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Imer-product array processor for retrieval of stored images represented by bipolar binary (+1,-1) pixels using partial input trinary pixels represented by (+1,-1)

An inner-product array processor is provided with thresholding of the inner product during each iteration to make more significant the inner product employed in estimating a vector to be used as the input vector for the next iteration. While stored vectors and estimated vectors are represented in bipolar binary (1,-1), only those elements of an initial partial input vector that are believed to be common with those of a stored vector are represented in bipolar binary; the remaining elements of a partial input vector are set to 0. This mode of representation, in which the known elements of a partial input vector are in bipolar binary form and the remaining elements are set equal to 0, is referred to as trinary representation. The initial inner products corresponding to the partial input vector will then be equal to the number of known elements. Inner-product thresholding is applied to accelerate convergence and to avoid convergence to a negative input product.

Liu, Hua-Kuang

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

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

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

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.

Method for hyperspectral imagery exploitation and pixel spectral unmixing

An efficiently hybrid approach to exploit hyperspectral imagery and unmix spectral pixels. This hybrid approach uses a genetic algorithm to solve the abundance vector for the first pixel of a hyperspectral image cube. This abundance vector is used as initial state in a robust filter to derive the abundance estimate for the next pixel. By using Kalman filter, the abundance estimate for a pixel can be obtained in one iteration procedure which is much fast than genetic algorithm. The output of the robust filter is fed to genetic algorithm again to derive accurate abundance estimate for the current pixel. The using of robust filter solution as starting point of the genetic algorithm speeds up the evolution of the genetic algorithm. After obtaining the accurate abundance estimate, the procedure goes to next pixel, and uses the output of genetic algorithm as the previous state estimate to derive abundance estimate for this pixel using robust filter. And again use the genetic algorithm to derive accurate abundance estimate efficiently based on the robust filter solution. This iteration continues until pixels in a hyperspectral image cube end.

Lin, Ching-Fang

CMOS VLSI Active-Pixel Sensor for Tracking

An architecture for a proposed active-pixel sensor (APS) and a design to implement the architecture in a complementary metal oxide semiconductor (CMOS) very-large-scale integrated (VLSI) circuit provide for some advanced features that are expected to be especially desirable for tracking pointlike features of stars. The architecture would also make this APS suitable for robotic- vision and general pointing and tracking applications. CMOS imagers in general are well suited for pointing and tracking because they can be configured for random access to selected pixels and to provide readout from windows of interest within their fields of view. However, until now, the architectures of CMOS imagers have not supported multiwindow operation or low-noise data collection. Moreover, smearing and motion artifacts in collected images have made prior CMOS imagers unsuitable for tracking applications. The proposed CMOS imager (see figure) would include an array of 1,024 by 1,024 pixels containing high-performance photodiode-based APS circuitry. The pixel pitch would be 9 m. The operations of the pixel circuits would be sequenced and otherwise controlled by an on-chip timing and control block, which would enable the collection of image data, during a single frame period, from either the full frame (that is, all 1,024 ~ 1,024 pixels) or from within as many as 8 different arbitrarily placed windows as large as 8 by 8 pixels each. A typical prior CMOS APS operates in a row-at-a-time ( grolling-shutter h) readout mode, which gives rise to exposure skew. In contrast, the proposed APS would operate in a sample-first/readlater mode, suppressing rolling-shutter effects. In this mode, the analog readout signals from the pixels corresponding to the windows of the interest (which windows, in the star-tracking application, would presumably contain guide stars) would be sampled rapidly by routing them through a programmable diagonal switch array to an on-chip parallel analog memory array. The diagonal-switch and memory addresses would be generated by the on-chip controller. The memory array would be large enough to hold differential signals acquired from all 8 windows during a frame period. Following the rapid sampling from all the windows, the contents of the memory array would be read out sequentially by use of a capacitive transimpedance amplifier (CTIA) at a maximum data rate of 10 MHz. This data rate is compatible with an update rate of almost 10 Hz, even in full-frame operation

Pain, Bedabrata

Micro-Pixel Image Position Sensing Testbed

The search for Earth-mass planets in the habitable zones of nearby Sun-like stars is an important goal of astrophysics. This search is not feasible with the current slate of astronomical instruments. We propose a new concept for microarcsecond astrometry which uses a simplified instrument and hence promises to be low cost. The concept employs a telescope with only a primary, laser metrology applied to the focal plane array, and new algorithms for measuring image position and displacement on the focal plane. The required level of accuracy in both the metrology and image position sensing is at a few micro-pixels. We have begun a detailed investigation of the feasibility of our approach using simulations and a micro-pixel image position sensing testbed called MCT. So far we have been able to demonstrate that the pixel-to-pixel distances in a focal plane can be measured with a precision of 20 micro-pixels and image-to-image distances with a precision of 30 micro-pixels. We have also shown using simulations that our image position algorithm can achieve accuracy of 4 micro-pixels in the presence of lambda/20 wavefront errors.

astrometry

Soil moisture variability within remote sensing pixels

The effects of topography and the level of soil moisture on the variability of soil moisture within remote sensing pixels were assessed during the First ISLSCP Field Experiment (FIFE) during 1987 and 1989. Soil moisture data from flat, sloped, and valley-shaped pixels were obtained over a wide range of moisture conditions. Relative elevation data were obtained for each study area to create digital elevation models with which to quantify topographic variability. Within-pixel soil moisture variability was shown to increase with increased topographic heterogeneity. The flat pixel had significantly lower standard deviations and fewer outlier points than the slope and valley pixels. Most pixel means had a positive skewness, indicating that most pixels will have areas of markedly higher than average soil moisture.

Charpentier, Michael A.

Electromagnetic Properties of Filled, Pixellated Arrays

Filled arrays of bolometers are currently being employed for use in astronomy from the far-infrared through millimeter parts of the electromagnetic spectrum. Because of the large range of wavelengths for which this is applicable, the number of modes supported by a bolometric pixel will vary according to specific application. Withington et al. (2003) have built a formalism for treating the electromagnetic properties of such bolometers by propagating the second order statistical properties of the radiation through a canonical optical system. In this work, we use this formalism to construct beam pattern images of square pixels for various ratios of p/lambda where p is the pixel size and lambda is the wavelength. In the low mode limit, the diffraction effects cause the beam pattern to be circular with a quadrupole dependence of Stokes Q and U. High mode cases approach the geometric limit. The polarization in these cases can be seen to trace the pixel edges. The effective size of the beam has a direct impact on the inter-pixel coupling and sets the number of independent detectors in an astronomical focal plane. This technique illustrates and quantifies the relationship between pixel size and angular resolution limits for a given wavelength and telescope. This is especially true in the limit of low p/lambda. In this case, the diffraction due to pixelization is non-negligible for the calculation of the overall angular resolution of the telescope. In addition, for instruments that are polarization sensitive, this method also provides a quantitative method for determining the contribution of the instrument to the measured polarization.

Chuss, David T.

Selecting Pixels for Kepler Downlink

The Kepler mission monitors > 100,000 stellar targets using 42 2200 1024 pixel CCDs. Bandwidth constraints prevent the downlink of all 96 million pixels per 30-minute cadence, so the Kepler spacecraft downlinks a specified collection of pixels for each target. These pixels are selected by considering the object brightness, background and the signal-to-noise of each pixel, and are optimized to maximize the signal-to-noise ratio of the target. This paper describes pixel selection, creation of spacecraft apertures that efficiently capture selected pixels, and aperture assignment to a target. Diagnostic apertures, short-cadence targets and custom specified shapes are discussed.

Bryson, Stephen T.

Improving Photometry and Stellar Signal Preservation with Pixel-Level Systematic Error Correction

The Kepler Mission has demonstrated that excellent stellar photometric performance can be achieved using apertures constructed from optimally selected CCD pixels. The clever methods used to correct for systematic errors, while very successful, still have some limitations in their ability to extract long-term trends in stellar flux. They also leave poorly correlated bias sources, such as drifting moiré pattern, uncorrected. We will illustrate several approaches where applying systematic error correction algorithms to the pixel time series, rather than the co-added raw flux time series, provide significant advantages. Examples include, spatially localized determination of time varying moiré pattern biases, greater sensitivity to radiation-induced pixel sensitivity drops (SPSDs), improved precision of co-trending basis vectors (CBV), and a means of distinguishing the stellar variability from co-trending terms even when they are correlated. For the last item, the approach enables physical interpretation of appropriately scaled coefficients derived in the fit of pixel time series to the CBV as linear combinations of various spatial derivatives of the pixel response function (PRF). We demonstrate that the residuals of a fit of soderived pixel coefficients to various PRF-related components can be deterministically interpreted in terms of physically meaningful quantities, such as the component of the stellar flux time series which is correlated with the CBV, as well as, relative pixel gain, proper motion and parallax. The approach also enables us to parameterize and assess the limiting factors in the uncertainties in these quantities.

Kolodzijczak, Jeffrey J.

Fabrication of X-ray Microcalorimeter Focal Planes Composed of Two Distinct Pixel Types

We develop superconducting transition-edge sensor (TES) microcalorimeter focal planes for versatility in meeting the specifications of X-ray imaging spectrometers, including high count rate, high energy resolution, and large field of view. In particular, a focal plane composed of two subarrays: one of fine pitch, high count-rate devices and the other of slower, larger pixels with similar energy resolution, offers promise for the next generation of astrophysics instruments, such as the X-ray Integral Field Unit Instrument on the European Space Agencys ATHENA mission. We have based the subarrays of our current design on successful pixel designs that have been demonstrated separately. Pixels with an all-gold X-ray absorber on 50 and 75 micron pitch, where the Mo/Au TES sits atop a thick metal heatsinking layer, have shown high resolution and can accommodate high count rates. The demonstrated larger pixels use a silicon nitride membrane for thermal isolation, thinner Au, and an added bismuth layer in a 250-sq micron absorber. To tune the parameters of each subarray requires merging the fabrication processes of the two detector types. We present the fabrication process for dual production of different X-ray absorbers on the same substrate, thick Au on the small pixels and thinner Au with a Bi capping layer on the larger pixels to tune their heat capacities. The process requires multiple electroplating and etching steps, but the absorbers are defined in a single-ion milling step. We demonstrate methods for integrating the heatsinking of the two types of pixel into the same focal plane consistent with the requirements for each subarray, including the limiting of thermal crosstalk. We also discuss fabrication process modifications for tuning the intrinsic transition temperature (T(sub c)) of the bilayers for the different device types through variation of the bilayer thicknesses. The latest results on these 'hybrid' arrays will be presented.

Terms—Arrays