Theory of concentric designs for grating spectrometers

A concentric optical design for a grating spectrometer is described. General aberration theory is given for a family of designs of similar form, showing close similarities with the theory for conventional concentric imagers used in microlithography. Control of stray radiation in the concentric grating spectrometer is discussed.     

Accurate wavelength calibration method for flat-field grating spectrometers

A portable spectrometer prototype is built to study wavelength calibration for flat-field grating spectrometers. An accurate calibration method called parameter fitting is presented. Both optical and structural parameters of the spectrometer are included in the wavelength calibration model, which accurately describes the relationship between wavelength and pixel position. Along with higher calibration accuracy, the proposed calibration method can provide information about errors in the installation of the optical components, which will be helpful for spectrometer alignment.     

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.     

Using concentric circles and wedge grating for camera calibration

This paper presents a method for camera calibration based on the orthogonal vanishing point calibration using concentric circles grating and wedge grating. This method, which we believe is new, uses the high-precision characteristics of phase extraction to obtain the feature points, thus decreasing the calibration errors caused by the traditional marker extraction errors of gray pattern. According to the simulation experiment analysis results, the concentric circles grating was designed with seven periods and the wedge grating was designed with four periods. In the real measuring experiment, the grating target and the similar gray concentric circles target were used to calibrate the camera, respectively. Through comparing the reprojective errors of the two methods, the method proposed is proven to improve the calibration accuracy and robustness for the vanishing point calibration algorithm.     

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.     

Off-plane anastigmatic imaging in Offner spectrometers

In this paper, the imaging performance of an Offner concentric imaging spectrometer is analyzed when the spectrometer entrance slit is disposed arbitrarily on the plane that is parallel to the grating grooves and contains the common center of curvature. Astigmatism-corrected designs are obtained for off-plane incidence on the grating if one point on the slit is located on the Rowland circle of the primary mirror. In this case, the combined system of primary mirror plus diffraction grating provides two astigmatic line images oriented parallel and orthogonal to the plane of diffraction, with the former located on the same plane as the slit. Consequently, these images can be brought to a single focus on this plane by the tertiary mirror if its radius of curvature is chosen properly. In addition, coma aberration is simultaneously removed. These results can be applied to the design of two-mirror or three-mirror spectrometers, generalizing the concept of the best imaging circle and providing solutions to get anastigmatic imaging for two object points and two wavelengths.     

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.     

Combination of grating lenses for color splitting and imaging

A pair of planar reflection gratings is proposed and discussed for use in a color-splitting and imaging system, such as a projection-type color-scanner head. Red, green, and blue light reflected from a color subject are split by a color-splitting grating lens and imaged by an image-correction grating, consisting of three segments, onto three line sensors arranged in parallel. The phase-shift function of the image-correction grating was optimized for each color by numerical iteration with the ray-tracing method to suppress aberrations resulting from the wide view angle and the three different wavelengths. Gratings were designed and fabricated, and aberration suppression was experimentally confirmed.     

Planar reflection grating lens for compact spectroscopic imaging system

A compact spectroscopic imaging device consisting of a planar reflection grating lens, a probe fiber array, and a two-dimensional image sensor was proposed and discussed. Reflected or luminescent lights from a subject are coupled to the probe fibers, guided to fiber output ends, radiated into the air, diffracted by the grating lens with wavelength-dependent angle, and focused onto lines on the image sensor. Two-dimensional intensity distribution on the image sensor can give one-dimensional spectrum distribution along a specified direction. A grating lens was designed with a fiber array and a CCD image sensor for 100-nm wavelength range and 10-mm fiber array width. A spectral resolution of 5 nm and a spatial resolution of 0.25 mm were experimentally confirmed.     

Phase grating design for a dual-band snapshot imaging spectrometer

Infrared spectral features have proved useful in the identification of threat objects. Dual-band focal-plane arrays (FPAs) have been developed in which each pixel consists of superimposed midwave and long-wave photodetectors [Dyer and Tidrow, Conference on Infrared Detectors and Focal Plane Arrays (SPIE, Bellingham, Wash., 1999), pp. 434-440]. Combining dual-band FPAs with imaging spectrometers capable of interband hyperspectral resolution greatly improves spatial target discrimination. The computed-tomography imaging spectrometer (CTIS) [Descour and Dereniak, Appl. Opt. 34, 4817-4826 (1995)] has proved effective in producing hyperspectral images in a single spectral region. Coupling the CTIS with a dual-band detector can produce two hyperspectral data cubes simultaneously. We describe the design of two-dimensional, surface-relief, computer-generated hologram dispersers that permit image information in these two bands simultaneously.     

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.     

Convex approximation to the likelihood criterion for aperture synthesis imaging

Aperture synthesis allows one to measure visibilities at very high resolutions by coupling telescopes of reasonable diameters. We consider the case where visibility amplitudes and phase are measured separately. It leads to an estimation problem where the noise model yields a nonconvex data-likelihood criterion. We show how to optimally approximate the noise model while keeping the criterion convex. This approximation has been validated both on simulations and on experimental data.     

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.     

Hard-X-ray dark-field imaging using a grating interferometer

Imaging with visible light today uses numerous contrast mechanisms, including bright- and dark-field contrast, phase-contrast schemes and confocal and fluorescence-based methods. X-ray imaging, on the other hand, has only recently seen the development of an analogous variety of contrast modalities. Although X-ray phase-contrast imaging could successfully be implemented at a relatively early stage with several techniques, dark-field imaging, or more generally scattering-based imaging, with hard X-rays and good signal-to-noise ratio, in practice still remains a challenging task even at highly brilliant synchrotron sources. In this letter, we report a new approach on the basis of a grating interferometer that can efficiently yield dark-field scatter images of high quality, even with conventional X-ray tube sources. Because the image contrast is formed through the mechanism of small-angle scattering, it provides complementary and otherwise inaccessible structural information about the specimen at the micrometre and submicrometre length scale. Our approach is fully compatible with conventional transmission radiography and a recently developed hard-X-ray phase-contrast imaging scheme. Applications to X-ray medical imaging, industrial non-destructive testing and security screening are discussed.     

Two types of multi-moderator neutron spectrometers: Gamma-ray insensitive type and high-efficiency type

Two types of multi-moderator neutron spectrometers were developed; one is a gamma-ray insensitive type, and the other is a high-efficiency type. An indium activation detector is loaded in the former spectrometer, which can measure the photon-dominant pulsed neutron field such as in the primary photon beam of a high-energy medical electron accelerator. The latter, in which a ³He counter is loaded, is so sensitive that it can measure leakage neutrons from a well shielded facility or even the skyshine neutrons. The response functions of the spectrometers were measured by thermal and mono-energetic neutron standard fields, and were also calculated by the one-dimensional discrete ordinates transport code, ANISN. The measured and calculated responses showed generally good agreement. A benchmark measurement of ²⁵²Cf fission neutrons by using these two spectrometers agreed well with the calculated spectrum. The spectrometers were used in the measurements of neutrons produced by a medical electron accelerator and of skyshine neutrons from an intense 14 MeV neutron source facility.     

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.