December 2003

NASA/CR-2003-212678

Photogrammetry and Videogrammetry Methods

Development for Solar Sail Structures

Jonathan T. Black

Joint Institute for Advancement of Flight Sciences

Langley Research Center, Hampton, Virginia
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to the

advancement of aeronautics and space science. The

NASA Scientific and Technical Information (STI)

Program Office plays a key part in helping NASA

maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the lead center for NASA’s

scientific and technical information. The NASA STI

Program Office provides access to the NASA STI

Database, the largest collection of aeronautical and

space science STI in the world. The Program Office is

also NASA’s institutional mechanism for

disseminating the results of its research and

development activities. These results are published by

NASA in the NASA STI Report Series, which

includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant phase

of research that present the results of NASA

programs and include extensive data or

theoretical analysis. Includes compilations of

significant scientific and technical data and

information deemed to be of continuing

reference value. NASA counterpart of peerreviewed formal professional papers, but having

less stringent limitations on manuscript length

and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or of

specialized interest, e.g., quick release reports,

working papers, and bibliographies that contain

minimal annotation. Does not contain extensive

analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or co-sponsored by NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from NASA

programs, projects, and missions, often

concerned with subjects having substantial

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and

technical material pertinent to NASA’s mission.

Specialized services that complement the STI

Program Office’s diverse offerings include creating

custom thesauri, building customized databases,

organizing and publishing research results ... even

providing videos.

For more information about the NASA STI Program

Office, see the following:

• Access the NASA STI Program Home Page at

http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA STI Help Desk

at (301) 621-0134

• Phone the NASA STI Help Desk at

(301) 621-0390

• Write to:

 NASA STI Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076-1320
National Aeronautics and

Space Administration

Langley Research Center Prepared for Langley Research Center

Hampton, Virginia 23681-2199 under Cooperative Agreement NCC1-03008

December 2003

NASA/CR-2003-212678

Photogrammetry and Videogrammetry Methods

Development for Solar Sail Structures

Jonathan T. Black

Joint Institute for Advancement of Flight Sciences

Langley Research Center, Hampton, Virginia
Available from:

NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)

7121 Standard Drive 5285 Port Royal Road

Hanover, MD 21076-1320 Springfield, VA 22161-2171

(301) 621-0390 (703) 605-6000

The use of trademarks or names of manufacturers in the report is for accurate reporting and does not constitute an

official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics

and Space Administration.
iii

ABSTRACT 

Responding to recent advances in materials manufacturing, specifically 

membrane production, the space community has begun to focus considerable attention on 

gossamer technologies as a means of reducing launch costs and volumes. Ultralightweight and inflatable gossamer space structures are designed to be tightly packaged 

for launch, then deploy or inflate once in space. These properties will allow for in-space 

construction of very large structures 10 to 100 meters in size such as solar sails, inflatable 

antennae, and space solar power stations using a single launch. Solar sails are perhaps 

the most studied of the gossamer technologies because of the propellantless propulsion 

they provide. Gossamer structures do, however, have significant complications. Their 

low mass and high flexibility characteristics make them difficult to test on the ground. 

The added mass and stiffness of attached measurement devices can significantly alter the 

static and dynamic properties of the structure, necessitating an alternative approach for 

characterization. 

This report discusses the development and application of metrology methods 

called photogrammetry and videogrammetry that make accurate measurements from 

photographs. These methods have been adapted for the static and dynamic 

characterization of gossamer structures, as four specific solar sail applications 

demonstrate. The applications prove that high-resolution, full-field, non-contact static 

measurements of solar sails using dot projection photogrammetry are possible as well as 

full-field, non-contact, dynamic characterization using dot projection videogrammetry. 

The accuracy of the measurement of the resonant frequencies and operating deflection 

shapes that were extracted surpassed expectations. While other non-contact measurement 

methods exist, they are not full-field and require significantly more time to take data. 
iv

ACKNOWLEDGEMENTS 

 The author would like to thank Dr. Keith Belvin, Dr. Kara Slade, Mr. Tom Jones, 

Dr. Adrian Dorrington, Dr. Paul Danehy, and all the members of the Ultra-lightweight 

and Inflatable Structures group at NASA Langley Research Center (LaRC) for their 

commitment to excellence and their drive to explore, the members of the Structural 

Dynamics Branch at LaRC for their hospitality, Prof. Robert Blanchard of George 

Washington University for his guidance, Dr. Jack Leifer of the University of Kentucky 

and Dr. Joe Blandino of James Madison University for their collaboration and creativity, 

his thesis advisor Dr. Paul Cooper of George Washington University for his direction, 

thesis committee member Prof. Robert Sandusky of George Washington University, and 

his friends and family for their love and support. 

 The author would especially like to thank his NASA advisor, Mr. Richard Pappa 

of LaRC whose kindness, generosity, and devotion have made working at NASA an 

edifying and broadening experience. He has taught me more than I ever could have 

imagined and my gratitude runs deeper than I ever could express. 
v

TABLE OF CONTENTS

ABSTRACT ........................................................................................................iii

ACKNOWLEDGEMENTS....................................................................................iv

TABLE OF CONTENTS .......................................................................................v

LIST OF FIGURES ............................................................................................viii

LIST OF TABLES................................................................................................xi

1. INTRODUCTION..............................................................................................1

1.1 Measurement Methods...............................................................................1

1.2 Objective.....................................................................................................2

2. GOSSAMER STRUCTURES...........................................................................3

2.1 Overview.....................................................................................................3

2.2 Solar Sails ..................................................................................................5

3. PHOTOGRAMMETRY AND VIDEOGRAMMETRY.........................................6

3.1 Overview.....................................................................................................6

3.2 The Photogrammetric Process ...................................................................7

3.2.1 Camera Calibration ..............................................................................8

3.2.2 High Contrast Images ........................................................................10

3.2.3 Target Marking and Matching and the Bundle Adjustment.................12

3.2.4 Point Cloud ........................................................................................13

3.3 Videogrammetry .......................................................................................14

4. HARDWARE..................................................................................................15

4.1 Still Cameras ............................................................................................15

4.2 Video Camera...........................................................................................17

4.3 Projectors .................................................................................................19
vi

5. ACCURACY, PRECISION, AND REPEATABILITY......................................21

5.1 Overview...................................................................................................21

5.2 Photogrammetric Error Estimates.............................................................22

5.3 Camera-Related Factors ..........................................................................23

5.4 Noise Tests...............................................................................................26

6. RETRO-REFLECTIVE VS PROJECTED TARGETS ....................................36

6.1 Retro-reflective Targets ............................................................................36

6.2 Projected Targets .....................................................................................38

7. STATIC SHAPE MEASUREMENT EXAMPLES ...........................................42

7.1 Low Density Full-field Two Meter Kapton Solar Sail.................................42

7.1.1 Test Setup..........................................................................................42

7.1.2 Images ...............................................................................................44

7.1.3 Photogrammetric Processing.............................................................45

7.1.4 Error Estimates ..................................................................................46

7.1.5 Results...............................................................................................47

7.2 Wrinkle Test of Two Meter Kapton Solar Sail ...........................................49

7.2.1 Test Setup..........................................................................................49

7.2.2 Images ...............................................................................................50

7.2.3 Photogrammetric Processing.............................................................51

7.2.4 Error Estimates ..................................................................................52

7.2.5 Results...............................................................................................53

7.3 High Density Full-field Two Meter Kapton Solar Sail ................................55
vii

7.3.1 Test Setup..........................................................................................55

7.3.2 Images ...............................................................................................56

7.3.3 Photogrammetric Processing.............................................................57

7.3.4 Error Estimates ..................................................................................60

7.3.5 Results...............................................................................................60

8. DYNAMIC ANALYSIS OF A TWO METER VELLUM SOLAR SAIL.............65

8.1 Test Setup ................................................................................................65

8.2 Measurements..........................................................................................67

8.3 Results......................................................................................................69

9. CONCLUSIONS.............................................................................................76

9.1 Static Tests...............................................................................................76

9.2 Dynamic Test............................................................................................77

9.3 Future Work..............................................................................................78

9.4 Related Work............................................................................................79

REFERENCES....................................................................................................81

APPENDIX A – CALIBRATION TRACKING......................................................85
viii

LIST OF FIGURES 

Figure 1 – Gossamer structures........................................................................................... 4 

Figure 2 – James Webb Space Telescope ........................................................................... 4 

Figure 3 – Aerial photogrammetry example....................................................................... 7 

Figure 4 – Radial lens distortion angles.............................................................................. 9 

Figure 5 – Retro-reflective targets .................................................................................... 11 

Figure 6 – Underexposed image of a 7 m boom used in photogrammetric measurement 11 

Figure 7 – Matching and triangulation of points .............................................................. 13 

Figure 8 – Exported point cloud and best-fit straight line ................................................ 14 

Figure 9 – Digital still cameras......................................................................................... 16 

Figure 10 – Pulnix TM-1020-15 digital video camera with ring light ............................. 18 

Figure 11 – Projectors....................................................................................................... 20

Figure 12 – Noise test setup.............................................................................................. 26 

Figure 13 – Olympus E20n plots of a stationary point over time..................................... 28 

Figure 14 – Kodak DCS 760M plots of a stationary point over time ............................... 29 

Figure 15 – Pulnix TM-1020-15 plots of a stationary point over time............................. 30 

Figure 16 – Occurrence density plots demonstrating biases............................................. 34 

Figure 17 – Migration of a measurement of a target centriod in time .............................. 35 

Figure 18 – Target contrast comparison test..................................................................... 39 

Figure 19 – Comparison of multiple exposure times using dot projection....................... 40 
ix

Figure 20 – Two meter Kapton solar sail test article........................................................ 43 

Figure 21 – Kapton two meter full field test setup ........................................................... 43 

Figure 22 – Images used in photogrammetric processing (2 of 4) ................................... 44 

Figure 23 – Marked points in upper right corner of the solar sail test article................... 45 

Figure 24 – Results for low density measurements of the solar sail test article ............... 48 

Figure 25 – Two meter Kapton solar sail test article........................................................ 49 

Figure 26 – Images used in photogrammetric processing (2 of 4) ................................... 51 

Figure 27 – Camera locations with fields of view ............................................................ 52 

Figure 28 – Marked points in upper left corner of the area imaged ................................. 52 

Figure 29 – Results for wrinkle measurement of the solar sail test article ....................... 54 

Figure 30 – Two views of contour surface ....................................................................... 54 

Figure 31 – Two meter Kapton solar sail test article rotated slightly with billow............ 56 

Figure 32 – Images used in photogrammetric processing (2 of 4) ................................... 57 

Figure 33 – Marked points in lower right 0.01 m2

 of solar sail test article ...................... 59 

Figure 34 – Results for high density full-field measurement of the solar sail test article 62 

Figure 35 – Two views of the contour surface generated................................................. 63 

Figure 36 – Two meter four quadrant Vellum solar sail test article ................................. 66 

Figure 37 – Test setup for dynamic characterization........................................................ 67 

Figure 38 – Comparison of frequency response functions for a single point ................... 71 
x

Figure 39 – Overlayed magnitudes of frequency response functions for all measured 

points..................................................................................................................... 71 

Figure 40 – First deflection shape comparison for Vellum solar sail test article ............. 73 

Figure 41 – Second deflection shape comparison for Vellum solar sail test article ......... 73 

Figure 42 – Third deflection shape comparison for Vellum solar sail test article............ 73 

Figure 43 – Fourth deflection shape comparison for Vellum solar sail test article .......... 74 

Figure 44 – Fifth deflection shape comparison for Vellum solar sail test article ............. 74 
xi

LIST OF TABLES 

Table 1 – Still camera specifications ................................................................................ 16 

Table 2 – Video camera specifications ............................................................................. 18 

Table 3 – Standard deviations of noise plots .................................................................... 31 

Table 4 – Photogrammetric error estimates...................................................................... 46 

Table 5 – Comparison of two photogrammetric error estimates ...................................... 53 

Table 6 – Comparison of all photogrammetric error estimates ........................................ 60 

Table 7 – Identified resonant frequencies of the 2 m Vellum solar sail ........................... 70 

Table A-1 – Calibration parameters for Olympus E20n cameras..................................... 85 

Table A-2 – Calibration parameters for Kodak DCS 760M cameras............................... 87 

Table A-3 – Residual estimates for one Olympus E20n and one Kodak DCS 760M ...... 87 
xii
1

1. INTRODUCTION 

The average cost to place a payload into low earth orbit aboard a U.S. expendable 

launch vehicle is approximately $20,000 per kilogram with payload size restricted to 

approximately 65 cubic meters. Visionary plans within the government and private 

sector call for deploying large spacecraft with huge apertures, sun shields, and solar 

arrays; spacecraft with prohibitively high launch and assembly costs using traditional 

methods of construction. For such satellites to be feasible, a new class of structures using 

gossamer technology is under development. This unique technology uses ultra-thin 

membranes and inflatable booms to reduce launch volumes by a factor of 50 and launch 

mass by a factor of 10. Gossamer structures will not only fly as satellite components, but 

also as stand-alone spacecraft. Solar sails will be among the first to demonstrate the full 

potential of gossamer technology [1-8] 

1.1 Measurement Methods 

Photogrammetry is the science of making accurate shape measurements from 

photographs [9]. Using high contrast retro-reflective targets, static shape 

characterizations of gossamer test articles, such as inflatable antennae, have been 

achieved in previous work at the NASA Langley Research Center (LaRC) [10-13]. 

Videogrammetry expands the methods and techniques of close-range photogrammetry 

and applies them to a sequence of images to generate a series of the 3-D models produced 

with standard photogrammetry. The models are then linked to create dynamic data for 

such tasks as modal analysis and deployment tracking. Attached retro-reflective targets, 

however, may alter the static and dynamic behavior of the membranes. Therefore, to 

effectively measure ultra-thin membranes without physically attaching targets, totally 
2

non-contact projected circular targets were used in conjunction with photogrammetry [14, 

15]. 

1.2 Objective 

Current solar sail development at LaRC is focused in three areas: materials 

development, analytical model development and validation, and experimental methods. 

The techniques developed here apply to the second and third research areas. High quality 

structural analytical models require highly accurate, high-resolution measurements of 

solar sail test articles for validation. Non-contact, full-field measurements of this nature 

have never before been achieved with sufficient resolution and quality to adequately 

perform this task. This report details the development of non-contact photogrammetric 

and videogrammetric methods for use on Earth and potentially in space for the static and 

dynamic characterization of solar sails. Also included are an analysis of the accuracy and 

precision of the methods, a discussion of the hardware and its effects on the final results, 

strengths and weaknesses of the methods, and suggestions for future work. 
3

2. GOSSAMER STRUCTURES 

The term gossamer is generally applied to ultra-low-mass space structures. 

Frequently these structures are designed to be tightly packaged for launch, and then to 

deploy or inflate once in space. These properties will enable construction of a variety of 

structures that are impractical using current space hardware. Solar sails in particular have 

been the focus of many research and development efforts because of the unique 

propulsion they provide. 

2.1 Overview 

 Most gossamer space structures rely on ultra-thin membranes and inflatable tubes 

to achieve a reduction compared to standard space hardware in launch mass by as much 

as 10 times and in launch volume by as much as 50 times. The technology has been 

adapted for possible use in a wide variety of applications, including deployable ballutes 

for aerobraking on Mars, telescope sunshields, and membrane space solar arrays. Solar 

sails are another gossamer application receiving considerable research and development 

funding at NASA and are discussed in the following section. [1, 3-6, 8, 16] 

 In addition to satellite components, research into stand-alone gossamer spacecraft 

has progressed and can be categorized based on structure size, shown in Figure 1 below. 

Inflatable apertures include telescopes and antennae from 10 to 70 meters in diameter, 

solar sails range from 70 to 200 meters per side, and space solar power stations may be 

up to square kilometers in size. These spacecraft will serve many purposes, including 

studying planets orbiting distant stars, propelling satellites on inter-stellar voyages, and 

providing clean energy on Earth [4, 6]. 
4

(a) Inflatable apertures 10’s m (b) Solar sails 100’s m (c) Space solar power arrays 1 km 

Figure 1 – Gossamer structures

Results have been so promising, in fact, that several NASA missions planned for 

the next decade, including the GEOStorm solar sail mission and the James Webb Space 

Telescope (Figure 2), as well as more long-range possibilities such as a Mercury sample 

return, will make use of membrane structures up to hundreds of square meters in size [1, 

4-7, 17, 18]. Missions of this type are impossible today using traditional space hardware 

due to the complexity, time, weight restrictions, and high cost of multiple launches and 

in-space assembly. Gossamer technology, however, will allow spacecraft of this type to 

be launched as a single package. 

Figure 2 – James Webb Space Telescope 

22 x 10 m

Sunshield
5

2.2 Solar Sails 

Solar sails are among the most studied members of the gossamer family because 

of the unique propellantless propulsion they provide. Through the momentum transfer of 

reflected photons of sunlight (sail membranes have highly reflective surfaces) solar sails 

can generate a small but continuous acceleration on the order of 1.0 mm/s2. This constant 

thrust allows travel in non-Keplerian orbits enabling smaller versions less than 100 

meters on a side (square sail) to hold an approximately stationary location relative to the 

Sun or the Earth, such as a polar observing satellite. GEOStorm, a 70 meter square solar 

sail, will hold position slightly in front of the L1 Lagrange Point, at 0.98 astronomical 

units (AU) from the Sun and give warning of solar flares. Larger sails, over 150 meters 

per side, will be able to reach Jupiter in only two years and Pluto in just a decade [3, 6, 

17, 19]. 

A useful level of continuous acceleration is achievable for only a solar sail with 

very low areal mass densities. The pressure provided by sunlight is just 9.12x10-6 N/m2

at one AU, meaning that the spacecraft must be very large, as discussed above, and very 

lightweight – less than approximately 20 grams per square meter overall, including 

payload – to generate acceptable acceleration [7, 20]. Suitable membranes are less than 5 

μm thick with areal densities less than 7 g/m2

 [21, 22]. For comparison, standard 8.5 x 

11 inch white paper is 100 μm thick with a density of 75 g/m2

. While static and dynamic 

characterization of structures normally requires the attachment of accelerometers or other 

measurement sensors, the added mass and stiffness of potentially hundreds of these 

physically attached devices could drastically alter the properties of the membrane 

structure being evaluated. Therefore, a totally non-contact measurement method such as 

photogrammetry is preferred. 
6

3. PHOTOGRAMMETRY AND VIDEOGRAMMETRY 

 Photogrammetry and videogrammetry were selected as the measurement methods 

for study and development because of their unique ability to take full-field, non-contact 

data. Both are mature and complicated metrology methods that will be described here in 

abridgement. 

3.1 Overview 

 Photogrammetry is defined as the science of making three-dimensional 

measurements from photographs. The majority of these measurements are generated 

from aerial photographs and used to create topographic surface maps of large areas or 

land features. Close-range photogrammetry, the technique detailed below, measures 

objects several orders of magnitude closer to the camera in much greater detail than aerial 

topography. It is a complex and mature scientific method that will be only briefly 

discussed here. For comprehensive coverage, see References 9-13 and 23-25. Specific to 

the applications discussed here, photogrammetry can be thought of as generating 

computer models from photographs, as shown in Figure 3. Several aerial photographs, 

such as the one in Figure 3(a) of a building in Frankfurt, Germany, were used to create 

the 3-D digital model shown in Figure 3(b) [26]. 
7

 (a) Aerial photograph (b) Computer model 

Figure 3 – Aerial photogrammetry example 

 In Figure 3 only the corners and edges of the building were used to create the 

model, yielding a low measurement density. The building sides were all assumed to be 

perfectly flat, and no information concerning possible surface features was obtained (the 

surface detail in the computer model was mapped from the images, not calculated). 

Applied to gossamer structures, measuring only the corners and edges of a square solar 

sail 100 meters on a side will not provide adequate detail about surface features or 

contours, making accurate static and dynamic characterization impossible. To increase 

the density of measurement points, a grid of targets is used. The final result of a 

photogrammetric measurement performed in this manner is a three-dimensional “point 

cloud” that can serve as a detailed computer model. The models can then be evaluated to 

generate any desired measurements. 

3.2 The Photogrammetric Process 

 The basic photogrammetric process can be broken up into four steps as follows: 

camera calibration, high contrast images, target marking and matching, and bundle 
8-- 

adjustment. Each of these steps builds upon the previous to generate high-quality surface 

measurements. 

3.2.1 Camera Calibration 

 The first step in the photogrammetric process is the calibration of the cameras. 

This procedure, described in detail in References 9-11 and 25, calculates the focal length 

(zoom), location of the principal point, radial lens distortion, and decentering lens 

distortion of each camera. While some of these parameters can be estimated, such as the 

focal length of the lens and the principal point location, the calibration process measures 

them to micrometer precisions. For example, the principal point can be estimated to be at 

the center of the imager; however imperfections in the lens and internal camera 

components, slight inaccuracies in the manufacturing and assembly processes, etc. cause 

this assumption to be inaccurate. Knowledge of the lens distortion and the location of the 

principal point enable the computer to compensate for any deviation of the recorded 

image from that recorded by an ideal pin-hole camera. 

The radial and decentering (tangential) lens distortions are described by Equations 

1-3 and 4-5 respectively: 

7

3

5

2

3

1 δr = K r + K r + K r (1) 

2

0

2

0

2

r = (x − x ) + ( y − y ) (2) 

r r y y r

r r x x r

y

x

( )/

( )/

0

0

= −

= −

δ δ

δ δ

 (3) 

[ 2( ) ] 2 ( )( ) 2 0 0

2

0

2

1 δx = P r + x − x + P x − x y −y (4) 

[ 2( ) ] 2 ( )( ) 1 0 0

2

0

2

2 δy = P r + y − y + P x − x y −y (5) 

}
9

where δr is the radial displacement of an image point, (x,y) are the coordinates of the 

object point on the imager, (x0,y0) are the coordinates of the principal point, K1, K2, and 

K3 are calculated radial coefficients, and P1 and P2 are calculated tangential coefficients 

[9, 25]. 

The radial distortion (δr) is caused by variation in angular magnification as a 

function of angle of incidence. It creates either a “barrel” or a “pin cushion” effect in 

which images appear to billow toward or away from the center. As rays of light pass 

through the lens and aperture of the camera, they are distorted slightly by the glass and 

the fact that the aperture is not actually an infinitesimally small point. As shown in 

Figure 4, angles i (angle of incidence) and α are equal only for the ideal case 

corresponding to no refraction through the lens and an infinitesimally small aperture. In 

reality, however, the rays of light bend when passing through the lens and aperture, 

meaning that not only are i and α not equal, but the ratio of i to α is not constant over all 

values of i. This discrepancy is called the radial lens distortion, which is resolved into 

two components, δrx and δry in Equation 3 above. The maximum radial lens distortions 

for the cameras used in the applications in Chapters 7 and 8 are as high as 240 microns, 

corresponding to tens of pixels at the edges of the imager (see Appendix A). 

i

α

Figure 4 – Radial lens distortion angles 

Imager 

Object 

Aperture 
10

 Equations 4 and 5 show the calculation of the decentering, or tangential, lens 

distortion. This distortion is caused by any misalignment of the lens components, and the 

coefficients P1 and P2 depend on the camera focus setting. In general, as a camera is 

focused, pieces of glass within the lens move relative to each other. This movement is 

not exact, however, and the glass pieces tend to be slightly misaligned causing the 

rotational symmetry of the lens to be imperfect, creating a tangential distortion. Because 

the lens misalignment, and therefore P1 and P2, is unique for every focus setting, a 

constant focus setting must be maintained after calibrating the camera. To ensure that the 

focus setting could be repeatedly set to the same value, every camera discussed below 

was calibrated and used exclusively at infinity focus [9, 25]. 

Using focal length, principal point location, radial lens distortion, and decentering 

lens distortion values calculated in the camera calibration process, the photogrammetric 

software automatically removes any distortions of the images due to those parameters, 

enabling accurate measurements. To correct for possible changes in the calibrations over 

time and maintain measurement accuracy, the cameras were re-calibrated periodically. 

The parameters obtained from multiple calibrations are listed in Appendix A. 

3.2.2 High Contrast Images 

 Figures 5 and 6 show the second step in the photogrammetric process, the taking 

of high-contrast images. Traditionally, high contrast for measurement purposes is 

obtained using attached retro-reflective targets, shown in Figure 5, and underexposed 

images, shown in Figure 6. The camera flash illuminates the targets, which reflect light 

back to the camera hundreds of times brighter than a diffuse white surface. The 

underexposure darkens the rest of the image to the point where only the bright targets are 
11

clearly visible, creating a binary white-on-black image as shown in Figure 6. The binary 

nature of the images permits automatic and accurate detection of the target locations. 

While retro-reflective targets are highly effective and considered the industry standard, 

the added thickness, mass, and stiffness, combined with the required attachment time for 

potentially thousands of targets necessitate an alternative non-contact method for use on 

solar sails. The development and application of an approach using projected dots of light 

as targets is discussed in Chapters 6 through 8. 

 (a) With camera flash off (b) With camera flash on 

Figure 5 – Retro-reflective targets 

Figure 6 – Underexposed image of a 7 m boom used in photogrammetric measurement 

Illuminated 

Targets 
12

3.2.3 Target Marking and Matching and the Bundle Adjustment 

 In the third step of the photogrammetric process, multiple binary (high-contrast) 

images are loaded into the photogrammetric software and associated with the appropriate 

lens and camera calibration parameters. The targets are marked to sub-pixel accuracy 

using a centroiding process based on a least squares matching (LSM) algorithm with an 

elliptical template to account for off-normal viewing angles (see References 11 and 23), 

and the resulting points corresponding to the exact centers of the targets are matched 

across the photographs, as shown in Figure 7. An algorithm called a bundle adjustment is 

then run (step four) which simultaneously iterates on the camera locations and 

orientations from which the photographs were taken – a process called resection – and 

also calculates the 3-D point locations and corresponding precision values – a process 

called intersection. To obtain these point locations in three-dimensional space, a line is 

projected from each camera to the point, also shown in Figure 7. Note that projected 

light rays are infinitesimally wide, so in general the rays from multiple cameras never 

intersect. However, they do establish the bounds of an intersection region. The 

intersection region in space is assumed to contain the true point location. This method of 

calculating point locations requires each target to appear and be marked in at least two 

images. Note that using more photographs in the photogrammetric process increases the 

redundancy and hence the accuracy. 
13

.

.

.

.

.

.

. . . .

.

.

.

.

.

. .

. .

.

1

3

5

1

1

1

1

3

3

3

3

5

5

5

5

Figure 7 – Matching and triangulation of points 

3.2.4 Point Cloud 

The final result of the photogrammetric process is a set of 3-D points called a 

point cloud that, with an axis and scale defined, can be exported and measured. Figure 8 

shows a simple example in which photogrammetry was used to measure the straightness 

of the seven meter inflatable boom in Figure 6. The curved line shows the measured 

locations of the targets on the boom and is compared with a best-fit straight line. Note 

that the graph shown in Figure 8 is intended only to demonstrate one of many types of 

possible measurements from photogrammetric data and is not meant to provide any 

specific results. 

Imagers 
14

Figure 8 – Exported point cloud and best-fit straight line 

3.3 Videogrammetry 

Videogrammetry expands the methods and techniques of photogrammetry to 

multiple time steps creating dynamic data. The first images from multiple synchronized 

sequences of images are processed as a stand-alone photogrammetry project. The points 

are then tracked through the sequences of images with the camera locations assumed to 

be stationary, and at each time step the intersection is performed creating individual sets 

of three-dimensional points. The sets of points can then be linked together, tracking the 

movement of the point cloud from the first time step throughout the entire image 

sequence. This dynamic data can then be animated and analyzed. For a more detailed 

discussion of videogrammetry, see References 13 and 24. 

Max Deviation = 0.01m
15

4. HARDWARE 

 The hardware required for photogrammetric and videogrammetric measurements 

are separated into two categories: cameras and projectors. All of the cameras and 

projectors used to make measurements are described in detail, as well as the advantages 

and disadvantages of using each. 

4.1 Still Cameras 

 Photogrammetry, as discussed previously, uses photographs to make static shape 

measurements. While large format film cameras can be more accurate than digital 

cameras because of their greater resolution, digital images are preferred for the 

applications discussed in the following chapters due to the ease of import of measurement 

data and analysis with computers. Several different digital still cameras are available to 

consumers and professionals. The applications discussed below will demonstrate a 

progression from consumer grade hardware and software to test the feasibility of the 

method for solar sail applications to professional and custom equipment to refine the 

process and generate high quality measurements. The applications in Sections 7.1 and 

7.2 used four consumer grade Olympus E20n cameras (Figure 9(a)) while the application 

in Section 7.3 used four professional Kodak DCS 760M cameras (Figure 9(b)). These 

chapters also discuss the pros and cons of the transition from the consumer cameras to the 

professional. Figure 9 shows the cameras with attached ring flashes, which provide more 

uniform illumination of targets than standard built-in flashes. Specifications for both 

cameras are listed in Table 1 below. 
16

 (a) Olympus E20n with ring flash (b) Kodak DCS 760M with ring flash 

Figure 9 – Digital still cameras 

 Table 1 – Still camera specifications 

Olympus E20n Kodak DCS 760M 

CCD size (pixels) 2560 x 1920 3032 x 2008 

CCD size (mm) 8.704 x 6.582 27.288 x 18.072 

Dynamic Range 8 bit color 12 bit monochrome 

Lenses 

Type Non-removable Removable 

Focal Length (mm) 9 – 36 Variable (25.0) 

Aperture f/2.0 – f/11.0 Variable (f/2.8 – f/22) 

 The professional-grade Kodak camera has obvious improvements over the 

consumer-grade Olympus camera, as indicated by the data shown in Table 1. It has a six 

megapixel imager versus the five megapixel Olympus. The charge coupled device 

(CCD) imager in the Kodak is physically larger than the Olympus increasing its light 

sensitivity, and the Kodak has a greater dynamic range. The Olympus is manufactured 

with an attached zoom (variable focal length) lens while the lens of the Kodak is 

removable meaning the camera can be fitted with a variety of fixed focal length and 

zoom lenses. Parenthetical values in Table 1 denote the values for the lens used in the 

applications. The aperture size is variable on both cameras to allow the user to change 

the amount of light striking the imager. Larger apertures, while enabling shorter 

exposure times used to eliminate blurring when taking photographs with a hand-held 
17

camera, result in a shorter depth of field than smaller apertures. Accordingly, small 

apertures (f/9.0 – f/11.0) were used in both cameras to ensure that objects both close to 

and far from the cameras would be simultaneously in focus. The differences in the two 

cameras with respect to the accuracy and precision of the measurements they provide are 

discussed in detail in Chapter 5. While the results obtained using the professional camera 

are considerably better than those obtained using the consumer camera, the improvement 

comes at a price. The Kodak DCS 760M is approximately six times the cost of the 

Olympus E20n. 

It should also be noted that digital cameras are capable of performing many 

operations that enhance the produced images. Color balancing, image compression, antialiasing filters, sharpening, etc. all make the image look better, but complicate scientific 

measurements by altering or adding interpolation. To minimize the negative impact of 

the enhancements, all filters and sharpening were turned off and the images were stored 

with the least amount of compression possible. 

4.2 Video Camera 

Videogrammetry, like photogrammetry, relies on multiple images from various 

viewing angles to generate the desired 3-D models. To yield a sequence of images in 

time, the method requires multiple images at each time step, necessitating two or more 

synchronized video cameras. The Pulnix TM-1020-15 digital video camera (Figure 10) 

is a high quality scientific video camera, and a two-camera synchronized Pulnix system 

was used for the videogrammetry test. Figure 10 shows the camera with an attached fiber 

optic ring light used to provide even illumination of the retro-reflective targets. The 
18

specifications for this camera are listed in Table 2 below. As noted previously, 

parenthetical values indicate the parameters of the specific lens used in the test. 

Figure 10 – Pulnix TM-1020-15 digital video camera with ring light 

Table 2 – Video camera specifications 

Pulnix TM-1020-15 

CCD size (pixels) 1008 x 1018 

CCD size (mm) 9.072 x 9.162 

Frame Rate (Hz) Variable, 15 max 

Dynamic Range 10 bit monochrome 

Lens 

Type Removable 

Focal Length (mm) Variable (12.5) 

Aperture Variable (f/1.4 – f/22.0) 

 The TM-1020-15 has a one megapixel resolution, lower than either of the still 

cameras discussed in Section 4.1, but does have a large 9 μm pixel size like the Kodak 

DCS 760M. This resolution is typical, however, of scientific-grade video cameras 

operating at maximum frame rates of 15 Hz. At one megabyte per image, fifteen images 

per second, and two cameras, the system computer must store 30 MB of data each second 

at maximum frame rates. During data collection the image sequences are stored in the 

computer’s RAM and are only copied to the disk after the test. The video cameras have 
19

dynamic ranges and lens properties that are similar to those of the still cameras. All of 

the cameras discussed above enable non-contact, full-field, simultaneous data collection. 

4.3 Projectors 

 As discussed previously, traditional photogrammetry uses attached retro-reflective 

targets that would add unacceptable mass and stiffness to the ultra-thin membranes being 

measured. To avoid these unwanted effects, grids of circular targets were projected onto 

the test articles by the projectors shown in Figure 11. Figure 11(a) shows the Kodak 

Ektagraphic, a consumer-grade 35 mm slide projector that uses a fairly low-power 

incandescent bulb. 

The modest intensity of the Ektagraphic combined with the high reflectivity of the 

aluminized solar sail membranes necessitated exposure times as long as 30 seconds to 

obtain images of optimal contrast. To combat these long exposure times, a theater 

version of the Kodak Ektagraphic (Figure 11(b)) was subsequently used. It uses a highpower halogen bulb thereby producing higher intensity patterns than the consumer 

version. The greater intensity allows the exposure times of the cameras to be decreased 

significantly. To upgrade another step to professional hardware, a Geodetic Systems Inc. 

(GSI) Pro-Spot projector (Figure 11(c)) was used in the application discussed in Section 

7.3. It is a high-intensity flash projector capable of projecting up to 22,500 dots versus 

the maximum of 5,500 dots for the other projectors. The Pro-Spot is part of GSI’s turnkey industrial photogrammetry system, but was purchased separately for use in 

measuring solar sail test articles. 
20

 (a) Kodak Ektagraphic (b) Kodak Ektagraphic Theater 

 (c) Geodetic Systems Inc. Pro-Spot (d) Proxima LX2 Digital 

Figure 11 – Projectors 

 The Proxima LX2 digital projector (Figure 11(d)) was used for the 

videogrammetry application. Again a consumer product, its low intensity and resolution 

would limit its usefulness in measurements of highly reflective membranes. The 

projector did not, however, negatively affect the accuracy or precision of the 

videogrammetric measurement here because the test article in the experiment is 

comprised of diffuse white (non-aluminized) Vellum membranes. The major advantage 

of the digital projector is its ability to project custom dot patterns from computer files that 

can be easily and rapidly altered. 
21

5. ACCURACY, PRECISION, AND REPEATABILITY 

 Accuracy, precision, and repeatability quantify the error and noise present in a 

measurement. The photogrammetric measurements discussed here have three sources of 

experimental error and noise: the cameras, the projector, and the imaged targets 

(measured object). Any, or more likely all of these components or bodies may move 

slightly during data collection or in some other manner introduce noise and error that 

detract from the overall quality of the measurement. The error caused by the cameras and 

targets are tracked or estimated by the photogrammetry software, and are examined in 

detail below. The error caused by the third body in the system, the projector, is not, 

however, accounted for individually as in the case of the other two bodies. Rather, the 

projector is assumed to be stationary, and the error and noise for which it is responsible is 

grouped with the other two error sources. 

 

5.1 Overview 

The quality of any measurement can be described by three separate terms, 

accuracy, precision, and repeatability. The accuracy of a measurement expresses how 

close the process came to producing the true value. It can only be determined by 

comparing the results obtained using one measurement method to the results obtained 

from a higher quality system known to be at least twice as accurate. In the case of the 

measurements discussed here, higher quality comparable systems were not available for 

the static cases; however the level of maturity of photogrammetry as a scientific process, 

the error estimates produced by the software, and qualitative assessment are considered 

sufficient validations of the measurements. In the dynamic case, the videogrammetric 

results were compared with those of a high-end laser vibrometry system. 
22

The precision of a process can be thought of as the resolution of the measurement. 

For example, the measured weight of a cruise ship is usually precise to about one ton 

whereas the measured weight of a human being is usually precise to about one pound. 

The precision of the photogrammetric measurements performed below is discussed in the 

next section. Finally, the repeatability of the system is the ability of a process to generate 

the same results while measuring the same object multiple times. These three factors are 

all relevant to a discussion of the overall quality of a scientific measurement. [23, 25] 

5.2 Photogrammetric Error Estimates

The commercial photogrammetry software used in the applications below reports 

three error estimates: marking residual, tightness, and precision [23]. These estimates 

are calculated either directly at the end of the photogrammetric process or by error 

propagation techniques. A finite amount of error is present in all of the initial steps of the 

photogrammetric process, from the camera calibration to the capturing of the images to 

the marking of targets. These errors are embedded within the inputs of the bundle 

adjustment algorithm and are therefore propagated through the calculation. The software 

tracks or estimates the errors inputted into the algorithm, and produces precision 

information after the processing is complete. The marking residuals and tightness 

information are calculated independently at the end of the process and are described 

below. 

Photogrammetric precisions are usually expressed as ratios of the form 1:10,000, 

meaning one part in 10,000. In this case, if the measured object is one meter in size, the 

measurement would be precise to one meter divided by 10,000, or 0.1 millimeters (100 

microns). The manner in which this error information is presented varies depending on 
23

the software package, but for all of the applications discussed here there is a 95% 

probability (plus or minus two standard deviations) that the true location of the point falls 

within the error ellipsoid created from the precision numbers for the X, Y, and Z 

directions. X, Y, and Z precisions for each three dimensional point are calculated by the 

error propagation technique discussed previously. Tightness estimates are calculated by 

determining how close the projected rays come to intersecting the point (see Section 3.2), 

and residuals are calculated for each point on each image by determining how far the 

point in the image is from the point projected from the calculated 3-D location. Precision 

estimates are reported in working units of the project, tightness estimates in percentages, 

and marking residuals in pixels [23]. 

5.3 Camera-Related Factors 

Physical properties of the cameras used the photogrammetric process have a 

significant impact on the precision and accuracy of the measurement. The type of 

imager, type of lens, quality of manufacture, etc. are important contributing factors. 

Several properties of the Olympus cameras detract from maximum achievable accuracy 

when compared with the Kodak cameras. While both Olympus E20n and Kodak DCS 

760M cameras use CCD imagers, the E20n has a five megapixel resolution compared to 

the six megapixel DCS 760M (Table 1). The higher resolution of the professional 

camera yields a greater number of pixels per target and therefore increases the amount of 

information being used in the LSM centroiding phase, making the process more accurate 

at finding the exact center of the targets. The physical size of the pixels on the Kodak 

imager is 9.0 microns versus the smaller 3.4 microns of the Olympus. Larger pixels have 

a greater sensitivity to light and reduce the amount of noise present in images, and are 
24

therefore nominally twice as precise [25]. In summary, the Kodak DCS 760M has a 

greater number of more sensitive pixels than the Olympus E20n, which makes it more 

precise in scientific measurements. 

 The third row of Table 1 shows the difference in the dynamic range of the two 

cameras. The consumer Olympus is an eight-bit color camera that produces standard 

eight-bit images while the professional Kodak is a monochrome twelve-bit camera. The 

increase in the dynamic range of the professional over the consumer camera again yields 

a greater sensitivity to light and therefore accuracy. Another limiting factor of the 

Olympus camera is its color CCD. To produce color images, most cameras attempt to 

mimic the structure of the human eye. The cones of the eye, which sense color, are 

comprised of three separate types. Approximately 60 percent of the cones see only green, 

30 percent see only red, and 10 percent see only blue. The brain then combines the 

intensity information from each of these sets to create a single, cohesive color image. 

Like the cones of the human eye, each pixel on a digital imager can only see one color. 

Most CCD’s are comprised of 50 percent green pixels, 25 percent red pixels, and 25 

percent blue pixels arranged in what is called a Bayer checkerboard pattern, roughly 

paralleling the distribution of cones in the eye. For each image, the on-board camera 

processor runs an interpolation algorithm to assign each pixel intensity values for the 

other two colors it cannot see, thereby creating a cohesive image. The interpolation 

reduces the effective resolution of color compared to monochrome cameras for 

photogrammetric measurements [27]. 

 Information regarding the lenses of the two cameras is also listed in Table 1. The 

built-in zoom lens on the Olympus has several more glass pieces through which light 

must pass to reach the imager, leading to greater distortion of the light rays and again 
25

decreasing its accuracy. The fixed focal length lenses used on the Kodak cameras are 

inherently more stable for precision photogrammetric measurements than zoom lenses. 

 From the above discussion one might receive the impression that the consumer 

Olympus cameras are drastically less accurate than the professional Kodak cameras, 

which is not the case. The Olympus E20n is a high-quality single lens reflex (SLR) 

consumer camera (fixed lens) that has produced measurement precisions up to 1:30,000, 

or one-fourth that of top-end industrial turn-key systems at less than one fiftieth of the 

cost [28]. The Kodak DCS 760M camera is approximately five times the cost of the 

Olympus camera, yet only doubles or triples its measurement precision. In effect, it is 

easy to get an answer with photogrammetry using basic hardware, but as with any 

measurement system, a principle of diminishing returns applies making it expensive to 

obtain the highest measurement precision and accuracy. 

 As stated previously, videogrammetric measurements were performed using only 

two Pulnix TM-1020-15 video cameras instead of the four cameras used in the static 

measurements. More cameras with greater resolution and higher frame rates can be 

added to the system, but with each improvement comes a requirement for higher 

computer bandwidth and a larger total amount of data that must be stored by the 

computer per unit time. To maximize the accuracy with only two cameras, however, the 

TM-1020-15 does use large 9.0 micron pixels and a monochrome CCD. Noise level tests 

for the Olympus, Kodak, and Pulnix systems were conducted and are discussed in the 

following section, and the precision of the individual measurements are discussed in the 

sections detailing the four application examples. 
26

5.4 Noise Tests 

 Knowledge of the signal-to-noise ratio of experimental data is important to 

understanding the results of a test. It is essential that results are obtained from actual 

response of the system and not from background noise inherent in every experiment. 

Related to photogrammetry, the noise level of the camera systems is one of the factors 

governing measurement resolution, meaning features cannot be characterized with 

confidence below the noise floor. For dynamic data the noise floor determines the 

smallest displacements from one frame to the next that can be detected. 

 The noise floor of each of the camera systems was measured by tracking the 

calculated position of stationary points over a period of time. The still camera systems 

took time-lapse images over several minutes while the video cameras simply recorded 

stationary points as part of a dynamic measurement. The test setup is shown in Figure 12 

below. 

Figure 12 – Noise test setup 

 Three boards with attached retro-reflective targets on strips of black tape were 

imaged. Because attached instead of projected targets were used, the third source or body 

of error (projector) was eliminated allowing direct calculation of the noise from only the 
27

cameras and targets. The slender boards on the left and right were mounted on stationary 

stands while the square board in the middle was allowed to swing freely to establish a 

baseline against which to compare the stationary points (see Reference 24). For all three 

cases (one for each camera type), the computed locations of the points on the stationary 

sidepieces were plotted versus frame number, called epochs, to generate the desired noise 

measurements and are shown in Figures 13, 14, and 15. Also shown in these figures is 

the difference between the maximum and minimum points in the series, denoted by the ∆

value. Note that in Figures 13 and 14 one epoch is equal to 12 seconds and in Figure 15 

each epoch is equal to one fifth of a second. 
28

(a) Left camera 

(b) Right camera 

Figure 13 – Olympus E20n plots of a stationary point over time 

∆≅ 0.2 

∆≅ 0.8 

∆≅ 0.2 

∆≅ 0.4 
29

(a) Left camera 

(b) Right camera 

Figure 14 – Kodak DCS 760M plots of a stationary point over time 

∆≅ 0.5 

∆≅ 0.3 

∆≅ 0.3 

∆≅ 0.3 
30

(a) Left camera 

(b) Right camera 

Figure 15 – Pulnix TM-1020-15 plots of a stationary point over time 

∆≅ 0.1 

∆≅ 0.1 

∆≅ 0.07 

∆≅ 0.04 
31

Table 3 – Standard deviations of noise plots 

Olympus Kodak Pulnix 

Left Right Left Right Left Right 

X Position 

Mean (pixels) 464.252 233.428 2786.975 2697.373 945.641 948.920 

Y Position 

Mean (pixels) 371.400 591.491 352.901 187.241 712.623 866.843 

σx (pixels) 0.077 0.15 0.11 0.046 0.014 0.0086 

σy (pixels) 0.050 0.036 0.049 0.065 0.015 0.0067 

2 σ (pixels) 0.125 0.185 0.155 0.110 0.030 0.015 

Overall Noise 

(pixels) 0.185 0.155 0.030 

 The plots in Figures 13 through 15 show the calculated center of a stationary point 

using the Olympus, Kodak, and Pulnix camera systems. Ideally these graphs would 

exhibit no trends or bias, and simply show a random scatter plot, as would be expected 

from noise. Bias is evident, however, in Figures 13 and 14 and will be discussed below. 

Table 3 shows the means and standard deviations (σ) of the plots in Figures 13, 14 and 

15, without correction for the trends. The row labeled “2 σ (pixels)” indicates that 95% 

(2*σ where σ is the average of σx and σy) of the noise in the left camera of the Olympus 

system falls within 0.125 pixels of the mean value and within 0.185 pixels of the mean 

value in the right camera. The larger of the two values, 0.185 pixels, is considered the 

overall noise floor of the Olympus system. Similarly, the overall noise floors of the 

Kodak and Pulnix systems are calculated to be 0.155 and 0.030 pixels respectively. 

 Expressed as a ratio of noise to number of pixels in the x-direction on the imager, 

the Olympus E20n noise floor is 1:14,000, the Kodak DCS 760M noise floor is 1:20,000, 

and the Pulnix TM-1020-15 noise floor is 1:34,000. Note that with the trends removed, 

the noise estimates for the Olympus and Kodak systems can be reduced by at least a 

factor of two. The targets imaged in photogrammetric measurements usually appear at 

least five pixels in diameter, and are therefore well above the level of disturbance caused 
32

by noise present in the systems. The motion of the object recorded from one image to the 

next in the videogrammetry test was also well above the noise floor of the system. 

 The plots in Figures 13 and 14 above show unexpected trends in the movement of 

a photographed stationary point. Obviously the calculated position of a stationary point 

should not move in any predictable manner over time, meaning the apparent motion is 

caused by random noise present in the system. This noise might include air currents, 

ground vibrations, settling of the tripod or board stand, electronic static, camera heating 

etc. The Olympus and Kodak camera systems were tested until the trend appeared to 

level, leading to the disparity in number of epochs used. 

 To examine the effects of the biases present in the noise data from each camera 

system, the total spread of the series was printed on the plots in Figures 13 – 15. The 

spread, ∆, is equal to the difference in the maximum point value in the series and the 

minimum point value in the series. Figure 13 shows that the Olympus cameras have the 

largest ∆’s, caused by the most pronounced trends in the data. The Pulnix cameras 

(Figure 15) have the smallest ∆’s, as little or no bias affects the system. A larger ∆ value 

indicates more uncertainty in the location of the photographed points and a greater 

probability of noise influencing the measurements. 

 To visualize the biases, occurrence densities are plotted in Figure 16 for each 

camera system. The graphs were generated by dividing the ∆ value for each series into 

14 equal blocks and summing the occurrence of points within each block. Density plots 

for the most biased of the four series from each of Figures 13, 14, and 15 are shown. 

Figure 16(c) shows an approximately symmetric bell curve versus those in Figures 16(a) 

and 16(b) in the Pulnix TM-1020-15 series, expected from random noise with little or no 

bias. Most of the points are clustered near the average value of the series, with a minimal 
33

number of extreme points lying outside the curve. Figures 16(a) and 16(b) by contrast 

show asymmetric curves of the Olympus E20n and Kodak DCS 760M data heavily 

influenced by a disproportionate number of points at extreme values of the series. These 

curves clearly demonstrate that the biases present in the Kodak and Olympus camera 

systems affect the stationarity and therefore randomness of the data, and lead to the 

conclusion that external, non-random factors influenced the systems. 
34

0

1

2

3

4

5

6

7

8

9

233.199233.231233.264233.297233.330233.363233.396233.429233.462233.495233.528233.560233.593233.626233.894

Pixles

Fre

quenc

y

(a) Right Olympus E20N camera measured X position 

0

5

10

15

20

25

352.833352.849352.865352.881352.897352.913352.929352.945352.961352.977352.993353.009353.025353.041

Pixels

Fre

quenc

y

(b) Left Kodak 760M camera measured Y position 

0

10

20

30

40

50

60

866.825866.828866.831866.834866.837866.840866.843866.846866.849866.852866.855866.858866.861866.864

Pixels

Frequency

(c) Right Pulnix TM-1020-15 camera measured Y position 

Figure 16 – Occurrence density plots demonstrating biases 
35

The biases in the data cause the calculated centers of stationary targets to migrate 

over time. All of the point centroids in each of the images migrate in a diagonal fashion 

as shown in Figure 17, a trend that has been observed in other tests. The exact cause of 

this migration is still under investigation, but is likely due to global effects such as 

camera heating or tripod settling. Again it should be noted that the size of the measured 

targets (signal) is much larger than any biases or noise present in the systems. 

Figure 17 – Migration of a measurement of a target centriod in time
36

6. RETRO-REFLECTIVE VS PROJECTED TARGETS 

 High resolution photogrammetric measurements rely on high-contrast images and 

a high density of targets. For example, the general shape of the boards in Figure 12 could 

have been measured using only the four corners and four edges, but this does not provide 

information about the object’s surface shape. Attaching retro-reflective targets to the 

face of the board enables measurement of its contour and surface features, in addition to 

the edge and corner locations. Projected targets can be used instead of retro-reflective 

targets to avoid altering the responses of the measured objects, but introduce 

experimental and numerical complications discussed here. 

6.1 Retro-reflective Targets 

Retro-reflective targets are manufactured in a variety of shapes and sizes. 

Circular targets can be punched from sheets of retro-reflective material, peeled off sheets 

of individual targets, or cut from rolls of tape with targets spaced at a precise, repeating 

interval. Specific shapes or patterns of targets can be identified as individual codes by 

photogrammetry software, and pieces of carbonite can be machined to sub-micrometer 

precision with targets at exact spacing. Retro-reflective targets have been used to 

measure objects ranging in size from the 305-meter Arecibo Observatory [29, 30], to a 

five meter inflatable lenticular reflector [10], to micro air vehicles less than 20 

centimeters in size. This method of targeting is considered the industry standard in 

photogrammetric measurements [31]. 

 Retro-reflective targets used in conjunction with flash illumination, fast shutter 

speeds, and small apertures appear as bright white circles on a black, underexposed 

background (see Figures 5 and 6). Retro-reflective material is manufactured by bonding 
37

small, silver-coated glass spheres to a substrate, usually a paper-based material. The 

spheres are approximately 50 microns in diameter and they are attached using about 25 

microns of epoxy. The coating on the top halves of the spheres is then chemically 

removed, leaving only the side by side reflective hemispheres, resulting in a range of 

intense reflections approximately ±60o from normal. 

 For the majority of close-range photogrammetric applications, the thickness, 

weight, and attachment time associated with using retro-reflective targets are 

inconsequential compared to the superior results they provide. When used in gossamer 

applications, however, the added mass and stiffness may seriously alter the static and 

dynamic properties being measured. The average thickness of a retro-reflective target is 

100 microns including the substrate, significantly greater than solar sail membranes, 

which can be less than five microns thick. Aside from the additional thickness, the mass 

and stiffness associated with adding retro-reflective targets to a membrane can have a 

great impact on its static and dynamic properties. Consider a square solar sail membrane 

100 meters on a side. At 10,000 square meters in size, this membrane has a mass of just 

70 kg based on a seven gram per square meter areal density. Assuming a modest 

measurement density of 10 targets per square meter – some applications use 2500 targets 

per square meter – 100,000 retro-reflective targets would have to be attached to the 

surface of the sail. The combined mass of these targets may be as much as that of the sail 

itself. Such a large number of targets would also require an impractical amount of time 

to attach. 

 In addition to the physical drawbacks discussed above, a small geometric 

distortion occurs when using retro-reflective targets. Light from the camera flash reflects 

off the targets, not the object to which they are attached, meaning that in reality the target 
38

and not the object surface is being measured. The center of the target may be anywhere 

from 50 to 75 microns from the surface of the object, and adds uncertainty to the 

measurement, especially when imaging ultra-thin, wrinkled membranes. 

6.2 Projected Targets 

 As an alternative to physically attaching retro-reflective targets, white circular 

targets were projected onto the solar sail test articles. Called dot projection, this targeting 

method has several advantages over attached targets. Projected targets do not add mass 

or stiffness to the object, they do not have to be individually attached, and because the 

light reflects off the surface of the object, it is the actual surface that is measured instead 

of the optical center of a target located slightly above the surface. Target patterns, sizes, 

and densities can also be varied with ease, and there is no risk of membrane damage 

associated with changing the pattern. 

 The major drawback of dot projection when used on reflective surfaces such as 

solar sails involves the non-uniform contrast of the projected patterns. Within the ±60o

range of retro-reflective targets, almost identical amounts of light will be reflected by all 

of the targets (a result of the geometry of the spheres of which the material is comprised) 

regardless of angle to the camera or the reflective properties of the material being 

measured. The dot projection technique, however, requires a single stationary projector 

with multiple cameras imaging the created pattern, meaning only this single source of 

light is used instead of multiple flashes. For materials that scatter light in all directions 

more or less equally such as diffuse white surfaces like projector screens, the relationship 

of the camera location to the light source location is inconsequential. The same level of 

contrast is expected from virtually all camera positions. If the material being measured is 
39

not diffuse but, for example, specular as in the case of the solar sails, each incident light 

ray is reflected almost entirely in one direction according to the principle of angle of 

incidence equals angle of reflection. Therefore contrast of the pattern varies with camera 

angle, with camera locations closer to the angle of reflection seeing greater light intensity 

than camera locations farther from the angle of reflection. For wrinkled membrane 

surfaces in which the normal direction to the surface varies with location on the 

membrane, pattern contrast not only varies with camera angle, but also with target 

location yielding a set of images with non-uniform contrast in each individual image and 

also across other images. 

 Figures 18 and 19 show a test preformed to demonstrate the contrast challenges 

associated with using dot projection to measure highly reflective membrane surfaces 

versus diffuse white surfaces. Figure 18 shows the setup used to compare the reflective 

surface of an aluminized wrinkled Kapton membrane with the matte white surface of 

Vellum. A dot pattern was projected onto the area indicated and was imaged by a camera 

at multiple shutter speeds. Figure 19 shows the images generated at three different 

exposure times. 

Figure 18 – Target contrast comparison test 

Area Imaged 

Aluminized 

Kapton 

Matte White 

Vellum 
40

 (a) 2.5 second exposure (b) 10.0 second exposure 

(c) 30.0 second exposure 

Figure 19 – Comparison of multiple exposure times using dot projection 

All of the images in Figure 19 display the non-uniform contrast gradient that 

occurs when photographing the Kapton membranes, shown on the left, as well as 

demonstrating the necessity for long exposure times. The image in Figure 19(a) has 

sufficient contrast in the Vellum membrane to make the photogrammetric measurements 

at exposure times of just 2.5 seconds compared to the 30 second exposure time in Figure 

19(c) to generate adequate contrast in the Kapton sail. Also evident in the lower left 

corner of Figure 19(c) are the hot spots created by membrane curling. The long exposure 

times, contrast gradients, and hot spots will be discussed in greater detail in Chapter 7. 
41

 Another complication associated with dot projection occurs in the area of 

dynamics. In the case of retro-reflective targets attached to the object, dynamic data can 

be generated for specific object points as well as the object as a whole. Attached targets 

allow three-degree-of-freedom tracking, meaning that each target can be tracked in the x, 

y, and z directions. When using dot projection, however, the projector and therefore the 

pattern, remain stationary. Projected targets on a moving structure can only displace 

along the rays of light, either towards or away from the projector, making in-plane 

motion nearly impossible to characterize. However dot projection does measure the 

correct shape of the structure at each instant of time, even though it cannot follow 

specific object points. This type of point movement (only along the rays of light) implies 

videogrammetry using dot projection is very similar to laser vibrometry measurements 

(see Chapter 8), which will be used as a standard against which the videogrammetry 

results are compared. 
42

7. STATIC SHAPE MEASUREMENT EXAMPLES 

 The three measurement examples discussed in this chapter were conducted for 

dual purposes: to develop measurement methods suitable for use on actual solar sail 

spacecraft and to obtain measurements for validation of structural analytical models. The 

experiments used low-fidelity, generic solar sail test articles currently at NASA Langley 

Research Center. These low-fidelity test articles are sub-scale models manufactured from 

solar sail quality materials but are not directly scalable to full size solar sails. The 

developed methods will be applied to other current and future high-fidelity gossamer test 

structures and space missions. 

 The first example is a low density full-field measurement of the test article, the 

second is a high resolution measurement of the wrinkle pattern of a small section of the 

sail, and the final example is full-field high resolution test to simultaneously characterize 

the wrinkle pattern of the sail as well as a large amplitude global deformation. 

7.1 Low Density Full-field Two Meter Kapton Solar Sail 

 The experiment described below was designed to assess the feasibility of using 

projected circular targets instead of attached retro-reflective targets on highly reflective 

membrane surfaces. It was intended as a demonstration of the technique and was not 

expected to generate a high resolution characterization of surface details. 

7.1.1 Test Setup 

 The two meter per side, square, aluminized Kapton solar sail test article shown in 

Figure 20 was selected for static shape measurement because of its continuity (other test 

articles are divided into four quadrants and do not have steady-state wrinkle patterns). 
43

The Kodak Ektagraphic projector (Figure 11(a)) created a pattern of approximately 400 

dots and four Olympus E20n cameras shown in Figure 9(a) (f/9.0, no sharpening) at 

approximately 90o separation at the corners of the sail simultaneously photographed the 

sail, as shown in Figure 21. Four synchronized cameras were used instead of a single 

roving hand-held camera to avoid possible membrane movement between images. 

Figure 20 – Two meter Kapton solar sail test article 

Figure 21 – Kapton two meter full field test setup 

Camera 

Projector Point Cloud 
44

7.1.2 Images

Figure 22 shows actual images used in the photogrammetric processing, with the 

dot pattern clearly visible on the surface of the sail. The images are underexposed to 

create high-contrast targets discussed in Chapter 3. 

Figure 22 – Images used in photogrammetric processing (2 of 4) 

 Several trouble spots are evident in the images in Figure 22. The long exposure 

time (30 seconds) required to obtain the images due to the reflective nature of the 

membrane allowed ambient light to also image on the sail, causing the background to 

appear much brighter than desired. In the left image of Figure 22, ambient light imaging 

on the upper right corner of the sail drastically reduced the contrast between the dots and 

the membrane in that area, leading to a loss of target information. Also, there are several 

“hot spots” in areas where the sail curled, reflecting much more light into the camera than 

in the rest of image and washing out all data (i.e. targets) in that particular region. Two 

hot spots due to edge curling are visible in both bottom corners of the image on the left 

and another is visible in the upper left corner of the image on the right. The low density 

of the dot pattern creates a low resolution measurement condition, meaning only the 

overall shape and not the intricate wrinkle pattern seen in Figure 20 can be adequately 

characterized from these images. While the long exposure time, hot spots, and low 
45

resolution do not preclude measurement, they detract from the achievable accuracy and 

precision of the process and will be addressed in the application discussed in Section 7.2. 

7.1.3 Photogrammetric Processing 

 Figure 21 shows an image of the point cloud and camera locations created from 

the 3-D Viewer in the photogrammetry software, which can be studied to verify that the 

project processed correctly and that the setup and result are as expected. The four camera 

stations (one in each corner of the sail) and the final point cloud are positioned as 

expected. This result demonstrates that the four camera positions have been resected 

successfully and that the point location calculations have produced a nearly planer threedimensional cloud, expected when measuring a predominantly flat membrane. 

Figure 23 demonstrates how the imperfections in the images in Figure 22 affect 

the photogrammetric processing of the project. It shows a close up view of the upper 

right corner of the sail in the left image of Figure 22 after the processing was completed. 

Figure 23 – Marked points in upper right corner of the solar sail test article 

As discussed earlier, the ambient light in the room led to a loss of data in this region of 

the membrane. Some targets in the area are not visible and therefore could not be 
46

marked. Several other targets do not have sufficient contrast to be marked using the 

automatic LSM process and therefore were marked by hand, reducing precision. The 

greatest amount of wrinkling occurs at the corners of the membrane making them 

important in the measurement. The ambient light, therefore, has caused a loss of 

accuracy and data in one of the most critical areas of the sail. 

7.1.4 Error Estimates 

 The error estimates, discussed in Chapter 5, calculated by the photogrammetry 

software for this application are listed in Table 4 below. The largest residual is an 

estimation of the accuracy of the project. Residuals less than one pixel are considered 

acceptable error for the highly reflective membranes discussed here. In this application, 

due to the low contrast and marking of several of the targets by hand, the largest residual 

was quite high at 4.8 pixels, and only 63% of the points were accurate to less than one 

pixel residual. The average of all the precision values for all of the points in the project 

was calculated to be 0.16 mm, meaning that overall for the two meter sail, the 

measurements were precise to 1:12,500. Despite the faults in the images, reasonable data 

were still obtained; however the residual and precision numbers do suggest that a great 

deal of improvement is possible. Methods for obtaining such improvements will be 

shown in Section 7.2. 

Table 4 – Photogrammetric error estimates 

Largest Residual 4.8 pixels 

Points below 1 

pixel residual 63.0% 

Average Precision 

(mm) 0.160 

Precision (parts per 

unit object size) 1:12,500 
47

7.1.5 Results 

 The coordinates of the three-dimensional points (point cloud) corresponding to 

centers (centriods) of the targets were exported for measurement. These data were 

imported into a contour mapping program, which was used to visualize the membrane 

shape. The first step in the visualization involves the creation of a continuous surface 

from the imported, discrete data – a process called gridding. A grid consists of a set of 

the maximum number of uniformly spaced points creating the continuous surface that do 

not exceed a 100 x 100 matrix. Several different algorithms may be selected by the user 

to create the grid, depending on the amount of smoothing and interpolation desired. The 

default method is a Kriging algorithm that follows trends in the data creating ridges and 

valleys instead of bull’s-eyes around higher points and holes around lower points. The 

Kriging algorithm is a natural choice for displaying wrinkle patterns and was used to grid 

the data in Sections 7.2 and 7.3. For the low-resolution condition here, however, a Local 

Polynomial gridding algorithm was selected. The Local Polynomial method uses a 

weighted least squares fit around each inputted point, creating a series of small, joined 

surfaces instead of a single continuous surface. This algorithm produced better results 

than the Kriging for the mostly planar data gathered here. Subsequently the grid can be 

displayed in a variety of different plots, some of which are shown below. [32] 

The results of the mapping for the gathered photogrammetry data are shown in 

Figure 24. The contour plot and contour surface show the overall low-resolution shape of 

the membrane. These types of surface measurements are useful for assessing the overall 

shape of the structure (e.g. is it warped or flat), but are of little value for characterizing 

wrinkle patterns, which requires high-resolution data. However this experiment does 

demonstrate the feasibility of using non-contact dot projection photogrammetry to obtain 
48

surface shape models of highly reflective aluminized membranes. A test to measure 

wrinkle pattern and amplitudes of this same test article is detailed in Section 7.2. 

(a) Contour map 

(b) Contour surface (Z Position amplified) 

Figure 24 – Results for low density measurements of the solar sail test article 

A B 

D C

A

B C

D Y Position (m) 

X Position (m) 

Z Position (m) 
49

7.2 Wrinkle Test of Two Meter Kapton Solar Sail 

The wrinkle test described here was performed to investigate if dot projection 

photogrammetry could successfully characterize small amplitude surface features on 

highly reflective solar sail membranes. Such data are important for validation of analytic 

structural models and will lead to better prediction of the contribution of wrinkling to loss 

in propulsive efficiency, to predicting and preventing localized hot spots, to 

understanding membrane dynamics, and to providing an indication of the corresponding 

film stress. 

7.2.1 Test Setup 

The same two meter aluminized Kapton solar sail test article used in Section 7.1 

and shown again in Figure 25 was selected. 

Figure 25 – Two meter Kapton solar sail test article 

The observed wrinkle pattern is a complex phenomena significantly affected by the seam 

running across the middle of the membrane, discrete corner loads, and gravity. The 

pattern is marginally stable, changing somewhat with small external disturbances such as 

Area Imaged 
50

slight air currents. To obtain a consistent set of images, the four cameras were again fired 

simultaneously freezing the shape. Using traditional attached retro-reflective targets in 

this application is clearly inappropriate. 

The theater version of the Kodak Ektagraphic projector (Figure 11(b)) was used to 

create a grid of approximately 5100 dots on a 0.9 x 0.5 meter area on the right side of the 

sail, as indicated in Figure 24. The same four Olympus E20n cameras (Figure 9(a)) used 

in Section 7.1 arranged in the same configuration, one in each corner, simultaneously 

photographed the grid (f/9.0, no sharpening) instead of a single roving camera, again 

done to eliminate the chance of inadvertent membrane movement. The reflectivity of the 

aluminized coating of the Kapton that led to the use of long exposure times in Section 7.1 

was again a complicating factor, but was compensated for much more effectively. The 

higher powered projector and smaller distances involved allowed exposure times below 

30 seconds, and the cameras were set to identical exposure values instead of the identical 

shutter speeds used previously. The exposure value, which indicates the over- or underexposure of the image, of –1.0 set different shutter speeds in each camera ranging from 

15 to 30 seconds, resulted in images of similar contrast. 

7.2.2 Images 

Two of the images used in the processing are shown in Figure 26. The images are 

nearly optimal white-on-black images. Ambient room lighting has been eliminated and 

while the contrast gradient is still present, each image contains useful data out to the 

corners of the projected pattern. Note that while hot spots still caused a loss of data in the 

image on the right, the nearly uniform contrast in all of the images enabled redundancy 
51

that minimized the negative impact of the hot spots on the final outcome. In general the 

location of hot spots varies from one image to the next. 

 

Figure 26 – Images used in photogrammetric processing (2 of 4)

7.2.3 Photogrammetric Processing 

Figure 27 shows an image of the completed project created with the 3-D Viewer 

in the photogrammetry software. The graphic shows the camera stations at 

approximately 90o angles of separation, their relative orientations and fields of view, and 

the final point cloud, all appearing as expected. Figure 28 is a magnified view of the 

upper left corner of the grid visible in Figure 26, after the target marking was completed. 

Evident is a higher resolution compared with the data in Section 7.1, indicating that the 

data points are sufficiently dense to measure the visible wrinkles. The greater density, 

however, does have a drawback; it is highly computationally and labor intensive to 

calculate the positions of over 5000 points. The measurement in Section 7.1 required 

hours to process, while this measurement required almost one week (8 hours computing 

time on a 2.0 GHz processor, 30 hours data handling). Also apparent in Figure 28 is that 

sufficient contrast existed for the computer to accurately mark the centers of almost all 

the targets using LSM centroiding. Automatic centroiding minimized the need for the 
52

human intervention necessary in Section 7.1, thereby maximizing the accuracy of the 

marking process. The increase in the total time required to process the data resulted from 

the need to iterate on the solution. The automated functions in the photogrammetry 

software required multiple adjustments and corrections that were not necessary in the 

previous measurement example. 

1 2 

3 4 

Figure 27 – Camera locations with fields of view 

Figure 28 – Marked points in upper left corner of the area imaged 

7.2.4 Error Estimates 

Table 5 contains the estimated error quantities calculated by the photogrammetry 

software for this test along with those for the test described in Section 7.1. The largest 
53

residual from all 5000 points is only 1.8 pixels, and over 98 percent of the points are 

below a 1.0 pixel residual, giving high confidence that the measurements are accurate. 

The average precision was calculated to be 0.062 mm, yielding an overall precision on 

the area measured of 1:32,300. These numbers, combined with the high target density, 

allow for accurate measurement of wrinkles less than one millimeter in amplitude. 

Table 5 – Comparison of two photogrammetric error estimates 

Experiment in: Section 7.1 Section 7.2 

Largest Residual 4.8 pixels 1.8 pixels 

Points below 1 pixel 

residual 63.0% 98.9% 

Average Precision 

(mm) 0.160 0.062 

Precision (parts per 

unit object size) 1:12,500 1:32,300 

Table 5 shows that the measurements in this section are a marked improvement in 

measurement residuals and precision over Section 7.1, demonstrating for the first time 

that high quality, high-resolution measurements can be obtained for these structures using 

dot projection photogrammetry. Improvements in hardware and technique led to the 

gains, and further advances, detailed in Section 7.3, will produce still better 

measurements. 

7.2.5 Results 

A contour map (Figure 29(a)) and a shaded relief map (Figure 29(b)) were created 

using the exported 3-D coordinates from the photogrammetric process. These maps, 

normally used for displaying topographic land features, clearly characterize the visible 

wrinkles in the Kapton membrane and the seam cutting horizontally across the center. 

The wrinkle amplitude can be determined in Figure 30 by examining the two views of the 
54

contour surface. The smallest wrinkle amplitude is approximately 0.25 mm and the 

average wrinkle amplitude is approximately 5.0 mm. The seam and wrinkles of the 

membrane are clearly visible in these results and match the pattern seen in Figure 25. 

Note the amplitude in the Z-direction has been exaggerated for better viewing. 

 (a) Contour map (b) Shaded relief map 

Figure 29 – Results for wrinkle measurement of the solar sail test article 

 

Figure 30 – Two views of contour surface 

These results demonstrate that it is possible using careful experimental technique 

to make non-contact photogrammetric measurements of highly reflective membranes that 

accurately characterize their static shape, including wrinkling. These measurements are 

the first of sufficient quality to validate analytical models of this configuration. More 

powerful projectors will allow high-resolution measurements such as these on even large 

gossamer structures. 

Y Position (m) 

X Position (m) Y Position (m) Z Position (m) 
55

7.3 High Density Full-field Two Meter Kapton Solar Sail 

The high density full-field test described here was designed to generate 

measurements of comparable resolution to the results in Section 7.2 over the entire 

surface of the two meter Kapton solar sail instead of over only a small section. It was 

intended to demonstrate the ability of dot-projection photogrammetry to simultaneously 

characterize medium-amplitude wrinkles and large-amplitude surface features. 

7.3.1 Test Setup 

 The same square two meter Kapton solar sail test article was used once again, 

however, it was rotated slightly, as shown in Figure 31, to create a slight billow in the 

bottom half of the membrane to demonstrate the ability of the method to simultaneously 

measure both medium-amplitude wrinkles and global non-planar shapes. Four Kodak 

DCS 760M cameras (Figure 9(b)) again at 90o

 angles of separation at the corners of the 

membrane photographed (f/11.0, no sharpening) a grid of approximately 10,800 targets 

created by the GSI ProSpot (Figure 11(c)) flash projector. The use of the Kodak cameras 

and the ProSpot projector signify a transition to professional grade hardware, as stated in 

previous chapters, to yield full-field, high-resolution, high precision measurements of 

currently available two meter solar sail structures. To the extent possible NASA will 

apply these methods to even larger solar sail scale models (10 m and 20 m) to be 

manufactured in the near future. Experimental methods developed here will be used and 

possibly extended further as required. 
56

Figure 31 – Two meter Kapton solar sail test article rotated slightly with billow 

7.3.2 Images 

 Two images used in the photogrammetric processing are shown in Figure 32. As 

discussed in Chapter 3, the images are monochromatic and underexposed. Ambient room 

lighting was minimized, but data was still lost due to the intensity of the flash projector. 

Because of the billow in the sail and the angles involved, a percentage of the light 

reflected by the membrane fell onto the floor. The high intensity of the projector meant a 

large amount of light, when scattered in all directions by the floor, imaged back onto the 

membrane. These images of the light on the floor were of sufficient intensity to wash out 

the original points. This loss of data will be discussed further in Section 7.3.3. Curling 

of the membrane and the large distances involved again led to hot spots in the images; 
57

however the loss of data at these points was compensated for again by the redundancy of 

four cameras. 

 

Figure 32 – Images used in photogrammetric processing (2 of 4)

7.3.3 Photogrammetric Processing 

 A three dimensional point cloud similar to those seen in Figures 21 and 27 in 

Sections 7.1 and 7.2 again resulted from the photogrammetric processing. The time 

required to generate the final project, however, was much greater than in the two previous 

examples. The measurement in Section 7.2 required 8 hours of computer time and 30 

hours of data handling whereas this project required approximately 90 hours on a 2.0 

GHz processor and an additional 80 hours of data handling. The current photogrammetry 

software was not designed to process such a large number of points, over 10,000 in this 

measurement, or to handle such close point spacing. The loss of data caused by hot spots 

and the image of the floor, shown in the top portion of Figure 33(a), added to the overall 

complexity of the processing, making this an extremely demanding and complicated 

measurement. Figure 33(b) shows how the redundant use of four cameras allows for 

useful data to still be gathered from this area. A combination of the four cameras 

effectively cover the region and yield useful data (each target must be marked in at least 
58

two images to be located in 3D space). Also evident in Figure 33 is the ability of the 

software to mark the projected dots using the LSM centroiding, as well as the true 

resolution of the projected pattern (impossible to see in Figure 32). In this case, the 

number of dots per square meter is nominally half as high as that used for the 

measurement in Section 7.2, but it is the highest currently achievable with the available 

hardware. Note the highest density Pro Spot slide projects 22,500 targets in a circular 

pattern. The position and shape of the test article dictated that for full coverage of the 

sail, only a portion of targets could be used. Approximately 10,800 dots were projected 

onto the membrane, and with the small size of the targets and the distance from the test 

article to the cameras (approximately three meters), some dots appeared as small as five 

pixels in diameter with as little as five pixels spacing. Higher pattern resolution or larger 

dots are therefore impractical for this measurement given the current hardware 

configuration. 
59

(a) Un-useable data in top half of image 

 

(b) Other three camera images 

Figure 33 – Marked points in lower right 0.01 m2 of solar sail test article 
60

7.3.4 Error Estimates 

 Error estimates for all three static shape measurements discussed thus far are 

listed in Table 6. The largest residual of the above project was slightly higher than that in 

Section 7.2 and can be explained by the relatively poor quality of the data. Even with 

this poor quality, however, over 95% of the points had under a one pixel residual. The 

most important improvement of this measurement over the previous one is evident in the 

precision numbers. Over the four square meters of membrane area imaged, the Kodak 

system was precise to 59 microns versus 62 microns over less than 0.5 square meters 

imaged previously, meaning that the overall precision increased from 1:32,300 to 

1:50,800. While this test represents another significant improvement in measurement 

precision, it also substantiates the principle of diminishing returns mentioned in Chapter 

6. The system used in the above test relied on professional hardware costing almost ten 

times that of the system used in Sections 7.1 and 7.2. Combined with a significant 

increase in processing time, this system represents a substantial investment that only 

doubled the resulting measurement precision. 

Table 6 – Comparison of all photogrammetric error estimates 

Experiment In: Section 7.1 Section 7.2 Section 7.3 

Largest Residual 4.8 pixels 1.8 pixels 2.7 pixels 

Points below 1 pixel 

residual 63.0% 98.9% 95.5% 

Average Precision 

(mm) 0.160 0.062 0.059 

Precision (parts per 

unit object size) 1:12,500 1:32,300 1:50,800 

7.3.5 Results 

 While Section 7.3.4 provides little justification for the added cost of the 

professional system, the results more than compensate for the fact that the price increase 
61- 

was far greater than the precision increase. The contour map and shaded relief map 

shown in Figure 34 clearly characterize all the medium-amplitude wrinkles, the seam, 

and the billow seen in Figure 31. These plots detail the entire surface of the test article 

instead of just a small area as in Section 7.2. Figure 35 shows two views of the contour 

surface generated from the data. The wrinkles are clearly evident, but in addition it is 

possible to see the true size of the billow compared to the wrinkles. The measured 

wrinkles are on average five millimeters in amplitude, matching the measurement in 

Section 7.2, while the billow is almost ten times that size. Also apparent in Figure 35 is 

the tendency of the membrane to curl at the edges. 
62

(a) Contour map 

(b) Shaded relief map 

Figure 34 – Results for high density full-field measurement of the solar sail test article 
63

(a) Top view 

(b) Perspective view 

Figure 35 – Two views of the contour surface generated 

 While it is impossible to obtain a quantitatively accurate comparison of the results 

obtained photogrammetrically to the actual shape of the membrane due to the lack of any 

more accurate measurement system, qualitative validation can be performed. Careful 

X Position (m) 

Y Position (m)
64-- 

examination of the membrane shown in Figure 31 reveals patterns of wrinkles that begin 

in the corners of the membrane and progress in straight lines diagonally toward the 

center. The same trends are visible in Figures 34 and 35. These figures also show the 

seam cutting across the center of the membrane visible in Figure 31. The billow occurs 

in identical locations in all three figures, and in the lower left quarter of the membrane 

the last of the wrinkles curves toward the center instead of running in a straight line. This 

qualitative validation combined with the maturity of the photogrammetric technique and 

the quality of this particular measurement gives high confidence that these results are 

accurate. 

 The shape characterization produced above is unique. A realistic solar sail model 

has never before been produced in a full-field, totally non-contact manner to this 

resolution. These surface models are of sufficient quality to be used for validation of 

analytical models and for supporting development of hardware and software tools for 

future measurements and use in space, achieving both of the goals expressed prior to 

Section 7.1. 
65

8. DYNAMIC ANALYSIS OF A TWO METER VELLUM SOLAR SAIL 

 Structural dynamic characterization is also important for the development and 

validation of analytical models supporting future designs of gossamer structures in 

general and solar sails in particular. In the dynamic analysis of these structures, as in the 

static characterization, non-contact measurement is necessary to avoid altering the 

responses of the objects being measured. Videogrammetry, discussed in Chapter 3, 

expands the methods and techniques of photogrammetry to multiple time steps yielding 

dynamic data. While other non-contact dynamic measurement techniques exist, they are 

not full-field. It was hoped that the dynamic data generated would be useful in simply 

tracking the overall shape of the membrane as a function of time. The accuracy of the 

measurement of the resonant frequencies and operating deflection shapes that were 

extracted, however, surpassed expectations. 

8.1 Test Setup 

 Figure 36 shows the two meter solar sail test article measured in this application. 

The test article membranes are 100 micron thick (thinnest commercially available) 

Vellum, a diffuse white material ideal for dot projection since it scatters light almost 

equally in all directions regardless of the angle of incidence. This property enables the 

Vellum to yield a grid of uniform contrast from any camera angle. The test article is not 

designed to approximate actual solar sail material as is the test article used in the first 

three applications, but is designed as a research tool for measurement method 

development. Figure 37 shows the test setup used in the experiment. A grid of 49 dots 

was created on the right quadrant of the four quadrant solar sail by the digital projector 

shown in Figure 11(d) and retro-reflective targets were attached to the booms. A long-
66

stroke electrodynamic shaker attached to the tip of the lower right boom excited the 

structure with a pseudo-random forcing function. A scanning laser vibrometer measured 

the frequency response function of the sail quadrant and its corresponding operating 

deflection shapes, and is used below as a standard against which to compare and 

determine the validity of the videogrammetry results. 

Figure 36 – Two meter four quadrant Vellum solar sail test article 
67

Figure 37 – Test setup for dynamic characterization 

8.2 Measurements 

 The scanning laser vibrometer system is an industry standard for determining 

modal frequencies and shapes of structures. The user defines a measurement grid – in 

this case the same grid used in the videogrammetry – and at each point the displacement 

or response to an input force is measured. Using the calculated power spectral densities 

and cross spectral density of these input and output signals, the vibrometer software 

generates the frequency response function (FRF) for each measured point, as well as 

coherence functions, phase angles, and other modal analysis data. Relevant modal 

frequencies are then selected by the user – usually at peaks in the FRF – and animated by 

the software, as shown below. The laser vibrometer is a complete modal analysis system 

used for both gathering and analyzing vibration data. [33, 34] 
68

The question then arises: if the scanning laser vibrometer is such a powerful 

system, why study videogrammetry? As the name implies, the vibrometer can scan or 

measure multiple points, but does so one point at a time. At each point the measured 

signal (response vs. time) is divided into blocks for each of which the software calculates 

a Fast Fourier Transform (FFT). Variations of this technique, often combined with 

windowing, are used to smooth the data. Each block is then discritized into samples 

depending on the desired resolution of the measurement. An artifact of the analogue antialiasing filter requires that the number of samples equals 2.56 times the number of FFT 

lines. These FFT lines define the resolution of the measurement by: 

FFT n

BW ∆f = (6) 

Where ∆f is the resolution, BW is the bandwidth of the measurement (i.e. from 0 to 10 

Hz), and nFFT is the number of FFT lines. At high resolutions, therefore, the vibrometer 

measures thousands of FFT lines at each point, 1600 in this application, to produce 

detailed results. However this form of data acquisition by scanning each point 

individually is slow at low frequencies, requiring several hours to run one test. 

Videogrammetry is attractive because of its ability to measure all of the points 

simultaneously. For the results presented below, the cameras recorded data for 

approximately 26 seconds gathering a total of only 384 frames each instead of several 

sets of 3200 samples (twice the number of frequency lines) taken by the vibrometer at 

each point. While the videogrammetric results shown below are arguably not as clean as 

the vibrometer data, they are full-field, simultaneous measurements taken in just a few 

seconds instead of hours. [33 – 35] 
69

8.3 Results 

The position versus time videogrammetry data was loaded into modal analysis 

software for interpretation where two different computational methods were used. The 

first involved overlaying the time histories of individual points and calculating the 

Fourier transform of the joint history. The software then animated the Operating 

Deflection Shapes (ODS) at each peak in the frequency domain [36]. The second method 

of analysis calculated frequency response functions. Here only one degree of freedom 

was used, the out-of-plane displacement in the Z direction, identical to that used by the 

vibrometer. As stated above, an FRF is calculated by dividing either the output spectral 

density or the cross spectral density by the input spectral density, the difference in the 

two methods generating the coherence function [35]. For the videogrammetry 

experiment the input signal was not measured, so a reference point was specified 

enabling the software to divide out the input and calculate the FRF’s (Figures 38 and 39) 

and animate shapes again at the peaks in the frequency domain [37]. The combined 

results of both of these methods of analysis are compared against the results of the laser 

vibrometer measurements in Table 7 below. While neither the ODS or FRF method is 

currently considered to be entirely accurate, some combination of the two will likely 

capture all dynamics below 5 Hz [38]. Note that the non-linear nature of the deflection 

shapes, their coupling, and the inability to compensate for atmospheric damping mean 

that the shapes shown in Figures 40 through 44 are not actually mode shapes, and that the 

frequencies listed in Table 7 are not actually modal frequencies. These can alternatively 

be referred to as “structural resonances” and “resonant frequencies.” 
70

Table 7 – Identified resonant frequencies of the 2 m Vellum solar sail 

Laser Vibrometer Videogrammetry 

1.75 Hz 1.77 Hz (ODS) 

2.49 Hz (FRF, ODS) 2.65 Hz 2.81 Hz (ODS) 

3.34 Hz 3.28 Hz (FRF) 

3.67 Hz 3.69 Hz (ODS, FRF) 

4.74 Hz 4.75 Hz (ODS, FRF) 

 Examination of Table 7 reveals good correlation between the results found using 

laser vibrometry and videogrammetry. While several inconsistencies are evident, overall 

the modal frequencies were measured to within 0.2 Hz of each other. Figure 38 shows 

the overlayed magnitude of the three frequency response functions (videogrammetry 

ODS, videogrammetry FRF, and laser vibrometer) of a single point. It is clear how the 

two methods of analyzing the videogrammetry data were used in conjunction to 

approximate the laser vibrometer data. The first large peak in the magnitude of the 

vibrometer data has a corresponding peak in the videogrammetry ODS data, while the 

second vibrometer peak corresponds to a peak in the videogrammetry FRF. Note that 

while it is customary to show a phase angle plot with the magnitude plot, in this case no 

useful information is contained in the phase data, and it is therefore not shown. The 

randomness and scatter in Figure 38, even in the high quality vibrometer data, indicates a 

high degree of modal coupling, non-linearity, and noise present in the system. 
71

Figure 38 – Comparison of frequency response functions for a single point 

Figure 39 – Overlayed magnitudes of frequency response functions for all measured 

points 

Figure 39 shows the magnitudes of the frequency response functions for all of the 

points for each of the three analysis methods. The visible scatter in the vibrometer data 

again indicates the complexity of characterizing solar sail structures. Also evident is the 

fact that peaks in one or both sets of videogrammetry data generally correspond to peaks 

in the vibrometer data. The frequencies listed in Table 7 were selected by analyzing the 

damping and the deflection shape at each of these peaks. Clean shapes and low damping 
72

were considered to be the true structural resonance shapes and the corresponding 

frequencies considered to be the true resonant frequencies of the system. 

Apparent in both Figures 38 and 39 is the bandwidth limitation of the 

videogrammetry system. While the bandwidth of the vibrometer can be customized for 

each scan (in this case set from 0 to 10 Hz), the maximum frequency at which 

videogrammetry can generate data, or Nyquist frequency, is always one half of the 

sampling rate. In this case the cameras ran at slightly less than 15 Hz yielding a Nyquist 

frequency of just over 7 Hz. Nyquist is important because recorded motion caused by 

modes occurring above it reflects back into the measured spectrum creating peaks at 

frequencies where resonance does not exist, an effect called aliasing [39]. While the laser 

vibrometer has anti-aliasing filters to compensate for the effect, the videogrammetry 

system does not. The multiple peaks below 1.0 Hz in the videogrammetry FRF are 

believed to have been caused by aliased boom modes. Compensating for aliasing will be 

a challenge for future videogrammetry work. 

Figures 40 through 44 show the deflection shapes for each of the modal 

frequencies listed above, again comparing the laser vibrometry shapes and the 

videogrammetry shapes. In general, the videogrammetry shapes are noisier than the 

shapes obtained using the vibrometer, which is to be expected due to the disparity in data 

volumes, but overall there is good correlation, especially at higher frequencies. 
73

 (a) 1.75 Hz Laser Vibrometer (b) 1.77 Hz Videogrammetry (ODS)

Figure 40 – First deflection shape comparison for Vellum solar sail test article 

 (a) 2.65 Hz Laser Vibrometer (b) 2.49 Hz Videogrammetry (FRF) 

Figure 41 – Second deflection shape comparison for Vellum solar sail test article 

 (a) 3.34 Hz Laser Vibrometer (b) 3.28 Hz Videogrammetry (FRF) 

Figure 42 – Third deflection shape comparison for Vellum solar sail test article 
74

 (a) 3.67 Hz Laser Vibrometer (b) 3.69 Hz Videogrammetry (FRF) 

Figure 43 – Fourth deflection shape comparison for Vellum solar sail test article 

 (a) 4.74 Hz Laser Vibrometer (b) 4.75 Hz Videogrammetry (FRF) 

Figure 44 – Fifth deflection shape comparison for Vellum solar sail test article 

The first two shapes shown in Figures 40 and 41 are basically boom driven 

modes. The first deflection shape shows that the booms are in phase, and the second 

shows the booms to be out of phase with the membrane following in a first order fashion. 

Figure 42 shows the third deflection shape of the system, with the booms in phase and the 

membrane in a second order configuration. The fourth deflection shape (Figure 43) 

shows the booms to be in phase with a large amplitude first order billow of the 

membrane. Finally, the fifth deflection shape in Figure 44 shows a saddle configuration 
75

for the membrane. In all of the figures videogrammetry produced similar shapes at 

similar frequencies as the vibrometer, demonstrating the potential of the full-field noncontact dynamic characterization technique. As stated previously, videogrammetry can 

only measure frequencies up to approximately one half the frame rate of the cameras 

without hardware alterations. This limitation will not generally be a hindrance for use on 

gossamer structures, however, because due to their size the dominant modes will usually 

occur below 5.0 Hz. Also, the displacement of the test article must be large enough to be 

detected by the cameras, whereas the vibrometer is much more sensitive. The above 

results show videogrammetry to be capable, with some refinement, of achieving full-field 

non-contact dynamic measurements of solar sail structures. 
76

9. CONCLUSIONS 

 Accurate static and dynamic characterization of solar sail test articles is vital for 

creating and validating high-fidelity analytical models, developing space quality 

hardware, and future advancement of the technology. Obtaining accurate static and 

dynamic measurements of the highly reflective ultra-thin membranes, however, is not a 

trivial task. Photogrammetry, the selected measurement method, usually relies on 

physically attached retro-reflective targets. The mass and stiffness these targets add to 

the five micron thick membranes, however, alter the static and dynamic properties the 

method is attempting to characterize. Therefore a totally non-contact technique called 

dot projection was used instead. 

As with any adaptation of an established measurement method to a unique task and 

field, many questions arise about the accuracy of the results. Zoom lenses, color imagers, 

projector intensity, camera heating, highly flexible test articles, reflective object surfaces, 

and many other factors both complicate the measurements and affect their accuracy and 

resolution. Accordingly, a detailed study was performed to understand the effects of 

these parameters and quantify their impact on the measurement method. The three static 

shape applications of dot projection photogrammetry describe refinements in technique 

and hardware and produced noticeable gains in measurement quality from one test to the 

next. 

9.1 Static Tests 

 Three experiments to statically characterize a two meter aluminized Kapton solar 

sail test article were performed. The first test yielded a model of the global shape of the 

article, but did not achieve the full accuracy or resolution potential of the dot projection 
77

photogrammetry technique. The second test focused on a small portion of the membrane. 

Using the same cameras as the first test, a more powerful projector, and technique 

refinement, accurate modeling of surface features as small as 0.25 mm was achieved. 

These measurements, the first totally non-contact wrinkle characterization of solar sail 

membranes using photogrammetry, are of sufficient quality and resolution to be used for 

analytical model validation. The third and final static test used professional hardware to 

generate high resolution surface measurements of the entire two meter sail with an even 

higher quality. These tests have paved the way for other high resolution, non-contact, 

full-field dot projection measurements on current and future solar sail test articles and 

will enable the validation and refinement of analytical models that will be used to design 

future space missions. 

9.2 Dynamic Test 

 Dynamic measurements were performed using an adaptation of photogrammetry 

to time-dependant data called videogrammetry, a method that produces a series of 3-D 

surface models in time. The data were exported to a modal analysis software package 

where two different methods were used to reduce the data and yield resonance 

frequencies and deflection shapes. These data were compared to data from a scanning 

laser vibrometer. While the videogrammetry results show good correlation to those 

obtained from the turn-key industrial system, they are not quite as clean, but the method 

is full-field and all of the data was acquired in seconds instead of the hours required by 

the vibrometer. The ability of the system to generate data of sufficient quality to be used 

for actual dynamic analysis instead of simply tracking the overall shape of the object in 
78

time is an important breakthrough that may allow for more detailed measurements in 

space than previously thought possible. 

 

9.3 Future Work 

For the foreseeable future, providing high-fidelity analytical models of solar sails 

and other gossamer structures will be the most critical issue in the development of the 

technology. Static and dynamic characterization techniques that can be used reliably to 

provide the necessary measurement accuracy and precision for these structures are 

needed to validate these analytical models. Accordingly, work should continue to focus 

on hardware, software, and technique refinement in static measurements to achieve 

higher resolution on a global scale while decreasing computation time, as well as on 

refining the videogrammetric analysis. A detailed study must be performed to investigate 

thermal or other effects seen in Chapter 5. Finally, implementing a static measurement 

system in vacuum is necessary for future solar sail testing and for adapting the hardware 

for use in space. 

As computers become ever faster and more powerful and prices continue to drop, 

consumers will have inexpensive access to capability that just a few years ago required 

substantial capital investment. It is foreseeable, therefore, that completely automated real 

time photogrammetry and videogrammetry systems could be developed and implemented 

for use on gossamer structures both in the laboratory and in space. Developing and 

implementing measurement systems that provide continuous static and dynamic data for 

the control systems of these structures is a realistic goal that may be achievable by the 

time NASA flies its first solar sail sometime before the end of the decade. 
79

9.4 Related Work 

The applications presented above represent only a portion of the work completed 

in this area over the past year and a half. These four applications were selected for the 

concise development story they tell, not for the completeness of the coverage they 

provide. Other work performed by the author using photogrammetry and 

videogrammetry includes that found in References 8, 12, 13, 24, and 38, as well as the 

following publications: 

Black, J. T., “Photogrammetry and Videogrammetry Methods for Solar Sails and Other 

Gossamer Structures,” AIAA Student Conference Region I, College Park, Maryland, 

April, 2003. 

Leifer, J., Black, J. T., Belvin, K. W., and Behun, V., “Evaluation of Shear Compliant 

Boarders for Wrinkle Reduction in Thin Film Membrane Structures,” 44th

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials 

Conference, 4th Gossamer Spacecraft Forum, Norfolk, Virginia, April 2003, AIAA 

2003-1984. 

Johnston, J. D., Blandino, J. R., Black, J. T., and Pappa, R. S., “Structural Analysis and 

Testing of a 1/20th Scale NGST Sunshield Membrane Layer,” 44th

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials 

Conference, 4th Gossamer Spacecraft Forum, Norfolk, Virginia, April 2003, AIAA 

2003-1742. 

 Photogrammetric measurements have also been taken to determine the 

straightness of a 7 m solar sail quality boom after a deployment in vacuum at LaRC, to 

determine the radial expansion of polyethylene cylinders as a function of pressure (to be 

published by AIAA in April 2004), to characterize the wrinkle pattern of various 
80

configurations of horizontally supported solar sail quality membranes (to be published by 

AIAA in April 2004), to determine the accuracy of photogrammetry performed using 

various camera systems, and to measure the sag caused by gravity in a 10 m solar sail 

membrane quadrant under various load conditions (to be published by AIAA in April 

2004). 
81

REFERENCES 

[1] Jenkins, C. H. M. (editor), Gossamer Spacecraft: Membrane and Inflatable Structures 

Technology for Space Applications, Vol. 191, Progress in Astronautics and 

Aeronautics, AIAA, Reston, VA, 2001. 

[2] Wertz, J. R. and Larson, W. J. (editors), Space Mission Analysis and Design, Space 

Technology Library, Microcosm Press, El Segundo, CA, 1999. 

[3] Chmielewski, A. B., Moore, C., and Howard, R., “The Gossamer Initiative,” IEEE 0-

7803-5846-5/00, 2000. 

[4] Belvin, W. K., “Solar Sails: Structures and Materials Subsystem,” Presentation at 

Technical Interchange Meeting, Structural Dynamics Branch, NASA Langley 

Research Center, Hampton, VA, April 2002. 

[5] Nella, J., et al., “Next Generation Space Telescope (NGST) Observatory Architecture 

and Performance,” http://www.stsci.edu/ngst/, TRW Space and Electronics / 

International Society for Optical Engineering (SPIE) Article, November 2002. 

[6] Chmielewski, A. B., “Overview of Gossamer Structures,” Gossamer Spacecraft: 

Membrane and Inflatable Structures Technology for Space Applications, Jenkings, C. 

H. M., ed., AIAA, Vol. 191, 2001, pp. 1-33. 

[7] McInnes, C. R., Solar Sailing – Technology, Dynamics and Mission Applications,

Praxis Publishing Ltd, Chichester, UK, 1999. 

[8] Pappa, R. S., Black, J. T., and Blandino, J. R., “Photogrammetric Measurement of 

Gossamer Spacecraft Membrane Wrinkling,” Society for Experimental Mechanics 

Annual Conference, Charlotte, NC, June 2003. 

[9] Mikhail, E. M., Bethel, J. S., and McGlone, J. C., Introduction to Modern 

Photogrammetry, John Wiley & Sons, New York, NY, 2001. 
82

[10] Pappa, R. S., Giersch, L. R., and Quagliaroli, J. M., “Photogrammetry of a 5m 

Inflatable Space Antenna With Consumer Digital Cameras,” Experimental 

Techniques, Society for Experimental Mechanics, Vol. 25, No. 4, July/August 2001, 

pp. 21-29. 

[11] Giersch, L. R., “Pathfinder Photogrammetry Research for Ultra-Lightweight and 

Inflatable Space Structures,” NASA/CR-2001-211244, November 2001. 

[12] Pappa, R. S., Jones, T. W., Black, J. T., Walford, A., Robson, S., and Shortis, M. R., 

“Photogrammetry Methodology Development for Gossamer Space Structures,” Sound 

and Vibration, Vol. 36, No. 8, August 2002, pp. 12-21. 

[13] Pappa, R. S., Black, J. T., Blandino, J. R., Jones, T. W., Danehy, P. M., and 

Dorrington, A. A., “Dot Projection Photogrammetry and Videogrammetry of 

Gossamer Space Structures,” Journal of Spacecraft and Rockets, Vol. 40, No. 6, 

Nov.-Dec. 2003, pp. 858-867. 

[14] Ganci, G., and Brown, J., “Developments in Non-Contact Measurement Using 

Videgorammetry,” Geodetic Services, Inc., Boeing Large Scale Metrology Seminar, 

2002. 

[15] Greenwood, J. A., Darve, C., Bernstein, R., Black, E., and Kubik, D., “Failure-mode 

Metrology using Projected Target Videogrammetry,” Coordinate Measurement 

Systems Committee Conference, Albuquerque, New Mexico, August, 2001. 

[16] Gnoffo, P. A. and Anderson, B. P., “Computational Analysis of Towed Ballute 

Interactions,” 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 

St. Louis, Missouri, AIAA 2002-2997, 24-26 June 2002, p. 13. 

[17] West, J. L. and Derbes, B., “Solar Sail Vehicle System Design for the GEOStorm 

Warning Mission,” AIAA 2000-5326, 2000. 
83

[18] McInnes, C. R., “Solar Sail Mission Opportunities,” Royal Astronomical Society 

Discussion Meeting,10 May 2002. 

[19] Benford, G., “Assisting the Sun: Beamed Power in Space,” Aerospace America, 

Vol. 41, No. 6, June 2003. 

[20] Virgin, L. and Holland, D., “Post-Buckling Dynamic Structural Modeling and 

Analysis of Square Solar Sail Configurations,” Seminar given at NASA Langley 

Research Center, August 2001. 

[21] Hiscox, J., “Sailing to Mars,” Marsbugs: The Electronic Astrobiology Newsletter, 

Vol. 9, No. 27, p. 6, 25 July 2002. 

[22] Spieth, D. and Zubrin, R., “Ultra-Thin Solar Sails for Interstellar Travel – Phase I 

Final Report,” NASA Institute for Advanced Concepts, Pioneer Astronautics Inc., 

December 1999. 

[23] Eos Systems, Inc., PhotoModeler Pro User’s Manual, Version 5, Vancouver, B.C., 

Canada, 2003. 

[24] Black, J. T. and Pappa, R. S., “Videogrammetry Using Projected Circular Targets: 

Proof-of-Concept Test,” NASA/TM-2003-212148, February 2003. 

[25] Atkinson, K. B., ed., Close Range Photogrammetry and Machine Vision, Whittles 

Publishing, Caithness, Scotland, 2001. 

[26] Institute of Photogrammetry, Agricultural Facility, University of Bonn, [on-line] 

http://www.ipb.uni-bonn.de/. 

[27] Rabbani, M., “Introduction to Electronic Imaging Systems,” SPIE Education 

Services Program, Short Course Notes, June 2002. 

[28] Geodetic Services Inc., [on-line] http://www.geodetic.com/. 
84

[29] Goldsmith, P., “Resetting the Arecibo Primary Reflector Surface,” National 

Astronomy and Ionosphere Center Newsletter, Number 32, March 2001. 

[30] Edmundson, K. and Baker, L., “Photogrammetric Measurement of the Arecibo 

Primary Reflector Surface,” Coordinate Measurement Systems Committee 

Conference, Albuquerque, NM, August 2001. 

[31] Avery-Dennison Corp., “Specifications for Heat Fused Durable Preformed 

Pavement Markings Incorporating Preapplied Visibeads, 90 Mil,” 2003 

[32] Golden Software, Inc., Surfer 8 – Contouring and 3D Surface Mapping for Scientists 

and Engineers, User’s Guide, Golden, Colorado, 2002. 

[33] Polytech, “Polytech Scanning Vibrometer Software 7.1,” 2002. 

[34] Polytech, “Polytech Scanning Vibrometer Theory Maual 7.1,” 2002. 

[35] Hardin, J. C., Introduction to Time Series Analysis, National Aeronautics and Space 

Administration, NASA RP-1145, November 1990. 

[36] Batel, M., “Operational Modal Analysis – Another Way of Doing Modal Testing,” 

Sound and Vibration, Vol. 36, No. 8, August 2002, pp. 22-27. 

[37] Vibrant Technology, Inc., ME’scope VES, Visual Engineering System, Operating 

Manual, Jamestown, CA, 2001. 

[38] Blandino, J. R., Pappa, R. S., and Black J. T., “Modal Identification of Membrane 

Structures with Videogrammetry and Laser Vibrometry,” 44th

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials 

Conference, 4th Gossamer Spacecraft Forum, Norfolk, VA, AIAA Paper 2003-1745, 

April 2003. 

[39] Ewins, D. J., Modal Testing: Theory and Practice, John Wiley & Sons Inc., New 

York, NY, 1984. 
85

APPENDIX A – CALIBRATION TRACKING 

 Calibrating the cameras used in the photogrammetric process is vital to achieving 

accurate measurements. The parameters listed in Tables A-1 and A-2 were obtained from 

calibrations performed on the dates listed and are as follows: Focal Length is the exact 

zoom setting of the camera, Format Size is the exact size of the CCD imager, Format 

Ratio is the Format Width divided by the Format Height, Principal Point coordinates are 

the exact center of the image on the CCD, and K1, K2, P1, and P2 are the radial and 

descentering lens distortion parameters, all of which are described in detail in Section 

3.2.1. Table A-3 shows estimates of the radial distortion for one Olympus camera and 

one Kodak camera calculated using the constants in Tables A-1 and A-2 and Equations 1-

5 in Section 3.2.1. 

 Tables A-1 and A-2 show that over time small changes in the calibration 

parameters do occur. These changes can be caused by a number of factors, including 

repeated use, settling of the lenses and internal camera components, vibrations, thermal 

warping, etc. It is important to note that while maintaining up-to-date calibrations of all 

of the cameras is vital to attaining maximum accuracy in photogrammetric 

measurements, the observable deviations in all of the parameters listed below do not 

follow any predictable pattern which may indicate a systemic flaw. The parameters vary 

over time by less than ten percent. 

Table A-1 – Calibration parameters for Olympus E20n cameras 

Camera Date 

Focal 

Length 

(mm) 

Format 

Size W 

(mm) 

Format 

Size H 

(mm) 

Format 

Ratio 

(W/H) 

Principal 

Point X 

(mm) 

Principal 

Point Y 

(mm) 

 Jan-02 9.1599 8.7042 6.5280 1.3334 4.3821 3.1998 

 Jul-02 9.1930 8.7004 6.5280 1.3328 4.3805 3.1900 

1 Nov-02 vac 9.1782 8.7088 6.5280 1.3341 4.3672 3.1850 

 May-03 9.0775 8.6201 6.4660 1.3331 4.3077 3.1640 

 
86

 Jan-02 9.1611 8.7082 6.5280 1.3340 4.3454 3.1578 

2 Jul-02 9.1978 8.7060 6.5280 1.3336 4.3317 3.1427 

 Nov-02 vac 9.1936 8.7119 6.5280 1.3345 4.3328 3.1361 

 

 Jan-02 9.1732 8.7059 6.5280 1.3336 4.3454 3.1793 

3 Nov-02 vac 9.1835 8.7093 6.5280 1.3341 4.3321 3.1613 

 May-03 9.0035 8.5555 6.4179 1.3331 4.2349 3.1145 

 

 Jan-02 9.1294 8.7019 6.5280 1.3330 4.2313 3.2346 

4 May-03 8.1852 7.7838 5.8382 1.3333 3.7613 2.8928 

 Jan-02 9.1733 8.7078 6.5280 1.3339 4.3921 3.1654 

5 Jul-02 9.1795 8.7086 6.5280 1.3340 4.3814 3.1627 

 Nov-02 vac 9.1628 8.7150 6.5280 1.3350 4.3844 3.1528 

 

6 Jul-02 9.1690 8.7075 6.5280 1.3339 4.3255 3.1988 

Camera Date K1 K2 P1 P2 

 Jan-02 0.002235 -1.491E-05 -2.682E-05 6.639E-05 

 Jul-02 0.002487 -2.537E-05 -7.780E-05 1.428E-05 

1 Nov-02 vac 0.002476 -2.270E-05 -2.183E-05 6.675E-05 

 May-03 0.002521 -2.383E-05 3.316E-05 1.209E-05 

 

 Jan-02 0.002473 -1.529E-05 2.084E-05 3.185E-05 

2 Jul-02 0.002593 -2.829E-05 -1.264E-05 1.862E-05 

 Nov-02 vac 0.002421 -2.311E-05 -1.518E-08 3.918E-05 

 

 Jan-02 0.002376 -2.271E-05 6.969E-06 4.028E-06 

3 Nov-02 vac 0.002466 -2.475E-05 7.917E-06 6.676E-05 

 May-03 0.002446 -2.260E-05 8.106E-05 -9.308E-06 

 

 Jan-02 0.002393 -2.847E-05 -5.028E-06 -2.549E-05 

4 May-03 0.003092 -3.779E-05 1.070E-04 3.949E-05 

 

 Jan-02 0.002467 -2.663E-05 -8.715E-05 1.023E-05 

5 Jul-02 0.002519 -2.704E-05 -2.521E-05 -1.937E-06 

 Nov-02 vac 0.002582 -2.945E-05 2.317E-05 3.463E-05 

 

6 Jul-02 0.002475 -2.446E-05 -8.344E-05 -5.966E-05 

vac = in early November 2002 these cameras were used in vacuum chamber tests and 

were calibrated immediately thereafter 
87

Table A-2 – Calibration parameters for Kodak DCS 760M cameras 

Camera Date 

Focal 

Length 

(mm) 

Format 

Size W 

(mm) 

Format 

Size H 

(mm) 

Format 

Ratio 

(W/H) 

Principal 

Point X 

(mm) 

Principal 

Point Y 

(mm) 

 Oct-02 4.0 24.2855 27.2391 18.0000 1.5133 13.7492 9.1606 

155 Feb-03 23.7714 26.6274 17.6116 1.5119 13.4723 8.9743 

 May-03 23.9696 26.8440 17.7549 1.5119 13.6199 9.0644 

 

 Mar-03 23.3584 26.2020 17.3344 1.5116 13.3156 8.7496 

156 May-03 23.9087 26.8387 17.7563 1.5115 13.6591 8.9651 

 Apr-03 23.7165 26.6078 17.5997 1.5118 13.4136 8.9274 

159 May-03 24.0166 26.9576 17.8314 1.5118 13.5825 9.0585 

 Apr-03 23.9109 26.8404 17.7472 1.5124 13.6499 9.0456 

163 May-03 24.0115 26.9594 17.8272 1.5123 13.7150 9.0823 

Camera Date K1 K2 P1 P2 

 Oct-02 4.0 0.0001634 -2.670E-07 -2.710E-05 2.273E-05 

155 Feb-03 0.0001717 -2.697E-07 -3.332E-05 2.844E-06 

 May-03 0.0001679 -2.604E-07 -3.510E-05 2.237E-06 

 

 Mar-03 0.0001797 -2.919E-07 -2.256E-05 -1.352E-05 

156 May-03 0.0001718 -2.680E-07 -2.715E-05 -1.228E-05 

 

 Apr-03 0.0001726 -2.780E-07 -6.645E-06 9.491E-07 

159 May-03 0.0001681 -2.645E-07 -5.885E-06 1.700E-06 

 

 Apr-03 0.0001676 -2.649E-07 -3.301E-06 -7.875E-06 

163 May-03 0.0001666 -2.621E-07 -3.200E-06 -8.613E-06 

4.0 = release 4.0 of the photogrammetry software. Other calibrations from release 5.0. 

Table A-3 – Residual estimates for one Olympus E20n and one Kodak DCS 760M 

Radial 

Distance, r 

(mm) 

E20 δr 

(mm) 

E20 δrx

(mm) 

E20 δry

(mm) 

760Mδr 

(mm) 

760Mδrx

(mm) 

760Mδry

(mm) 

1 2.497E-03 1.888E-03 1.635E-03 1.676E-04 1.301E-04 1.009E-04

2 1.941E-02 1.467E-02 1.270E-02 1.335E-03 1.036E-03 8.035E-04

3 6.228E-02 4.708E-02 4.077E-02 4.470E-03 3.468E-03 2.690E-03

4 1.369E-01 1.035E-01 8.965E-02 1.048E-02 8.130E-03 6.307E-03

5 2.407E-01 1.819E-01 1.576E-01 2.017E-02 1.565E-02 1.214E-02

 

 Max Magnitude (mm) = 2.407E-01 2.017E-02
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Photogrammetry and Videogrammetry Methods Development for Solar 

Sail Structures

5a. CONTRACT NUMBER

NCC1-03008

 6. AUTHOR(S)

Black, Jonathan T.

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

NASA Langley Research Center

Hampton, VA 23681-2199

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

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

Thesis submitted to the faculty of The School of Engineering and Applied Science of The George Washington University in partial

satisfaction of the requirements for the degree of Master of Science, August 29, 2003.

An electronic version can be found at http://techreports.larc.nasa.gov/ltrs/ or http://ntrs.nasa.gov. Technical Monitor: Richard S. Pappa

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 39

Availability: NASA CASI (301) 621-0390 Distribution: Standard

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

This report discusses the development and application of metrology methods called photogrammetry and videogrammetry that 

make accurate measurements from photographs. These methods have been adapted for the static and dynamic characterization 

of gossamer structures, as four specific solar sail applications demonstrate. The applications prove that high-resolution, 

full-field, non-contact static measurements of solar sails using dot projection photogrammetry are possible as well as full-field, 

non-contact, dynamic characterization using dot projection videogrammetry. The accuracy of the measurement of the resonant 

frequencies and operating deflection shapes that were extracted surpassed expectations. While other non-contact measurement 

methods exist, they are not full-field and require significantly more time to take data.

15. SUBJECT TERMS

Photogrammetry; Videogrammetry; Optical measurement techniques; Dot projection; Solar sails; Gossamer spacecraft; 

Structural test methods

18. NUMBER

 OF 

 PAGES

102

19b. TELEPHONE NUMBER (Include area code)

(301) 621-0390

a. REPORT

U

c. THIS PAGE

U

b. ABSTRACT

U

17. LIMITATION OF 

 ABSTRACT

UU

Prescribed by ANSI Std. Z39.18

Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

23-629-80-01

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

NASA/CR-2003-212678

16. SECURITY CLASSIFICATION OF:

The 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 Department of Defense, Washington Headquarters Services, Directorate for Information Operations and 

Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person 

shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01- 12 - 2003