscopic Laser Induced Breakdown Spectrometer’’. Anal. Chem. 1999. 71(22): 5157-5164. 22. E. Voigtman. ‘‘Gated Peak Integration Versus Peak Detection in White Noise’’. Appl. Spectrosc. 1991. 45(2): 237-241. 23. V. Margetic, A. Pakulev, A. Stockhaus, M. Bolshov, K. Niemax, R. Hergenro¨der. ‘‘A Comparison of Nanosecond and Femtosecond Laser-Induced Plasma Spectroscopy of Brass Samples’’. Spectrochim. Acta B. 2000. 55(11): 1771-1785.
