OPSIAL Manual. v Xiaofeng Tan. All Rights Reserved
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1 OPSIAL Manual v Xiaofeng Tan. All Rights Reserved
2 1. Introduction Spectral Calculator & Fitter (SCF) Automated Analyzer (AA) Working Principles and Workflows of OPSIAL RT Model Workflow of SCF Workflow of AA Tutorial References
3 1. Introduction OPSIAL (Optical Plasma Spectral CalculatIon And Parameters RetrievaL) is software package for calculating emission spectra of plasmas and for automatically determining chemical species and important plasma parameters (i.e., chemical species, mixing ratios, plasma LTE temperature, and electron density) of a plasma from its emission spectra. It is comprised of two major components: 1) Spectral Calculator & Fitter, 2) Automated Analyzer. 1.1 Spectral Calculator & Fitter (SCF) The SCF uses an ultra-fast line-by-line (LBL) radiation transport (RT) algorithm developed by Dr. Tan (Tan, X. An ultrafast line-by-line algorithm for calculating spectral Transmittance and radiance, J. Quant. Spectrosc. Radiat. Transfer, 129, p , 2013) for calculating emission spectra of a plasma based on line of sight (LOS) information of the plasma specified by the user through the graphical interface of OPSIAL. Highlighted features of SCF include: An ultra-fast LBL algorithm for performing accurate first-principles calculations of emission spectra of plasmas. Covering the 150 nm 1000 nm spectral range. Including all ionic and neutral atomic species in the NIST and CFA atomic databases. Supporting multiple LOS segments. Supporting spectral emission calculations for both LTE and NLTE conditions. Automatically fitting to the input plasma emission spectrum by optimizing chemical species mixing ratios, temperatures (LTE and NLTE), and pressures of the plasma. 1.2 Automated Analyzer (AA) The AA uses patented technology (Tan, X. Method for automatically determining chemical species, mixing ratios, temperatures, and electron density in plasmas from observed emission spectra, patent pending # , 2016) for automatically determining chemical species, mixing ratios, plasma LTE temperatures, and electron density in a plasma from its emission spectra. Highlighted features include: Fully automated analysis workflow that does not require human interventions. Automatically identifying chemical species (covering all atomic species in the NIST and CFA databases) in a plasma from its emission spectra. Producing quantitative metrics for the species identification, including sensitivity and specificity. Automatically determining the mixing ratios of the identified species, plasma LTE temperature, and electron density. 3
4 Automatically estimating wavelength correction for the input emission spectrum. Based on first-principles methods and a built-in performance library and does not require user s training of the chemical identifier. Supporting input spectra with either calibrated spectral radiance or with arbitrary spectral radiance units. 2. Working Principles and Workflows of OPSIAL The working principles and workflows of the OPSIAL code are briefly described in this manual. For detailed information on the methods used in OPSIAL, please refer to the references in the References section of this manual. 2.1 RT Model Tan s (2003) ultra-fast LBL RT model is used to quickly calculate emission spectra of the plasma. This RT method is based on fast convolution of spectral line profile using the Fast Fourier Transform (FFT) method. The theoretical framework for applying this method to the RT calculation in OPSIAL is briefly described as follows. Solutions to the equation of radiative transfer (Goody and Yung 1989) for calculating spectral transmittance and radiance in plasmas require calculation of optical depth as a function of the path though the LOS. In numerical approaches, this calculation is decomposed into calculations of the optical depth through a number of homogenous segments along the LOS. Within each of these LOS segments, temperature, pressure, and species mole fractions are assumed to be uniform. In a LBL model, the wavelength-dependent optical depth for a gas mixture in a homogeneous segment is given by:!!!!! τ ν; T, P, U!, U!,, U!! =! U! S!,! V σ!,!, γ!,! ; ν ν!,!, (1) where τ ν; T, P, U!, U!,, U!! is the optical depth that depends on the wavenumber ν, temperatures T and total pressure P, and the column densities U!, U!,, U!! of the N! species in the segment; S!,! is the line strength for the i-th line of species α that has N! lines in total; V σ!,!, γ!,! ; ν ν!,! is the line profile for the i-th line of species α whose central wavenumber is ν!,! ; σ!,! and γ!,! are the Doppler width and the collision broadened half width (HWHM) for the i-th line of species α, respectively. For simplicity, it may be assumed in OPSIAL that Doppler and collision broadening are the only line broadening mechanisms in the plasma and as a result the line profile in the emission spectrum is Voigt. The collision broadening of spectral lines are attributed to the collisions of the carrier species with gas species and electrons in the plasma. The broadening with gas species may be approximated as: 4
5 γ!,! = 0.08!!"!!!.! P, (2) where T! is the gas kinetic temperature of the plasma in K and P is the pressure in atm. In eq. (2), it is assumed that all species in the plasma are subject to a same broadening with the surrounding gas in the plasma. Collision broadening with electrons may be obtained from various experimental data sources or from theoretical values such as those in the Stark-B database ( Instead of calculating the optical depth using eq. (1) directly, which requires a lot of computational power when N! s are large, a solution to eq. (1) in the Fourier transform space is sought. Eq. (1) can be easily rewritten in Fourier transform space using the convolution theorem:!!!!! τ k; T, P, U!, U!,, U!! =! U! S!,! exp σ!!,! k! γ!,! k ikν!,!, (3) where k is the Fourier transform variable of wavenumber ν. If the LOS information (i.e., T, P, U!, U!,, U!! ) and the spectral line information (i.e., S!,! for all lines of all species) are known, one can sum over all the terms in the right side of eq. (3) to get the Fourier transform coefficients of the optical depth and then performs an inverse Fourier transform to get the real optical depth. 2.1 Workflow of SCF The workflow of SCF is very straightforward. It involves specifying LOS parameters (i.e., species, mixing ratios, temperatures, pressures) of the plasma for spectral calculations in the Calculator mode or specifying an input spectrum and LOS parameters to be optimized and their bounds in the Fitter mode. The workflows of the two modes are self-explanatory in the OPSIAL graphic front-end. 2.2 Workflow of AA Fig. 1 depicts the workflow of the AA in OPSIAL. The input emission spectrum (300) is comprised of wavelength and spectral radiance pairs in which at least two emission peaks are present. There is no upper limit to the number of emission peaks that can be handled by OPSIAL. The input data can be in units of calibrated spectral radiance or in arbitrary units. Currently, emission peaks in the spectral range of 150 nm to 1000 nm are used by OPSIAL for analysis. A Spectral Feature Extraction (SFE, 302) method is used to extract the emission peak information from the input spectrum. It performs de-noising, emission peak identification, and continuum baseline removal from the input emission spectrum. An important aspect of the SFE is that it fits the emission peaks in the emission spectrum to an appropriate peak function and accurately determine the positions, heights, and widths of all emission peaks in the input spectrum that form the spectral features (304) for further use. OPSIAL uses Gaussian to fit all peaks in the 5
6 emission spectrum for simplicity. A Reference Spectral Library (RSL, 308) is used in OPSIAL and is comprised of a collection of key and value pairs for all atomic species in the NIST and Harvard CFA atomic databases. OPSIAL AA assumes the LTE condition and a single LOS segment. The key field of an entry in the RSL is comprised of LTE temperatures ranging from 800 K to K with a step size of 1000 K and emission instrument slit (Gaussian assumed) widths ranging from cm -1 to 2.6 cm -1 in a geometric sequence with a common ratio of 2. The value field of an entry in the RSL is comprised of peak descriptions extracted from emission spectra calculated with the RT code using the corresponding key field of the entry as input together with additional LOS conditions such as LOS length (e.g., 1 cm) and LOS pressure (e.g., 1 atm). The extracted spectral features (304) of the input spectrum are compared with the value fields of the entries in the RSL. Two peaks are considered a potential match if the difference of the positions is within a wavelength threshold specified in the additional match parameters (310) by the user. The linear correlation coefficient of the positions of the paired peaks is checked against a threshold specified in the match parameters and the entry in the RSL is ignored if the coefficient does not meet the threshold. For an RSL entry that passes the above check, two feature vectors are formed by OPSIAL using the integrated intensities of the peaks in the RSL entry and in the input spectrum, respectively. A match score is calculated using the following equation: S = 1!!!!!!! (!) (!)!!!!!!!! (!)!!! (!)!!!!!!!!!!, (4) where X! (!) and X! (!) are the integrated intensities of the peaks in the input spectrum and in the RSL entry in the wavelength range of the input spectrum, respectively; N1 and N2 are the number of peaks in the input spectrum and in the RSL entry, respectively; and N is the number of unique peaks present in both the input spectrum and the entry of the RSL. It can be seen that eq. (4) is the cosine similarity between the two feature vectors times the ratio of the number of common peaks over the total number of peaks. The minimum number of common peaks and the maximum number of the strongest peaks in the RSL entry to use in calculating match scores are also specified in the additional math parameters (310). OPSIAL features a Performance Library (PL, 318) that is constructed and trained using result of ~6000 random computer experiments, each of which contains 1 to 5 randomly generated species with randomly generated mixing ratios and plasma LTE temperatures. The same LOS conditions as used in constructing the RSL are used in the computer experiments. The results of the random computer experiments are used to generate performance metrics for the species identifier of OPSIAL, such as the True Positive Rate (TPR) and the False Positive Rate (FPR) as functions of the match score. TPRs and FPRs are fitted to empirical expressions as follows: 6
7 TPR = 1 S e!!/!!"#, (5) and FPR = 1 S e!!/!!"#, (6) where S is the match score; τ!"# and τ!"# are constants to be fitted. For each species, a cutoff match score S!"#$%% is determined according to the following equation: TPR + FPR = 1 S e!!!"#$%%/!!"# + e!!!"#$%%/!!"# = R, (7) where R is a threshold specified by the user. In OPSIAL, the match score is converted into match index during species identification. The match index is defined as: I = S/S!"#$%%. (8) OPSIAL features a method for performing wavelength calibration, LTE temperatures estimation, and species identification of the input spectrum. The workflow of the method is as follows. Firstly, peaky spectral features are extracted by the SFE. The relative intensities of these features are then compared to those of the entries of the RSL to calculate match scores. Secondly, overall match score (OMS) values are calculated to facilitate estimation of plasma LTE temperatures and wavelength shift in the input spectrum. The OMS is defined as:! OMS T; Δw =!! S α; T; Δw /N!, (9) where OMS T; Δw is a function of the plasma LTE temperatures T and the wavelength shift Δw; S α; T; Δw is the match score of species α; and the summation is over for all species. The OMS are calculated for all the LTE temperatures in the RSL and for all Δws in a specified wavelength range. The wavelength shift of the input spectrum is estimated with the Δw associated with the largest OMS. Plasma LTE temperatures is estimated using the match-score weighted average of all the temperatures in the OMS at the estimated wavelength shift Δw! : T! = e!"#!;!!!!"#!!!"#!;!!!!, (10) where T! is the estimated plasma LTE temperature; Δw! is the estimated wavelength shift by. Thirdly, a species is identified if its match index calculated from eqs. (7) and (8) is greater than 1.0. Once a species is identified, the TPR and FPR for the identification are then calculated from eq. (5), (6), and (8). Finally, for an identified species, a species-specific wavelength calibration is determined by fitting the extracted emission peak positions of the matched peaks to the positions in the RSL for that specific species. A final wavelength calibration is determined using the 7
8 match-index weighted average of all the species-specific wavelength calibrations. The identified species, estimated temperature LTE T!, and guessed initial mixing ratios (320), together with additional LOS information (e.g., LOS length and pressure) (324) specified by the user, are sent to a Saha equation solver code and the RT code (324) to calculate an emission spectrum (326). The chi-squared of the difference of the calculated spectrum and the input spectrum are minimizing by varying the mixing ratios and the LTE temperature using a gradient-descent based optimizer. The final mixing ratios and LTE temperature are determined when the optimization converges. The electron density of the plasma is determined by solving the Saha equation at these conditions. 8
9 Emission spectrum of plasma 300 Spectral feature extraction Spectral features Calculate match scores Match scores Identify Species and estimate temperatures Species, temperature, and mixing ratios Solve Saha equation and calculate emission spectrum with RT code Reference spectral library Match parameters Performance library 320 Performance parameters Additional LOS information Calculated emission spectrum Plasma parameter optimization Emission spectrum of plasma Converged? Yes Plasma parameters 330 No 332 Figure 1. Flowchart of the Automated Analyzer. 9
10 It is important to note that the construction of the PL of OPSIAL is a very time-consuming process and that results of more randomly computer simulations are still being constantly added to the PL to improve the accuracy of the species identifier of OPSIAL. As a consequence, it is important for the user to keep updating the PL comes with a release of OPSIAL. 3. Tutorial In this tutorial, we are going to analyze the first LIBS spectrum of Mars taken by the ChemCam instrument boarding the NASA rover Curiosity *. The spectrum can be seen online at Step 1. Start OPSIAL and select the Automated Analyzer tab so that we can have OPSIAL automatically determine species, mixing ratios, temperature, and electron density. Load file Mars_First_Spectrum_part.dat inside path examples/chemcam of the OPSIAL installation directory. This spectrum covers the nm spectral range. Select Arbitrary Units in the Spectrum Radiance Units to have OPSIAL use the relative intensities of the spectrum to perform analysis. Step 2. Make sure the following parameters in the Automated Analyzer are set to the following values: Identify Species & Estimate LTE Temperature. Check this radio box to have OPSIAL identify species and estimate plasma LTE temperature. Spectrum Slit Width: 0.2 nm. This is the slit width of the spectrum as seen from the width of the peaks in the spectrum. TPR + FPR: 1.2. This is the threshold used in eq. (7) for calculating cutoff match scores for species. LOS Length in cm: 1.0. This is an estimated LOS length of the plasma created by the ChemCam instrument. LOS Pressure in atm: This is the average air pressure on the surface of Mars. Number of Optimization Iterations: 30. This is number of iterations for fitting to the input spectrum to determine the mixing ratios and the LTE plasma temperature. Min. Number of Peaks to Match: 4. This is the minimum number of peaks to match between the input spectrum and a spectrum in the reference library in order for the reference spectrum to be considered as a potential match to the input spectrum. * We are very grateful to Dr. R. C. Wiens and Dr. A. Shaner for the assistance on retrieving the spectrum from the ChemCam online databases. 10
11 Other parameters on the Automated Analyzer should normally take the defaults values since those are the values with which the OPSIAL species identifier is trained. A screenshot after this step is shown in Fig. 2. Figure 2. Settings of OPSIAL in Step 2. Step 3. Execute the Action Start Calculation/Analysis menu command or click the button with two gears on the toolbar. OPSIAL starts to identify species in the plasma and estimates the LTE plasma temperature. The result looks like the following: **************************************************************** Optical Plasma Spectral Identification & AnaLysis (OPSIAL) The Autonomous Species & Temperature Module (LTE Only) (c) 2016 Xiaofeng Tan, Ph.D., All Rights Reserved. **************************************************************** >>> Start Analysis at :12:03 <<< Successfully read 2048 lines of data from /Users/xtan/opsial/examples/ChemCam/Mars_First_Spectrum_part1.dat! Identifying species and estimating temperature... Finished estimating temperature! ======================================================================== Fe % 1% e+00 * w e-03 11
12 Mg % 5% e-01 * w e-03 Si % 8% e+00 * w e-02 Ti % 10% e-01 * w e-02 Est. T: e+04 K Est. Wavelength Scaling: e-01 * w e-02 ======================================================================== It is worth mentioning that the PL used by OPSIAL is still being actively developed (i.e., more and more training data are being generated to train the species identifier and to generate updated PL). As a result, the version of OPSIAL the user uses may produce different species as shown above due to the differences between the PLs. Step 4. Now in the Automated Analyzer, check the radio box Determine Species, Mixing Ratios, LTE Temperature, and Electron Density and then execute the Action Start Calculation/Analysis menu command or click the corresponding button on the toolbar. This time OPSIAL performs an optimization to determine the mixing ratios and LTE temperature after the species identification and temperature estimation. The result looks like the following: -- Segment #1 (w/ #1 next to the detector) Information -- T = K, P = 0.06 ATM, Length = 0.01 m. Mole fraction for Fe: e-06 Mole fraction for Mg: e-07 Mole fraction for Si: e-06 Mole fraction for Ti: e-06 Sum of mole fractions: e-05 Electron density = e+17 cm^-3. Note that the mixing ratios determined with Arbitrary Units selected for the Spectrum Radiance Units in the Automated Analyzer are relative mixing ratios but not absolute mixing ratios. The calculated spectrum with the optimized mixing ratios and the plasma LTE temperature is plotted together with the input spectrum are shown in Fig
13 Figure 3. Calculated and input spectra in Step 4. References Tan, X. An ultrafast line-by-line algorithm for calculating spectral Transmittance and radiance, J. Quant. Spectrosc. Radiat. Transfer, 129, p , Tan, X. Method for automatically determining chemical species, mixing ratios, temperatures, and electron density in plasmas from observed emission spectra, patent pending (application # ), Goody, R. M.; Yung, Y.L. Atmospheric radiation: theoretical basis, 2nd ed. NewYork: Oxford;
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