Accurate and precise wavelength calibration for wide bandwidth array spectrometers

Calibrating the wavelength scale of an array spectrometer typically involves measurements of lines at well-known wavelengths from a calibration lamp such as a mercury-argon source. This process is relatively straightforward when the lines are well separated, relative to the bandwidth of the spectrometer. When the spectrometer's bandwidth is large, compared with the distance between calibration wavelengths, it becomes increasingly difficult to accurately locate lines in the calibration spectrum. Even calibrations for instruments with a modest bandwidth of 12 nm can be difficult. Here we present results from a simple approach to improve the accuracy of wavelength calibration for an instrument with a large bandwidth (12 nm, center-to-center pixel spacing 3.3 nm). A monochromator has been used to filter the source so that each calibration line can be measured separately. For ten spectrometers, we were able to achieve accuracy better than 0.12 nm, or 0.09 nm on average; this is less than 3% of the pixel spacing. We anticipate this approach will be useful for improving the accuracy of measurements on array spectrometers and particularly in transferring multivariate calibrations between instruments.     

Multivariate calibration and instrument standardization for the rapid detection of diethylene glycol in glycerin by Raman spectroscopy

The transfer of a multivariate calibration model for quantitative determination of diethylene glycol (DEG) contaminant in pharmaceutical-grade glycerin between five portable Raman spectrometers was accomplished using piecewise direct standardization (PDS). The calibration set was developed using a multi-range ternary mixture design with successively reduced impurity concentration ranges. It was found that optimal selection of calibration transfer standards using the Kennard-Stone algorithm also required application of the algorithm to multiple successively reduced impurity concentration ranges. Partial least squares (PLS) calibration models were developed using the calibration set measured independently on each of the five spectrometers. The performance of the models was evaluated based on the root mean square error of prediction (RMSEP), calculated using independent validation samples. An F-test showed that no statistical differences in the variances were observed between models developed on different instruments. Direct cross-instrument prediction without standardization was performed between a single primary instrument and each of the four secondary instruments to evaluate the robustness of the primary instrument calibration model. Significant increases in the RMSEP values for the secondary instruments were observed due to instrument variability. Application of piecewise direct standardization using the optimal calibration transfer subset resulted in the lowest values of RMSEP for the secondary instruments. Using the optimal calibration transfer subset, an optimized calibration model was developed using a subset of the original calibration set, resulting in a DEG detection limit of 0.32% across all five instruments.     

Intercomparison of reflectances observed by GOME and SCIAMACHY in the visible wavelength range

We compare the Earth reflectances of the spectrometers Global Ozone Monitoring Experiment (GOME) and Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) over their overlapping wavelength range (240-800 nm). The goal is to investigate the quality of the radiometric calibration of SCIAMACHY using calibrated GOME data as a reference. However, severe degradation of the GOME instrument in the UV since 2001 prevents it from being a reliable reference below 500 nm. Above 500 nm, GOME is reliable and we find substantial disagreement between GOME and SCIAMACHY, of the order of 15%-20%, which we can attribute completely to the current calibration problems of SCIAMACHY. These numbers are supported by a previous study in which SCIAMACHY was compared with the imager Medium Resolution Imaging Spectrometer (MERIS) onboard the Envisat satellite.     

Calibration transfer of partial least squares jet fuel property models using a segmented virtual standards slope-bias correction method

Fifteen pure molecular chemicals were used to transfer near-IR partial least squares (PLS) models of jet fuel properties between two dispersive near-IR instruments by a novel calibration transfer, standardization, method. PLS was applied to establish models for quantitative analysis of jet fuels properties. The modeled jet fuel properties include: API gravity; %aromatics; cetane index; density; distillation temperatures for 10%, 20%, 50% and 90% recovered volume; flashpoint; freeze point, %hydrogen content; %saturates; and viscosity. The transfer of the PLS models requires that spectra of only 15 pure chemicals be acquired on the primary and secondary instruments. The spectra of the chemicals are then segmented into distinct spectral regions which are subsequently used to digitally construct spectra of virtual standards which mimic jet fuel spectra in the training set. The resulting virtual standards for the primary and secondary instruments are then predicted using the PLS models, and the prediction values are regressed to provide a simple but effective slope and bias correction for transfer. SVSSB calibration transfer of 7 jet fuels properties shows better performance than PDS, for example, in the case of cetane index Root Mean Square Error of Prediction (RMSEP_c) of SVSSB and PDS corrected secondary instrument relative to primary instrument prediction are 0.19 and 0.27 respectively. SVSSB and PDS show comparable performance of the other 6 jet fuel properties. For example, RMSEP_c of SVSSB and PDS corrected secondary of % hydrogen content of secondary instrument relative to the primary instrument prediction are 0.015 and 0.014 respectively. The Segmented Virtual Standards Slope and Bias Method (SVSSB) performs as well as using real jet fuel standards to generate a slope and bias correction, and also as well as conventional Piecewise Direct Standardization (PDS), while eliminating the need to maintain either the complex fuel standards or the primary instrument.     

Wavelength interval selection in multicomponent spectral analysis by moving window partial least-squares regression with applications to mid-infrared and near-infrared spectroscopic data

A new wavelength interval selection procedure, moving window partial least-squares regression (MWPLSR), is proposed for multicomponent spectral analysis. This procedure builds a series of PLS models in a window that moves over the whole spectral region and then locates useful spectral intervals in terms of the least complexity of PLS models reaching a desired error level. Based on a proposed theory demonstrating the necessity of wavelength selection, it is shown that MWPLSR provides a viable approach to eliminate the extra variability generated by non-composition-related factors such as the perturbations in experimental conditions and physical properties of samples. A salient advantage of MWPLSR is that the calibration model is very stable against the interference from non-composition-related factors. Moreover, the selection of spectral intervals in terms of the least model complexity enables the reduction of the size of a calibration sample set in calibration modeling. Two strategies are suggested for coupling the MWPLSR procedure with PLS for multicomponent spectral analysis: One is the inclusion of all selected intervals to develop a PLS calibration model, and the other is the combination of the PLS models built separately in each interval. The combination of multiple PLS models offers a novel potential tool for improving the performance of individual models. The proposed procedures are evaluated using two open-path Fourier transform infrared data sets and one near-infrared data set, each having different noise characteristics. The results reveal that the proposed procedures are very promising for vibrational spectroscopy-based multicomponent analyses and give much better prediction than the full-spectrum PLS modeling.     

Design and testing of a two-monochromator reference spectrofluorimeter for high-accuracy total radiance factor measurements

A two-monochromator reference spectrofluorimeter has been developed at the National Research Council of Canada in accordance with International Commission on Illumination and American Society for Testing and Materials colorimetry standards to permit high-accuracy total spectral radiance factor measurements of fluorescent materials. This fully automated instrument employs a xenon-arc light source, all-reflective optics, two grating monochromators with order-sorting filters, a cooled photomultiplier tube analyzing detector, and a calibrated silicon photodiode monitor detector. The instrument operating range is 250-1050 nm with a selectable bandpass (optimized for a 5-nm resolution), and the measurement geometry is 45 degrees annular illumination and 0 degrees viewing (45/0). We describe the instrument's design, testing, and verification procedures. Systematic errors that have been determined and corrected for include instrument polarization, beam nonuniformity, wavelength shifts, stray light, and system drift. The wavelength accuracy and reproducibility are estimated to better than +/-0.1 and +/-0.03 nm, respectively. The photometric short-term repeatability and long-term reproducibility are estimated to be better than +/-0.15% and +/-0.5%, respectively. The overall photometric accuracy is better than 1% of the value over a wide range of reflectances, and the reproducibility of the color specification of a fluorescent material is better than 0.25 DE(ab) units.     

Investigation of electrolyte measurement in diluted whole blood using spectroscopic and chemometric methods

The feasibility of using near-infrared (NIR) spectroscopy in combination with partial least-squares (PLS) regression was explored to measure electrolyte concentration in whole blood samples. Spectra were collected from diluted blood samples containing randomized, clinically relevant concentrations of Na+, K+, and Ca2+. Sodium was also studied in lysed blood. Reference measurements were made from the same samples using a standard clinical chemistry instrument. Partial least squares (PLS) was used to develop calibration models for each ion with acceptable results (Na+, R2 = 0.86, CVSEP = 9.5 mmol/L; K+, R2 = 0.54, CVSEP = 1.4 mmol/L; Ca2+, R2 = 0.56, CVSEP = 0.18 mmol/L). Slightly improved results were obtained using a narrower wavelength region (470-925 nm) where hemoglobin, but not water, absorbed indicating that ionic interaction with hemoglobin is as effective as water in causing measurable spectral variation. Good models were also achieved for sodium in lysed blood, illustrating that cell swelling, which is correlated with sodium concentration, is not required for calibration model development.     

Near-infrared analysis of whole kernel barley: comparison of three spectrometers

This study was conducted to develop calibration models for determining quality parameters of whole kernel barley using a rapid and nondestructive near-infrared (NIR) spectroscopic method. Two hundred and five samples of whole barley grains of three winter-habit types (hulled, malt, and hull-less) produced over three growing seasons and from various locations in the United States were used in this study. Among these samples, 137 were used for calibration and 68 for validation. Three NIR instruments with different resolutions, one Fourier transform instrument (4 cm(-1) resolution), and two dispersive instruments (8 nm and 10 nm bandpass) were utilized to develop calibration models for six components (moisture, starch, beta-glucan, protein, oil, and ash) and the results were compared. Partial least squares regression was used to build models, and various methods for preprocessing of spectral data were used to find the best model. Our results reveal that the coefficient of determination for calibration models (NIR predicted versus reference values) ranged from 0.96 for moisture to 0.79 for beta-glucan. The level of precision of the model developed for each component was sufficient for screening or classification of whole kernel barley, except for beta-glucan. The higher resolution Fourier transform instrument gave better results than the lower resolution instrument for starch and beta-glucan analysis. The starch model was most improved by the increased resolution. There was no advantage of using a higher resolution instrument over a lower resolution instrument for other components. Most of the components were best predicted using first-derivative processing, except for beta-glucan, where second-derivative processing was more informative and precise.     

Monitoring the calibration status of a measuring instrument by astochastic model

The paper discusses a class of stochastic models for evaluating the optimal calibration interval in measuring instruments. The model is based on the assumption that the calibration status of a measuring instrument can be monitored by means of one observable parameter. The observable parameter is undergoing a stochastic drift process. The paper introduces and compares stochastic drift models of different nature, and estimates the first passage time of the monitored parameter on a preset limit. The calibration interval is determined as a suitable percentile of the distribution function of the first passage time. A preliminary validation of the model, based on a sample of experimental data collected on a class of instruments, is finally reported     

Determination of glucose in human aqueous humor using Raman spectroscopy and designed-solution calibration

Glucose concentrations of in vitro human aqueous humor (HAH) samples from cataract patients were determined using 785 nm Raman spectra and partial least squares (PLS) calibration. PLS models were created from spectra of prepared calibration solutions rather than aqueous humor samples. Spectra were obtained with an excitation energy (100 mW for 150 s), which was higher than can be applied in vivo, to decrease the models' contribution to prediction uncertainty. The solutions contained experimentally designed levels of glucose, bicarbonate, lactate, urea, and ascorbate. Multiplicative signal correction of spectra helped compensate for the +/-20% drift in laser power observed at the sample over six noncontiguous days of data collection. Seventeen HAH samples containing 38-775 mg/dL of glucose exhibited a root-mean-square error (RMSEP) of 22 mg/dL, coefficient of determination (r(2)) of 0.989, and bias of 6 mg/dL when predicted from lower energy (30 s) spectra collected contemporaneously with fifty calibration spectra. Similar results were obtained even when spectral data were gathered separately for human aqueous humor samples and calibration samples: 10 HAH samples, calibrated on 25 solutions measured 3.6 weeks earlier, exhibited an RMSEP of 23 mg/dL, r(2) of 0.992, and bias of 9 mg/dL. The results demonstrate progress toward the determination of glucose levels in patient-derived aqueous humor using laboratory-derived "artificial aqueous humor" calibration solutions.     

Cross calibration of SeaWiFS and MODIS using on-orbit observations of the Moon

Observations of the Moon provide a primary technique for the on-orbit cross calibration of Earth remote sensing instruments. Monthly lunar observations are major components of the on-orbit calibration strategies of SeaWiFS and MODIS. SeaWiFS has collected more than 132 low phase angle and 59 high phase angle lunar observations over 12 years, Terra MODIS has collected more than 82 scheduled and 297 unscheduled lunar observations over nine years, and Aqua MODIS has collected more than 61 scheduled and 171 unscheduled lunar observations over seven years. The NASA Ocean Biology Processing Group Calibration and Validation Team and the NASA MODIS Characterization Support Team use the USGS RObotic Lunar Observatory (ROLO) photometric model of the Moon to compare these time series of lunar observations over time and varying observing geometries. The cross-calibration results show that Terra MODIS and Aqua MODIS agree, band to band, at the 1%-3% level, while SeaWiFS and either MODIS instrument agree at the 3%-8% level. The combined uncertainties of these comparisons are 1.3% for Terra and Aqua MODIS, 1.4% for SeaWiFS and Terra MODIS, and 1.3% for SeaWiFS and Aqua MODIS. Any residual phase dependence in the ROLO model, based on these observations, is less than 1.7% over the phase angle range of -80° to -6° and +5° to +82°. The lunar cross calibration of SeaWiFS, Terra MODIS, and Aqua MODIS is consistent with the vicarious calibration of ocean color products for these instruments, with the vicarious gains mitigating the calibration biases for the ocean color bands.     

State-of-the art comparability of corrected emission spectra. 1. Spectral correction with physical transfer standards and spectral fluorescence standards by expert laboratories

The development of fluorescence applications in the life and material sciences has proceeded largely without sufficient concern for the measurement uncertainties related to the characterization of fluorescence instruments. In this first part of a two-part series on the state-of-the-art comparability of corrected emission spectra, four National Metrology Institutes active in high-precision steady-state fluorometry performed a first comparison of fluorescence measurement capabilities by evaluating physical transfer standard (PTS)-based and reference material (RM)-based calibration methods. To identify achievable comparability and sources of error in instrument calibration, the emission spectra of three test dyes in the wavelength region from 300 to 770 nm were corrected and compared using both calibration methods. The results, obtained for typical spectrofluorometric (0°/90° transmitting) and colorimetric (45°/0° front-face) measurement geometries, demonstrated a comparability of corrected emission spectra within a relative standard uncertainty of 4.2% for PTS- and 2.4% for RM-based spectral correction when measurements and calibrations were performed under identical conditions. Moreover, the emission spectra of RMs F001 to F005, certified by BAM, Federal Institute for Materials Research and Testing, were confirmed. These RMs were subsequently used for the assessment of the comparability of RM-based corrected emission spectra of field laboratories using common commercial spectrofluorometers and routine measurement conditions in part 2 of this series (subsequent paper in this issue).     

Spectral simulation methodology for calibration transfer of near-infrared spectra

A spectrum simulation method is described for use in the development and transfer of multivariate calibration models from near-infrared spectra. By use of previously measured molar absorptivities and solvent displacement factors, synthetic calibration spectra are computed using only background spectra collected with the spectrometer for which a calibration model is desired. The resulting synthetic calibration set is used with partial least squares regression to form the calibration model. This methodology is demonstrated for use in the analysis of physiological levels of glucose (1-30 mM) in an aqueous matrix containing variable levels of alanine, ascorbate, lactate, urea, and triacetin. Experimentally measured data from two different Fourier transform spectrometers with different noise levels and stabilities are used to evaluate the simulation method. With the more stable instrument (A), well-performing calibration models are obtained, producing a standard error of prediction (SEP) of 0.70 mM. With the less stable instrument (B), the calibration based solely on synthetic spectra is less successful, producing an SEP value of 1.58 mM. For cases in which the synthetic spectra do not describe enough spectral variance, an augmentation protocol is evaluated in which the synthetic calibration spectra are augmented with the spectra of a small number of experimentally measured calibration samples. For instruments A and B, respectively, augmentation with measured spectra of nine samples lowers the SEP values to 0.64 and 0.85 mM.     

Long-term analysis of GOME in-flight calibration parameters and instrument degradation

Since 1995, the Global Ozone Monitoring Experiment (GOME) has measured solar and backscattered spectra in the ultraviolet and visible wavelength range. Now, the extensive data set of the most important calibration parameters has been investigated thoroughly in order to analyze the long-term stability and performance of the instrument. This study focuses on GOME in-flight calibration and degradation for the solar path. Monitoring the sensor degradation yields an intensity decrease of 70% to 90% in 240-316 nm and 35% to 65% in 311-415 nm. The spectral calibration is very stable over the whole period, although a very complex interaction between predisperser temperature and wavelength was found. The leakage current and the pixel-to-pixel gain increased significantly during the mission, which requires an accurate correction of the measured radiance and irradiance signals using proper calibration parameters. Finally, several outliers in the data sets can be directly assigned to instrument and satellite anomalies.     

Spectral variable selection for partial least squares calibration applied to authentication and quantification of extra virgin olive oils using Fourier transform Raman spectroscopy

The limits of quantitative multivariate assays for the analysis of extra virgin olive oil samples from various Greek sites adulterated by sunflower oil have been evaluated based on their Fourier transform (FT) Raman spectra. Different strategies for wavelength selection were tested for calculating optimal partial least squares (PLS) models. Compared to the full spectrum methods previously applied, the optimum standard error of prediction (SEP) for the sunflower oil concentrations in spiked olive oil samples could be significantly reduced. One efficient approach (PMMS, pair-wise minima and maxima selection) used a special variable selection strategy based on a pair-wise consideration of significant respective minima and maxima of PLS regression vectors, calculated for broad spectral intervals and a low number of PLS factors. PMMS provided robust calibration models with a small number of variables. On the other hand, the Tabu search strategy recently published (search process guided by restrictions leading to Tabu list) achieved lower SEP values but at the cost of extensive computing time when searching for a global minimum and less robust calibration models. Robustness was tested by using packages of ten and twenty randomly selected samples within cross-validation for calculating independent prediction values. The best SEP values for a one year's harvest with a total number of 66 Cretian samples were obtained by such spectral variable optimized PLS calibration models using leave-20-out cross-validation (values between 0.5 and 0.7% by weight). For the more complex population of olive oil samples from all over Greece (total number of 92 samples), results were between 0.7 and 0.9% by weight with a cross-validation sample package size of 20. Notably, the calibration method with Tabu variable selection has been shown to be a valid chemometric approach by which a single model can be applied with a low SEP of 1.4% for olive oil samples across three different harvest years.     

Transfer of multivariate classification models between laboratory and process near-infrared spectrometers for the discrimination of green Arabica and Robusta coffee beans

Analogous to the situation found in calibration, a classification model constructed from spectra measured on one instrument may not be valid for prediction of class from spectra measured on a second instrument. In this paper, the transfer of multivariate classification models between laboratory and process near-infrared spectrometers is investigated for the discrimination of whole, green Coffea arabica (Arabica) and Coffea canefora (Robusta) coffee beans. A modified version of slope/bias correction, orthogonal signal correction trained on a vector of discrete class identities, and model updating were found to perform well in the preprocessing of data to permit the transfer of a classification model developed on data from one instrument to be used on another instrument. These techniques permitted development of robust models for the discrimination of green coffee beans on both spectrometers and resulted in misclassification errors for the transfer process in the range of 5-10%.     

Comparison of two multiplicative signal correction strategies for calibration transfer without standards

Two multiplicative signal correction (MSC) algorithms are compared for the standardization of data from two near-infrared (NIR) spectrometers. Absorbance spectra were measured from 1000-2200 nm for a set of 45 jet fuel samples. Data from one instrument were standardized to match data from a second instrument using windowed MSC (W-MSC) and moving window MSC (MW-MSC). For W-MSC user-defined windows were selected and for MW-MSC the window size was optimized based on a two-step procedure: 1) assigning a cut off window to avoid over-processing and 2) selection of a specific window size based on sample leverage. For reproducibility studies performed over time on a single instrument, data extending through the last day of the study (63 days outside the calibration) required no preprocessing except a peak alignment correction on day 58. For analysis between the two instruments, successful results were obtained using a sub-region of the data from 1000–1700 nm processed by MW-MSC using a 441 point window. A method of selecting an appropriate window size is proposed based on statistical significance testing.     

Tandem triple-pass Fabry-Perot interferometer for applications in the near infrared

A standard tandem triple-pass scanning Fabry-Perot interferometer of the Vernier type for applications in the near infrared is described. The Fabry-Perot etalons have been coated with a specially designed dielectric multilayer stack with low loss factors and a uniform reflectivity of (92.5 +/- 1.0)% between 730 and 860 nm. The performances of the instrument, such as resolution, total transmission, and contrast, are equivalent to conventional tandem Fabry-Perot spectrometers but over the whole near-infrared wavelength range. Applications of the system to Brillouin scattering on semiconductors in the transparent wavelength regime and high-resolution spectroscopy of vertical cavity surface-emitting lasers are given.     

The use of crystal phosphors based on rare-earth elements to determine the spectral resolution and to calibrate the wavelength scale of luminescence spectrometers

The results of an investigation of the crystal phosphor Y₂O₂S:Er,Yb to determine the possibility of using it to measure the spectral resolution and to calibrate the wavelength scale of luminescence spectrometers are presented. The luminescence spectrum of the crystal phosphor was measured on three spectrofluorescence instruments when excited by a laser with λ_max = 960 nm and with ultraviolet excitation with λ_max = 383 nm, the optical arrangements of which differ considerably in the radiation recording channel. The difference in the wavelength positions of the maxima of the spectra of the neon lamp used for calibration and of the crystal phosphor investigated is estimated.     

High-accuracy spectrometer for measurement of regular spectral transmittance

A high-accuracy spectrometer has been developed for measuring regular spectral transmittance. The spectrometer is an automated, single-beam instrument that is based on a grating monochromator, reflecting optics, and an averaging sphere detector unit with a silicon photodiode. The uncertainties related to wavelength calibration, detector nonlinearity, system instability, beam displacement, polarization, stray light, interreflections, and beam uniformity are determined for the visible spectral range from 380 to 780 nm. A total uncertainty of 3 × 10(-4) (1σ) is estimated for transmittance measurements of homogeneous neutral-density filters. The uncertainty of the wavelength scale is 0.06 nm. As a specific application, calibration of V(λ)-correction filters is studied. To verify the accuracy of the transmittance measurements, a comparison of the measured and predicted transmittances of a sample of high-purity fused silica is made, revealing agreement at the 5 × 10(-4) level.