Automated Quantitative Spectroscopic Analysis Combining Background Subtraction, Cosmic Ray Removal, and Peak Fitting | Spectroscopy

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  Automated Quantitative Spectroscopic Analysis CombiningBackground Subtraction, Cosmic Ray Removal, and Peak Fitting Timothy M. James, a Magnus Schlo ¨sser, b Richard J. Lewis, a Sebastian Fischer, b Beate Bornschein, b Helmut H. Telle a, * a   Department of Physics, College of Science, Swansea University, Singleton Park, Swansea, SA2 8PP United Kingdom b  Institute for Technical Physics (ITeP), Tritium Laboratory Karlsruhe (TLK), Karlsruhe Institute of Technology (KIT), P.O. Box 3640, 76021 Karlsruhe, Germany An integrated concept for post-acquisition spectrum analysis wasdeveloped for in-line (real-time) and off-line applications that preservesabsolute spectral quantification; after the initializing parameter setup,only minimal user intervention is required. This spectral evaluation suiteis composed of a sequence of tasks specifically addressing cosmic rayremoval, background subtraction, and peak analysis and fitting, togetherwith the treatment of two-dimensional charge-coupled device array data.One may use any of the individual steps on their own, or may excludesteps from the chain if so desired. For the background treatment, thecanonical rolling-circle filter (RCF) algorithm was adopted, but it wascoupled with a Savitzky–Golay filtering step on the locus-array generatedfrom a single RCF pass. This novel only-two-parameter procedure vastlyimproves on the RCF’s deficiency to overestimate the baseline level inspectra with broad peak features. The peak analysis routine developedhere is an only-two-parameter (amplitude and position) fitting algorithmthat relies on numerical line shape profiles rather than on analyticalfunctions. The overall analysis chain was programmed in NationalInstrument’s LabVIEW; this software allows for easy incorporation of this spectrum analysis suite into any LabVIEW-managed instrumentcontrol, data-acquisition environment, or both. The strength of theindividual tasks and the integrated program sequence are demonstratedfor the analysis of a wide range of (although not necessarily limited to)Raman spectra of varying complexity and exhibiting nonanalytical lineprofiles. In comparison to other analysis algorithms and functions, ournew approach for background subtraction, peak analysis, and fittingreturned vastly improved quantitative results, even for  ‘‘ hidden ’’  details inthe spectra, in particular, for nonanalytical line profiles. All software isavailable for download. Index Headings:  Automated baseline subtraction; Cosmic ray removal;Peak analysis; Quantitative spectroscopic analysis; Raman spectroscopy;Rolling-circle filter. INTRODUCTION Analytical (laser) spectroscopy techniques have becomecommonplace in a wide range of applications in, e.g., analyticalchemistry, chemical processing, biomedical research, andnanotechnology. Absolute and relative quantifiable results aswell as chemometric classification, based on the recordedspectra, are of vital importance in all of these fields. Generally,spectral responses are treated numerically during post-acquisi-tion analysis, namely, to (i) remove background, (ii) eliminatespurious cosmic ray events, (iii) fit spectral line profiles, or a combination. If not applied with care, each of these measuresmay affect the quantitative information contained in the spectra and also may influence detection limits. Note that spectra of complex specimens are often evaluated using, e.g., principalcomponent analysis (PCA)/chemometrics instead of peakfitting; the aim then is classification rather than precisequantification.Most modern data analysis software packages, either commercial or user-written, incorporate some or all theaforementioned post-acquisition functionality. But, normallythe full analysis chain, i.e., acquisition ! spectra correction ! data analysis, is only semiautomatic (i.e., some or all partsrequire human input, and one often encounters strong modeldependence in the chosen correction routines). Furthermore,they are often  ‘‘ black-box ’’  implementations, and the sophis-tication of individual procedures can vary significantly,depending on which user community is targeted. This variationbecomes problematic in situations (i) where near real-time(feedback) response is required to maintain stable operationalconditions, and (ii) when experiments run over extendedperiods of time (weeks, months or even years), and thusperpetual user attention is often out of the question.Specific in-line experiments that may be seen as exemplaryfor being affected by all the above-mentioned effects andcaveats are encountered in the International Thermonuclear Experimental Reactor (ITER) project and in the KarlsruheTritium Neutrino (KATRIN) experiment. For example, theKATRIN experiment  1 is set up to measure the neutrino massby means of analyzing the electron-energy spectra associatedwith the  b -decay of tritium, bound to run nearly continuouslyover a period of three to five years. Thus automation of anymonitoring and control mechanisms during the gathering of spectral information is paramount. Besides the recording of the b -decay spectrum itself, knowledge of the temporal stabilityand chemical composition of the tritium gas feed from the inner tritium loop into the source tube of KATRIN is of ultimateimportance. 2 Thus the amount and the purity of the tritium gasinjection have to be monitored continuously and can berealized by using a laser Raman system. 3 The Raman system’srequirements for data treatment and analysis procedures arerather demanding:(i) The operation and analysis procedure needs to beautomated, unstaffed, able to run for 60 days nonstop, andprovide real-time feedback of the gas composition (specificallyT 2 , DT, and HT) to the KATRIN run-control.(ii) Acquisition and analysis time need to be minimized toenable fast feedback of the monitored gas composition.(iii) The extracted Raman line intensities have to be freefrom systematic shifts to provide reliable and quantifiableresults, and the precision of the analysis output has to be of theorder 0.1 %  or better. Received 20 June 2012; accepted 18 March 2013 * Author to whom correspondence should be sent. E-mail: 10.1366/12-06766 Volume 67, Number 8, 2013 APPLIED SPECTROSCOPY  949 0003-7028/13/6708-0949/0   2013 Society for Applied Spectroscopy  These requirements lead to some specific problems encoun-tered in the evaluation of recorded (Raman) spectra. For example, the baseline in the spectra may change nonlinearlywith time, and transient changes in the gas composition canoccur. Both changes affect the sensitivity of KATRIN or, for that matter, any other experiments experiencing such baselinevariations. The former change is mainly encountered in long-term operations, caused by, e.g., temperature effects, thegeneration of color centers in the Raman cell window, (trace)generation of chemical reaction products, 4 or a combination;the latter change is due to system-specific injection of freshgases, and retraction of   ‘‘ waste. ’’ Any post-acquisition analysis still has to work fast andreliably under the aforementioned circumstances, and it shouldincorporate subtasks to deal with background subtraction,cosmic ray removal, and quantitative spectral line evaluation.This analysis should happen with as little user intervention aspossible and should be fast enough to provide the desired near real-time response. The latter response should not be tooproblematic for KATRIN Raman monitoring, where responsetimes of approximately 60–100 s are specified. However, in thecontext of the ITER project, the requirements are much morechallenging, since real-time process control with responsetimes of less than or equal to 1 s are required.Furthermore, it should be possible to seamlessly link theevaluation procedure to any data acquisition process, ideally torun in parallel to an acquisition to provide near real-timeanalysis; but which, conversely, is equally applicable to other  ‘‘ off-line ’’  evaluation of spectra. Also, it would be advanta-geous if such an integrated routine were suitable for other experimental situations in which spectra are generated in needof similar data treatment.For example, recently depolarization measurements for theQ-branch Raman lines of the hydrogen isotopologues and other molecules have been carried out by our group. 5 Thesemeasurements may require very long acquisition times of upto the order of 1000 s, rather than the few seconds in theaforementioned dynamic KATRIN and ITER response de-mands, to gather the related spectra of huge intensitydifferences with the necessary high signal-to-noise ratio. Suchlong signal integration times lead to a large number of cosmicray events captured by the charge-coupled device (CCD)detector during an acquisition, and the cosmic ray removal taskwould need to be able to deal with this outcome. To provideaccurate depolarization ratios for individual rotational Ramanlines—even those with weak intensity or overlapping with eachother—the precision in the peak evaluation would need to beeven higher than for the monitoring and control tasks inKATRIN, ITER, or other experiments.The integrated spectrum analysis procedure described hereevolves from cosmic ray removal via astigmatism correctionand background subtraction to peak intensity extraction. Theinterplay of individual spectra treatment steps and the successof the overall concept are presented for some selectedexamples. It should be noted that parts of the analysisprocedure described in this publication have been successfullyapplied to KATRIN-related measurements 2,6 and other Ramanexperiments. 7,8 Once operating parameters are set, it constitutesa fully automated procedure for post-acquisition data treatment of (Raman) spectra and analysis of spectral line peaks. Thenecessity for model input has been reduced to the lowest levelpossible while maintaining full control on the methods.It is worth noting that by no means are we the first to attempt to assemble a suite for the evaluation of Raman spectra. SinceRaman spectroscopy has become a widely accepted analyticalmethod, nearly all manufacturers of related instrumentationprovide software packages that incorporate data acquisition,pre-evaluation data treatment, and final spectrum evaluation. Inaddition, quite a few research groups have attempted to tailor certain aspects to specific needs in their work (e.g., Reisner et al. 9 and Vicarra Rossel 10 ). Three aspects of all approachesseem to be common: (i) usually, the data evaluation is gearedtoward chemometrics, i.e., sort-of   ‘‘ pattern-recognition ’’ against library data; exact quantification is often of lesser interest; (ii) because the chemometric aspect is the key in most of the published works, detailed information on the pre-evaluation procedures is normally sparse (e.g., it is not alwaysclear how well the particular, selected procedure would suit quantification, as we require in our research); and (iii) data acquisition and evaluation are normally sequential. DATA ANALYSIS METHODS The overall analysis procedure described here is composedof a sequence of individual steps, each associated with its ownLabVIEW subroutine (subVI); these subroutines also can beused on their own, in principle. The schematic flow chart for this concept is shown in Fig. 1; the individual routines aredescribed in the sections below, in the sequence as they areexecuted in the overall program chain.For   ‘‘ on-line ’’  applications, all steps are fully incorporatedinto a program flow and require only minimal user interventionduring the initial set-up; for off-line applications, the sequenceshown in Fig. 1 is overlaid with a graphical front end. Bysetting option switches in the program flow, individual steps inthe sequence may be skipped, should they not be required for a particular spectrum analysis. It should be noted that LabVIEWstands out when seamless integration of instrument control,data acquisition, and signal analysis is desired. A similar LabVIEW approach, albeit for the analysis of biochemicalsamples and chemometric evaluation, has been described byVicarra Rossel. 10 Of course, all individual tasks may beprogrammed differently; thus, the underlying generic algo-rithms for each are summarized in a supplemental materialdocument wherein we also provide download options for thedocumented programs. Cosmic Ray Removal.  In any spectrum recorded by photondetectors, cosmic ray events are encountered on a frequent but random basis. For CCD array detectors, they manifest themselves as (mostly) single-pixel responses where theparticular pixel carries a far greater intensity in comparisonwith that of neighboring pixels. For accurate analysis of suchaffected spectra, the cosmic-ray events need to be removed.Numerous techniques and algorithms exist that can beimplemented for cosmic ray removal from one-dimensional(1D) or two-dimensional (2D) spectral recordings (e.g.,Home, 11 Kelson, 12 Li and Dai, 13 and Mozharov et al. 14 ). Sincein the work described here we only deal with 1D spectrumtraces, we do not elaborate further on 2D methodology (for a brief summary on the latter, see Section 1 of the supplementalmaterial).Having sets of spectra recorded over time, like in our case(large sets of spectra are recorded during KATRIN runs andduring off-line control measurements), the least complicatedand very efficient method for identifying and eliminating 950  Volume 67, Number 8, 2013  cosmic rays is the use of spectral difference comparison.Comparing at least two consecutive spectra recordings and thendetermining the signal difference pixel by pixel implement thisconcept. If the absolute value of this difference is less than a threshold, the two spectral data points are averaged, and thisaverage is taken as the  ‘‘ cleaned ’’  output value; otherwise, thesmaller valued data point is taken as the output value. Thethreshold value has to be set large enough not to becompromised by noise fluctuations but small enough toefficiently capture the majority of cosmic ray events that canhave a wide range of random amplitudes. We have dubbed thisprocess  ‘‘ temporal ’’  cosmic ray removal (TCRR), and it isrepeated for the selected set of rows or binning segments of thedetector chip, and for the full set of spectra.It should be noted that TCRR has certain limitations. TCRRworks assuming that cosmic ray events are random and sparse,whereas the spectral features of interest are static for consecutive spectra. This assumption is no longer valid for very long acquisition times. As the acquisition time expands,the probability that cosmic rays will strike the detector in thesame or in close-proximity places in consecutive acquisitionsincreases. Hence, an acquisition time threshold will beencountered, where the simple (two back-to-back acquisitionsonly) temporal routine will no longer remove all cosmic rays.Above this threshold, more than two consecutive acquisitionswill be needed to ensure the spectra are completely clean of cosmic rays.In principle, one could see this multiple-comparisonapproach to be akin the differentiation method described byMozharov et al., 14 who for a multitude of repeat measurements,differentiated the spectra along the time axis at each pixel(wavelength) position. The cosmic rays show up as disconti-nuities in the derivative spectrum, and they can be eliminatedvia neighboring pixel replacement.The routine TCRR has been tested on high- and low-intensity spectra for various acquisition times; for eachmeasurement series, cosmic ray events left in the spectra werecounted. The number of cosmic rays present in a spectrum willvary depending on the location, shielding, and time of day.Based on the test measurements with our PIXIS:2KB(Princeton Instruments) and Synapse FIOP (Horiba) detectors,the TCRR routine removed all cosmic rays with only twoconsecutive spectra for acquisition times for an individualspectrum of up to approximately 600 s (normally, acquisitiontimes are much shorter than this value). Above this value, threeor more consecutive spectra were required. The numbers statedhere may change for other detectors and measurement conditions. However, the results show that TCRR can be verysuccessful and that for short acquisition times almost alwaysonly two consecutive spectra are needed to remove all cosmicrays. Astigmatism Correction.  All optical systems suffer from a certain degree of astigmatism, i.e., distortion of straight lines bycurved optical components. As a consequence, in a relativelyshort focal length (small f-number) spectrograph with widedispersion, the shift of a line maximum within pixel rows near the top and bottom edges of a CCD array detector can be quitesevere. The simplest approach to correcting astigmatismaberration in a well-aligned CCD-array detector is to shift allindividual rows until full alignment with a selected linemaximum in a reference row is achieved. This  ‘‘ per-row ’’ approach consists of two steps: (i) characterization of theastigmatism curvature; and (ii) interpolation for the (fractional-value) pixel shift, an interpolation that also includes a fractionalshift correction associated with the slight change of astigma-tism as a function of wavelength. The implementation of thisprocedure is based on our earlier work on Raman spectroscopyof hydrogen isotopologues 15 and is described in more detail inthe supplemental material section. Background Removal.  The removal of background fromspectral data has been subject to many studies, and numerousalgorithms have been developed for a variety of methodolo-gies. However, it has to be noted that because of the largevariation of individual needs for such post-acquisition data  F IG . 1. Flowchart for integrated, sequential evaluation procedure, indicatingthe action of each individual step. APPLIED SPECTROSCOPY  951  treatment, in different spectroscopic techniques and individualexperiments, particular procedures may not be universallysuccessful. Over the past few years, some efficient procedureshave been described and cross-compared, normally based onwell-established theories, but incorporating novel algo-rithms. 16,17 Although these procedures may be judged as quitesuccessful, it is equally clear that some approaches are time-consuming (e.g., Schulze et al. 18 state for their method that   ‘‘ it requires further development for in-line or real-time applica-tions ’’ ), or they need extensive user intervention for their overall success. However, for real-time evaluation of spectra that may suffer nonlinear variation of background and noise,and that are accumulated continuously over extended periodsof time, processing speed is of the essence and user intervention should be reduced to a minimum. For example,the planned Raman monitoring in the KATRIN experiment or the future ITER fusion experiment will generate spectra everyfew seconds to minutes, over periods of several months for individual measurement campaigns, with the need for frequent feedback for measurement or process control.We have explored the various published methodologies andfound the rolling circle filter (RCF) concept to have high meritsfor background removal in conjunction with such months-longtasks and for dealing with odd-shaped and time-varying baselines. RCF requires no further user intervention onceparameters have been set for the specific task, but it canthereafter cope automatically with nearly any not-too-suddenvariation in background or noise during long measurement periods. Next, we describe our particular approach and themodifications we made to the basic methodology. Althoughthis new approach to the RCF methodology was specificallydeveloped with the KATRIN and ITER experiments in mind, it has already been used successfully in other experiments. 7,8  Rolling Circle Filter.  The RCF routine was originallyproposed by Mikhailyuk et al. 19 The associated canonicalRCF is described, e.g., in Brandt et al. 20 The concept of theaction of the RCF is visualized in Fig. 2. As suggested by itsname, it is broadly equivalent to rolling a circle of radius  r  below a measured array of points, treating the array as a rigidsurface. The vertical locus at the top of the circle thus rolled istaken as an estimate of the varying background level. For thiswork, the RCF was implemented in LabVIEW, as summa-rized in the supplemental material accompanying thispublication. Savitzky–Golay Coupled Advanced Rolling Circle Filter(SCARF).  The canonical RCF algorithm has a seriousdeficiency, namely, that the baseline level is overestimated if a gap (e.g., a peak or broad unresolved feature) is encounteredwhose baseline width,  w , is larger than double the RCF-circleradius, i.e.,  w  2 r  . Then, the propagating circle  ‘‘ rolls into thegap ’’  (see Fig. 2), thus subtracting more than the actualbackground. But, simply increasing the RCF-circle to muchlarger values does not necessarily fully solve the problem, aswill be shown in the examples below.Our proposed SCARF algorithm can ameliorate thisdeficiency. Simply put, it works by applying a Savitzky–Golayfiltering (SGF) step to the locus-array generated from a singleRCF pass. Two key parameters in the SGF algorithm have tobe set appropriately, namely, (i) the number of side points,  s  r  , to be included (the number of side points corresponds to thehalf-width of the SGF window), and (ii) the polynomial order   n of the smoothing process. Note that in this work thepolynomial order was always  n  =  3 (but this can be alteredif so desired). It also should be stressed that the SGF-step isapplied to the background estimate, and not to the spectral data itself.The procedure is surprisingly robust even if parameters werenot set to their optimum values. However, care should still betaken to choose a suitable value of   r   in the RCF segment of theroutine and the number of side points,  s . Specifically,  r   shouldbe as small as possible in order to capture details in thevariation of the baseline level but normally should not besmaller than the widest spectral peak of interest (i.e., 2 r    w max ), whose shape one wishes to preserve, sitting upon themoving baseline. For broad background features within themoving baseline, the limit of   r   may be reduced to ensure thebaseline is followed correctly. But, as a consequence of reducing 2 r   to values below  w max , the number of side pointsneeds to be increased. However, decreasing 2 r   too far mayhave unwanted, rather adverse effects, as shown in theexamples below. Finally, for most efficient removal of odd-shaped background from peaks of varying width multiplepasses of the routine may be required.To demonstrate the action of the standard RCF and theadvanced SCARF routines, we applied them for a range of filter parameters, specifically to (i) a synthetic line spectrumand (ii) a real Raman spectrum.In the first instance, a simple synthetic spectrum has beengenerated, consisting of a pure Gaussian line of full width half-maximum (FWHM)  w  =  10 pixel, sitting on an offset background dressed with random shot noise fluctuations. Theamplitude of the spectral line was changed from values just above the noise level to values at which the noise becomesnearly negligible. The default starting parameter for the RCFprocedure was  r   =  2 w . The results are summarized in Fig. 3and Table I; note that the entries in the table are the amplitudes,in units of counts, recuperated by peak-fitting the background-corrected spectra after filter treatment.Both the figure and table data clearly reveal that selecting thefilter parameters too small with respect to the base width of thepeak results in the filter rolling into the peak, and thussubtracting an incorrect value. It is clear that peaks of equalFWHM, but substantially different amplitude, exhibit different behavior. One notices that it is indeed the width at the base of the peak (here, the width points are taken at two times the noisefluctuations above the baseline) that is responsible for how far  F IG . 2. Action of the RCF on an example spectrum; the filter tends to roll intothe peak, overcompensating the background level. This deficiency is overcomeby using our SCARF filter routine. 952  Volume 67, Number 8, 2013
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