Determining the Pixel-to-Pixel Uncertainty in Satellite-Derived SST Fields
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Fan Wu↗
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On-Orbit Solar Dynamics Observatory (SDO) Star Tracker Warm Pixel Analysis
This paper describes the process of identification and analysis of warm pixels in two autonomous star trackers on the Solar Dynamics Observatory (SDO) mission. A brief description of the mission orbit and attitude regimes is discussed and pertinent star tracker hardware specifications are given. Warm pixels are defined and the Quality Index parameter is introduced, which can be explained qualitatively as a manifestation of a possible warm pixel event. A description of the algorithm used to identify warm pixel candidates is given. Finally, analysis of dumps of on-orbit star tracker charge coupled devices (CCD) images is presented and an operational plan going forward is discussed. SDO, launched on February 11, 2010, is operated from the NASA Goddard Space Flight Center (GSFC). SDO is in a geosynchronous orbit with a 28.5 inclination. The nominal mission attitude points the spacecraft X-axis at the Sun, with the spacecraft Z-axis roughly aligned with the Solar North Pole. The spacecraft Y-axis completes the triad. In attitude, SDO moves approximately 0.04 per hour, mostly about the spacecraft Z-axis. The SDO star trackers, manufactured by Galileo Avionica, project the images of stars in their 16.4deg x 16.4deg fields-of-view onto CCD detectors consisting of 512 x 512 pixels. The trackers autonomously identify the star patterns and provide an attitude estimate. Each unit is able to track up to 9 stars. Additionally, each tracker calculates a parameter called the Quality Index, which is a measure of the quality of the attitude solution. Each pixel in the CCD measures the intensity of light and a warns pixel is defined as having a measurement consistently and significantly higher than the mean background intensity level. A warns pixel should also have lower intensity than a pixel containing a star image and will not move across the field of view as the attitude changes (as would a dim star image). It should be noted that the maximum error introduced in the star tracker attitude solution during suspected warm pixel corruptions is within the specified 36 attitude error budget requirement of [35, 70, 70] arcseconds. Thus, the star trackers provided attitude accuracy within the specification for SDO. The star tracker images are intentionally defocused so each star image is detected in more than one CCD pixel. The position of each star is calculated as an intensity-weighted average of the illuminated pixels. The exact method of finding the positions is proprietary to the tracker manufacturer. When a warm pixel happens to be in the vicinity of a star, it can corrupt the calculation of the position of that particular star, thereby corrupting the estimate of the attitude.
Felikson, Denis↗
Pixelation Effects in Weak Lensing
Weak gravitational lensing can be used to investigate both dark matter and dark energy but requires accurate measurements of the shapes of faint, distant galaxies. Such measurements are hindered by the finite resolution and pixel scale of digital cameras. We investigate the optimum choice of pixel scale for a space-based mission, using the engineering model and survey strategy of the proposed Supernova Acceleration Probe as a baseline. We do this by simulating realistic astronomical images containing a known input shear signal and then attempting to recover the signal using the Rhodes, Refregier, and Groth algorithm. We find that the quality of shear measurement is always improved by smaller pixels. However, in practice, telescopes are usually limited to a finite number of pixels and operational life span, so the total area of a survey increases with pixel size. We therefore fix the survey lifetime and the number of pixels in the focal plane while varying the pixel scale, thereby effectively varying the survey size. In a pure trade-off for image resolution versus survey area, we find that measurements of the matter power spectrum would have minimum statistical error with a pixel scale of 0.09' for a 0.14' FWHM point-spread function (PSF). The pixel scale could be increased to ~0.16' if images dithered by exactly half-pixel offsets were always available. Some of our results do depend on our adopted shape measurement method and should be regarded as an upper limit: future pipelines may require smaller pixels to overcome systematic floors not yet accessible, and, in certain circumstances, measuring the shape of the PSF might be more difficult than those of galaxies. However, the relative trends in our analysis are robust, especially those of the surface density of resolved galaxies. Our approach thus provides a snapshot of potential in available technology, and a practical counterpart to analytic studies of pixelation, which necessarily assume an idealized shape measurement method.
gravitational lensing↗
Photon-counting hexagonal pixel array CdTe detector: Spatial resolution characteristics for image-guided interventional applications
Purpose: High-resolution, photon-counting, energy-resolved detector with fast-framing capability can facilitate simultaneous acquisition of precontrast and postcontrast images for subtraction angiography without pixel registration artifacts and can facilitate high-resolution real-time imaging during image-guided interventions. Hence, this study was conducted to determine the spatial resolution characteristics of a hexagonal pixel array photon-counting cadmium telluride (CdTe) detector. Methods: A 650 μm thick CdTe Schottky photon-counting detector capable of concurrently acquiring up to two energy-windowed images was operated in a single energy-window mode to include photons of 10 keV or higher. The detector had hexagonal pixels with apothem of 30 μm resulting in pixel pitch of 60 and 51.96 μm along the two orthogonal directions. The detector was characterized at IEC-RQA5 spectral conditions. Linear response of the detector was determined over the air kerma rate relevant to image-guided interventional procedures ranging from 1.3 nGy/frame to 91.4 μGy/frame. Presampled modulation transfer was determined using a tungsten edge test device. The edge-spread function and the finely sampled line spread function accounted for hexagonal sampling, from which the presampled modulation transfer function (MTF) was determined. Since detectors with hexagonal pixels require resampling to square pixels for distortion-free display, the optimal square pixel size was determined by minimizing the root-mean-squared-error of the aperture functions for the square and hexagonal pixels up to the Nyquist limit. Results: At Nyquist frequencies of 8.33 and 9.62 cycles/mm along the apothem and orthogonal to the apothem directions, the modulation factors were 0.397 and 0.228, respectively. For the corresponding axis, the limiting resolution defined as 10% MTF occurred at 13.3 and 12 cycles/mm, respectively. Evaluation of the aperture functions yielded an optimal square pixel size of 54 μm. After resampling to 54 μm square pixels using trilinear interpolation, the presampled MTF at Nyquist frequency of 9.26 cycles/mm was 0.29 and 0.24 along the orthogonal directions and the limiting resolution (10% MTF) occurred at approximately 12 cycles/mm. Visual analysis of a bar pattern image showed the ability to resolve close to 12 line-pairs/mm and qualitative evaluation of a neurovascular nitinol-stent showed the ability to visualize its struts at clinically relevant conditions. Conclusions: Hexagonal pixel array photon-counting CdTe detector provides high spatial resolution in single-photon counting mode. After resampling to optimal square pixel size for distortion-free display, the spatial resolution is preserved. The dual-energy capabilities of the detector could allow for artifact-free subtraction angiography and basis material decomposition. The proposed high-resolution photon-counting detector with energy-resolving capability can be of importance for several image-guided interventional procedures as well as for pediatric applications.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
A Proposed Extension to the Soil Moisture and Ocean Salinity Level 2 Algorithm for Mixed Forest and Moderate Vegetation Pixels
The Soil Moisture and Ocean Salinity (SMOS)mission, launched in November 2009, provides global maps of soil moisture and ocean salinity by measuring the L-band (1.4 GHz) emission of the Earth's surface with a spatial resolution of 40-50 km.Uncertainty in the retrieval of soilmoisture over large heterogeneous areas such as SMOS pixels is expected, due to the non-linearity of the relationship between soil moisture and the microwave emission. The current baseline soilmoisture retrieval algorithm adopted by SMOS and implemented in the SMOS Level 2 (SMOS L2) processor partially accounts for the sub-pixel heterogeneity of the land surface, by modelling the individual contributions of different pixel fractions to the overall pixel emission. This retrieval approach is tested in this study using airborne L-band data over an area the size of a SMOS pixel characterised by a mix Eucalypt forest and moderate vegetation types (grassland and crops),with the objective of assessing its ability to correct for the soil moisture retrieval error induced by the land surface heterogeneity. A preliminary analysis using a traditional uniform pixel retrieval approach shows that the sub-pixel heterogeneity of land cover type causes significant errors in soil moisture retrieval (7.7%v/v RMSE, 2%v/v bias) in pixels characterised by a significant amount of forest (40-60%). Although the retrieval approach adopted by SMOS partially reduces this error, it is affected by errors beyond the SMOS target accuracy, presenting in particular a strong dry bias when a fraction of the pixel is occupied by forest (4.1%v/v RMSE,-3.1%v/v bias). An extension to the SMOS approach is proposed that accounts for the heterogeneity of vegetation optical depth within the SMOS pixel. The proposed approach is shown to significantly reduce the error in retrieved soil moisture (2.8%v/v RMSE, -0.3%v/v bias) in pixels characterised by a critical amount of forest (40-60%), at the limited cost of only a crude estimate of the optical depth of the forested area (better than 35% uncertainty). This study makes use of an unprecedented data set of airborne L-band observations and ground supporting data from the National Airborne Field Experiment 2005 (NAFE'05), which allowed accurate characterisation of the land surface heterogeneity over an area equivalent in size to a SMOS pixel.
Panciera, Rocco↗
A Cryogenic readout integrated circuit with analog pile-up and in-Pixel ADC for high frame rate Skipper CCD-in-CMOS Sensors
The Skipper CCD-in-CMOS Parallel Read-Out Circuit V2 (SPROCKET2) is designed to enable high frame rate readout of Skipper CCD-in-CMOS image sensors. The SPROCKET2 pixel is fabricated in a 65 nm CMOS process and occupies a 60$\mu$m $\times$ 60$\mu$m footprint. SPROCKET2 is intended to be heterogeneously integrated with a pixelated Skipper CCD-in-CMOS sensor, such that one readout pixel is connected to a multiplexed array of 16 active image sensor pixels, to match their spatial geometry. Our design benefits from the Skipper CCD-in-CMOS sensor's non-destructive readout capability to achieve exceptionally low noise through multi-sampling and averaging while optimizing for total power consumption. The pixel readout utilizes correlated double sampling to minimize 1/f noise and includes "pile-up" of ten successive samples in the analog domain before digitizing at a rate of 66.7 ksps. Measurement results of in-pixel serial SAR ADC show DNL and INL of ~0. 44 LSB and 0.58 LBS respectively. A large area array of 20,000 SPROCKET2 ADC pixels (multiplexed 1:16 to 320,000 sensor pixels) is currently under test. By reading out data over a 10 Gbps optical link, this pixel design enables a frame rate of $\sim$ 4 kfps for large sensing areas with minimal sensing deadtime. In the highest gain mode, the pixelated ADC has an input-referred resolution of 10$\mu$V with a simulated power consumption of 50$\mu$W. The pixel operates with constant current draw to minimize power-rail crosstalk.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Fully depleted CMOS pixel sensor development and potential applications
CMOS pixel sensors are often opposed to hybrid pixel sensors due to their very different sensitive layer. In standard CMOS imaging processes, a thin (about 20 μm) low resistivity epitaxial layer acts as the sensitive volume and charge collection is mostly driven by thermal agitation. In contrast, the so-called hybrid pixel technology exploits a thick (typically 300 μm) silicon sensor with high resistivity allowing for the depletion of this volume, hence charges drift toward collecting electrodes. But this difference is fading away with the recent availability of some CMOS imaging processes based on a relatively thick (about 50 μm) high resistivity epitaxial layer which allows for full depletion. This evolution extents the range of applications for CMOS pixel sensors where their known assets, high sensitivity and granularity combined with embedded signal treatment, could potentially foster breakthrough in detection performances for specific scientific instruments. One such domain is the Xray detection for soft energies, typically below 10 keV, where the thin sensitive layer was previously severely impeding CMOS sensor usage. Another application becoming realistic for CMOS sensors, is the detection in environment with a high fluence of non-ionizing radiation, such as hadron colliders. However, when considering highly demanding applications, it is still to be proven that micro-circuits required to uniformly deplete the sensor at the pixel level, do not mitigate the sensitivity and efficiency required. Prototype sensors in two different technologies with resistivity higher than 1 kΩ, sensitive layer between 40 and 50 μm and featuring pixel pitch in the range 25 to 50 μm, have been designed and fabricated. Various biasing architectures were adopted to reach full depletion with only a few volts. Laboratory investigations with three types of sources (X-rays, β-rays and infrared light) demonstrated the validity of the approach with respect to depletion, keeping a low noise figure. Especially, an energy resolution of about 400 eV for 5 keV X-rays was obtained for single pixels. The prototypes have then been exposed to gradually increased fluences of neutrons, from 10{sup 13} to 5x10{sup 14} neq/cm{sup 2}. Again laboratory tests allowed to evaluate the signal over noise persistence on the different pixels implemented. Currently our development mostly targets the detection of soft X-rays, with the ambition to develop a pixel sensor matching counting rates as affordable with hybrid pixel sensors, but with an extended sensitivity to low energy and finer pixel about 25 x 25 μm{sup 2}. The original readout architecture proposed relies on a two tiers chip. The first tier consists of a sensor with a modest dynamic in order to insure low noise performances required by sensitivity. The interconnected second tier chip enhances the read-out speed by introducing massive parallelization. Performances reachable with this strategy combining counting and integration will be detailed. (authors)
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Use of high-granularity CdZnTe pixelated detectors to correct response non-uniformities caused by defects in crystals
Following our successful demonstration of the position-sensitive virtual Frisch-grid detectors, we investigated the feasibility of using high-granularity position sensing to correct response non-uniformities caused by the crystal defects in CdZnTe (CZT) pixelated detectors. The development of high-granularity detectors able to correct response non-uniformities on a scale comparable to the size of electron clouds opens the opportunity of using unselected off-the-shelf CZT material, whilst still assuring high spectral resolution for the majority of the detectors fabricated from an ingot. Here, we present the results from testing 3D position-sensitive 15×15×10 mm 3 pixelated detectors, fabricated with conventional pixel patterns with progressively smaller pixel sizes: 1.4, 0.8, and 0.5 mm. We employed the readout system based on the H3D front-end multi-channel ASIC developed by BNL's Instrumentation Division in collaboration with the University of Michigan. We use the sharing of electron clouds among several adjacent pixels to measure locations of interaction points with sub-pixel resolution. By using the detectors with small-pixel sizes and a high probability of the charge-sharing events, we were able to improve their spectral resolutions in comparison to the baseline levels, measured for the 1.4-mm pixel size detectors with small fractions of charge-sharing events. These results demonstrate that further enhancement of the performance of CZT pixelated detectors and reduction of costs are possible by using high spatial-resolution position information of interaction points to correct the small-scale response non-uniformities caused by crystal defects present in most devices.
36 MATERIALS SCIENCE↗
Fast and Accurate Pixel Calibration of Tof Neutron Diffractometers with Machine Learning
At a spallation neutron source, neutron pulses of varying energies are generated, and the detection of neutrons by instrument detectors is recorded as time-of-flight from the emission of the neutron pulse to its arrival at specific detector pixels with high time resolution. The flight path of neutrons from the moderator to the sample and then to the detector must be precisely calibrated at the detector-pixel level using standard powders, so the neutron events from all pixels can be time-focused to produce high-resolution diffraction patterns. Modern time-of-flight neutron diffractometers at spallation neutron sources are equipped with two-dimensional detectors with millimeter-scale pixelations. The number of pixels in a diffraction instrument can reach millions, which makes a single-pixel-level calibration process time-consuming or even impossible with conventional refinement or fitting approaches. Here we present a machine-learning-aided calibration process using a train-and-predict approach, in which machine learning models are trained on the relationship between an individual pixel time-of-flight diffraction pattern and its diffraction constant. These models use a portion of the available pixels for training, and a good model then predicts the diffraction constants precisely and rapidly for large sets of pixel diffraction patterns.
detector pixel calibration↗
The Impact of Pixel Size on the Characterization of Deep Convective Clouds for Calibration
The NASA CERES project provides the scientific community the observed TOA SW and LW fluxes for climate monitoring and climate model validation. CERES utilizes hourly geostationary imager derived broadband fluxes, which rely on the channel radiances and associated cloud retrievals, are used to estimate the broadband fluxes between CERES observations. This requires stable and consistent cross-platform imager visible channel calibration. The CERES project utilizes deep convective clouds (DCC) as an invariant Earth target to both monitor the stability of sensors and for radiometric scaling. GSICS, an international collaboration, is also evaluating and implementing the DCC invariant target calibration methodology to provide consistent calibration coefficients across geostationary imagers anchored to the AquaMODIS or the NOAA-20 VIIRS calibration reference. Tropical DCC are the brightest, coldest, most Lambertian, top of the atmosphere Earth targets. The DCC invariant target calibration methodology relies on a large ensemble of tropical D CC-identified pixel-level reflectances, which are aggregated as probability density functions (PDF). By assuming the monthly PDF shape is otherwise consistent in time excepting shifts in reflectance caused by changes in the sensor calibration, the imager stability is monitored. Radiometric scaling is accomplished by ratioing the sensor pair DCC PDF reflectance values. The success of the DCC methodology relies on consistent PDF distributions. The goal of this study is to determine the impact of pixel resolution on the DCC reflectance distribution. Single SNPP-VIIRS 750-m and Landsat 8 OLI 30-m granules are aggregated to degrade the pixel resolution from the native level. The DCC pixels are identified using a BT threshold. Most of the brightest DCC pixels are also the coldest, although there are exceptions. It was found that increasing the BT threshold exponentially increased the number of darker pixels. The pixel resolution did not seem to impact the DCC reflectance PDF distribution for pixel resolutions less than 3 km, which suggests that imagers of varying pixel resolutions may be radiometrically scaled to each other using DCC targets.
DCC↗
Charge Loss and Charge Sharing Measurements for Two Different Pixelated Cadmium-Zinc-Telluride Detectors
As part of ongoing research at Marshall Space Flight Center, Cadmium-Zinc- Telluride (CdZnTe) pixilated detectors are being developed for use at the focal plane of the High Energy Replicated Optics (HERO) telescope. HERO requires a 64x64 pixel array with a spatial resolution of around 200 microns (with a 6m focal length) and high energy resolution (< 2% at 60keV). We are currently testing smaller arrays as a necessary first step towards this goal. In this presentation, we compare charge sharing and charge loss measurements between two devices that differ both electronically and geometrically. The first device consists of a 1-mm-thick piece of CdZnTe that is sputtered with a 4x4 array of pixels with pixel pitch of 750 microns (inter-pixel gap is 100 microns). The signal is read out using discrete ultra-low-noise preamplifiers, one for each of the 16 pixels. The second detector consists of a 2-mm-thick piece of CdZnTe that is sputtered with a 16x16 array of pixels with a pixel pitch of 300 microns (inter-pixel gap is 50 microns). Instead of using discrete preamplifiers, the crystal is bonded to an ASIC that provides all of the front-end electronics to each of the 256 pixels. what degree the bias voltage (i.e. the electric field) and hence the drift and diffusion coefficients affect our measurements. Further, we compare the measured results with simulated results and discuss to
Gaskin, Jessica↗
Characterization of Pixelated Cadmium-Zinc-Telluride Detectors for Astrophysical Applications
Comparisons of charge sharing and charge loss measurements between two pixelated Cadmium-Zinc-Telluride (CdZnTe) detectors are discussed. These properties along with the detector geometry help to define the limiting energy resolution and spatial resolution of the detector in question. The first detector consists of a 1-mm-thick piece of CdZnTe sputtered with a 4x4 array of pixels with pixel pitch of 750 microns (inter-pixel gap is 100 microns). Signal readout is via discrete ultra-low-noise preamplifiers, one for each of the 16 pixels. The second detector consists of a 2-mm-thick piece of CdZnTe sputtered with a 16x16 array of pixels with a pixel pitch of 300 microns (inter-pixel gap is 50 microns). This crystal is bonded to a custom-built readout chip (ASIC) providing all front-end electronics to each of the 256 independent pixels. These detectors act as precursors to that which will be used at the focal plane of the High Energy Replicated Optics (HERO) telescope currently being developed at Marshall Space Flight Center. With a telescope focal length of 6 meters, the detector needs to have a spatial resolution of around 200 microns in order to take full advantage of the HERO angular resolution. We discuss to what degree charge sharing will degrade energy resolution but will improve our spatial resolution through position interpolation.
Gaskin, Jessica↗
High-speed imaging at high x-ray energy: CdTe sensors coupled to charge-integrating pixel array detectors
Pixel Array Detectors (PADs) consist of an x-ray sensor layer bonded pixel-by-pixel to an underlying readout chip. This approach allows both the sensor and the custom pixel electronics to be tailored independently to best match the x-ray imaging requirements. Here we describe the hybridization of CdTe sensors to two different charge-integrating readout chips, the Keck PAD and the Mixed-Mode PAD (MM-PAD), both developed previously in our laboratory. The charge-integrating architecture of each of these PADs extends the instantaneous counting rate by many orders of magnitude beyond that obtainable with photon counting architectures. The Keck PAD chip consists of rapid, 8-frame, in-pixel storage elements with framing periods <150 ns. The second detector, the MM-PAD, has an extended dynamic range by utilizing an in-pixel overflow counter coupled with charge removal circuitry activated at each overflow. This allows the recording of signals from the single-photon level to tens of millions of x-rays/pixel/frame while framing at 1 kHz. Both detector chips consist of a 128×128 pixel array with (150 µm){sup 2} pixels.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Detector pixel calibration of time-of-flight neutron diffractometers accelerated by machine learning
Modern time-of-flight neutron diffractometers at spallation neutron source are equipped with two dimensional detectors with fine pixelations. The flight path of neutrons from the moderator to the sample and to the detector needs to be precisely calibrated at detector pixel level using standard powders so the diffraction data from all the detector pixels can be correctly time-focused to produce high resolution diffraction peaks. The number of pixels can reach to millions which makes a single-pixel calibration process time-consuming, or even impossible, with conventional fitting routine. Here we presented a machine learning aided calibration process via a “training and predict” process by training machine learning models with the relations between the individual pixel time-of-flight diffraction pattern and fitted diffraction constant. The training models take a portion of the available pixels to predict the diffraction constants precisely and rapidly for massive pixel diffraction patterns.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Estimation of proportions in mixed pixels through their region characterization
A region of mixed pixels can be characterized through the probability density function of proportions of classes in the pixels. Using information from the spectral vectors of a given set of pixels from the mixed pixel region, expressions are developed for obtaining the maximum likelihood estimates of the parameters of probability density functions of proportions. The proportions of classes in the mixed pixels can then be estimated. If the mixed pixels contain objects of two classes, the computation can be reduced by transforming the spectral vectors using a transformation matrix that simultaneously diagonalizes the covariance matrices of the two classes. If the proportions of the classes of a set of mixed pixels from the region are given, then expressions are developed for obtaining the estmates of the parameters of the probability density function of the proportions of mixed pixels. Development of these expressions is based on the criterion of the minimum sum of squares of errors. Experimental results from the processing of remotely sensed agricultural multispectral imagery data are presented.
Chittineni, C. B.↗
Effect of mixed (boundary) pixels on crop proportion estimation
In estimating acreage proportions of crop types in a segment using Landsat data, considerable problem is caused by the presence of mixed pixels. Due to lack of understanding of their spectral characteristics, mixed pixels have been treated in the past as pure while clustering and classifying the segment data. This paper examines this approach of treating mixed pixels as pure pixels and the effect of mixed pixels on the bias and variance of a crop type proportion estimate. First, the spectral response of a boundary pixel is modeled and an analytical expression for the bias and variance of a proportion estimate is obtained. This is followed by a numerical illustration of the effect of mixed pixels on bias and variance. It is shown that as the size of the mixed pixel class increases in a segment, the variance increases, however, such increase does not always affect the bias of the proportion estimate.
Chhikara, R. S.↗