Self-consistent algorithm for calibrating spectrometers to picometer accuracy over the entire wavelength range

Spectrometer calibration accuracies are of high importance for a wide range of applications. Typically, one calibrates the spectrometer with a calibration lamp, providing distinct and well-defined calibration lines. However, for small spectral ranges, where only two calibration lines are present, the calibration becomes inaccurate. We present a high-precision nonlinear wavelength calibration method, which is based on two or more reference lines from a calibration lamp. The additional key element introduced is a Fabry-Perot multilayer structure that yields multiple sharp transmission maxima of similar intensity over the full spectrometer range under broad-band illumination (e.g., white-light source). An iterative algorithm is put forward to obtain a self-consistent calibration of picometer precision over the full spectrometer range. In regions distant from calibration lines the accuracy is enhanced by at least a factor of two compared to conventional methods.     

Wavelength calibration of spectra measured by the Global Ozone Monitoring Experiment by use of a high-resolution reference spectrum

Earthshine spectra measured by the nadir-viewing Global Ozone Monitoring Experiment (GOME) spectrometer aboard the second European Remote Sensing (ERS-2) Satellite in the range of 240-790 nm are widely used for the retrieval of concentrations and vertical profiles of atmospheric trace gases. For the near-real-time delivery of ozone columns and profiles at the Royal Netherlands Meterological Institute, a tailor-made wavelength calibration method was developed. The method use a high-resolution (0.01-nm) solar spectrum as the reference spectrum and applies both a shift and a squeeze to the wavelengths in selected windows to find the optimal wavelength grid per window. This method provides a calibration accuracy of 0.002 nm below and 0.001 nm above 290 nm. The new wavelength calibration method can be used on any wavelength window, for example, to improve the calibration of spectra from the GOME Data Processor. A software package, GomeCal, which performs this recalibration, along with an improved polarization and radiometric correction, has been made and has been released via the World Wide Web. The method can be used for any high-resolution (ir)radiance spectrometer, such as the satellite instruments SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Cartography), Ozone Monitoring Instrument, and GOME-2.     

Prelaunch characterization of the Ozone Monitoring Instrument transfer function in the spectral domain

A method and an experimental measurement setup to accurately characterize the instrument transfer function in the spectral domain for hyperspectral spectrometers in the ultraviolet-visible wavelength range are described. The application to the on-ground calibration of the Ozone Monitoring Instrument (OMI) on board the Earth Observing System Aura satellite is presented and discussed. With this method and setup, based on an echelle grating, a sampling of the instrument transfer function in the spectral domain can be selected and is not limited by the spectral resolution and sampling of the spectrometer that is being characterized. The importance of accurately knowing the OMI instrument transfer functions in the spectral domain for in-flight differential optical absorption spectroscopy retrievals and wavelength calibration is discussed. The analysis of the OMI measurement data is presented and shows that the instrument transfer functions in the spectral domain as a function of wavelength and viewing angle can be determined with high accuracy.     

Determination of spectrometer-detector parameters from calibration spectra and the use of the parameters in spectrometer calibrations

The grating equation is used to generate quadratic calibration equations for multichannel detectors with perpendicular and tilted focal planes. The quadratic coefficients are not independent and contain terms that are used to solve for spectrometer-detector parameters. The parameters can be calculated from a quadratic fit at one spectrometer position, but more accurate values can be obtained from quadratic fits at two spectrometer positions. The calculations show that the detector focal plane is tilted by about two degrees. Once values for the spectrometer-detector parameters are obtained from calibrations using at least three lines at one or two spectrometer positions, only one calibration line at any spectrometer position is required to obtain accuracies on the order of 0.1 cm(-1) over a several thousand wavenumber range. The main cause of spectrometer drift is a change in the diffraction angle and/or the spectrometer included angle. This drift is almost totally compensated by the one-line calibration, which adjusts the diffraction angle. A neon pen lamp is used to generate the calibration spectra. Using standard air wavelengths compared to true wavelengths can produce calibration errors of 0.1 to 0.6 cm(-1); the magnitude depends on local conditions and how the laser wavelength is treated.     

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.     

Absolute spectral measurements of direct solar ultraviolet irradiance with a Brewer spectrophotometer

A methodology for the absolute calibration of spectral measurements of direct solar ultraviolet radiation, performed with a Brewer spectrophotometer is presented. The method uses absolute measurements of global and diffuse solar irradiance obtained practically simultaneously at each wavelength with the direct-Sun component. On the basis of this calibration, direct-Sun spectra, measured over a wide range of solar zenith angles at a high altitude site, were used to determine the extraterrestrial solar spectrum by applying the Langley extrapolation method. Finally this spectrum is compared with a solar spectrum derived from the airborne tunable laser absorption spectrometer 3 Space Shuttle mission, showing an agreement of better than +/-3%.     

Use of Eutectic Fixed Points to Characterize a Spectrometer for Earth Observations

A small palm-sized, reference spectrometer, mounted on a remote-controlled model helicopter is being developed and tested by the National Physical Laboratory (NPL) in conjunction with City University, London. The developed system will be used as a key element for field vicarious calibration of optical earth observation systems in the visible-near infrared (VNIR) region. The spectrometer is hand held, low weight, and uses a photodiode array. It has good stray light rejection and wide spectral coverage, allowing simultaneous measurements from 400 to 900 nm. The spectrometer is traceable to NPL’s primary standard cryogenic radiometer via a high-temperature metal-carbon eutectic fixed-point blackbody. Once the fixed-point temperature has been determined (using filter radiometry), the eutectic provides a high emissivity and high stability source of known spectral radiance over the emitted spectral range. All wavelength channels of the spectrometer can be calibrated simultaneously using the eutectic transition without the need for additional instrumentation. The spectrometer itself has been characterized for stray light performance and wavelength accuracy. Its long-term and transportation stability has been proven in an experiment that determined the “World’s Bluest Sky”—a process that involved 56 flights, covering 100,000 km in 72 days. This vicarious calibration methodology using a eutectic standard is presented alongside the preliminary results of an evaluation study of the spectrometer characteristics.     

Imaging spectroscopy for two-dimensional characterization of auroral emissions

A large throughput transmission spectrometer, with a grating on a prism as the diffraction element, has been developed to study altitude distributions of auroral emissions. The imaging spectrometer disperses spectrally in one dimension while spatial information is preserved in the orthogonal direction. The image is projected onto a CCD array detector. Image processing methods have been developed to calibrate for wavelength, uniform field, spectral sensitivity, curvature of field, and spatial mapping. Single images are processed to represent a measured signal brightness in a unit of Rayleighs/pixel, from which area integrations can be made for desired spatial-spectral resolution. System performance is ~1.5-nm resolution over a 450-nm bandwidth (420-870 nm). Two spectrometer systems of this design were operated simultaneously, one with additional optical instruments and an incoherent scatter radar at Sondrestrom, Greenland, and the other at Godhavn, Greenland, which lies 290 km to the northwest and nearly in the magnetic meridian of Sondrestrom. The developed system, calibration method, and examples of performance results are presented.     

Performance assessment of onboard and scene-based methods for Airborne Prism Experiment spectral characterization

Accurate spectral calibration of airborne and spaceborne imaging spectrometers is essential for proper preprocessing and scientific exploitation of high spectral resolution measurements of the land and atmosphere. A systematic performance assessment of onboard and scene-based methods for in-flight monitoring of instrument spectral calibration is presented for the first time in this paper. Onboard and ground imaging data were collected at several flight altitudes using the Airborne Prism Experiment (APEX) imaging spectrometer. APEX is equipped with an in-flight characterization (IFC) facility allowing the evaluation of radiometric, spectral, and geometric system properties, both in-flight and on-ground for the full field of view. Atmospheric and onboard filter spectral features present in at-sensor radiances are compared with the same features in reference transmittances convolved to varying instrument spectral configurations. A spectrum-matching algorithm, taking advantage of the high sensitivity of measurements around sharp spectral features toward spectrometer spectral performance, is used to retrieve channel center wavelength and bandwidth parameters. Results showed good agreement between spectral parameters estimated using onboard IFC and ground imaging data. The average difference between estimates obtained using the O(2) and H(2)O features and those obtained using the corresponding filter features amounted to about 0.3 nm (0.05 of a spectral pixel). A deviation from the nominal laboratory instrument spectral calibration and an altitude-dependent performance was additionally identified. The relatively good agreement between estimates obtained by the two approaches in similar spectral windows suggests they can be used in a complementary fashion: while the method relying on atmospheric features can be applied without the need for dedicated calibration acquisitions, the IFC allows assessment at user-selectable wavelength positions by custom filters as well as for the system on-ground.     

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.     

飞秒脉冲光谱测量对时域波形重建的影响

利用光谱相位还原直接电场重建法对飞秒脉冲激光时域波形进行重建,分析了光谱测量波长示值误差和光谱辐照度示值误差对于飞秒脉冲光谱测量的影响。使用低压汞灯对光谱仪波长校准,根据校准结果,对测量光谱蓝移和红移,通过数值模拟研究波长示值误差对重建脉冲波形的影响;利用光谱辐射照度标准装置对光谱仪光谱辐照度校准,通过增加白噪声模拟分析和各种常用反射片实验测量研究光谱辐照度示值误差对重建脉冲波形的影响。结果表明,光谱测量波长示值误差和光谱辐照度示值误差对于飞秒脉冲光谱测量的相对标准差在1%之内。     

阵列光电传感器的非线性校正

阵列光电传感器在接近饱和时表现出非线性,但是可以通过阵列传感器的线性区的系数外推得到修正,而且只需在一个波长位置测得曝光量与A/D转换值的响应曲线,将能够推广到任意波长位置。为此,利用最小二乘法进行多项式拟合和软件的非线性校正,在同等硬件配置的条件下,增加了线阵传感器的线性区,延拓了传感器的动态范围。在整个动态范围内,系统测量误差可以减少到±2%。此非线性校正方法也非常适用于光电阵列传感器的光谱仪生产厂的强度定标校正。     

Procedures for Wavelength Calibration and Spectral Response Correction of CCD Array Spectrometers

This work describes a procedure for acquiring a spectrum of an analyte over an extended range of wavelengths and validating the wavelength and intensity assignments. To acquire a spectrum over an extended range of wavelengths with a spectrometer with a charge coupled device (CCD) array detector, it is necessary to acquire many partial spectra, each at a different angular position of the grating, and splice the partial spectra into a single extended spectrum. The splicing procedure exposes instrument dependent artifacts. It is demonstrated that by taking a spectrum of a reference irradiance source and making spectral correction, the artifacts exposed by the splicing are removed from the analyte spectrum. This is because the irradiance reference spectrum contains the same artifacts as the analyte spectrum. The artifacts exposed by the splicing depend on the wavelength of the splice; therefore it is important to measure the irradiance reference spectrum for the same range of wavelengths used to measure the spectrum of the analyte solution. In other words, there is no general spectral correction factor which is applicable to spectra taken for different range of wavelengths. The wavelength calibration is also carried out by splicing many partial spectra from a source like a krypton lamp. However the wavelength assignments are not sensitive to the splicing procedure and the same wavelength calibration can be used for spectra acquired over different extended wavelength ranges. The wavelength calibration checks the validity of the setting of the grating angular position, and the assignment of wavelengths to individual pixels on the CCD array detector. The procedure is illustrated by measuring the spectrum of an orange glass and the spectrum of a suspension of microalgae.     

H2O: a frequency and wavelength standard from 0.5 to 5THz (18-160 cm-1)

Frequencies of H₂O pure rotational transitions from 0.5 to 5 THz have been measured with an accuracy of 1 part in 10⁸ using a tunable far-infrared spectrometer. Measured frequencies of more than a hundred spectral lines provide an excellent wavelength and frequency calibration standard for the far infrared     

In-flight energy calibration for the X-ray and gamma-ray spectrometers on the solar-A satellite

The electronically gated in-flight energy calibration is applied to the X-ray and gamma-ray spectrometers on a SOLAR-A satellite. The NaI X-ray spectrometer covering the 20–400 keV energy band is calibrated by an ²⁴¹Am radioactive source which decays by the simultaneous emission of 60 keV X-rays and 5.48 MeV alpha-particles. The X-ray calibration spectrum is accumulated in coincidence with an event tag pulse generated by the simultaneous detection of an X-ray and an alpha-particle. The BGO gamma-ray spectrometer covering the 0.2–10 MeV energy band is calibrated by a ⁶⁰Co radioactive source which decays by the simultaneous emission of 1.17 and 1.33 MeV gamma-rays and a beta-ray (maximum energy is 313 keV). The gamma-ray calibration spectrum is accumulated in a manner similar to the X-ray spectrometer. Since the present method enables to select the calibration pulse without the disadvantage of introducing extra pulses, it is suitable for a space experiment where external conditions and background counting rates can significantly change.     

Characteristics of an absolutely calibrated flat-field extreme ultraviolet spectrometer in the 10-130 A range for fusion plasma diagnostics

A flat-field extreme ultraviolet (EUV) spectrometer with a nominal 2400 grooves/mm aberration-corrected ruled grating has been developed to analyze the emission spectrum in the wavelength range of 10 to 130 A from large helical device (LHD) plasmas. Spectral properties such as resolution, sensitivity, contribution of higher-order light, and background stray light have been studied using emission spectra mainly from intrinsic impurities, e.g., C and Fe. It is found that the spectrometer well resolves closely existing spectral lines of highly ionized medium- and high-Z impurities even in a very short wavelength range such as 10 to 20 A. As a result, it allows one to study the charge state distribution of elements in high-temperature fusion plasma. The ruled grating was then replaced by a laminar type holographic grating for the comparative study. The spectral resolution for the ruled grating (Dlambda approximately 0.08 A at 33.73 A) is clearly better than the holographic grating (Dlambda approximately 0.13 A at 33.73 A). Both gratings well suppress the higher-order light, e.g., the second-order light is only less than 11% of the first-order light for C vi(33.73 A). Relative sensitivity calibration with the wavelength has been done using bremsstrahlung continuum from the LHD plasmas. Absolute intensity calibration has been done by comparing the spectral intensities directly with the absolutely calibrated 1200 grooves/mm EUV spectrometer in the overlapping range of 90-120 A due to the absence of a good branching pair in 10-130 A. As a typical result on the present spectrometer well-resolved n=2-3 full transition arrays from Ne- to Li-like ions are measured for Fe and Ti and wavelengths of the spectral array are tabulated for each charge state. Spectroscopic comparison is also made between the 1200 grooves/mm and 2400 grooves/mm gratings in a range of 50-130 A.     

On the electron microprobe analysis of structured magnetic thin films

The electron microprobe analysis of sputtered FeSi and sputtered or electroplated NiFe films with different structures is reported. The layer thicknesses are between 5 × 10² and 10⁴ Å. The sources of error of a wavelength dispersive spectrometer are compared with those of an energy dispersive spectrometer. Both have been tested by variation of the spectrometer geometry, the inclination of the thin film plane, and the chemical composition, surface roughness and thickness of the films. The calibration was made by X-ray fluorescence and atomic absorption analysis.     

A least squares procedure for calculating the calibration constants of a portable gamma-ray spectrometer

In this study, a least squares procedure for calculating the calibration constants of a portable gamma-ray spectrometer using the general inverse matrix method is presented. The procedure weights the model equations fitting to the calibration data, taking into account the variances in the counting rates and in the radioactive standard concentrations. The application of the described procedure is illustrated by calibrating twice the same gamma-ray spectrometer, with two independent data sets collected approximately 18 months apart in the same calibration facility.     

比较法真空标准漏孔校准方法研究

比较法校准真空标准漏孔是通过四极质谱计比较气体流量计提供的标准气体流量与被校真空标准漏孔产生的离子流获得校准值。主要介绍了比较法真空标准漏孔的校准方法、装置原理、校准过程及校准结果的处理等,并提出了减小测量不确定度的影响因素。     

Characteristics of the relation between wavelength and displacement in monochromators with a sine drive

In this paper, we analyze the wavelength variation as the structural parameters of monochromators with a sine drive and describe the procedures for wavelength calibration by the fitting method. It will be helpful to understand and to use the wavelength calibration method in synchrotron radiation beamlines commissioning and other grating scanning spectrometers.