Wavelength Calibration Research Articles

Performance results of HESP physical model

As a continuation to the published work on model based calibration technique with HESP(Hanle Echelle Spectrograph) as a case study, in this paper we present the performance results of the technique. We also describe how the open parameters were chosen in the model for optimization, the glass data accuracy and handling the discrepancies. It is observed through simulations that the discrepancies in glass data can be identified but not quantifiable. So having an accurate glass data is important which is possible to obtain from the glass manufacturers. The model's performance in various aspects is presented using the ThAr calibration frames from HESP during its pre-shipment tests. Accuracy of model predictions and its wave length calibration comparison with conventional empirical fitting, the behaviour of open parameters in optimization, model's ability to track instrumental drifts in the spectrum and the double fibres performance were discussed. It is observed that the optimized model is able to predict to a high accuracy the drifts in the spectrum from environmental fluctuations. It is also observed that the pattern in the spectral drifts across the 2D spectrum which vary from image to image is predictable with the optimized model. We will also discuss the possible science cases where the model can contribute.

Preliminary results of the solar corona spectroscopic observation of 9th March 2016 Total Solar Eclipse

Spectroscopy observation of solar corona has been carried out from 9th March 2016 Total Solar Eclipse expedition in Maba, East Halmahera. Due to limitation by the weather condition during the observation, the obtained data were not favorable. Because of the low signal to noise ratio, the wavelength calibration was not straightforward. To obtain the optimum results, steps for data reduction were performed as the following: selecting the finest data, extracting the 1D spectrum from 2D spectrum, and calibrating spectrum wavelength (including careful interpolation). In this preliminary result, we discuss the instrumentation, the data under investigation, the extraction process of spectrum, and the polynomial interpolation that has been used for extracting information from our data.

High-precision limit on variation in the fine-structure constant from a single quasar absorption system

The brightest southern quasar above redshift z = 1, HE 0515−4414, with its strong intervening metal absorption line system at zabs = 1.1508, provides a unique opportunity to precisely measure or limit relative variations in the fine-structure constant (Δα/α). A variation of just ∼3 parts per million (ppm) would produce detectable velocity shifts between its many strong metal transitions. Using new and archival observations from the Ultraviolet and Visual Echelle Spectrograph (UVES), we obtain an extremely high signal-to-noise ratio spectrum (peaking at S/N ≈ 250 pix−1). This provides the most precise measurement of Δα/α from a single absorption system to date, Δα/α = −1.42 ± 0.55stat ± 0.65sys ppm, comparable with the precision from previous, large samples of ∼150 absorbers. The largest systematic error in all (but one) previous similar measurements, including the large samples, was long-range distortions in the wavelength calibration. These would add an ∼2 ppm systematic error to our measurement and up to ∼10 ppm to other measurements using Mg and Fe transitions. However, we corrected the UVES spectra using well-calibrated spectra of the same quasar from the High Accuracy Radial velocity Planet Searcher, leaving a residual 0.59 ppm systematic uncertainty, the largest contribution to our total systematic error. A similar approach, using short observations on future well-calibrated spectrographs to correct existing high S/N spectra, would efficiently enable a large sample of reliable Δα/α measurements. The high-S/N UVES spectrum also provides insights into analysis difficulties, detector artefacts and systematic errors likely to arise from 25–40-m telescopes.

Evaluation of the Effect of near Infrared Spectrometer Wavelength Range and Calibration Algorithms on Prediction of Crushing Strength of Pharmaceutical Tablets

This study was aimed at understanding the effect of near infrared (NIR) spectrometer wavelength range and calibration approaches on the performance of pharmaceutical tablet crushing strength prediction methods. The study utilised a six-component tablet formulation, created with variability in excipient ratio and compression force. Method development was tested with two NIR spectrometers and three calibration approaches: spectral slope, partial least squares (PLS) and multiple linear regression (MLR). The sensors used in the study were based on diffuse reflectance sensing geometry with wavelength ranges of 1100–2498 nm and 1350–1800 nm. The three calibration approaches demonstrated an improved prediction of crushing strength with the longer wavelength range, indicative of its significant impact on method performance. It was established that the PLS approach reduced the impact of wavelength range on performance by maximising the covariance between crushing strength and the spectral features associated with baseline shift/slope change and excipient ratio. The MLR approach incorporated variables of physical/chemical nature to mitigate risks to method performance.

Alignment and absolute wavelength calibration of imaging Bragg spectrometers.

In the present and the next generation of fusion devices, imaging Bragg spectrometers are key diagnostics to measure plasma parameters in the hot core, especially ion temperature and plasma rotation. The latter quantities are routinely obtained using the Doppler-width and -shift of the emitted spectral lines, respectively. Line shift measurements require absolute accuracies Δλ/λ of about 10 ppm, where λ-is the observed wavelength. For ITER and the present fusion devices, spectral lines of He-and H-like argon, iron, and krypton as well as Ne-like tungsten are foreseen for the measurements. For these lines, Kα lines can be found, some in higher order, which fit into the narrow energy window of the spectrometers. For arbitrary wavelength settings, Kα lines are also used to measure the miscut of the spherical crystals; afterwards the spectrometers can be set according to the geometrical imaging properties using coordinate measurement machines. For the spectrometers measuring Lyα lines of H-like ions, fluorescence targets can provide in situ localized calibration lines on the spectra. The fluorescence targets are used best in transmission and are excited by the thermal x-ray radiation of the plasma. An analytic theory of fluorescence is worked out.

THE DATA REDUCTION PIPELINE FOR THE SDSS-IV MaNGA IFU GALAXY SURVEY

ABSTRACT Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) is an optical fiber-bundle integral-field unit (IFU) spectroscopic survey that is one of three core programs in the fourth-generation Sloan Digital Sky Survey (SDSS-IV). With a spectral coverage of 3622–10354 Å and an average footprint of ∼500 arcsec2 per IFU the scientific data products derived from MaNGA will permit exploration of the internal structure of a statistically large sample of 10,000 low-redshift galaxies in unprecedented detail. Comprising 174 individually pluggable science and calibration IFUs with a near-constant data stream, MaNGA is expected to obtain ∼100 million raw-frame spectra and ∼10 million reduced galaxy spectra over the six-year lifetime of the survey. In this contribution, we describe the MaNGA Data Reduction Pipeline algorithms and centralized metadata framework that produce sky-subtracted spectrophotometrically calibrated spectra and rectified three-dimensional data cubes that combine individual dithered observations. For the 1390 galaxy data cubes released in Summer 2016 as part of SDSS-IV Data Release 13, we demonstrate that the MaNGA data have nearly Poisson-limited sky subtraction shortward of ∼8500 Å and reach a typical 10σ limiting continuum surface brightness μ = 23.5 AB arcsec−2 in a five-arcsecond-diameter aperture in the g-band. The wavelength calibration of the MaNGA data is accurate to 5 km s−1 rms, with a median spatial resolution of 2.54 arcsec FWHM (1.8 kpc at the median redshift of 0.037) and a median spectral resolution of σ = 72 km s−1.

In situ wavelength calibration of the edge CXS spectrometers on JET.

A method for obtaining an accurate wavelength calibration over the entire focal plane of the JET edge CXS spectrometers is presented that uses a combination of the fringe pattern created with a Fabry-Pérot etalon and a neon lamp for cross calibration. The accuracy achieved is 0.03 Å, which is the same range of uncertainty as when neglecting population effects on the rest wavelength of the CX line. For the edge CXS diagnostic, this corresponds to a flow velocity of 4.5 km/s in the toroidal direction or 1.9 km/s in the poloidal direction.

Retrieval of Precise Radial Velocities from Near-infrared High-resolution Spectra of Low-mass Stars

Given that low-mass stars have intrinsically low luminosities at optical wavelengths and a propensity for stellar activity, it is advantageous for radial velocity (RV) surveys of these objects to use near-infrared (NIR) wavelengths. In this work, we describe and test a novel RV extraction pipeline dedicated to retrieving RVs from low-mass stars using NIR spectra taken by the CSHELL spectrograph at the NASA Infrared Telescope Facility, where a methane isotopologue gas cell is used for wavelength calibration. The pipeline minimizes the residuals between the observations and a spectral model composed of templates for the target star, the gas cell, and atmospheric telluric absorption; models of the line-spread function, continuum curvature, and sinusoidal fringing; and a parameterization of the wavelength solution. The stellar template is derived iteratively from the science observations themselves without a need for separate observations dedicated to retrieving it. Despite limitations from CSHELL’s narrow wavelength range and instrumental systematics, we are able to (1) obtain an RV precision of 35 m s−1 for the RV standard star GJ 15 A over a time baseline of 817 days, reaching the photon noise limit for our attained signal-to-noise ratio; (2) achieve ∼3 m s−1 RV precision for the M giant SV Peg over a baseline of several days and confirm its long-term RV trend due to stellar pulsations, as well as obtain nightly noise floors of ∼2–6 m s−1; and (3) show that our data are consistent with the known masses, periods, and orbital eccentricities of the two most massive planets orbiting GJ 876. Future applications of our pipeline to RV surveys using the next generation of NIR spectrographs, such as iSHELL, will enable the potential detection of super-Earths and mini-Neptunes in the habitable zones of M dwarfs.

TESTING THE WAVELENGTH DEPENDENCE OF COSMOLOGICAL REDSHIFT DOWN TO Δz ∼ 10−6

ABSTRACT At the core of the standard cosmological model lies the assumption that the redshift of distant galaxies is independent of photon wavelength. This invariance of cosmological redshift with wavelength is routinely found in all galaxy spectra with a precision of Δz ∼ 10−4. The combined use of approximately half a million high-quality galaxy spectra from the Sloan Digital Sky Survey (SDSS) allows us to explore this invariance down to a nominal precision in redshift of 10−6 (statistical). Our analysis is performed over the redshift interval 0.02 < z < 0.25. We use the centroids of spectral lines over the 3700–6800 Å rest-frame optical window. We do not find any difference in redshift between the blue and red sides down to a precision of 10−6 at z ≲ 0.1 and 10−5 at 0.1 ≲ z ≲ 0.25 (i.e., at least an order of magnitude better than with single galaxy spectra). This is the first time the wavelength-independence of the (1 + z) redshift law is confirmed over a wide spectral window at this precision level. This result holds independently of the stellar population of the galaxies and their kinematical properties. This result is also robust against wavelength calibration issues. The limited spectral resolution (R ∼ 2000) of the SDSS data, combined with the asymmetric wavelength sampling of the spectral features in the observed restframe due to the (1 + z) stretching of the lines, prevent our methodology from achieving a precision higher than 10−5, at z > 0.1. Future attempts to constrain this law will require high quality galaxy spectra at higher resolution (R ≳ 10,000).

First measurement of the edge charge exchange recombination spectroscopy on EAST tokamak.

An edge toroidal charge exchange recombination spectroscopy (eCXRS) diagnostic, based on a heating neutral beam injection (NBI), has been deployed recently on the Experimental Advanced Superconducting Tokamak (EAST). The eCXRS, which aims to measure the plasma ion temperature and toroidal rotation velocity in the edge region simultaneously, is a complement to the exiting core CXRS (cCXRS). Two rows with 32 fiber channels each cover a radial range from ∼2.15 m to ∼2.32 m with a high spatial resolution of ∼5-7 mm. Charge exchange emission of Carbon VI CVI at 529.059 nm induced by the NBI is routinely observed, but can be tuned to any interested wavelength in the spectral range from 400 to 700 nm. Double-slit fiber bundles increase the number of channels, the fibers viewing the same radial position are binned on the CCD detector to improve the signal-to-noise ratio, enabling shorter exposure time down to 5 ms. One channel is connected to a neon lamp, which provides the real-time wavelength calibration on a shot-to-shot basis. In this paper, an overview of the eCXRS diagnostic on EAST is presented and the first results from the 2015 experimental campaign will be shown. Good agreements in ion temperature and toroidal rotation are obtained between the eCXRS and cCXRS systems.

Precise limits on cosmological variability of the fine-structure constant with zinc and chromium quasar absorption lines

The strongest transitions of Zn and CrII are the most sensitive to relative variations in the fine-structure constant ($\Delta\alpha/\alpha$) among the transitions commonly observed in quasar absorption spectra. They also lie within just 40\AA\ of each other (rest frame), so they are resistant to the main systematic error affecting most previous measurements of $\Delta\alpha/\alpha$: long-range distortions of the wavelength calibration. While Zn and CrII absorption is normally very weak in quasar spectra, we obtained high signal-to-noise, high-resolution echelle spectra from the Keck and Very Large Telescopes of 9 rare systems where it is strong enough to constrain $\Delta\alpha/\alpha$ from these species alone. These provide 12 independent measurements (3 quasars were observed with both telescopes) at redshifts 1.0--2.4, 11 of which pass stringent reliability criteria. These 11 are all consistent with $\Delta\alpha/\alpha=0$ within their individual uncertainties of 3.5--13 parts per million (ppm), with a weighted mean $\Delta\alpha/\alpha = 1.2\pm1.7_{\rm stat}\pm0.9_{\rm sys}$ ppm (1$\sigma$ statistical and systematic uncertainties), indicating no significant cosmological variations in $\alpha$. This is the first statistical sample of absorbers that is resistant to long-range calibration distortions (at the $<$1 ppm level), with a precision comparable to previous large samples of $\sim$150 (distortion-affected) absorbers. Our systematic error budget is instead dominated by much shorter-range distortions repeated across echelle orders of individual spectra.

ON-LINE WAVELENGTH CALIBRATION OF PULSED LASER FOR CO2 DIFFERENTIAL ABSORPTION LIDAR

Abstract. Differential absorption lidar (DIAL) remote sensing is a promising technology for atmospheric CO2 detection. However, stringent wavelength accuracy and stability are required in DIAL system. Accurate on-line wavelength calibration is a crucial procedure for retrieving atmospheric CO2 concentration using the DIAL, particularly when pulsed lasers are adopted in the system. Large fluctuations in the intensities of a pulsed laser pose a great challenge for accurate on-line wavelength calibration. In this paper, a wavelength calibration strategy based on multi-wavelength scanning (MWS) was proposed for accurate on-line wavelength calibration of a pulsed laser for CO2 detection. The MWS conducted segmented sampling across the CO2 absorption line with appropriate number of points and range of widths by using a tunable laser. Complete absorption line of CO2 can be obtained through a curve fitting. Then, the on-line wavelength can be easily found at the peak of the absorption line. Furthermore, another algorithm called the energy matching was introduced in the MWS to eliminate the backlash error of tunable lasers during the process of on-line wavelength calibration. Finally, a series of tests was conducted to elevate the calibration precision of MWS. Analysis of tests demonstrated that the MWS proposed in this paper could calibrate the on-line wavelength of pulsed laser accurately and steadily.

ON-LINE WAVELENGTH CALIBRATION OF PULSED LASER FOR CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; DIFFERENTIAL ABSORPTION LIDAR

Differential absorption lidar (DIAL) remote sensing is a promising technology for atmospheric CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; detection. However, stringent wavelength accuracy and stability are required in DIAL system. Accurate on-line wavelength calibration is a crucial procedure for retrieving atmospheric CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; concentration using the DIAL, particularly when pulsed lasers are adopted in the system. Large fluctuations in the intensities of a pulsed laser pose a great challenge for accurate on-line wavelength calibration. In this paper, a wavelength calibration strategy based on multi-wavelength scanning (MWS) was proposed for accurate on-line wavelength calibration of a pulsed laser for CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; detection. The MWS conducted segmented sampling across the CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; absorption line with appropriate number of points and range of widths by using a tunable laser. Complete absorption line of CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; can be obtained through a curve fitting. Then, the on-line wavelength can be easily found at the peak of the absorption line. Furthermore, another algorithm called the energy matching was introduced in the MWS to eliminate the backlash error of tunable lasers during the process of on-line wavelength calibration. Finally, a series of tests was conducted to elevate the calibration precision of MWS. Analysis of tests demonstrated that the MWS proposed in this paper could calibrate the on-line wavelength of pulsed laser accurately and steadily.

First observation of SASE radiation using the compact wide-spectral-range XUV spectrometer at FLASH2

The Free-electron LASer in Hamburg (FLASH) has been extended with a new undulator line FLASH2 in 2014. A compact grazing-incident wide-spectral-range spectrometer based on spherical-variable-line-spacing (SVLS) gratings in the extreme ultraviolet (XUV) region was constructed to optimize and characterize the free-electron laser (FEL) performance at FLASH2. The spectrometer is equipped with three different concave SVLS gratings covering a spectral range from 1 to 62nm to analyze the spectral characteristics of the XUV radiation. Wavelength calibration and evaluation of the spectral resolution were performed at the plane grating monochromator beamline PG2 at FLASH1 before the installation at FLASH2, and compared with analytical simulations. The first light using self-amplified spontaneous emission from FLASH2 was observed by the spectrometer during a simultaneous operation of both undulator lines—FLASH1 and FLASH2. In addition, the spectral resolution of the spectrometer was evaluated by comparing the measured spectrum from FLASH2 with FEL simulations.

Wavelength calibration model for prism-type echelle spectrometer by reversely solving prism’s refractive index in real time

In an echelle spectrometer equipped with a prism cross-dispersion element, wavelength calibration is very difficult because of the complex, nonlinear interaction between the prism and the echelle grating. From the spectrometer geometry and the dispersion equations for the prism and the grating, a detailed mathematical model for wavelength calibration is derived that fits the refractive index of the prism in real time. An expression relating the refractive index, wavelength, and image coordinates is constructed, and standard wavelength sources and image positions are adopted to timely calculate the refractive index, which is affected by ambient factors such as temperature and air pressure. Experimental results indicate that the fitting accuracy of the refractive index in real time approaches 10−4, while the wavelength accuracy approaches 10−3 nm for the entire spectral range.

State of the Field: Extreme Precision Radial Velocities**The content of this publication emerged from presentations and discussion by the 150 participants in the Second Workshop on Extreme Precision Radial Velocities, held at Yale University. The talks and posters from this meeting are archived at http://eprv.astro.yale.edu.

The Second Workshop on Extreme Precision Radial Velocities defined circa 2015 the state of the art Doppler precision and identified the critical path challenges for reaching 10 cm s−1 measurement precision. The presentations and discussion of key issues for instrumentation and data analysis and the workshop recommendations for achieving this bold precision are summarized here. Beginning with the High Accuracy Radial Velocity Planet Searcher spectrograph, technological advances for precision radial velocity (RV) measurements have focused on building extremely stable instruments. To reach still higher precision, future spectrometers will need to improve upon the state of the art, producing even higher fidelity spectra. This should be possible with improved environmental control, greater stability in the illumination of the spectrometer optics, better detectors, more precise wavelength calibration, and broader bandwidth spectra. Key data analysis challenges for the precision RV community include distinguishing center of mass (COM) Keplerian motion from photospheric velocities (time correlated noise) and the proper treatment of telluric contamination. Success here is coupled to the instrument design, but also requires the implementation of robust statistical and modeling techniques. COM velocities produce Doppler shifts that affect every line identically, while photospheric velocities produce line profile asymmetries with wavelength and temporal dependencies that are different from Keplerian signals. Exoplanets are an important subfield of astronomy and there has been an impressive rate of discovery over the past two decades. However, higher precision RV measurements are required to serve as a discovery technique for potentially habitable worlds, to confirm and characterize detections from transit missions, and to provide mass measurements for other space-based missions. The future of exoplanet science has very different trajectories depending on the precision that can ultimately be achieved with Doppler measurements.

A HIGH-PRECISION NEAR-INFRARED SURVEY FOR RADIAL VELOCITY VARIABLE LOW-MASS STARS USING CSHELL AND A METHANE GAS CELL

ABSTRACT We present the results of a precise near-infrared (NIR) radial velocity (RV) survey of 32 low-mass stars with spectral types K2–M4 using CSHELL at the NASA InfraRed Telescope Facility in the K band with an isotopologue methane gas cell to achieve wavelength calibration and a novel, iterative RV extraction method. We surveyed 14 members of young (≈25–150 Myr) moving groups, the young field star ε Eridani, and 18 nearby (&lt;25 pc) low-mass stars and achieved typical single-measurement precisions of 8–15 m s−1with a long-term stability of 15–50 m s−1 over longer baselines. We obtain the best NIR RV constraints to date on 27 targets in our sample, 19 of which were never followed by high-precision RV surveys. Our results indicate that very active stars can display long-term RV variations as low as ∼25–50 m s−1 at ≈2.3125 μm, thus constraining the effect of jitter at these wavelengths. We provide the first multiwavelength confirmation of GJ 876 bc and independently retrieve orbital parameters consistent with previous studies. We recovered RV variabilities for HD 160934 AB and GJ 725 AB that are consistent with their known binary orbits, and nine other targets are candidate RV variables with a statistical significance of 3σ–5σ. Our method, combined with the new iSHELL spectrograph, will yield long-term RV precisions of ≲5 m s−1 in the NIR, which will allow the detection of super-Earths near the habitable zone of mid-M dwarfs.

Wavelet modulus maxima method for on-line wavelength location of pulsed lidar in CO_2 differential absorption lidar detection

Differential absorption lidar (DIAL) is an excellent technology for atmospheric CO2 detection. However, the accuracy and stability of a transmitted on-line wavelength are strictly required in a DIAL system. The fluctuation of a tunable pulsed laser system is relatively more serious than that of other laser sources, and this condition leads to a large measurement error for the lidar signal. These concerns pose a significant challenge in on-line wavelength calibration. This study proposes an alternative method based on wavelet modulus maxima for the accurate on-line wavelength calibration of a pulsed laser. Because of the different propagation characteristics of the wavelet transform modulus maxima between signal and noise, the singularities of a signal can be obtained by detection of the local modulus maxima in the wavelet transform maximum at fine scales. Simulated analysis shows that the method is more accurate than the general method such as quintic polynomial fitting and can steadily maintain high calibration precision at different signal-to-noise ratios (SNRs). Last, 16 groups of real experiments were conducted to verify the simulated analysis, which shows that the proposed method is an alternative for accurately calibrating an on-line wavelength. In addition, the proposed method is able to suppress noises in the process of wavelength calibration, which gives it an advantage in accurate on-line wavelength calibration with a low SNR.

Spectroscopic quantitation of tetrazolium formazan in nano-toxicity assay with interval-based partial least squares regression and genetic algorithm

Spectrophotometric quantitation of formazan in tetrazolium-based nanoparticle (NP) toxicity assay requires a robust calibration model immune to optical interference. For the first time, variant of partial least squares (PLS) regression models, such as, full-spectrum (250–700nm) PLS, interval PLS (iPLS), backward interval PLS (biPLS), and synergy interval PLS (siPLS) models have been adopted for formazan quantitation. Models were evaluated based on root mean square error of cross-validation (RMSECV), and prediction (RMSEP). The spectral variables in optimal iPLS, biPLS and siPLS models, as well as variables retained above a selection frequency threshold (for all intervals), were further refined in a genetic algorithm (GA). The results suggest that the optimal biPLS (140 variables, 5 LVs, RMSECV: 0.4438, RMSEP: 0.2936) and siPLS (88 variables, 5 LVs, RMSECV: 0.4401, RMSEP: 0.316) models were superior either to the full-spectrum PLS (4 LVs, RMSECV: 0.9674, RMSEP: 0.4618) or traditional single wavelength calibration (414nm, RMSECV: 2.0864, RMSEP: 2.1628). Minimum RMSEP (0.2976) was observed when GA was performed on spectral variables retained (above a threshold frequency) from the cumulative frequency distribution of all siPLS models. Finally, applicability of the selected PLS regression models in real NP toxicity assay is demonstrated.

Revised wavelength and spectral response calibrations for AKARI near-infrared grism spectroscopy: Cryogenic phase

Abstract We perform revised spectral calibrations for the AKARI near-infrared grism to correct quantitatively for the effect of the wavelength-dependent refractive index. The near-infrared grism covering the wavelength range of 2.5–5.0 μm, with a spectral resolving power of 120 at 3.6 μm, is found to be contaminated by second-order light at wavelengths longer than 4.9 μm, which is especially serious for red objects. First, we present the wavelength calibration considering the refractive index of the grism as a function of the wavelength for the first time. We find that the previous solution is positively shifted by up to 0.01 μm compared with the revised wavelengths at 2.5–5.0 μm. In addition, we demonstrate that second-order contamination occurs even with a perfect order-sorting filter owing to the wavelength dependence of the refractive index. Secondly, the spectral responses of the system from the first- and second-order light are simultaneously obtained from two types of standard objects with different colors. The response from the second-order light suggests leakage of the order-sorting filter below 2.5 μm. The relations between the output of the detector and the intensities of the first- and second-order light are formalized by a matrix equation that combines the two orders. The removal of the contaminating second-order light can be achieved by solving the matrix equation. The new calibration extends the available spectral coverage of the grism mode from 4.9 μm up to 5.0 μm. The revision can be used to study spectral features falling in these extended wavelengths, e.g., the carbon monoxide fundamental ro-vibrational absorption within nearby active galactic nuclei.