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NASA NTRS2002

The 12x32 Pop-Up Bolometer Array for the SHARC II Camera

SHARC II is a 350 micron facility camera for the Caltech Submillimeter Observatory (CSO) expected to come on-line in 2002. The key component of SHARC II is a 12x32 array of doped silicon 'pop-up' bolometers developed at NASA/Goddard and delivered to Caltech in March 2002. Each pixel is 1 mm x 1 mm, coated with a 400 Omega/square bismuth film, and located lambda/4 above a reflective backshort to maximize radiation absorption. The pixels cover the focal plane with greater than 95% filling factor. Each doped thermistor occupies nearly the full area of the pixel to minimize 1/f noise. We report some results from the first cold measurements of this array. The bolometers were located inside a dark cover, and 4x32 pixels were read simultaneously. In the best 25% of winter nights on Mauna Kea, SHARC II is expected to have an NEFD at 350 microns of 1 Jy s(sup 1/2) or better.

Dowell, C. Darren↗

NASA NTRS2004

Sunglint Research in the Lab, and Spatial Micro-Complexity

We are beginning a new investigation into polarized sunglint in a laboratory setting, using a wave tank. The wave tank has the capability of generating almost any combination of gravity and capillary waves under computer control, from simple sine waves to essentially random seas. Our aim is to perfect sunglint models, which have advanced little since the work of Cox and Munk in the 1950s using digitized photographs taken from an airplane. Sungllnt patterns, even when viewed from elevated platforms, but more and more so when viewed from low Earth orbit and beyond, have a kind of coherence and stability which transcends a pixel-by-pixel interpretation. The light forming the pattern is a sum of contributions from several or even many waves which are far from adjacent. Thus glint is a phenomenon that can only be understood in the large and never on a pixel-by-pixel basis.

Wiscombe, Warren↗

NASA NTRS2004

Recent History of Large-Scale Ecosystem Disturbances in North America Derived from the AVHRR Satellite Record

Ecosystem structure and function are strongly impacted by disturbance events, many of which in North America are associated with seasonal temperature extremes, wildfires, and tropical storms. This study was conducted to evaluate patterns in a 19-year record of global satellite observations of vegetation phenology from the Advanced Very High Resolution Radiometer (AVHRR) as a means to characterize major ecosystem disturbance events and regimes. The fraction absorbed of photosynthetically active radiation (FPAR) by vegetation canopies worldwide has been computed at a monthly time interval from 1982 to 2000 and gridded at a spatial resolution of 8-km globally. Potential disturbance events were identified in the FPAR time series by locating anomalously low values (FPAR-LO) that lasted longer than 12 consecutive months at any 8-km pixel. We can find verifiable evidence of numerous disturbance types across North America, including major regional patterns of cold and heat waves, forest fires, tropical storms, and large-scale forest logging. Summed over 19 years, areas potentially influenced by major ecosystem disturbances (one FPAR-LO event over the period 1982-2000) total to more than 766,000 km2. The periods of highest detection frequency were 1987-1989, 1995-1997, and 1999. Sub- continental regions of Alaska and Central Canada had the highest proportion (greater than 90%) of FPAR-LO pixels detected in forests, tundra shrublands, and wetland areas. The Great Lakes region showed the highest proportion (39%) of FPAR-LO pixels detected in cropland areas, whereas the western United States showed the highest proportion (16%) of FPAR-LO pixels detected in grassland areas. Based on this analysis, an historical picture is emerging of periodic droughts and heat waves, possibly coupled with herbivorous insect outbreaks, as among the most important causes of ecosystem disturbance in North America.

Potter, Christopher↗

NASA NTRS1994

Thermal Design of the Cassini Narrow Angle Camera

The Narrow Angle Camera (NAC) is one of two cameras in the Imaging Science Subsystem (ISS) on the Cassini Spacecraft (S/C), the second camera is a Voyager-inherited Wide Angle Camera (WAC). Cassini is currently planned to be launched in October 1997 and will arrive at Saturn for a four year tour in June 2004. The Narrow Angle Optics are a Ritchey Chretien type Optics, has a focal length of 2000 mm, a relative aperture of f/10.5, a spectral range of 200 to 1100 nm, 24 filters, a pixel field of view of 6.0 microradian/pixel, and has a field of view of 3.5 x 3.5 degrees. The sensor is a Charged Couple Device (CCD), 1024 x 1024 pixels with a pixel size of 12 x 12 um, a full well greater than 50,000 e-, on chip processing of up to 800,000 e- pixel summation, a dark current of less than 0.1 e-/pixel/sec at operating temperature, and a charge transfer efficiency of 0.99999 at operating temperature...

Hoffman, Pamela↗

NASA NTRS2005

Rover mast calibration, exact camera pointing, and camara handoff for visual target tracking

This paper presents three technical elements that we have developed to improve the accuracy of the visual target tracking for single-sol approach-and-instrument placement in future Mars rover missions. An accurate, straightforward method of rover mast calibration is achieved by using a total station, a camera calibration target, and four prism targets mounted on the rover. The method was applied to Rocky8 rover mast calibration and yielded a 1.1-pixel rms residual error. Camera pointing requires inverse kinematic solutions for mast pan and tilt angles such that the target image appears right at the center of the camera image. Two issues were raised. Mast camera frames are in general not parallel to the masthead base frame. Further, the optical axis of the camera model in general does not pass through the center of the image. Despite these issues, we managed to derive non-iterative closed-form exact solutions, which were verified with Matlab routines. Actual camera pointing experiments aver 50 random target image paints yielded less than 1.3-pixel rms pointing error. Finally, a purely geometric method for camera handoff using stereo views of the target has been developed. Experimental test runs show less than 2.5 pixels error on high-resolution Navcam for Pancam-to-Navcam handoff, and less than 4 pixels error on lower-resolution Hazcam for Navcam-to-Hazcam handoff.

camera handoff↗

NASA NTRS2007

GIFTS SM EDU Data Processing and Algorithms

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the processing algorithms involved in the calibration stage. The calibration procedures can be subdivided into three stages. In the pre-calibration stage, a phase correction algorithm is applied to the decimated and filtered complex interferogram. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected blackbody reference spectra. In the radiometric calibration stage, we first compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. During the post-processing stage, we estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. We then implement a correction scheme that compensates for the effect of fore-optics offsets. Finally, for off-axis pixels, the FPA off-axis effects correction is performed. To estimate the performance of the entire FPA, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation.

Tian, Jialin↗

NASA NTRS2007

GIFTS SM EDU Level 1B Algorithms

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) SensorModule (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the GIFTS SM EDU Level 1B algorithms involved in the calibration. The GIFTS Level 1B calibration procedures can be subdivided into four blocks. In the first block, the measured raw interferograms are first corrected for the detector nonlinearity distortion, followed by the complex filtering and decimation procedure. In the second block, a phase correction algorithm is applied to the filtered and decimated complex interferograms. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected spectrum. The phase correction and spectral smoothing operations are performed on a set of interferogram scans for both ambient and hot blackbody references. To continue with the calibration, we compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. We now can estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. The correction schemes that compensate for the fore-optics offsets and off-axis effects are also implemented. In the third block, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation. Finally, in the fourth block, the single pixel algorithms are applied to the entire FPA.

Tian, Jialin↗

NASA NTRS2007

Digital Signal Processing Techniques for the GIFTS SM EDU

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiance using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes several digital signal processing (DSP) techniques involved in the development of the calibration model. In the first stage, the measured raw interferograms must undergo a series of processing steps that include filtering, decimation, and detector nonlinearity correction. The digital filtering is achieved by employing a linear-phase even-length FIR complex filter that is designed based on the optimum equiripple criteria. Next, the detector nonlinearity effect is compensated for using a set of pre-determined detector response characteristics. In the next stage, a phase correction algorithm is applied to the decimated interferograms. This is accomplished by first estimating the phase function from the spectral phase response of the windowed interferogram, and then correcting the entire interferogram based on the estimated phase function. In the calibration stage, we first compute the spectral responsivity based on the previous results and the ideal Planck blackbody spectra at the given temperatures, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. In the post-calibration stage, we estimate the Noise Equivalent Spectral Radiance (NESR) from the calibrated ABB and HBB spectra. The NESR is generally considered as a measure of the instrument noise performance, and can be estimated as the standard deviation of calibrated radiance spectra from multiple scans. To obtain an estimate of the FPA performance, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is developed based on the pixel performance evaluation. This would allow us to perform the calibration procedures on a random pixel population that is a good statistical representation of the entire FPA. The design and implementation of each individual component will be discussed in details.

Tian, Jialin↗

NASA NTRS2006

Using Satellite Data to Characterize the Temporal Thermal Behavior of an Active Volcano: Mount St. Helens, WA

ASTER thermal infrared data over Mt. St Helens were used to characterize its thermal behavior from Jun 2000 to Feb 2006. Prior to the Oct 2004 eruption, the average crater temperature varied seasonally between -12 and 6 C. After the eruption, maximum single-pixel temperature increased from 10 C (Oct 2004) to 96 C (Aug 2005), then showed a decrease to Feb 2006. The initial increase in temperature was correlated with dome morphology and growth rate and the subsequent decrease was interpreted to relate to both seasonal trends and a decreased growth rate/increased cooling rate, possibly suggesting a significant change in the volcanic system. A single-pixel ASTER thermal anomaly first appeared on Oct 1, 2004, eleven hours after the first eruption - 10 days before new lava was exposed at the surface. By contrast, an automated algorithm for detecting thermal anomalies in MODIS data did not trigger an alert until Dec 18. However, a single-pixel thermal anomaly first appeared in MODIS channel 23 (4 um) on Oct 13, 12 days after the first eruption - 2 days after lava was exposed. The earlier thermal anomaly detected with ASTER data is attributed to the higher spatial resolution (90 m) compared with MODIS (1 m) and the earlier visual observation of anomalous pixels compared to the automated detection method suggests that local spatial statistics and background radiance data could improve automated detection methods.

Advanced Spaceborne Thermal Emission and Reflectio↗

NASA NTRS2005

Event-driven charge-coupled device design and applications therefor

An event-driven X-ray CCD imager device uses a floating-gate amplifier or other non-destructive readout device to non-destructively sense a charge level in a charge packet associated with a pixel. The output of the floating-gate amplifier is used to identify each pixel that has a charge level above a predetermined threshold. If the charge level is above a predetermined threshold the charge in the triggering charge packet and in the charge packets from neighboring pixels need to be measured accurately. A charge delay register is included in the event-driven X-ray CCD imager device to enable recovery of the charge packets from neighboring pixels for accurate measurement. When a charge packet reaches the end of the charge delay register, control logic either dumps the charge packet, or steers the charge packet to a charge FIFO to preserve it if the charge packet is determined to be a packet that needs accurate measurement. A floating-diffusion amplifier or other low-noise output stage device, which converts charge level to a voltage level with high precision, provides final measurement of the charge packets. The voltage level is eventually digitized by a high linearity ADC.

Doty, John P.↗

NASA NTRS2001

High speed CMOS imager with motion artifact supression and anti-blooming

An image sensor includes pixels formed on a semiconductor substrate. Each pixel includes a photoactive region in the semiconductor substrate, a sense node, and a power supply node. A first electrode is disposed near a surface of the semiconductor substrate. A bias signal on the first electrode sets a potential in a region of the semiconductor substrate between the photoactive region and the sense node. A second electrode is disposed near the surface of the semiconductor substrate. A bias signal on the second electrode sets a potential in a region of the semiconductor substrate between the photoactive region and the power supply node. The image sensor includes a controller that causes bias signals to be provided to the electrodes so that photocharges generated in the photoactive region are accumulated in the photoactive region during a pixel integration period, the accumulated photocharges are transferred to the sense node during a charge transfer period, and photocharges generated in the photoactive region are transferred to the power supply node during a third period without passing through the sense node. The imager can operate at high shutter speeds with simultaneous integration of pixels in the array. High quality images can be produced free from motion artifacts. High quantum efficiency, good blooming control, low dark current, low noise and low image lag can be obtained.

Pain, Bedabrata↗

NASA NTRS2006

Image sensor with motion artifact supression and anti-blooming

Pain, Bedabrata↗

NASA NTRS2008

The Impact of Soil Reflectance on the Quantification of the Green Vegetation Fraction from NDVI

The green vegetation fraction (Fg) is an important climate and hydrologic model parameter. A common method to calculate Fg is to create a simple linear mixing rnodeP between two NDVI endmembers: bare soil NDVI (NDVI(sub o)) and full vegetation NDVI (NDVI(sub infinity)). Usually it is assumed that NDVI(sub o), is close to zero (NDVI(sub o) approx.-0.05) and is generally chosen from the lowest observed NDVI values. However, the mean soil NDVI computed from 2906 samples is much larger (NDVI=0.2) and is highly variable (standard deviation=O. 1). We show that the underestimation of NDVI(sub o) yields overestimations of Fg. The largest errors occur in grassland and shrubland areas. Using parameters for NDVI(sub o) and NDVI(sub infinity) derived from global scenes yields overestimations of Fg ((Delta) Fg*) that are larger than 0.2 for the majority of U.S. land cover types when pixel NDVI values are 0.2<NDVI(sub pixel)<0.4. Figure 1 shows how the Fg overestimation varies for the most common land cover types in the conterminous U.S. for typical seasonal NDVI values. When using conterminous U.S. scenes to derive NDV(sub o) and NDVI(sub infinity), the overestimation is less (0.10-0.17 for 0.2<NDVI(sub pixel)<0.4). As a result, parts of the conterminous U.S. are affected at different times of the year depending on the local seasonal NDVI cycle. We propose using global databases of NDVI(sub o) along with information on historical NDVI(sub pixel) values to compute a statistically most-likely estimate of Fg (Fg*). Using in situ measurements made at the Sevilleta LTER, we show that this approach yields better estimates of Fg than using global invariant NDVI(sub o) values estimated from whole scenes (Figure 2). At the two studied sites, the Fg estimate was adjusted by 52% at the grassland and 86% at the shrubland. More significant advances will require information on spatial distribution of soil reflectance.

Montandon, L. M.↗

NASA NTRS2008

Array-scale performance of TES X-ray Calorimeters Suitable for Constellation-X

Having developed a transition-edge-sensor (TES) calorimeter design that enables high spectral resolution in high fill-factor arrays, we now present array-scale results from 32-pixel arrays of identical closely packed TES pixels. Each pixel in such an array contains a Mo/Au bilayer with a transition temperature of 0.1 K and an electroplated Au or Au/Bi xray absorber. The pixels in an array have highly uniform physical characteristics and performance. The arrays are easy to operate due to the range of bias voltages and heatsink temperatures over which solution better than 3 eV at 6 keV can be obtained. Resolution better than 3 eV has also been obtained with 2x8 time-division SQUID multiplexing. We will present the detector characteristics and show spectra acquired through the read-out chain from the multiplexer electronics through the demultiplexer software to real-time signal processing. We are working towards demonstrating this performance over the range of count rates expected in the observing program of the Constellation-X observatory. We mill discuss the impact of increased counting rate on spectral resolution, including the effects of crosstalk and optimal-filtering dead time.

Kilbourne, C. A.↗

NASA NTRS2008

Vision System Measures Motions of Robot and External Objects

A prototype of an advanced robotic vision system both (1) measures its own motion with respect to a stationary background and (2) detects other moving objects and estimates their motions, all by use of visual cues. Like some prior robotic and other optoelectronic vision systems, this system is based partly on concepts of optical flow and visual odometry. Whereas prior optoelectronic visual-odometry systems have been limited to frame rates of no more than 1 Hz, a visual-odometry subsystem that is part of this system operates at a frame rate of 60 to 200 Hz, given optical-flow estimates. The overall system operates at an effective frame rate of 12 Hz. Moreover, unlike prior machine-vision systems for detecting motions of external objects, this system need not remain stationary: it can detect such motions while it is moving (even vibrating). The system includes a stereoscopic pair of cameras mounted on a moving robot. The outputs of the cameras are digitized, then processed to extract positions and velocities. The initial image-data-processing functions of this system are the same as those of some prior systems: Stereoscopy is used to compute three-dimensional (3D) positions for all pixels in the camera images. For each pixel of each image, optical flow between successive image frames is used to compute the two-dimensional (2D) apparent relative translational motion of the point transverse to the line of sight of the camera. The challenge in designing this system was to provide for utilization of the 3D information from stereoscopy in conjunction with the 2D information from optical flow to distinguish between motion of the camera pair and motions of external objects, compute the motion of the camera pair in all six degrees of translational and rotational freedom, and robustly estimate the motions of external objects, all in real time. To meet this challenge, the system is designed to perform the following image-data-processing functions: The visual-odometry subsystem (the subsystem that estimates the motion of the camera pair relative to the stationary background) utilizes the 3D information from stereoscopy and the 2D information from optical flow. It computes the relationship between the 3D and 2D motions and uses a least-mean-squares technique to estimate motion parameters. The least-mean-squares technique is suitable for real-time implementation when the number of external-moving-object pixels is smaller than the number of stationary-background pixels.

Talukder, Ashit↗

NASA NTRS2009

SOI CMOS Imager with Suppression of Cross-Talk

A monolithic silicon-on-insulator (SOI) complementary metal oxide/semiconductor (CMOS) image-detecting integrated circuit of the active-pixel-sensor type, now undergoing development, is designed to operate at visible and near-infrared wavelengths and to offer a combination of high quantum efficiency and low diffusion and capacitive cross-talk among pixels. The imager is designed to be especially suitable for astronomical and astrophysical applications. The imager design could also readily be adapted to general scientific, biological, medical, and spectroscopic applications. One of the conditions needed to ensure both high quantum efficiency and low diffusion cross-talk is a relatively high reverse bias potential (between about 20 and about 50 V) on the photodiode in each pixel. Heretofore, a major obstacle to realization of this condition in a monolithic integrated circuit has been posed by the fact that the required high reverse bias on the photodiode is incompatible with metal oxide/semiconductor field-effect transistors (MOSFETs) in the CMOS pixel readout circuitry. In the imager now being developed, the SOI structure is utilized to overcome this obstacle: The handle wafer is retained and the photodiode is formed in the handle wafer. The MOSFETs are formed on the SOI layer, which is separated from the handle wafer by a buried oxide layer. The electrical isolation provided by the buried oxide layer makes it possible to bias the MOSFETs at CMOS-compatible potentials (between 0 and 3 V), while biasing the photodiode at the required higher potential, and enables independent optimization of the sensory and readout portions of the imager.

Pain, Bedabrata↗

NASA NTRS2008

Nano-Multiplication-Region Avalanche Photodiodes and Arrays

Nano-multiplication-region avalanche photodiodes (NAPDs), and imaging arrays of NAPDs integrated with complementary metal oxide/semiconductor (CMOS) active-pixel-sensor integrated circuitry, are being developed for applications in which there are requirements for high-sensitivity (including photoncounting) detection and imaging at wavelengths from about 250 to 950 nm. With respect to sensitivity and to such other characteristics as speed, geometric array format, radiation hardness, power demand of associated circuitry, size, weight, and robustness, NAPDs and arrays thereof are expected to be superior to prior photodetectors and arrays including CMOS active-pixel sensors (APSs), charge-coupled devices (CCDs), traditional APDs, and microchannelplate/ CCD combinations. Figure 1 depicts a conceptual NAPD array, integrated with APS circuitry, fabricated on a thick silicon-on-insulator wafer (SOI). Figure 2 presents selected aspects of the structure of a typical single pixel, which would include a metal oxide/semiconductor field-effect transistor (MOSFET) integrated with the NAPD. The NAPDs would reside in silicon islands formed on the buried oxide (BOX) layer of the SOI wafer. The silicon islands would be surrounded by oxide-filled insulation trenches, which, together with the BOX layer, would constitute an oxide embedding structure. There would be two kinds of silicon islands: NAPD islands for the NAPDs and MOSFET islands for in-pixel and global CMOS circuits. Typically, the silicon islands would be made between 5 and 10 m thick, but, if necessary, the thickness could be chosen outside this range. The side walls of the silicon islands would be heavily doped with electron-acceptor impurities (p+-doped) to form anodes for the photodiodes and guard layers for the MOSFETs. A nanoscale reach-through structure at the front (top in the figures) central position of each NAPD island would contain the APD multiplication region. Typically, the reach-through structure would be about 0.1 microns in diameter and between 0.3 and 0.4 nm high. The top layer in the reach-through structure would be heavily doped with electron-donor impurities (n+-doped) to make it act as a cathode. A layer beneath the cathode, between 0.1 and 0.2 nm thick, would be p-doped to a concentration .10(exp 17)cu cm. A thin n+-doped polysilicon pad would be formed on the top of the cathode to protect the cathode against erosion during a metal-silicon alloying step that would be part of the process of fabricating the array.

Zheng, Xinyu↗

NASA NTRS2009

Fabricating Radial Groove Gratings Using Projection Photolithography

Projection photolithography has been used as a fabrication method for radial grove gratings. Use of photolithographic method for diffraction grating fabrication represents the most significant breakthrough in grating technology in the last 60 years, since the introduction of holographic written gratings. Unlike traditional methods utilized for grating fabrication, this method has the advantage of producing complex diffractive groove contours that can be designed at pixel-by-pixel level, with pixel size currently at the level of 45 45 nm. Typical placement accuracy of the grating pixels is 10 nm over 30 nm. It is far superior to holographic, mechanically ruled or direct e-beam written gratings and results in high spatial coherence and low spectral cross-talk. Due to the smooth surface produced by reactive ion etch, such gratings have a low level of randomly scattered light. Also, due to high fidelity and good surface roughness, this method is ideally suited for fabrication of radial groove gratings. The projection mask is created using a laser writer. A single crystal silicon wafer is coated with photoresist, and then the projection mask, with its layer of photoresist, is exposed for patterning in a stepper or scanner. To develop the photoresist, the fabricator either removes the exposed areas (positive resist) of the unexposed areas (negative resist). Next, the patterned and developed photoresist silicon substrate is subjected to reactive ion etching. After this step, the substrate is cleaned. The projection mask is fabricated according to electronic design files that may be generated in GDS file format using any suitable CAD (computer-aided design) or other software program. Radial groove gratings in off-axis grazing angle of incidence mount are of special interest for x-ray spectroscopy, as they allow achieving higher spectral resolution for the same grating area and have lower alignment tolerances than traditional in-plane grating scheme. This is especially critical for NASA Constellation- X project that will utilize hundreds of gratings all of which need to be precisely aligned for x-ray observation of space.

Iazikov, Dmitri↗