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NASA NTRS1975

Measurement of the inertial properties of the Helios F-1 spacecraft

A gravity pendulum method of measuring lateral moments of inertia of large structures with an error of less than 1% is outlined. The method is based on the fact that in a physical pendulum with a knife-edge support the distance from the axis of rotation to the system center of gravity determines the minimal period of oscillation and is equal to the system centroidal radius of gyration. The method is applied to results of a test procedure in which the Helios F-1 spacecraft was placed in a roll fixture with crossed flexure pivots as elastic constraints and system oscillation measurements were made with each of a set of added moment-of-inertia increments. Equations of motion are derived with allowance for the effect of the finite pivot radius and an error analysis is carried out to find the criterion for maximum accuracy in determining the square of the centroidal radius of gyration. The test procedure allows all measurements to be made with the specimen in upright position.

Gayman, W. H.↗

NASA NTRS1979

The ability of the space telescope to detect extra-solar planetary systems

The space telescope can plan a key role in searching for and investigating the contents of extra-solar planetary systems. For about 90 nearby stars, positional variations due to major planets would be well within the astrometric capability of the wide-field/planetary camera system. Since the centroids of star images will be determined to within a milliarcsecond down to 22d magnitude, there will be an abundance of reference stars at very small angular distances from each planetary system candidate, and they will have small enough motions of their own to provide a reference frame of the stability required.

Baum, W. A.↗

NASA NTRS2009

Target-Tracking Camera for a Metrology System

An analog electronic camera that is part of a metrology system measures the varying direction to a light-emitting diode that serves as a bright point target. In the original application for which the camera was developed, the metrological system is used to determine the varying relative positions of radiating elements of an airborne synthetic aperture-radar (SAR) antenna as the airplane flexes during flight; precise knowledge of the relative positions as a function of time is needed for processing SAR readings. It has been common metrology system practice to measure the varying direction to a bright target by use of an electronic camera of the charge-coupled-device or active-pixel-sensor type. A major disadvantage of this practice arises from the necessity of reading out and digitizing the outputs from a large number of pixels and processing the resulting digital values in a computer to determine the centroid of a target: Because of the time taken by the readout, digitization, and computation, the update rate is limited to tens of hertz. In contrast, the analog nature of the present camera makes it possible to achieve an update rate of hundreds of hertz, and no computer is needed to determine the centroid. The camera is based on a position-sensitive detector (PSD), which is a rectangular photodiode with output contacts at opposite ends. PSDs are usually used in triangulation for measuring small distances. PSDs are manufactured in both one- and two-dimensional versions. Because it is very difficult to calibrate two-dimensional PSDs accurately, the focal-plane sensors used in this camera are two orthogonally mounted one-dimensional PSDs.

Liebe, Carl↗

NASA NTRS2004

Compact Optoelectronic Compass

A compact optoelectronic sensor unit measures the apparent motion of the Sun across the sky. The data acquired by this chip are processed in an external processor to estimate the relative orientation of the axis of rotation of the Earth. Hence, the combination of this chip and the external processor finds the direction of true North relative to the chip: in other words, the combination acts as a solar compass. If the compass is further combined with a clock, then the combination can be used to establish a threeaxis inertial coordinate system. If, in addition, an auxiliary sensor measures the local vertical direction, then the resulting system can determine the geographic position. This chip and the software used in the processor are based mostly on the same design and operation as those of the unit described in Micro Sun Sensor for Spacecraft (NPO-30867) elsewhere in this issue of NASA Tech Briefs. Like the unit described in that article, this unit includes a small multiple-pinhole camera comprising a micromachined mask containing a rectangular array of microscopic pinholes mounted a short distance in front of an image detector of the active-pixel sensor (APS) type (see figure). Further as in the other unit, the digitized output of the APS in this chip is processed to compute the centroids of the pinhole Sun images on the APS. Then the direction to the Sun, relative to the compass chip, is computed from the positions of the centroids (just like a sundial). In the operation of this chip, one is interested not only in the instantaneous direction to the Sun but also in the apparent path traced out by the direction to the Sun as a result of rotation of the Earth during an observation interval (during which the Sun sensor must remain stationary with respect to the Earth). The apparent path of the Sun across the sky is projected on a sphere. The axis of rotation of the Earth lies at the center of the projected circle on the sphere surface. Hence, true North (not magnetic North), relative to the chip, can be estimated from paths of the Sun images across the APS. In a test, this solar compass has been found to yield a coarse estimate of the North (within tens of degrees) in an observation time of about ten minutes. As expected, the accuracy was found to increase with observation time: after a few hours, the estimated direction of the rotation axis becomes accurate to within a small fraction of a degree.

Christian, Carl↗

NASA NTRS2007

Metrology Camera System Using Two-Color Interferometry

A metrology system that contains no moving parts simultaneously measures the bearings and ranges of multiple reflective targets in its vicinity, enabling determination of the three-dimensional (3D) positions of the targets with submillimeter accuracy. The system combines a direction-measuring metrology camera and an interferometric range-finding subsystem. Because the system is based partly on a prior instrument denoted the Modulation Sideband Technology for Absolute Ranging (MSTAR) sensor and because of its 3D capability, the system is denoted the MSTAR3D. Developed for use in measuring the shape (for the purpose of compensating for distortion) of large structures like radar antennas, it can also be used to measure positions of multiple targets in the course of conventional terrestrial surveying. A diagram of the system is shown in the figure. One of the targets is a reference target having a known, constant distance with respect to the system. The system comprises a laser for generating local and target beams at a carrier frequency; a frequency shifting unit to introduce a frequency shift offset between the target and local beams; a pair of high-speed modulators that apply modulation to the carrier frequency in the local and target beams to produce a series of modulation sidebands, the highspeed modulators having modulation frequencies of FL and FM; a target beam launcher that illuminates the targets with the target beam; optics and a multipixel photodetector; a local beam launcher that launches the local beam towards the multi-pixel photodetector; a mirror for projecting to the optics a portion of the target beam reflected from the targets, the optics being configured to focus the portion of the target beam at the multi-pixel photodetector; and a signal-processing unit connected to the photodetector. The portion of the target beam reflected from the targets produces spots on the multi-pixel photodetector corresponding to the targets, respectively, and the signal-processing unit centroids the spots to determine bearings of the targets, respectively. As the spots oscillate in intensity because they are mixed with the local laser beam that is flood illuminating the focal plane, the phase of oscillation of each spot is measured, the phase of sidebands in the oscillation of each spot being proportional to a distance to the corresponding target relative to the reference target A.

Dubovitsky, Serge↗

NASA NTRS1994

Global, quasi-steady dynamics of the distant solar wind 2: Deformation of the heliospheric current sheet

A three-dimensional (3-D) magnetohydrodynamic (MHD) numerical model is used to trace global deformations of the heliospheric current sheet (HCS) caused by large-scale dynamical interactions associated with corotating solar wind flows. Configurations incorporating the tilted-dipole geometry are investigated out past 30 AU for a variety of dipole tilt angles, alpha. Inclusion of the full, 3-D interplanetary dynamics allows north-south displacements and the east-west warping of the HCS by advective corotational effects to be accurately assessed for the first time. It is found that large-scale spatial correlations between velocity and density imposed at the coronal source (i.e., the geometric arrangement whereby regions of high-speed low-density material lying adjacent to areas of slow, dense flow interact obliquely under the influence of solar rotation) result in a distinctive pattern of deformation of the HCS. For an alpha = 30 deg tilted-dipole example, it is shown that typical zonal variations in radial velocity lead to significant folding of the HCS within about 5 AU of the Sun. By 10 AU, additional sharp bends appear near the latitudinal extremes of the HCS surface, where it is overtaken by shock fronts driven by 3-D corotating interaction regions (CIRs). Moreover, the model suggests that inside about 20 AU, major plasma structures are systematically organized, about the HCS, such that the greatest concentrations of material and magnetic field (the centroids of the 3-D CIR structures) are coincident with the folded crests of the HCS (near heliographic latitudes lambda = +/- alpha). Thus, in these circumstances many of the more interesting dynamical features inconveniently lie well away from the heliographic equator. At larger heliocentric distances, where neighboring CIRs begin to interact strongly, the warping of the HCS abates dramatically and the association between folds in the HCS and major field and density concentrations is weakened and ultimately breaks down. On the basis of the model calculations, quasi-steady deformations and related phenomena should figure prominently in the interplanetary medium, except during those periods when the magnetic dipole and solar spin axes are nearly aligned (alpha is approximately less than 10 deg). Even then, they may be of significance if there are any substantial local warps or kinks in the streamer belt.

Pizzo, V. J.↗

NASA NTRSDate not supplied

Terminal Tracking for the Lucy Trojan Asteroid Mission

The most recent NASA Discovery class mission to fly is the Lucy mission to the Trojan Asteroids of Jupiter. Launched in October of 2021, Lucy’s destination will be the unexplored Jupiter Trojan Asteroids that orbit the Sun at the stable L4 and L5 points ahead of, and behind Jupiter. This 12-yearmission will perform close flybys of 1 main belt asteroid, Donaldjohanson, and 7 Trojans asteroids: Eurybates and its satellite Queta, Polymele, Leucus, Orus, and the near equal mass Trojan binary pair, Patroclus andMenoetius. The large distance from earth for the encounters, the high relative velocities and sun incidence angles on approach,and the limited number of Earth observations of the Trojans,make the delivery knowledge highly uncertain. To reduce the delivery uncertainties and maximize science return, Lucy employs a Terminal Tracking System consisting of optical imaging, centroiding and state estimation of the Trojan asteroids on approach and through close approach. This paper presents the Lucy Terminal Tracking System implementation, a brief overview of the mission and the GN&C subsystem.

Philip G Good↗

NASA NTRS2011

Fine Guidance Sensing for Coronagraphic Observatories

Three options have been developed for Fine Guidance Sensing (FGS) for coronagraphic observatories using a Fine Guidance Camera within a coronagraphic instrument. Coronagraphic observatories require very fine precision pointing in order to image faint objects at very small distances from a target star. The Fine Guidance Camera measures the direction to the target star. The first option, referred to as Spot, was to collect all of the light reflected from a coronagraph occulter onto a focal plane, producing an Airy-type point spread function (PSF). This would allow almost all of the starlight from the central star to be used for centroiding. The second approach, referred to as Punctured Disk, collects the light that bypasses a central obscuration, producing a PSF with a punctured central disk. The final approach, referred to as Lyot, collects light after passing through the occulter at the Lyot stop. The study includes generation of representative images for each option by the science team, followed by an engineering evaluation of a centroiding or a photometric algorithm for each option. After the alignment of the coronagraph to the fine guidance system, a "nulling" point on the FGS focal point is determined by calibration. This alignment is implemented by a fine alignment mechanism that is part of the fine guidance camera selection mirror. If the star images meet the modeling assumptions, and the star "centroid" can be driven to that nulling point, the contrast for the coronagraph will be maximized.

Brugarolas, Paul↗

NASA NTRS2006

Range-Measuring Video Sensors

Optoelectronic sensors of a proposed type would perform the functions of both electronic cameras and triangulation- type laser range finders. That is to say, these sensors would both (1) generate ordinary video or snapshot digital images and (2) measure the distances to selected spots in the images. These sensors would be well suited to use on robots that are required to measure distances to targets in their work spaces. In addition, these sensors could be used for all the purposes for which electronic cameras have been used heretofore. The simplest sensor of this type, illustrated schematically in the upper part of the figure, would include a laser, an electronic camera (either video or snapshot), a frame-grabber/image-capturing circuit, an image-data-storage memory circuit, and an image-data processor. There would be no moving parts. The laser would be positioned at a lateral distance d to one side of the camera and would be aimed parallel to the optical axis of the camera. When the range of a target in the field of view of the camera was required, the laser would be turned on and an image of the target would be stored and preprocessed to locate the angle (a) between the optical axis and the line of sight to the centroid of the laser spot.

Howard, Richard T.↗

NASA NTRS2019

NICER Discovers Spectral Lines During Photospheric Radius Expansion Bursts from 4U 1820-30: Evidence for Burst-Driven Winds

We report the discovery with the Neutron Star Interior Composition Explorer (NICER) of narrow emission and absorption lines during photospheric radius expansion (PRE) X-ray bursts from the ultracompact binary 4U 1820 −30. NICER observed 4U 1820−30 in 2017 August during a low-flux, hard spectral state, accumulating about 60 ks of exposure. Five thermonuclear X-ray bursts were detected, of which four showed clear signs of PRE. We extracted spectra during the PRE phases and fit each to a model that includes a Comptonized component to describe the accretion-driven emission, and a blackbody for the burst thermal radiation. The temperature and spherical emitting radius of the fitted blackbody are used to assess the strength of PRE in each burst. The two strongest PRE bursts (burst pair 1) had blackbody temperatures of ≈0.6 keV and emitting radii of ≈100 km (at a distance of 8.4 kpc). The other two bursts (burst pair 2) had higher temperatures (≈0.67 keV) and smaller radii (≈75 km). All of the PRE bursts show evidence of narrow line emission near 1 keV. By coadding the PRE phase spectra of burst pairs 1 and, separately, 2, we find, in both coadded spectra, significant, narrow, spectral features near 1.0 (emission), 1.7, and 3.0 keV (both in absorption). Remarkably, all the fitted line centroids in the coadded spectrum of burst pair 1 appear systematically blueshifted by a factor of 1.046±0.006 compared to the centroids of pair 2, strongly indicative of a gravitational shift, a wind-induced blueshift, or more likely some combination of both effects. The observed shifts are consistent with this scenario in that the stronger PRE bursts in pair 1 reach larger photospheric radii, and thus have weaker gravitational redshifts, and they generate faster outflows, yielding higher blueshifts. We discuss possible elemental identifications for the observed features in the context of recent burst-driven wind models.

Strohmayer, T. E.↗

NASA NTRS2008

Measuring Positions of Objects using Two or More Cameras

An improved method of computing positions of objects from digitized images acquired by two or more cameras (see figure) has been developed for use in tracking debris shed by a spacecraft during and shortly after launch. The method is also readily adaptable to such applications as (1) tracking moving and possibly interacting objects in other settings in order to determine causes of accidents and (2) measuring positions of stationary objects, as in surveying. Images acquired by cameras fixed to the ground and/or cameras mounted on tracking telescopes can be used in this method. In this method, processing of image data starts with creation of detailed computer- aided design (CAD) models of the objects to be tracked. By rotating, translating, resizing, and overlaying the models with digitized camera images, parameters that characterize the position and orientation of the camera can be determined. The final position error depends on how well the centroids of the objects in the images are measured; how accurately the centroids are interpolated for synchronization of cameras; and how effectively matches are made to determine rotation, scaling, and translation parameters. The method involves use of the perspective camera model (also denoted the point camera model), which is one of several mathematical models developed over the years to represent the relationships between external coordinates of objects and the coordinates of the objects as they appear on the image plane in a camera. The method also involves extensive use of the affine camera model, in which the distance from the camera to an object (or to a small feature on an object) is assumed to be much greater than the size of the object (or feature), resulting in a truly two-dimensional image. The affine camera model does not require advance knowledge of the positions and orientations of the cameras. This is because ultimately, positions and orientations of the cameras and of all objects are computed in a coordinate system attached to one object as defined in its CAD model.

Klinko, Steve↗

NASA NTRS2003

The Spatial Distribution of Fluorescent H2 Emission Near T Tauri

New subarcsecond far-UV observations of T Tau with Hubble Space Telescope STIS show spatially resolved structure in the 2in. x 2in. area around the star. The structures are apparent in multiline emission of fluorescent H2 pumped by Ly(alpha). One emission structure follows the cavity walls observed around T Tau N in scattered light in the optical. A temperature of greater than or = l000 K is required to have a high enough population in the H2 to produce the observed fluorescent lines; in the cool environment of the T Tau system, shock heating is required to achieve this temperature at distances of a few tens of AU. Fluorescent H2 along the cavity wall represent the best evidence to date for the action of low-density, wide opening angle outflows driving cavities into the molecular medium at scales less than or = 100 AU. A southern region of emission consists of two arcs, with shape and orientation similar to the arcs of H2 2.12 microns and forbidden-line emission crossing the outflow associated with the embedded system T Tau S. This region is located near the centroid of forbidden-line emission at the blueshifted lobe of the north-south outflow.

Saucedo, Jose↗

NASA NTRS1993

Prelaunch optical characterization of the Laser Geodynamic Satellite (LAGEOS 2)

The optical range correction (the distance between the apparent retroreflective skin of the satellite and the center of mass) of the LAGEOS 2 was determined using computer analysis of theoretical and experimentally measured far field diffraction patterns, and with short pulse lasers using both streak camera-based range receivers and more conventional PMT-based range receivers. The three measurement techniques yielded range correction values from 248 to 253 millimeters dependent on laser wavelength, pulsewidth, and polarization, location of the receiver in the far field diffraction pattern and detection technique (peak, half maximum, centroid, or constant fraction). The Lidar cross section of LAGEOS 2 was measured at 4 to 10 million square meters, comparable to the LAGEOS 1.

Minott, Peter O.↗

NASA NTRS1960

Experimental and Theoretical Study of a Rectangular Wing in a Vortical Wake at Low Speed

A systematic study has been made, experimentally and theoretically, of the effects of a vortical wake on the aerodynamic characteristics of a rectangular wing at subsonic speed. The vortex generator and wing were mounted on a reflection plane to avoid body-wing interference. Vortex position, relative to the wing, was varied both in the spanwise direction and normal to the wing. Angle of attack of the wing was varied from -40 to +60. Both chordwise and spanwise pressure distributions were obtained with the wing in uniform and vortical flow fields. Stream surveys were made to determine the flow characteristics in the vortical wake. The vortex-induced lift was calculated by several theoretical methods including strip theory, reverse-flow theory, and reverse-flow theory including a finite vortex core. In addition, the Prandtl lifting-line theory and the Weissinger theory were used to calculate the spanwise distribution of vortex-induced loads. With reverse-flow theory, predictions of the interference lift were generally good, and with Weissinger's theory the agreement between the theoretical spanwise variation of induced load and the experimental variation was good. Results of the stream survey show that the vortex generated by a lifting surface of rectangular plan form tends to trail back streamwise from the tip and does not approach the theoretical location, or centroid of circulation, given by theory. This discrepancy introduced errors in the prediction of vortex interference, especially when the vortex core passed immediately outboard of the wing tip. The wake produced by the vortex generator in these tests was not fully rolled up into a circular vortex, and so lacked symmetry in the vertical direction of the transverse plane. It was found that the direction of circulation affected the induced loads on the wing either when the wing was at angle of attack or when the vortex was some distance away from the plane of the wing.

Smith, Willard G.↗

NASA NTRS1994

On the temperature and velocity through the photosphere of a sunspot penumbra

We investigate the structure in depth of a sunspot penumbra by means of the inversion code of the radiative transfer equation proposed by Ruiz Cobo & del Toro Iniesta (1992), applied to a set of filtergrams of a sunspot, scanning the Fe I line at 5576.1 A, with a sampling interval of 30 mA, from -120 to 120 mA from line center (data previously analyzed by Title et al. 1993). The temperature structure of this penumbra is obtained for each of the 801 pixels selected (0.32 sec x 0.32 sec). On the average, the temperatures seem to decrease as we move inward, but the differences are of the order of the rms values (approximately equal 100-200 K) at a given distance to sunspot center. The outer parts of the penumbra have also a bigger curvature in the T versus log tau(sub 5) relation than the inner parts. We realize, however, that these differences might be influenced by possible stray light effects. Compared to the quiet Sun, penumbral temperatures are cooler at deep layers and hotter at high layers. A mean penumbral model atmosphere is presented. The asymmetries observed in the intensity profile (the line is magnetically insensitive) are deduced to be produced by strong gradients of the line-of-sight velocity that sharply vary spatially along slices of almost constant distance to sunspot center. These variations suggest that such gradients are not only needed to explain the broadband circular polarization observed in sunspots (see Sanchez Almeida & Lites 1992) but are a main characteristic of the fine-scale penumbra. The results are compatible with an Evershed flow present everywhere, but its gradient with depth turns out to vary so that the flow seems to be mainly concentrated in some penumbral fibrils when studied through Dopplergrams. Finally, as by-products of this study, we put constraints to the practical usefulness of the Eddington-Barbier relation, and we explain the values of the Fourier Dopplergrams to be carrying information of layers around the centroid of the generalized response function of Dopplergrams to velocity fluctuations.

Del Toro Iniesta, J. C.↗

NASA NTRS2005

Thermal Imaging of Earth for Accurate Pointing of Deep-Space Antennas

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

Ortiz, Gerardo↗

NASA NTRS1999

The Geoscience Laser Altimeter System (GLAS) for the ICESAT Mission

Accurate measurements of surface heights and atmospheric backscatter have been demonstrated with the SLA, MOLA and LITE space lidar. Recent MOLA measurements of the Mars surface have 40 cm resolution and have reduced the global uncertainty in Mars topography from a few km to approx. 10 m. GLAS is a next generation lidar being developed as part of NASA's Icesat Mission for Earth orbit . The GLAS design combines a 10 cm precision surface lidar with a sensitive dual wavelength cloud and aerosol lidar. GLAS will precisely measure the heights of the Earth's polar ice sheets, determine the height profiles of the Earth's land topography, and profile the vertical backscatter of clouds and aerosols on a global scale. GLAS will fly on a small dedicated spacecraft in a polar orbit at 598 km altitude with an inclination of 94 degrees. GLAS is scheduled to launch in summer 2001 and to operate continuously for a minimum of 3 years with a goal of 5 years. The primary mission for GLAS is to measure the seasonal and annual changes in the heights of the Greenland and Antarctic ice sheets. GLAS will measure the vertical distance to the ice sheet from orbit with 1064 nm pulses from a Nd:Yag laser at 40 Hz. Each 5 nsec wide laser pulse is used for a single range measurement. When over land GLAS will profile the heights of the topography and vegetation. The GLAS receiver uses a I m diameter telescope and a Si APD detector. The detector signal is sampled by an all digital receiver which records each surface echo waveform with I nsec resolution and a stored echo record lengths of either 200, 400, or 600 samples. Analysis of the echo waveforms within the instrument permits discrimination between cloud and surface echoes. Ground based echo analysis permits precise ranging, determining the roughness or slopes of the surface as well as the vertical distributions of vegetation illuminated by the laser, Errors in knowledge of the laser beam pointing angle can bias height measurements of sloped surfaces. For surfaces with 2 deg. slopes, knowledge of pointing angle of the beam centroid to about 8 urad is required to achieve 10 cm height accuracy. GLAS uses a stellar reference system (SRS) to determine the pointing angle of each laser firing relative to inertial space. The SRS uses a high precision star camera oriented toward local zenith whose measurements are combined with a gyroscope to determine the inertial orientation of the SRS optical bench. The far field pattern of each laser pulse is measured with a laser reference system (LRS). Optically measuring each laser far field pattern relative to the star camera and gyroscope permits the angular offsets of each laser pulse to be determined. GLAS will also determine the vertical distributions of clouds and aerosols by measuring atmospheric backscatter profiles at both 1064 and 532 nm. The 1064 nm measurements use an analog detector and profile the height and vertical structure of thicker clouds. Measurements at 532 nm use new highly sensitive photon counting detectors, and measure the height distributions of very thin clouds and aerosol layers. With averaging these can be used to determine the height of the planetary boundary layer. The instrument design and expected performance will be discussed.

Abshire, James B.↗

NASA NTRS2004

Determining Sizes of Particles in a Flow from DPIV Data

A proposed method of measuring the size of particles entrained in a flow of a liquid or gas would involve utilization of data from digital particle-image velocimetry (DPIV) of the flow. That is to say, with proper design and operation of a DPIV system, the DPIV data could be processed according to the proposed method to obtain particle sizes in addition to particle velocities. As an additional benefit, one could then compute the mass flux of the entrained particles from the particle sizes and velocities. As in DPIV as practiced heretofore, a pulsed laser beam would be formed into a thin sheet to illuminate a plane of interest in a flow field and the illuminated plane would be observed by means of a charge-coupled device (CCD) camera aimed along a line perpendicular to the illuminated plane. Unlike in DPIV as practiced heretofore, care would be taken to polarize the laser beam so that its electric field would lie in the illuminated plane, for the reason explained in the next paragraph. The proposed method applies, more specifically, to transparent or semitransparent spherical particles that have an index of refraction different from that of the fluid in which they are entrained. The method is based on the established Mie theory, which describes the scattering of light by diffraction, refraction, and specular reflection of light by such particles. In the case of a particle illuminated by polarized light and observed in the arrangement described in the preceding paragraph, the Mie theory shows that the image of the particle on the focal plane of the CCD camera includes two glare spots: one attributable to light reflected toward the camera and one attributable to light refracted toward the camera. The distance between the glare spots is a known function of the size of the particle, the indices of refraction of the particle material, and design parameters of the camera optics. Hence, the size of a particle can be determined from the distance between the glare spots. The proposed method would be implemented in an algorithm that would automatically identify, and measure the distance between, the glare spots for each particle for which a suitable image has been captured in a DPIV image frame. The algorithm (see figure) would begin with thresholding of data from the entire image frame to reduce noise, thereby facilitating discrimination of particle images from the background and aiding in the separation of overlapping particles. It is important not to pick a threshold level so high that the light intensity between a given pair of glare spots does not fall below the threshold value, leaving the glare spots disconnected. The image would then be scanned in a sequence of rows and columns of pixels to identify groups of adjacent pixels that contain nonzero brightnesses and that are surrounded by pixels of zero brightness. Each such group would be assumed to constitute the image of one particle. Each such group would be further analyzed to determine whether the image was saturated; saturated particle images must be rejected because the locations of glare spots in saturated images cannot accurately be determined. Within each unsaturated particle image, the centroids (deemed to be the locations) of the glare spots would be determined by means of gradients of brightness distributions and three-point horizontal and three-point vertical Gaussian estimates based on the brightness values of the brightest pixels and the pixels adjacent to them. If the brightness of a given particle image contained only one peak, then it would be assumed that a second glare spot did not exist and that image would be rejected.

Wernet, M. P.↗