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Various boundary layer parameters and transducer shape effect on Measurement error of random pressure field by finite size transducer
In many of today's telescopes the effects of surface errors on image quality and scattered light are very important. The influence of optical fabrication surface errors on the performance of an optical system is discussed. The methods developed by Hopkins (1957) for aberration tolerancing and Barakat (1972) for random wavefront errors are extended to the examination of mid- and high-spatial frequency surface errors. The discussion covers a review of the basic concepts of image quality, an examination of manufacturing errors as a function of image quality performance, a demonstration of mirror scattering effects in relation to surface errors, and some comments on the nature of the correlation functions. Illustrative examples are included.
Error probability for communication system correlators with noisy reference signals
The present investigation is concerned with the presentation of a simplified model of the spatial structure of forecast error statistics, a comparison of the model with actual numerical weather prediction results, and the extent to which simplifying assumptions made in the model are justified. A stochastic-dynamic model is derived for the spatial structure of the global atmospheric mass-field forecast error. The model states that the relative potential vorticity of the forecast error is random. The covariance function of the model's solutions is found to be governed by a simple deterministic equation. The agreement between the stochastic model and actual mass-field forecast errors fields for 12-36 h periods validates the assumptions on which the model is derived. Within this period, the difference between the potential voriticity fields of the atmosphere and of the numerical forecasts used in the comparison is well represented by white noise.
Random figure errors from the polishing process plus particles on the main mirrors in a telescope cause an extended point spread function (PSF) declining approximately as the inverse square of the sine of the angle from a star from about 100 micro-rad to a right angle. The decline in at least one case, and probably in general, proceeds as the inverse cube at smaller angles where the usual focal plane aperture radius is chosen. The photometric error due to misalignment by one Airy ring spacing with an aperture of n rings depends on the net variance in the figure. It is approximately 60/(n+1)(3) when using the data of Kormendy (1973). A typical value is 6 x 10 to the -5th power per ring of misalignment with n = 100 rings. The encircled power may be modulated on a time scale of hours by parts per thousand in a wavelength dependent manner due to relative humidity effects on mirror dust. The scattering according to an inverse power law is due to a random walk in aberration height caused by a multitude of facets and slope errors left by the polishing process. A deviation from such a law at grazing emergence may permit monitoring the dust effects.
An analysis was made to determine the effect of transmission errors on the quality of data transferred from the Terminal Area Air Traffic Model to a remote site. Data formating schemes feasible within the operational constraints of the data link were proposed and their susceptibility to both random bit error and to noise burst were investigated. It was shown that satisfactory reliability is achieved by a scheme formating the simulation output into three data blocks which has the priority data triply redundant in the first block in addition to having a retransmission priority on that first block when it is received in error.
A report discusses a proposal to use thermal (long-wavelength infrared) images of the Earth, as seen from spacecraft at interplanetary distances, for pointing antennas and telescopes toward the Earth for Ka-band and optical communications. The purpose is to overcome two limitations of using visible images: (1) at large Earth phase angles, the light from the Earth is too faint; and (2) performance is degraded by large albedo variations associated with weather changes. In particular, it is proposed to use images in the wavelength band of 8 to 13 m, wherein the appearance of the Earth is substantially independent of the Earth phase angle and emissivity variations are small. The report addresses tracking requirements for optical and Ka-band communications, selection of the wavelength band, available signal level versus phase angle, background noise, and signal-to-noise ratio. Tracking errors are estimated for several conceptual systems employing currently available infrared image sensors. It is found that at Mars range, it should be possible to locate the centroid of the Earth image within a noise equivalent angle (a random angular error) between 10 and 150 nanoradians at a bias error of no more than 80 nanoradians
The scene identification probabilities (Pij) are fundamentally important in evaluations of the top-of-the-atmosphere (TOA) radiation-flux errors due to the scene misidentification. In this paper, the scene identification error probabilities were empirically derived from data collected in 1985 by the Earth Radiation Budget Experiment (ERBE) scanning radiometer when the ERBE satellite and the NOAA-9 spacecraft were rotated so as to scan alongside during brief periods in January and August 1985. Radiation-flux error computations utilizing these probabilities were performed, using orbit specifications for the ERBE, the Cloud and Earth's Radiant Energy System (CERES), and the SCARAB missions for a scene that was identified as partly cloudy over ocean. Typical values of the standard deviation of the random shortwave error were in the order of 1.5-5 W/sq m, but could reach values as high as 18.0 W/sq m as computed from NOAA-9.
The fundamental objective is to determine the information available in ground-based millimeter-wave measurements of stratospheric constituent profiles, to identify the optimum method of retrieving this profile information, and to characterize the errors in the final result. A secondary objective is to produce retrieval software for operational use with Network for the Detection of Stratospheric Change (NDSC) measurements of O3, H2O, ClO, and perhaps N2O. Tests were performed on existing ozone retrieval programs in support of ongoing NDSC field measurements. The results show that if random spectral errors and retrieval bias errors are considered, accuracy of the retrieved profile is about 5 percent from 20-50 km, and about 10 percent from 50-60 km.
The single-breath method represents a simple noninvasive technique for the assessment of capillary blood flow across the lung. However, this method has not gained widespread acceptance, because its accuracy is still being questioned. A rigorous procedure is described for estimating pulmonary blood flow (PBF) using data obtained with the aid of the single-breath method. Attention is given to the minimization of data-processing errors in the presence of measurement errors and to questions regarding a correction for possible loss of CO2 in the lung tissue. It is pointed out that the estimations are based on the exact solution of the underlying differential equations which describe the dynamics of gas exchange in the lung. The reported study demonstrates the feasibility of obtaining highly reliable estimates of PBF from expiratory data in the presence of random measurement errors.
NASA Space Shuttle Challenger SIR-B ocean scenes are used to derive directional wave spectra for which speckle noise is modeled as a function of Rayleigh random phase coherence downrange and Poisson random amplitude errors inherent in the Doppler measurement of along-track position. A Fourier filter that preserves SIR-B image phase relations is used to correct the stationary and dynamic response characteristics of the remote sensor and scene correlator, as well as to subtract an estimate of the speckle noise component. A two-dimensional map of sea surface elevation is obtained after the filtered image is corrected for both random and deterministic motions.
Analysis of more than 36 years of time series of seven parameters measured in the NSO/AFRL/Sac Peak K-line monitoring program elucidates five elucidates five components of the variation: (1) the solar cycle (period approx. 11 years), (2) quasi-periodic variations (periods approx 100 days), (3) a broad band stochastic process (wide range of periods), (4) rotational modulation, and (5) random observational errors. Correlation and power spectrum analyses elucidate periodic and aperiodic variation of the chromospheric parameters. Time-frequency analysis illuminates periodic and quasi periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (1) and (2) at time scales in the range approx 0.1 - 10 years. These results using only full-disk data further suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as those being produced by NASA's Kepler observatory. Component (3) consists of variations over a range of timescales, in the manner of a 1/f random noise process. A timedependent Wilson-Bappu effect appears to be present in the solar cycle variations (1), but not in the stochastic process (3). Component (4) characterizes differential rotation of the active regions, and (5) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The recent data suggest that the current cycle is starting late and may be relatively weak. The data analyzed in this paper can be found at the National Solar Observatory web site http://nsosp.nso.edu/cak_mon/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters.
A television tube is a useful way to record a many-element picture such as is obtained from an echelle spectrograph. The signal on the tube target is scanned and relayed to the data-processing center where it must be reconstituted into the scene that was present in the focal plane of the spectrograph camera. A typical television frame will contain four million bits of information which must be processed to remove transmission errors and random noise pulses, to remove periodic noise, to correct for optical and electrical distortion, to remove sensitivity variations across the face of the tube, to calibrate from the photoelectrons back to incident energy, and to provide a wavelength scale. Results of a study of these problems is presented.
The determination of satellite orbits for use in geodesy using range-only data has been examined. A recently developed recursive algorithm for rectification of the nominal orbit after processing each observation has been tested. It is shown that when a synchronous satellite is tracked simultaneously with a subsynchronous geodetic target satellite, the orbits of each may be readily determined by processing the range information. Random data errors and satellite perturbations are included in the examples presented.
Formulas are presented to calculate the landing point of a spacecraft on Mars. The areographic latitude is taken as the angle between a plumb line at the landing point and the plane perpendicular to the axis of rotation of Mars relative to the sun. The ephemeral time of the upper culmination of the sun at the landing point is used to determine areographic longitude. A coupled system and a topocentric system of coordinates are introduced to develop the first series of equations. Both errors which are independent random quantities and systematic errors are considered, as well as the influence of the distance of the landing point from the boundary of the area of polar night.
Two sites in Canada were selected for detailed analysis of the ESMR-6/ snow relationships. Data were analyzed for February 1976 for site 1 and January, February and March 1976 for site 2. Snowpack water equivalents were less than 4.5 inches for site 1 and, depending on the month, were between 2.9 and 14.5 inches for site 2. A statistically significant relationship was found between ESMR-6 measurements and snowpack water equivalents for the Site 2 February and March data. Associated analysis findings presented are the effects of random measurement errors, snow site physiolography, and weather conditions on the ESMR-6/snow relationship.
The author has identified the following significant results. Results indicated that the LANDSAT data and the classification technology can estimate the small grains area within a sample segment accurately and reliably enough to meet the LACIE goals. Overall, the LACIE estimates in a 9 x 11 kilometer segment agree well with ground and aircraft determined area within these segments. The estimated c.v. of the random classification error was acceptably small. These analyses confirmed that bias introduced by various factors, such as LANDSAT spatial resolution, lack of spectral resolution, classifier bias, and repeatability, was not excessive in terms of the required performance criterion. Results of these tests did indicate a difficulty in differentiating wheat from other closely related small grains. However, satisfactory wheat area estimates were obtained through the reduction of the small grain area estimates in accordance with relative amounts of these crops as determined from historic data; these procedures are being further refined.
Geodetic positioning using range, integrated Doppler, and interferometric observations from a constellation of twenty-four Global Positioning System satellites is analyzed. A summary of the proposals for geodetic positioning and baseline determination is given which includes a description of measurement techniques and comments on rank deficiency and error sources. An analysis of variance comparison of range, Doppler, and interferometric time delay to determine their relative geometric strength for baseline determination is included. An analytic examination to the effect of a priori constraints on positioning using simultaneous observations from two stations is presented. Dynamic point positioning and baseline determination using range and Doppler is examined in detail. Models for the error sources influencing dynamic positioning are developed. Included is a discussion of atomic clock stability, and range and Doppler observation error statistics based on random correlated atomic clock error are derived.