Noise contributions for imaging spectrometers

In the past decade imaging spectrometers for observation of the Earth were developed to use the complete information of a spectrum as a major tool in the study of physical and biological processes of the Earth. Instead of a few relatively broad spectral bands (line detector), this imager concept provides for the detection of many contiguous narrow spectral bands by applying the technology of matrix detectors. The change from one-dimensional to two-dimensional solid-state imagers makes it necessary to carry out the specific signal-to-noise ratio (SNR) analysis of such detectors. A simulation of maximum and minimum radiances for typical spectral signatures of the Earth (water, vegetation) and the verification of these radiances with modular optoelectronic scanner data provide the means for calculation of electrons generated at the matrix detector. For a hypothetical sensor, water-minimum and vegetation-maximum signals are calculated, and the degradation of the SNR caused by image smear of two-dimensional solid-state imagers is demonstrated.     

Convex grating types for concentric imaging spectrometers

The properties of convex gratings fabricated by electron-beam lithography are investigated. Three grating types are shown. The first is a single-panel, true blazed grating in which the blaze angle stays constant relative to the local surface normal. This grating provides high peak efficiencies of approximately 88% in the first order and 85% in the second order. The second grating has two concentric panels, with each panel blazed at a different angle. This type permits flexibility in matching the grating response to a desired form. The third type has a groove shape that departs from the sawtooth blazed profile to increase the second-order bandwidth. All these types are difficult or impossible to produce with conventional techniques. The gratings compare favorably with conventional (holographic and ruled) types in terms of efficiency and scatter. Simple scalar models are shown to predict the wavelength response accurately. These gratings allow the optical designer to realize fully the considerable advantages of concentric spectrometer forms.     

Fast line-shape correction procedure for imaging Fourier-transform spectrometers

An instrument line-shape correction method adapted to imaging Fourier-transform spectrometers is demonstrated. The method calibrates all pixels on the same spectral grid and permits a direct comparison of the spectral features between pixels such as emission or absorption lines. Computation speed is gained by using matrix line-shape integration formalism rather than properly inverting the line shape of each pixel. A monochromatic source is used to characterize the spectral shift of each pixel, and a line-shape correction scheme is then applied on measured interferograms. This work is motivated by the emergence of affordable infrared CCD cameras that are currently being integrated in imaging Fourier-transform spectrometers.     

Stationary anastigmatic mounts of concave gratings

The general equations for parameters of concave grating mounts that provide stationary and superstationary astigmatism at the wavelength of correction are derived for the first time, to the best of our knowledge. These can be used to design grating multi/demultiplexers for wavelength-division multiplexed optical communication systems and high-resolution, narrow-band spectrographs. Important special cases of stationary anastigmatic mounts and their performance are presented.     

Spectral calibration requirement for Earth-looking imaging spectrometers in the solar-reflected spectrum

Earth-looking imaging spectrometers operating in the solar-reflected spectrum measure spectra of the total upwelling radiance for each spatial element in an image. These measurements are used to derive physical parameters of the Earth's surface and atmosphere from the energy, molecular absorption, and constituent scattering characteristics expressed in each spectrum. To achieve these quantitative objectives, the measured spectra must be spectrally, radiometrically, and spatially calibrated. The ubiquitous presence of numerous, strong, narrow atmosphere and solar absorptions in the upwelling spectral radiance in conjunction with the narrow spectral channels of imaging spectrometers forms the basis for a general spectral calibration requirement. In order to determine the requirement for spectral calibration accuracy, a sensitivity analysis has been completed for imaging spectrometers with contiguously sampled spectral channel response functions of 5, 10, and 20 nm full width at half-maximum from 400 to 2500 nm. This sensitivity analysis shows that spectral calibration errors of 10% and 5% cause significant, spectrally distinct errors in the measured radiance throughout the solar-reflected spectrum. These errors result from the sensitivity of the measured radiance to the exact convolution of the narrow channels of imaging spectrometers with the upwelling spectral radiance that contains narrow atmosphere and solar absorptions. These errors are systematic and add directly to the radiometric calibration uncertainty for every spectrum in the image. This analysis establishes that a spectral calibration accuracy approaching 1% of the full width at half-maximum throughput of the spectral response function for both spectral channel position and shape is necessary to suppress these errors in the measured radiance spectrum.     

Spectral characterization and calibration of AOTF spectrometers and hyper-spectral imaging systems

The goal of this article is to present a novel method for spectral characterization and calibration of spectrometers and hyper-spectral imaging systems based on non-collinear acousto-optical tunable filters. The method characterizes the spectral tuning curve (frequency-wavelength characteristic) of the AOTF (Acousto-Optic Tunable Filter) filter by matching the acquired and modeled spectra of the HgAr calibration lamp, which emits line spectrum that can be well modeled via AOTF transfer function. In this way, not only tuning curve characterization and corresponding spectral calibration but also spectral resolution assessment is performed simultaneously over the whole imaging plane. The obtained results indicated that the proposed method is efficient, accurate and feasible for routine calibration of AOTF spectrometers and hyper-spectral imaging systems and thereby a highly competitive alternative to the existing calibration methods.     

Design of Dyson imaging spectrometers based on the Rowland circle concept

We aim to show that Dyson imaging spectrometers can be easily designed by applying the concept of the Rowland circle to refracting surfaces. This allows us to conceive an analytical procedure that is based on the removal of astigmatism at two wavelengths. Following this procedure, high-optical-quality spectrometers can be designed even for high speeds. Root-mean-square spot radii less than 2.5 μm are obtained for speeds as high as f/1.5, slit lengths of 15 mm, and wavelength ranges of 0.4-1.7 μm. Design examples are presented for classical Dyson spectrometers in which the detector is glued to the glass plane surface and for spectrometers with an air gap between this surface and the image plane.     

Optimized superstationary anastigmatic mounts of concave gratings

Two subfamilies of concave grating superstationary anastigmatic mounts that provide minimum chromatic aberrations are described. The obtained approximate formulas can be used to design flat-field spectrographs and multi/demultiplexers for optical communication networks. Two specific mounts and their performance are presented.     

Systematic design of an anastigmatic lens axicon

We present an analytical method for systematic optical design of a double-pass axicon that shows almost no astigmatism in oblique illumination compared to a conventional linear axicon. The anastigmatic axicon is a singlet lens with nearly concentric spherical surfaces applied in double pass, making it possible to form a long narrow focal line of uniform width. The front and the back surfaces have reflective coatings in the central and annular zones, respectively, to provide the double pass. Our design method finds the radii of curvatures and axial thickness of the lens for a given angle between the exiting rays and the optical axis. It also finds the optimal position of the reflecting zones for minimal vignetting. This method is based on ray tracing of the real rays at the marginal heights of the aperture and therefore is superior to any paraxial method. We illustrate the efficiency of the method by designing a test axicon with optical parameters used for a prototype axicon, which was manufactured and experimentally tested. We compare the optical characteristics of our test axicon with those of the experimental prototype.     

Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information

A modulation transfer function-based optimization method is described that generates optimal spectral and spatial uniformity of response from compact pushbroom imaging spectrometer designs. Such uniformity is essential for extracting accurate spectroscopic information from a pushbroom imaging spectrometer for Earth-observing remote sensing applications. Two simple and compact spectrometer design examples are described that satisfy stringent uniformity specifications.     

Modeling the noise equivalent radiance requirements of imaging spectrometers based on scientific applications

The derivation of radiometric specifications for imaging spectrometers from the visible to the short-wave infrared part of the spectrum is a task based on the requirements of potential scientific applications. A method for modeling the noise equivalent radiance at-sensor level is proposed. The model starts with surface reflectance signatures, transforms them to at-sensor signatures, and combines signatures of various applications with regard to performance requirements. The wavelength-dependent delta radiances are then derived at predefined radiance levels by use of a model of the sensor performance. The model is applied with regard to the upcoming Airborne Prism Experiment imaging spectrometer system. A combination of various potential application disciplines forms the basis of the experiment. The results help in the definition of radiometric levels for laboratory calibration of the noise equivalent radiance levels, the quantization of the signal, and the spectral range of an instrument to be designed.     

Analysis of computed tomographic imaging spectrometers. I. Spatial and spectral resolution

Computed tomographic imaging spectrometers measure the spectrally resolved image of an object scene in an entirely different manner from traditional whisk-broom or push-broom systems, and thus their noise behavior and data artifacts are unfamiliar. We review computed tomographic imaging spectrometry (CTIS) measurement systems and analyze their performance, with the aim of providing a vocabulary for discussing resolution in CTIS instruments, by illustrating the artifacts present in their reconstructed data and contributing a rule-of-thumb measure of their spectral resolution. We also show how the data reconstruction speed can be improved, at no cost in reconstruction quality, by ignoring redundant projections within the measured raw images.     

Mechanical disturbances in Fourier spectrometers

Fourier spectrometers are sensitive to many kinds of disturbance. This focus is mainly on those connected to mechanical vibrations, assessing the relationships between the mechanical inputs and the deriving effects on the spectra. Mechanical vibrations have two main effects on the spectra, the addition of signals due to direct sensitivity to vibrations of the detectors (e.g., through piezoelectric effect) and the changes of the interferogram due to the interferometer optical components motion. The Fourier transform spectrometer considered in this study is based on the constant optical path step sampling achieved by using the interferogram of a reference laser as a trigger so, ideally insensitive to mirrors speed changes, however, the analysis will show how the effects of delays in the sampling chain can compromise the benefits of this configuration. The effects of the vibration of the interferometer optical alignment are considered as well, showing the effect produced on the interferograms and eventually on the spectra. Despite their nonmechanical nature, detector nonlinearity and internal optical reflections are considered as well because their effects, similar to the mechanical ones, could be confused with the latter while in spectra diagnostic it is often important to be able to distinguish between the two. For all the analyzed effects the quantitative relationships between the mechanical disturbances' amplitudes and spectral observed effects are derived.     

Improvement of mass spectrometers

Recent progress in the improvement of mass spectrometers at Osaka University is presented. Mass spectrometers are designed by using the computer program TRIO, which calculates the ion trajectories in the third order approximation. Several high-performance mass spectrometers are proposed and some of them have been constructed and examined. Two different kinds are described in detail: one is a single focusing mass spectrometer with large incident and exit angles and the other is a double focusing mass spectrometer with field arrangement QQHQC (quadrupole, quadrupole, homogeneous magnetic sector, quadrupole, cylindrical electric sector). High resolution and high sensitivity are attained simultaneously.