June 2002

NASA/TM-2002-211739

Photogrammetry Methodology Developmentfor Gossamer Spacecraft Structures

Richard S. Pappa and Thomas W. JonesLangley Research Center, Hampton, Virginia

Jonathan T. BlackJoint Institute for Advancement of Flight SciencesGeorge Washington UniversityLangley Research Center, Hampton, Virginia

Alan WalfordEos System, Inc., Vancouver, Canada

Stuart RobsonUniversity College London, London, United Kingdom

Mark R. ShortisUniversity of Melbourne, Parkville, Australia

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June 2002

NASA/TM-2002-211739

Photogrammetry Methodology Developmentfor Gossamer Spacecraft Structures

Richard S. Pappa and Thomas W. JonesLangley Research Center, Hampton, Virginia

Jonathan T. BlackJoint Institute for Advancement of Flight SciencesGeorge Washington UniversityLangley Research Center, Hampton, Virginia

Alan WalfordEos System, Inc., Vancouver, Canada

Stuart RobsonUniversity College London, London, United Kingdom

Mark R. ShortisUniversity of Melbourne, Parkville, Australia

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Photogrammetry Methodology Development forGossamer Spacecraft Structures

Richard S. Pappa Thomas W. Jones Jonathan T. BlackNASA Langley Research Center NASA Langley Research Center George Washington University

Hampton, VA 23681 Hampton, VA 23681 Hampton, VA 23681

Alan Walford Stuart Robson Mark R. ShortisEos Systems, Inc. University College London University of Melbourne

Vancouver, Canada London, United Kingdom Parkville, Australia

ABSTRACT

Photogrammetry--the science of calculating 3Dobject coordinates from images--is a flexible and robustapproach for measuring the static and dynamiccharacteristics of future ultra-lightweight and inflatablespace structures (a.k.a., Gossamer structures), such aslarge membrane reflectors, solar sails, and thin-filmsolar arrays. Shape and dynamic measurements arerequired to validate new structural modeling techniquesand corresponding analytical models for theseunconventional systems. This paper summarizesexperiences at NASA Langley Research Center overthe past three years to develop or adaptphotogrammetry methods for the specific problem ofmeasuring Gossamer space structures. Turnkeyindustrial photogrammetry systems were not considereda cost-effective choice for this basic research effortbecause of their high purchase and maintenance costs.Instead, this research uses mainly off-the-shelf digital-camera and software technologies that are affordable tomost organizations and provide acceptable accuracy.

INTRODUCTION

Photogrammetry is the science of measuring thesize and location of 3D objects using photographs.1 Theclassical application (known as topographicphotogrammetry) is for creating aerial land surveys andmaps. There are also many ground-based applications(known as non-topographic or close-rangephotogrammetry) in such diverse fields as archaeology,bioengineering, civil engineering, computer animation,forensic analysis, historical preservation, mechanicalinspection, plant engineering, ship construction, andsurgery.2 Modern close-range photogrammetry uses

digital imaging sensors3 and computer data analysis andoften measures hundreds or thousands of object points.The fundamental theory is based on surveyingprinciples.4 When dealing with time sequences ofimages, the term “videogrammetry” or “videometrics”is used to describe this technology.5 Photogrammetryoffers the simplicity of taking photographs coupledwith good to excellent measurement precision.

New analytical and experimental methods forshape and dynamic characterization of future Gossamerspace structures, such as large membrane reflectors,solar sails, and thin-film solar arrays, are beingdeveloped at the NASA Langley Research Center(LaRC) and elsewhere.6 Accurate analytical methodsare required for confident design of new or evolvedstructural concepts and for mission simulations.Correspondingly, experimental methods are requiredfor measuring the shape and dynamic characteristics ofresearch test articles and prototypes, which willtypically be scale models, in either air or vacuumenvironments. Accurate test data are needed to validateanalytical methods for these structures in one or moreof the following three conditions: stationary (staticshape), vibrating (modes of vibration), or deploying(deployment dynamics).

The selected technical focus for making thesemeasurements is close-range photogrammetry, aflexible and robust technology with demonstratedpotential for measuring Gossamer-type structures.7-9

Static shape measurements are the simplest to make,requiring two or more still photographs of the structurefrom convergent viewing directions. Vibrationmeasurements are more difficult to obtain, requiringsynchronized image sequences from multiple cameras.

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With vibrating structures, off-line data analysis issimpler than real-time analysis, which needs specialhardware and software and can be limited bycomputational speed to a few simultaneousmeasurement points. The most difficult situation isquantitative measurement of the unsteady dynamiccharacteristics of inflating or deploying structures. Thiscase is like vibration measurement, but must alsohandle large geometry changes and target obstructionsthat can occur as a function of time.

Industrial photogrammetry systems are availablefor making highly accurate (1 part in 100,000+)structural measurements.10,11 However, they were notconsidered a cost-effective choice for this basicresearch effort (which includes collaborative researchand development in academia and small businesses)because of their high purchase and maintenance costs.To the extent possible, this work uses consumer digital-camera and software technologies that are affordable tomost organizations and provide acceptable accuracy.Occasionally, a Geodetic Services Inc. V-STARSindustrial photogrammetry system can be borrowed formeasurement comparisons.†

The objective of this paper is to document initialexperiences at the NASA Langley Research Centerusing various hardware and software forphotogrammetry of Gossamer research structures. Thepaper has two sections. The first section summarizesexperiences with seven laboratory test articles,illustrating some advantages and challenges of image-based measurement of Gossamer structures. The secondsection explains the ten main steps of close-rangephotogrammetry using recent data from a 2-m solar sailmodel as an example.

TEST ARTICLES

Figure 1 shows seven Gossamer-class test articlesmeasured with photogrammetry at LaRC. The firstthree are flight prototypes suitable for use in space(Figs. 1a-1c), and the others are generic researchstructures built for technology development purposesonly. The following subsections discuss salient points

†Throughout the paper, references to specific commercial items used

in this research are not an official endorsement or promotion of any

product by NASA or the United States government.

of each project.

1. 5-m inflatable parabolic reflector

Figure 1a is a 5-m-diameter inflatable parabolicmembrane reflector, which weighs only about 4 kg. Inspace, it can serve as either a microwave antenna or asolar concentrator. The 3D coordinates of 521 attachedretroreflective targets were measured withphotogrammetry using four Kodak DC290 (2.1-megapixel) digital cameras. These cameras had thehighest resolution of any consumer model at the time.The test occurred in a closed chamber to minimize aircurrents. Estimated measurement precisions were1:28,000 (1 part in 28,000) in the horizontal direction,1:14,000 in the vertical direction, and 1:5,000 in thecamera direction. Later tests showed that measurementprecision would improve somewhat by increasing thenumber of camera locations (from four to nine), theirangular separation, or the image resolution. The focallength of a best-fit parabolic surface for themeasurements was 3.050 m, which closely correlatedwith the design focal length of 3.048 m. The root-mean-square deviation from an ideal parabolic shape wasabout 1.5 mm. Additional details of this work arepublished elsewhere.12

2. 1-m flexible Fresnel lens

Figure 1b shows test configurations for static-shape(top) and dynamic (bottom) measurements of a 1-m-long, membrane solar concentrator. These testssupported development of a proposed space flightexperiment.13 The test article is a patented, flexibleFresnel lens that refracts light onto a narrow line ofsolar cells, requiring only 12% of the cell area oftraditional spacecraft solar arrays, which reducesweight and cost. In service, a 3x8-m array wouldcontain 280 of these pop-up lenses. Two cameras werearranged to measure the static shape of the lens withprojected circular dots. Although the projected dots hadgood contrast without spraying the lens with a diffusecoating (not permitted in this case), target centroidscould not be accurately obtained because of the prismsmolded into the membrane. Vibration tests were thenconducted using 40 adhesive circular targets and twoclose-up miniature video cameras for stereovideogrammetry. The bottom of Fig. 1b shows a typicalimage pair. Image sequences were successfully

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processed to obtain 3D target coordinates versus time.A scanning laser vibrometer (with sub-micronprecision) made corroborative vibration measurementsfor comparison. Factors affecting the achievablephotogrammetric accuracy in this application were:

• Marginal target image size at edge of field of view,• Image intensity variation over larger targets, and• Variation in background image intensity due to

surface reflection and transmission characteristics.

3. 15-m inflated, rigidized tube

Long slender tubes proposed for solar sail supportstructures and other Gossamer spacecraft are difficultphotogrammetry test objects. Figure 1c shows a 15-m-long, rigidized aluminum-laminate inflatable tube witha length-to-diameter ratio of 100 hanging vertically.The cross-sectional shape and straightness of the tubesignificantly affect the axial strength and bucklingproperties,14 so photogrammetric measurements ofthese quantities were desired. The thinness of the tubewall prevented installation of traditional adhesivetargets without risking local damage, so anunconventional measurement approach was designed. Astationary camera on a tall ladder photographed the tubeagainst a dark background as the tube was rotatedaxially in 30-degree steps. In each photograph, thedistances from the edges of the tube to two stationaryplumb lines were measured. These dimensions gave thedesired cross-sectional shape and straightness of thetube over most of its length.

4. 0.7-m oscillating Kapton membrane

The four images in Fig. 1d show one epoch (instantof time) of a 40-sec, 300-frame video sequence of anoscillating Kapton membrane with 100 illuminatedretroreflective targets. A metal frame tensioned themembrane by its corners into a slightly warped shape,and the frame was suspended by strings. Anelectrodynamic shaker attached to the bottom of theframe slowly moved the membrane back and forth at10.0 sec per period. The image sequence captured fourperiods of the repetitive motion. High membranetension and slow speed of motion avoided localvibration of the membrane. This dataset, representingthe rigid-body motion of the structure, is a good testcase for development of new or improved motion

analysis software. Accurate photogrammetric analysisof the sequence should show four identical periods of arigid, warped surface swaying back and forth in themanner described above. The same motion analysissoftware can then be applied to flexible-body datasetsto identify structural dynamic modal parameters(assuming the vibration is large enough to detect withcameras).15 Note that both upper images in Fig. 1d havea “hot spot” from reflection of a light source located atanother camera. It is impossible to measurephotogrammetry targets there. The hot spots changelocation as the membrane oscillates.

5. 3-m hexapod reflector

Figure 1e shows a 3-m-diameter, reflectivemembrane research structure developed by ILC Dover,Inc., Tennessee State University and NASA Langleyfor active shape and vibration control experiments. It isnot an actual spacecraft concept, but contains genericcomponents of proposed inflatable Gossamerobservatories. The structure uses a Stewart Platformconfiguration, also known as a hexapod--a design forcontrolling all six degrees-of-freedom of the triangularfeed platform. On all six tapered tubes holding the feedplatform and on the membrane boundary arepiezoelectric actuators that can dampen (or create)vibrations. Control experiments will compare variousfeedback circuits or algorithms to sense and adjust thestatic shape or dynamics of the system using theactuators to optimize a selected performance objective.Photogrammetry can measure the membrane shapebefore and during the control experiments. The right-hand side of Fig. 1e shows about 550 dots projectedonto the back of the membrane,16 which also has areflective aluminum coating like the front surface. Twocameras, one on either side, photographed the dots.Although the surface is shiny, sufficient photographiccontrast was obtained in a darkened room with longimage exposure times (about 30 sec) for accuratemeasurement of the static shape.

6. 4.5-m inflatable tripod

Understanding the deployment dynamics ofGossamer space structures is a key element of makingthem a reliable and practical technology.Videogrammetry (photogrammetry using imagesequences) is a logical way to measure deployment

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dynamics of Gossamer structures by tracking discretetargets on the structure with multiple cameras.17 Figure1f shows three stages of inflation of a simple tripodconstructed of black, 150-micron-thick, polyethylenetubing. Basic-research investigations used this materialbecause it is inexpensive and rugged enough towithstand many inflation/deflation cycles. Low-pressure air inflated all three legs simultaneously in thisexperiment. Clearly, a significant issue for reliablevideogrammetric tracking of targets on inflatingstructures is obstruction of targets by folds of thematerial or by other members. Some successful real-time target tracking occurred in this experiment for upto two of the three legs simultaneously using twosynchronized cameras; however, targets werefrequently lost from view of either or both cameras.Recording the entire deployment sequence, and thenpost-processing the images in reserve order, generally isthe best approach for obtaining 3D target trajectories indeployment tests. Algorithms for extrapolating paths oftargets that move temporarily out of view can improvetracking performance.

7. Partial 10-m and two complete 2-m solar sailmodels

Fig. 1g shows three solar sail structural testarticles.18 The large one on the left is half of a four-quadrant, 10-m sail concept (the length of each edge is10 m). Those on the right are 2-m scale models ofdifferent sail designs. These research structures are in a16-m-diameter vacuum chamber, large enough toaccommodate testing of a complete 10-m solar sailmodel in both horizontal and vertical orientations. Allthree structures use aluminized Kapton membranes (25-micron-thick) that are shiny, but with sufficient diffusereflection for 3D photogrammetry. Useful spacemissions require sail sizes of at least 70 m withmembrane thicknesses of less than 7 microns. The 10-mtest article has 80 distributed, 28.5-mm-diameter,retroreflective targets for laser vibrometry andphotogrammetry measurements of overall shape anddynamic characteristics. High-density dot projectionhas also been used on a portion of the four-quadrant, 2-m sail, shown in the lower-right corner of Fig. 1g, tomeasure its static shape with high spatial resolution.Note that the four-quadrant, 2-m sail has four individualtriangular membrane sections, tensioned by slenderaluminum rods running between them.

PHOTOGRAMMETRY

Figure 2 is a flowchart of the ten main steps ofphotogrammetry consistent with PhotoModeler Pro, oneof the software programs used in this research. Theremainder of the paper discusses each step individuallyusing data from a recent test of the four-quadrant, 2-msolar sail as an illustrative example. Note that theflowchart is a “closed loop” since lessons learned ineach application lead to method improvements in laterapplications.

Step 1: Establish measurement objectives andaccuracy requirements

The seven projects discussed in the precedingsection show how photogrammetry can measure a widevariety of structures, using a variety of experimentalmethods. There are only three top-level measurementobjectives for Gossamer structures (static shape, modesof vibration, and deployment dynamics), but there aremany ways to estimate each type of data. Establishingspecific measurement objectives and accuracyrequirements is important for selecting proper testmethods.

An important consideration in developing ground-test objectives is a good understanding of missionrequirements and important design issues so they can beadequately validated. For example, with solar sails, thetwo biggest technical concerns (at least in earlydemonstration experiments) is proper deployment of thesail and controllability. Next is the ability of the sail toaccelerate as expected using the momentum exchangeimparted by sunlight (photon) reflection. All threeaspects relate to one of the types of data thatphotogrammetry can measure. Specifically,photogrammetry can measure deployment dynamicsand modes of vibration, which relate to the deploymentand attitude control aspects, respectively. Sailacceleration performance in space relates directly to theoperational shape of the deployed membrane, whichcan also be determined with photogrammetry.

A good estimate of the required measurementaccuracy for each photogrammetry project is alsoimportant, avoiding both under- and over-estimating therequirements. Under estimation can lead to

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unacceptable or unreliable measurements. Overestimation can waste time and resources because thecost versus accuracy relationship is one of diminishingreturns at higher accuracy levels. Photogrammetricaccuracy (specified in parts per thousand of the largestdimension of the structure) can vary by more than threeorders of magnitude depending on the method andequipment used, ranging from 1:1,000,000 with large-format film cameras to under 1:1000 with low-resolution consumer cameras and manual featuremarking in images.

Step 2: Select and calibrate suitable camerasand lenses

Modern close-range photogrammetry uses digitalcameras almost exclusively rather than traditional filmor analog (for video) equipment because of severaladvantages, including:

1. The images are immediately available forcomputer analysis (using removable storagemedia or cable connection),

2. The photogrammetrist can take many extrapictures at the test site at no additional cost usingdifferent camera and lighting settings and selectthe best images later for the analysis, and

3. The measurement accuracy can be higher than forstandard 35-mm film, which can shift relative tothe camera lens. Also, image transmissions (forvideo) are higher quality using digital data lines.

There are also some disadvantages of digitalcameras compared with film or analog (for video)equipment, including:

1. Higher prices (at least 3x higher than comparablefilm cameras), but these are fully recovered byeliminating film and developing costs,

2. Maximum image resolution capability is stillachieved by medium- or large-format filmcameras designed and calibrated forphotogrammetry, and

3. Cable-length limitations of digital video systems,which is typically less than 10 m withoutincreased noise.

Figure 3 describes two types of digital camerasused in this research. There are at least 200 other

models of consumer, scientific, and professionaldigital cameras on the market, many with similarspecifications. Four Olympus E-20 and two PulnixTM-1020-15 cameras are available at LaRC for static-shape and dynamic measurements of Gossamerstructures, respectively. Several other types of camerasare also available for data comparisons.

Accurate photogrammetry requires preciseknowledge of the optical characteristics of each camera,referred to as the internal camera parameters. Theprocess of measuring these properties is called cameracalibration.19 At a minimum, the following informationis required for each camera: sensor format (pixel sizeand number of pixels), principal point (intersection ofoptical axis with the imaging sensor), photogrammetricprincipal distance (distance from projection center ofthe lens to the principal point), and lens distortioncharacteristics (radial, decentering, and possiblyothers). Note that the photogrammetric principaldistance is synonymous with the focal length of the lenswhen focused at infinity.

The PhotoModeler Pro software contains a simpleprocedure for computing internal camera parameters byanalyzing photographs of a grid of targets projectedonto a flat wall. To illustrate the procedure, Fig. 4shows typical photos of the camera calibration grid. It isa rectangular mosaic of black and white triangles with acoded dot pattern in each corner. The procedure usessix camera locations and eight photographs. Threelocations are on the left side and three on the right sideof the grid at low, medium, and high elevations. Thefourth photograph on each side is at medium elevationwith the camera rotated 90 degrees. The user alsomeasures and inputs the distance between the upper-leftand lower-right corners of the projected grid.PhotoModeler uses a mostly automated procedure toprocess the eight photographs. Camera parameterscomputed by the method are: format aspect ratio,principal point, photogrammetric principal distance,two coefficients of radial lens distortion (usually thelargest component of lens distortion), and twocoefficients of decentering lens distortion (caused byany misalignment in the lens). Note that industrial orother close-range photogrammetry systems may use amore comprehensive calibration procedure with manyadditional images and non-planar target locations.

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Step 3: Select type, size, and distribution oftargets

Photogrammetry achieves the best accuracy usinghigh-contrast, solid-colored circles as targets. Targetscan be light-colored on dark background or dark-colored on light background, the former being morecommon. Targets cover each part of the structure withenough density to define its shape, usually withoutbeing placed at specific locations, though there can beadvantages to placing some targets at knowncoordinates. Circular targets appear in photographs aselongated ellipses, with the elongation depending onviewing angle. Accurate calculation of target centers(centroids) for photogrammetry requires both axes ofthe ellipse to be about five pixels in size or larger.

This research uses three types of solid-coloredcircular targets: diffuse, retroreflective, and projected.Diffuse materials, such as common white paper, reflectlight in all directions. Retroreflective materials, such ashighway road signs or markers, reflect light mostlyback in the direction of its source, significantlyincreasing visibility in that direction alone. Projectedtargets, typically white dots from a standard slideprojector, are an attractive alternative for static-shapemeasurements of delicate Gossamer structures, but arenot as useful as attached targets for dynamicmeasurements because they do not move with thestructure. Photogrammetry can measure the 3D shape ofa structure at each instant of time with projected dots;however, motion time histories of specific points on thestructure cannot be obtained without interpolation orother assumptions.

Figure 5 shows retroreflective and projectedcircular targets. Figure 5a is a retroreflector on a blackbackground, with and without the camera flash turnedon. Without illumination, the target is dull gray in color.With illumination, it is bright white--many timesbrighter than a diffuse white surface. If the exposure isoptimized for the retroreflective dots in the images, asin Fig. 1d, illuminated retroreflective targets appear asbright white dots on a dark background and areexcellent photogrammetric targets that computersoftware can automatically locate and mark.

Figure 5b compares white dots projected onto twodifferent membrane materials. The left-hand side is

aluminized Kapton, the same material used for the solarsails in Fig. 1g. It is mainly a specular surface(reflecting light at the same angle as the incident angle),but has a small diffusivity (reflecting light in everydirection). The right-hand side is matte Mylar film,which is mainly diffuse. Diffuse materials are muchbetter for photogrammetry since they give moreuniform target contrast from different viewingdirections relative to the projector. In Fig. 5b, theprojector is directly in front of the membranes and thecamera is about 30 degrees to the left side.

Membrane materials for proposed Gossamerstructures are often reflective or transparent, which aredifficult materials to measure with photogrammetry.Special ground test articles may be manufactured with adiffuse white coating on one or both sides of shiny andtransparent membranes to simplify photogrammetrywith dot projection.

Step 4: Design the photogrammetric geometryand take the photographs

Designing the photogrammetric geometry (a.k.a.,“network design”) involves selecting an adequatenumber and distribution of camera positions.20 Ageneral guideline is to place cameras at convergentviewing angles, in both the horizontal and verticaldirections if possible, at about 70 to 90 degrees angularseparation, plus or minus 30 degrees. A key feature ofclose-range photogrammetry with bundle adjustment isthat the camera locations and orientations do not haveto be measured, but are calculated by the software alongwith the desired target coordinates. The bundleadjustment, which is the data reduction procedurepreferred by the photogrammetric community, uses aniterative non-linear least squares solution. Althoughdetails of this process are beyond the scope of thispaper, a brief discussion is provided in Step 8 below.

Each point of interest on the object must appear inat least two photographs for 3D determination, althoughfour or more photographs are preferred for improvedleast-squares accuracy and reliability. With knowledgeof at least one other constraint, such as knowing that allobject points lie on a plane, photogrammetry can alsouse a single camera location. This capability isparticularly useful for real-time measurements to reducecomputational requirements. Gossamer structure tests

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will usually use two or more camera locations tocompute 3D structural coordinates without assumptionsor constraints.

Figure 6 shows the equipment for dot-projectionphotogrammetry of the 2-m solar sail model (or othersmall test articles). This is a staged photograph--theactual test configuration was somewhat different. Tominimize hot spots in the images, the projector wasmoved to the floor and angled up toward the sail atabout 45 degrees, causing the main light beam to reflectmostly above the cameras. Forty pictures were shotusing eight camera locations in front of the sail (fouracross at each of two tripod heights) and with fiveimage exposure settings at each location. With the roomdarkened, a standard 35-mm slide projector had enoughpower to project about 1500 dots with adequate contraston only the lower-right corner of this shiny membrane,indicated by dashed lined lines in Fig. 6. The size ofthis area is about 835 x 585 mm. Theater projectorswith higher power are available for larger structures.

Photogrammetry requires targets with goodcontrast that are in reasonable focus. Generally, the bestway to take the photographs is using a small aperturesetting (f/8 or higher) to obtain good depth of field (i.e.,the depth in the object that is simultaneously in focus)while minimizing, or even eliminating, focusingrequirements. Using a small aperture and focusing thecamera to optimize depth of field, it is possible tosimultaneously focus all objects in the picture from ashort distance in front of the camera out to the horizon.However, using a small aperture requires a slowershutter speed or brighter illumination to obtain adequateimage exposure. Tripods should be used with exposuretimes longer than about 30 msec to avoid cameramovement. Most consumer digital cameras have zoomlenses, and it is important to be sure that they are setproperly. Normally either the minimum or maximumzoom setting (focal length) and infinity focus are usedto simplify the process and improve repeatability. Anychanges in the zoom or focus settings require newcamera calibration data.

Figure 7 shows the best pair of images among the40 that were taken of the 2-m solar sail. The contrast inthese images is higher than observed with the naked eyefor this reflective membrane. Contrast enhancementoccurred using long camera exposure settings of about

30 sec (i.e., long integration times). The images wereshot using the longest focal length of the camera (36mm) so that the photographer stayed as far away fromthe membrane as possible to avoid causing air currentsthat would move the sensitive film. For the images inFig. 7, the cameras were about 3 m from the structureand separated by about 3.5 m. Maximizing the testarticle image size in each photo increases accuracy. Theprojected dots in the left photograph occupy 85% of theimage and in the right photograph, they occupy 74%. Ahot spot occurs in the right image from slight twistingof the membrane edge that redirected the main lightbeam toward the camera. The occurrence of hot spotson shiny materials with dot projection is almostunavoidable.

Photographic images are inherently non-dimensional (e.g., one cannot tell from photographsalone if the solar sail is 2 m or 20 m in size). Forscaling purposes and for initial calculation of cameralocations and orientations, ten light-colored adhesivetargets were placed on the membrane and are visible inthe photos with close examination. The measureddistance between a widely separated pair of adhesivetargets provided physical scaling for the resulting 3Dphotogrammetric model.

Step 5: Select data analysis software andimport the images

Close-range photogrammetry traditionally has beena specialized technology with relatively few softwaredevelopers. Most photogrammetry software is one ofthe following three types: 1) Part of a turnkey systemand interfaces with one particular camera only, 2)Developed and used by an individual or consulting firmand not available for sale, or 3) Research code writtenat universities and used primarily by its developers andstudents. However, with rapidly increasing capabilitiesof digital cameras and personal computers in recentyears, some general-purpose photogrammetry softwarehas appeared on the market. These products can analyzeimages from any source. PhotoModeler Pro, one of theconsumer software products, has been used successfullythroughout this research. The remainder of the paperdescribes the photogrammetric analysis of the solar sailimages in Fig. 7 with PhotoModeler. Other softwareproducts provide similar capabilities.

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First, the images are transferred from the camerasto the computer. Most digital cameras use removable,solid-state memory cards about the size of a matchbox,available in capacities as high as 512 MB. For theOlympus E-20 camera used to take the solar sailpictures, each card holds up to 150 JPEG images at themaximum resolution of 2560 x 1920 pixels. The card isremoved from the camera, inserted in a peripheral cardreader attached to the computer, and the images aretransferred just as floppy disk files are copied. ThePhotoModeler software is then started, and the imagesare selected and imported into the program for analysis.

Next, the user associates each image with itsspecific, previously calibrated camera (the cameras canbe entirely different types). This allows the properinternal camera parameters, obtained from calibration,to be used with each image. Traditionally,photogrammetric measurement of stationary objectsuses only one roving camera, and there are someaccuracy advantages of this approach (by running aself-calibration procedure during the data analysis).However, many Gossamer structures are so flimsy theycan change shape from unintentional air currentscreated by a roving photographer. In addition, testsunder vacuum conditions cannot easily use a rovingcamera. These situations require multiple stationarycameras. Multiple time-synchronized cameras are alsonecessary for 3D dynamic measurements.

Step 6: Mark the target locations in each image

Data analysis begins by marking the locations ofthe targets in the images. In other words, the x-ycoordinates of the centroid of each elliptical target,projected white dots in this case, must be marked asaccurately as possible in each image. An importantaspect of precision photogrammetry is the availabilityof subpixel interpolation algorithms that locate thecenter of solid-colored ellipses to an accuracy of one-tenth of a pixel or less.21 The 3D spatial measurementprecision obtained with photogrammetry is directlyrelated to this subpixel interpolation factor. Forexample, the overall three-dimensional measurementprecision improves by approximately a factor of two ifthe center of ellipses is calculated to a precision of 1/20of a pixel rather than to 1/10 of a pixel.

PhotoModeler contains a robust subpixel marking

tool for circular targets. Individual targets are markedby clicking them with the mouse, or all targets in arectangular region of the image can be selected andmarked collectively. The latter approach is called“automatic marking” (or auto-marking) and although itis not entirely automatic, does greatly simplify subpixeltarget marking in projects with large numbers of points,such as in dot-projection tests.

Auto-marking requires the selection of anappropriate intensity threshold, which is then used todetermine the number and location of targets in theimages. The software assumes that parts of the imagewith intensities below the selected threshold contain notargets. The user selects an area of the image to analyze(in this case the entire image is selected), and theninteractively moves a slider bar to adjust and select athreshold value. Figure 8 shows various displays thatoccurred in the left solar sail image as the slider movedfrom 255 (pure white) down to zero (pure black). Theobjective is to choose as low a threshold as possiblewithout seeing too much noise in the image or havingthe targets join together. With dot projection on thisshiny membrane, there is uneven illumination so asingle threshold value will not work for the entireimage. A threshold intensity of 70 was selected as acompromise to get as many correctly marked targetsautomatically as possible. Note that target markingprocedures may be significantly different and moreautomatic in other photogrammetry systems.

Figure 9 shows the automatically marked points forthis image. Most targets were detected and marked withthe exception of several in the upper-center of themembrane located in the brightest region and several onthe right edge of the membrane located in the darkestregion. There are a few other targets in the image thatwere not found automatically, and they were marked byhand in a second step. PhotoModeler required 70 sec ona 2.2-GHz computer to calculate the subpixel locationof 1500 targets using a least-squares matchingalgorithm. Two other marking algorithms are availablethat are faster but also less accurate.

Step 7: Identify which points in the imagesrefer to the same physical point

The second step of the data analysis is to match themarked points in one image with their corresponding

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points in the other images. This process is called“referencing” the points. When a point is initiallymarked on an image, it is assigned a uniqueidentification number. Then, when a marked point onone image is referenced to a marked point on anotherimage, the software reassigns the same identificationnumber to both points indicating they are the samephysical location on the structure. In the beginning ofthe data analysis, the user must perform this referencingoperation manually until a certain minimum number ofpoints (at least six) are referenced on all photos, atwhich time the user “processes” the data. Processingthe data runs a photogrammetric bundle adjustmentalgorithm, described in Step 8.

When these calculations finish (typically in a fewseconds), the user returns to the Referencing phase. Atthis point, automatic helper tools are available to speedup the process. These tools appear as a result of theinitial processing of the data, which yields the spatiallocation and orientation angles of the cameras. Now,the images are said to be “oriented.” In a typicalPhotoModeler project without control points (specialpoints with known coordinates), the camera locationsand orientations calculated above are relative quantitieswith respect to one of the cameras, usually Camera 1.At this point, it is a good idea to verify that the softwarepositioned the cameras properly, which can be checkedeasily in the graphical 3D viewer available inPhotoModeler. The viewer shows small camera icons attheir locations and orientations relative to targets withcalculated 3D coordinates, displayed as small dots.Controls are available to rotate or resize the 3D graphicfor better viewing.

Figure 10 illustrates the use of an interactive,referencing helper tool. The user selects one or morepoints in the first image to reference in the otherimages. For example, select Point 5820 in Fig. 10a.Once the images are oriented, the software knows thedirection of a light ray from Point 5820 on the structureto the first camera. It projects this ray onto theremaining images. The photogrammetric term for thisprojected line is an “epipolar line.” The user knows thatthe desired point should be somewhere along the line.In most cases, this greatly simplifies referencing thepoint. In Figure 10b, the corresponding target in Image2 is the only one directly on the epipolar line, located inthe third column of points.

PhotoModeler also contains fully automaticreferencing algorithms for applications with two ormore images (which is standard). These algorithmswork best with at least three images, but there is also anew technique for auto-referencing two images ofplanar or near-planar structures. The constraintprovided by the surface shape allows the software towork with the normally ambiguous case of twophotographs. The algorithm asks the user to select threeor more points with 3D coordinates that define the near-planar surface. The software calculates the equation ofthis plane, then automatically searches for andreferences pairs of points using the epipolar line and auser-specified distance from the indicated plane. It isdifficult to see in the images, but the measurementregion in the 2-m solar sail test is, in fact, not planarenough for this algorithm to reference the entire imagesimultaneously. As will be clear later, the right-handsail quadrant is significantly displaced outward at thetop--by more than 5 cm--from the lower quadrant. Thisgeometry required auto-referencing to be performed intwo steps, a separate operation for each region.

Notice in Fig. 10 that many small, bright spotsappear throughout the images. The Kapton membranefor this solar sail model is perforated, and the brightspots are from light reflected by the edges of the holes.These spots cause small errors in the calculatedcentroids of the targets, but the effects are minimal.

Step 8: Process, scale, and rotate the data

The third and final step of the data analysis is to“process” the data using the bundle adjustmentalgorithm. In the technical literature, several variationsof the bundle adjustment method appear, with differentuser options and levels of sophistication.22 As discussedin the preceding section, the data are processed initiallyafter referencing at least six points in each image. Thisorients the images. Then the user returns to referencing(and marking, if necessary) additional points. It is oftenbetter not to reference all remaining points at this time,but stop after adding some additional points and re-process the data. With the 2-m solar sail images, pointswere referenced and processed mostly in two large sets(the lower-left and upper-right regions). Then someadditional points were added that did not auto-mark orauto-reference previously, such as on the curved edges.

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This approach avoids wasting time if for some reasonthe algorithms fail to handle a large number ofadditional points, usually because of referencing errors.Referencing errors can be located and fixed more easilyif a limited number of new points are added at each stepof the procedure.

The bundle adjustment algorithm does two thingssimultaneously: 1) Computes the spatial locations andorientation angles of each camera, and 2) Computes the3D coordinates of all referenced points and estimatestheir measurement precision. Bundle adjustment isalways an iterative solution (since the underlying mathis non-linear), and hence the calculations continue untila specified consistency or maximum number ofiterations occurs. If the object points are distributed onthe structure and the photographs are at suitable angles,the bundle adjustment will usually run successfully. Inmany cases, camera self-calibration or field-calibrationare added to the bundle adjustment equations during thedata processing to improve the internal consistency ofthe solution and the accuracy of the point coordinates.

These steps were followed with the twophotographs of the 2-m solar sail, and the coordinatesof all targets were successfully determined usingsuccessive bundle adjustment calculations. The resultwas 1449 photogrammetrically computed 3D pointsdescribing the static shape of the structure. Followingeach bundle adjustment, the camera locations andorientations were displayed in the PhotoModeler 3DViewer. The cameras always appeared to be in theirproper positions and orientations, adding confidencethat the software was working properly. Recall that thesoftware computes the camera positions andorientations from the images.

At this point, the set of 3D points (a.k.a., the “pointcloud”) can be scaled to physical units and translatedand rotated to any desired coordinate system. Scalingand changing coordinate systems in PhotoModeler is asimple matter of selecting two distant points in animage, entering their separation distance in engineeringunits, and then selecting three points to define thecoordinate system. (The three points specify the neworigin, direction of a designated axis, and the plane ofanother designated axis.) In this test, two of the tensmall adhesive dots placed on the membrane were usedfor scaling, and three of the projected dots defined the

coordinate system. In some photogrammetry projects,these scaling and coordinate system points may belocated off the structure, e.g., on a rigid frame or otherstationary support structure.

Step 9: Examine results and export foradditional analyses

Figure 11 shows two views of the final structuralmodel displayed as a point cloud in the 3D Viewer.Note that it was impossible to mark a region of targetsat the hot spot in the right-hand image, so the resulting3D model contains a hole at this location. There is alsoa gap between the two individual membrane sectionsbecause projected dots on the slender aluminum tubebetween the membranes were larger than the tubediameter and therefore the centroids could not beaccurately calculated.

It is easier to see the shape of the membrane byexamining cross-sectional slices through the model atvarious elevations, shown in Fig. 12. These contourswere created by exporting the 3D data fromPhotoModeler in ASCII format and doing cubic-splinecurve fits to the data points on five horizontal rows ofdots. Note that this plot uses different scales on the xand y axes, so the out-of-plane membrane shape (Zdirection) is amplified in the plot by about 20x relativeto the horizontal dimension (X direction). The datashow a significant displacement of the upper regionrelative to the lower region by up to 6 cm. This warpedshape, caused by the two upper rods of the sail bendingconsiderably forward by gravity, was the initialconfiguration of the structure. Later (for the picture inFig. 6), the upper rods were pulled back and tied in astraighter position by cords. Curling of the membraneedges is also apparent in Fig. 12.

Photogrammetric precision achieved in the projectcan also be examined using the exported data. Figure 13shows two principal parameters, largest markingresidual and tightness, that can be studied. The plotsshow the results for the 1449 3D points sorted indescending order. Marking residuals are the least-squares error distances in the camera image planes.Residuals under 1.0 pixel indicate sub-pixelmeasurement precision. In this application, half of thepoints had residuals less than 0.20 pixel, which is goodconsidering the shiny nature of the membranes and

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suboptimal target contrast. Points with the largestresiduals were manually marked points located on thetwisted membrane edges.

The second plot in Fig. 13 shows thephotogrammetric tightness, which measures themaximum distance (as a percentage of the object size)between any pair of projected light rays from theimages to the object point. Due to measurement errors,light rays extending from marked points in separateimages to the same object point in space never intersect.The closeness, or tightness, of the intersection isanother indication of measurement precision. In thisapplication, half of the points had tightness less than0.016%, equivalent to 1 part in 6250.

Step 10: Lessons learned and how to improvethe methods?

Some lessons learned in this 2-m solar sailphotogrammetry application using projected dots astargets that can benefit later projects are:

1. As expected, shiny membranes are difficult, thoughnot impossible, to measure with dot projection. Ifpossible, future solar sail ground test articlesshould use a diffuse white membrane coating (onone side is adequate), which would simplify andimprove shape measurements with dot projection.

2. Higher-power projectors with a variety of lensesare needed to measure complete solar sails of 2-min size and larger at various projection distancesand angles.

3. A convenient way to move the projector todifferent locations was not available in the test.With a shiny membrane, finding the projectorlocation and direction that minimizes hot spots inthe images is helpful.

4. Lightly tensioned membranes move easily from aircurrents generated by walking near them. Usingmultiple simultaneous cameras is preferable tousing a single roving camera to avoid this problem.Multiple cameras fired remotely from outside aclosed chamber are best to completely avoidunintentional air currents.

5. The use of three or more images from convergentviewing directions simplifies target referencingcompared with the use of only two images,particularly for non-planar surfaces. An effective

camera network for a square solar sail test wouldconsist of one camera in each corner pointingtoward the hub of the sail.

CONCLUSIONS

This paper summarized experiences at NASALangley Research Center during the past three years todevelop or adapt photogrammetry methods forGossamer-type spacecraft and components. Theresearch used mainly off-the-shelf digital-camera andsoftware technologies that are affordable to mostorganizations and provide acceptable accuracy. Thefirst part of the paper discussed seven successfulapplications on a variety of research structures. Thesecond part discussed the ten main steps ofphotogrammetry (consistent with the PhotoModeler Procommercial software program) using data from a recent2-m solar sail test with projected dots as an example.Solar sails require highly reflective membranes for theiroperation in space (they are propelled by reflectingsunlight), but shiny membranes are difficult test objectsbecause photogrammetry uses the diffuse component ofreflected light, not the specular component. The staticshape of the 2-m solar sail was successfully determined,but required long image exposure times of about 30 sec.Using a diffuse white coating on future test articles cansimplify shape measurements. Many other lessons werelearned in these initial applications that will improvefuture photogrammetry projects with Gossamerstructures.

ACKNOWLEDGMENTS

The authors acknowledge the contributions andsupport of Alpheus Burner, Paul Danehy, MarkHutchinson, and Keith Belvin of NASA LaRC, VaughnBehun of Swales Aerospace, Joe Blandino of JamesMadison University, Gary Robertson of ShapeQuest,Inc., and former students Louis Giersch and JessicaQuagliaroli, in the development of photogrammetrymethods for Gossamer spacecraft structures.

REFERENCES1Mikhail, E. M., Bethel, J. S., and McGlone, J. C.,Introduction to Modern Photogrammetry, John Wiley& Sons, New York, NY, 2001.2Atkinson, K. B. (editor), Close Range Photogrammetryand Machine Vision, Whittles Publishing Company,

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Scotland, UK, 2001.3Shortis, M. R. and Beyer, H. A., “Sensor Technologyfor Digital Photogrammetry and Machine Vision,”ibid., pp. 106-155.4Cooper, M. A. R. and Robson, S., “Theory of CloseRange Photogrammetry,” ibid., pp. 9-51.5El-Hakim, S. F. (editor), Videometrics and OpticalMethods for 3D Shape Measurement, SPIE ProceedingsNo. 4309, Jan. 2001.6Jenkins, C. H. M. (editor), Gossamer Spacecraft:Membrane and Inflatable Structures Technology forSpace Applications, Vol. 191, Progress in Astronauticsand Aeronautics, AIAA, Reston, VA, 2001.7L’Garde, Inc., “Photogrammetry Capability,”http://www.lgarde.com/capabilities/photo.html.8Giersch, L. R., “Pathfinder Photogrammetry Researchfor Ultra-Lightweight and Inflatable Space Structures,”M.S. Thesis, George Washington University, Aug.2001 (also published as NASA CR-2001-211244, Nov.2001).9Dharamsi, U. K., Evanchik, D. M., and Blandino, J. R.,“Comparing Photogrammetry with a ConventionalDisplacement Measurement Technique on a SquareKapton Membrane,” AIAA paper 2002-1258, April2002.10Geodetic Services, Inc., Melbourne, FL, V-STARSIndustrial Photogrammetry Systems,http://www.geodetic.com.11Imetric SA, Porrentruy, Switzerland, 3D ImageMetrology Systems, http://www.imetric.com.12Pappa, R. S., Giersch, L. R., and Quagliaroli, J. M.,“Photogrammetry of a 5-m Inflatable Space AntennaWith Consumer Digital Cameras,” ExperimentalTechniques, July/Aug. 2001, pp. 21-29.13Pappa, R. S., Woods-Vedeler, J. A., and Jones, T. W.,“In-Space Structural Validation Plan for a Stretched-Lens Solar Array Flight Experiment,” Proceedings ofthe 20th International Modal Analysis Conference, Feb.2002, pp. 461-471.14Watson, J. J., “Static-Test Results for theCharacterization of Inflatable Rigidizable Columns,”AIAA Paper 2001-1269, April 2001.15Pappa, R. S., Lassiter, J. O., and Ross, B. P.,“Structural Dynamics Experimental Activities in Ultra-

Lightweight and Inflatable Space Structures,” AIAAPaper 2001-1263, April 2001.16Jones, T. W. and Pappa, R. S., “Dot ProjectionPhotogrammetric Technique for Shape Measurementsof Aerospace Test Articles,” AIAA Paper 2002-0532,Jan. 2002.17Shortis, M. R. and Snow, W. L., “VideometricTracking of Wind Tunnel Aerospace Models at NASALangley Research Center,” The PhotogrammetricRecord, Vol. 15, No. 85, 1997, pp. 673-689.18Slade, K. N., Belvin, W. K., and Behun, V., “SolarSail Loads, Dynamics, and Membrane Studies,” AIAApaper 2002-1265, April 2002.19Fryer, J. G., “Camera Calibration,” Close RangePhotogrammetry and Machine Vision, edited by K. B.Atkinson, Whittles Publishing, Scotland, UK, 2001, pp.156-179.20Fraser, C. S., “Network Design,” ibid., pp. 256-281.21West, G. A. W. and Clarke, T. A., “A Survey andExamination of Subpixel Measurement Techniques,”SPIE Proceedings No. 1395, Sept. 1990, pp. 456-463.22Granshaw, S. I., “Bundle Adjustment Methods inEngineering Photogrammetry,” PhotogrammetricRecord, Vol. 10, No. 56, 1980, pp. 181-207.

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a) 5-m inflatable parabolic reflector

f) 4.5-m inflatable tripod

d) 0.7-m oscillating Kapton membranewith retroreflective targets

Fig. 1. Gossamer test articles.

g) Partial 10-m and two complete 2-m solar sail models

e) 3-m hexapod reflector for active control experiments(projected dots on stretched membrane reflector)

b) 1-m flexible Fresnel lens(1-projected dots, 2-adhesive targets)

c) 15-m inflated,rigidized tube

1

2

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9. Examine results & export for additional analyses

10. Lessons learned and how to improve the methods?

2. Select and calibrate suitable cameras and lenses

3. Select type, size, and distribution of targets

4. Design the photogrammetric geometry& take the photographs

5. Select data analysis software & import the images

1. Establish measurement objectives& accuracy requirements

6. Mark the target locations in each image(can be automatic)

7. Identify which points in the images refer to the same physical point(can be automatic)

8. Process, scale, and rotate the data

Fig. 2. The 10 steps of photogrammetry.

Fig. 3. Camera characteristics.

Used for static shape measurementsOlympus E-20 color digital SLR camerasCCD: 2560 x 1920 pixels, 8.704 x 6.528 mmNon-removable lens: 9 - 36 mm, f/2.0 - f/11Shutter speed: 1/640 - 60 sec

Used for dynamic measurementsPulnix TM-1020-15 monochrome digital video camerasCCD: 1008 x 1018 pixels, 9.072 x 9.162 mmRemovable lens: 24 - 85 mm, f/2.8 - f/22Up to 30 frames per sec

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Fig. 6. Equipment for photogrammetry of 2-m solar sail model using projected dots.

Fig. 4. Camera calibration images.

Fig. 5. Retroreflective and projected circular targets.

a) Retroreflectors appear bright whitewhen illuminated from camera position

With cameraflash off

With cameraflash on

b) Comparison of projected dots on shiny (left)and diffuse-white (right) membranes

Slide projector

Olympus E-20digital cameras

Region measured withphotogrammetry

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Fig. 8. Left image displayed at various binary intensity thresholds.

Fig. 7. Best images of lower-right corner (835 x 585 mm) of 2-m solar sail model

70 40

200 160

130 100

Left image Right image

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Fig. 9. Automatically marked points using an intensity threshold of 70.

Fig. 10. Epipolar line assists target referencing.

a) Select a point in Image 1 (e.g., #5820) b) Corresponding point in Image 2 is on the epipolar line

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Fig. 11. Two views of 3D point model (1449 points).

Fig. 13. Distribution of largest marking residuals and tightness (descending order).

Fig. 12. Out-of-plane membrane shape at various elevations.

90% of pts < 0.74 pixel50% of pts < 0.20 pixel

90% of pts < 0.052 %50% of pts < 0.016 %

A

D

C

B

E

ABCE D

REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 1. AGENCY USE ONLY (Leave blank)

2. REPORT DATE

June 2002 3. REPORT TYPE AND DATES COVERED

Technical Memorandum 4. TITLE AND SUBTITLE

Photogrammetry Methodology Development for Gossamer Spacecraft Structures

5. FUNDING NUMBERS WU-755-06-00-11

6. AUTHOR(S) Richard S. Pappa Alan Walford Thomas W. Jones Stuart Robson Jonathan T. Black Mark R. Shortis

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center Hampton, VA 23681-2199

8. PERFORMING ORGANIZATION REPORT NUMBER

L-18200

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration Washington, DC 20546-0001

10. SPONSORING/MONITORING AGENCY REPORT NUMBER

NASA/TM-2002-211739

11. SUPPLEMENTARY NOTESPappa and Jones: Langley Research Center, Hampton, Va; Black: George Washington University; Walford: Eos System, Inc.,Vancouver, Canada; Robson: University College London, London, United Kingdom; Shortis: University of Melbourne, Parkville, Australia. Presented as paper number AIAA-2002-1375, April 22-25, 2002.

12a. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified-Unlimited Subject Category 39 Distribution: Standard Availability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words) Photogrammetry--the science of calculating 3D object coordinates from images--is a flexible and robust approach for measuring the static and dynamic characteristics of future ultra-lightweight and inflatable space structures (a.k.a., Gossamer structures), such as large membrane reflectors, solar sails, and thin-film solar arrays. Shape and dynamic measurements are required to validate new structural modeling techniques and corresponding analytical models for these unconventional systems. This paper summarizes experiences at NASA Langley Research Center over the past three years to develop or adapt photogrammetry methods for the specific problem of measuring Gossamer space structures. Turnkey industrial photogrammetry systems were not considered a cost-effective choice for this basic research effort because of their high purchase and maintenance costs. Instead, this research uses mainly off-the-shelf digital-camera and software technologies that are affordable to most organizations and provide acceptable accuracy.

14. SUBJECT TERMS

Close-Range Photogrammetry, Videogrammetry, Gossamer Spacecraft, Ultra- 15. NUMBER OF PAGES

23 Lightweight and Inflatable Space Structures, Optical Measurement Techniques 16. PRICE CODE

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OF REPORT Unclassified

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