GEOLOGICAL SURVEY PROFESSIONAL PAPER 1046-D

Prepared on belmlf of the

National Aeronautics and Space Administration

Experimental Photogrammetry 

of Lunar Images

By SHERMAN S. C. WU and H. J. MOORE

APOLLO 15-17 ORBITAL INVESTIGATIONS 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 104 6-D

Prepared on behalf of the

National Aeronautics and Space Administration

An experimental photogrammetric study, using 

Apollo orbital photographs for geologic 

studies of the Moon and the exploration of 

the Moon and other planetary bodies

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1980
UNITED STATES DEPARTMENT OF THE INTERIOR 

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY 

H. William Menard, Director

Library of Congress Cataloging in Publication Data

Wu, Sherman S. C.

Experimental photogrammetry of lunar images.

(Apollo 15-17 orbital investigations) (Geological Survey professional

paper ; 1046-D)

Bibliography: p. D22-D23.

1. Moon Photographic measurements. 2. Moon Maps. I. Moore, 

Henry J., joint author. II. United States. National Aeronautics 

and Space Administration. III. Title. IV. Series. V. Series: 

United States. Geological Survey. Professional paper ; 1046-D.

QB595.W8 559.9'1 80-607010

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402

Stock number 024-001-03300-3
CONTENTS

Page

Abstract________________________________ Dl

Introduction __________________________________ 1

Cameras and photography.--_____________________________ 2

Lunar topographic camera ________________ 2

Mapping camera ____________________________ 3

Panoramic camera _________________________ 3

Methods and procedures-_____________________ 4

Equipment and materials __________________________ 4

Control and leveling _________________________ 4

Methods of measurement ________________________ 5

Precision of measurement _____________________________ 5

Mapping camera photography ______________________ 5

Panoramic and lunar topographic camera photography __ 6

Page

Topographic maps ____—____ ——— __ —————— ——— -___ D6

Vertical mapping camera photography__———_________ 6

Oblique mapping camera ___________________— — — - 8

Panoramic camera photography _______ —— — — _____ 8

Profiles ____-_____---_—_—__—-_——--—----- 10

Crater geometry _____________ ——— _ ___________________ 10

Lunar flows ______—__________ — _________—— ____— 10

Lunar surface roughness ____ —— — __ — —— —— — ____— 13

Bistatic-radar method--------- —— - ————— —— — ——— 14

Photogrammetric method ___ —— ___ — ——— ______——— 15

Reading error problem _______ —— __ — — —— ______— 15

Results of comparison------------- —— - — __ —— — -—— 17

Conclusion _______________----_—______ — — ______———— 21

References cited _______ — __ —— — --- — - ——— — - — — --- 22

ILLUSTRATIONS

[Plates are in pocket]

PLATE 1. Experimental lunar topographic map of scabland region north of Aristarchus Plateau.

2. Experimental topographic map of southeast Krieger area.

3. Experimental lunar topographic map of a mare dome north of the Aristarchus Plateau.

4. Experimental topographic map of area north of Diophantus.

Page

FIGURE 1. Graph showing regression curves determined from standard error in elevation measurement (SE ) and local sun

elevation angles _____________________________________________________________ —— ____— D6

2. Vertical photograph of scabland region north of Aristarchus Plateau ___________ —— __________ —— ___ —— ______ 7

3. Oblique photograph of Alphonsus__________________________________________________ —— ____ —— ___ 8

4. Contour map of Alphonsus _____________________________________________— — _________ —— _______ 9

5. Profiles and rim-crest elevations of Linne ___________________________________________________ —— __— 11

6. Photograph showing lava flows in Mare Imbrium ______________________—— —— ____ ——— _____ — _____ 12

7. Map and profiles of Imbrium flow lobe ______________________________________________„__-_______ 13

8. Photograph showing flow lobe in basin north of King _________________________ —— __ _______________________ 14

9. Histograms illustrating effect of reading error on semilogarithmic slope-probability distributions _____ —— — ——— 16 

10-13. Graphs showing—

10. Effect of photogrammetric reading error on statistical descriptors of slope-probability distribution __ ——— _ 17

11. Slope-probability distributions of lunar cratered plains measured by photogrammetry and radar ___——— 19

12. Slope-probability distributions of lunar uplands measured by photogrammetry and radar ______________ 20

13. Generalized relations between algebraic standard deviation and slope length as determined using

photogrammetric method _______________________________—_________________________ 21

TABLES

Page

TABLE 1. General features, films, and remarks for Apollo cameras used in experimental photogrammetric studies _______ D3

2. Nominal errors in elevation related to Apollo photographs and analytical stereoplotiers _______________ 5

3. Coefficients of regression curves determined from all standard errors and local sun elevation angles for each

measured point ___________________________________________________________________________ 5

4. Experimental topographic maps prepared in support of Photogeology Apollo 15-17 (NASA experiment S-222) ____ 7

5. Profiles prepared for studies of crater dimensions _______________ ______________________________________ 11

6. Statistical parameters of slope-probability distributions using Apollo photographs and stereophotogrammetry ___ 18

ill

APOLLO 15-17 ORBITAL INVESTIGATIONS

EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES

By SHERMAN S. C. Wu and H. J. MOORE

ABSTRACT

High-quality cameras capable of making reliable measurements 

and topographic maps were carried aboard the orbiting Command 

and Service Modules during Apollo missions 14, 15, 16, and 17. In 

addition to providing selenodetic control and topographic maps with 

scales of 1: 10, 000,1: 50,000, and 1: 250,000, photographs taken by 

these cameras can be used to obtain quantitative data for specialized 

scientific studies such as: (1) the relation between stereophotogrammetric measurements and illumination conditions, (2) measurement 

of structural deformation, (3) crater geometry and lunar landforms, 

(4) rheological properties of lunar flows, and (5) fine-scale lunar surface roughness.

Experimental photogrammetric studies have produced results applicable to the exploration of the Moon and other planetary bodies. 

Optimum illumination conditions for lunar stereophotogrammetric 

studies include sun elevation angles near 30°. Lower sun elevation 

angles result in excessive shadows, and much higher angles result in 

loss of scene contrast. For any given scene, local slope and albedo 

affect stereophotogrammetric measurements. Lunar results may be 

applied to other planetary bodies devoid of thick atmospheres.

Topographic maps prepared from vertical Apollo 15-17 mapping 

camera photographs can be prepared with contour intervals as small 

as 50 m depending on map scale, local roughness, illumination, and 

other conditions. Oblique photographs taken by the mapping camera 

can be used to prepare topographic maps with contour intervals of 50 

m or larger. Panoramic camera photographs taken by Apollos 15-17 

can be used to prepare topographic maps of fine-scale features with 

form-line intervals near 5 m under ideal conditions.

For scientific purposes, the small- and large-scale topographic 

maps can be used to determine subtle structural deformations of the 

lunar surface. Certain geologic features and shapes of small lunar 

landforms can be portrayed at a fine scale with an accuracy never 

before possible.

The geometry of lunar craters—the most ubiquitous lunar 

landform—has been determined using profiles and topographic maps 

prepared from Apollo 15-17 photographs with high accuracy. These 

profiles and maps required a revision of equations describing lunar 

craters.

Profiles of lunar volcanic and impact melt flows using the 

stereophotogrammetric method established the thicknesses and 

widths of the flows. When combined with theory and with lunar 

topographic maps to establish the gradient of the flow, it has been 

shown that the materials of mare flows had a yield strength about 

the same as basalt lava in Hawaii and that material of the flow of 

impact melt north of the crater King had a yield strength larger than 

the mare flow. Additionally, structural tilts of the maria after the 

mare flow formed were negligible, but some local warping occurred.

Stereophotogrammetric measurements on the high-resolution 

panoramic camera photographs of Apollos 15-17 and the lunar topographic camera photographs of Apollo 14 have been used to determine lunar surface roughness and slope-probability distributions at 

scale lengths of 17 to 25 m and larger. These data form a basis for 

comparison of the Apollo 14-16 bistatic-radar method of determining 

lunar surface roughness and slope-probability distributions at comparable scale lengths. The photogrammetric and radar methods 

agree on four major points: (1) lunar maria are smoother than 

uplands, (2) the magnitude of the algebraic standard deviations of 

slope-probability distributions for lunar maria are comparable for 

both methods, (3) maria appear rougher at small scale lengths than 

at large scale lengths, and (4) slope-probability distributions are typically semilogarithmic, but they vary and may be gaussian and complex.

Although the potential uses of Apollo photographs in special scientific studies have not been fully realized, existing studies employing 

the photographs and maps prepared from them have been profitable. 

Achievement of required mensuration for special scientific studies 

requires close coordination between the photogrammetrist and the 

user.

INTRODUCTION

In a substantial improvement over all previous 

Apollo lunar missions, the Command and Service 

Modules of the Apollo 15, 16, and 17 missions carried 

camera equipment capable of obtaining high-quality 

topographic and selenodetic data for the Moon from 

orbit. Equipment on each spacecraft included a mapping camera, a stellar camera, a laser altimeter, and a 

high-resolution panoramic camera. Accurate topographic measurements of the lunar surface in support 

of quantitative geologic studies can be made using the 

photographs returned to Earth by these later Apollo 

missions. Apollo 14 carried a lunar topographic camera 

(Hycon) in orbit from which quantitative topographic 

data could be obtained. Previous missions, as well as 

Apollos 14-17, carried Hasselblad cameras. Stereoscopic Hasselblad photographs of the lunar surface 

taken from orbit by the Apollo 11, 12, and 14 missions 

provided improved topographic data of selected features and were used in prelanding studies of the Apollo 

16 landing site (Descartes).

This paper is one of four separately bound chapters 

summarizing Apollo 15-17 orbital investigations: (1) 

"Stratigraphy of Part of the Lunar Nearside" (Chapter

Di
D2 APOLLO 15-17 ORBITAL INVESTIGATIONS

A, Wilhelms, 1980), (2) "Lunar Remote Sensing and 

Measurements" (Chapter B, Moore and others, 1980), 

(3) "Geometric Interpretation of Lunar Craters" (Chapter C, Pike, 1980), and (4) "Experimental Photogrammetry of Lunar Images" (Chapter D, this paper). This 

paper summarizes experimental photogrammetric 

studies done chiefly in support of special lunar research 

projects. Photogrammetric results described in this 

paper do not include the systematic topographic mapping being conducted by the Defense Mapping Agency 

(Kinsler, 1975) or the selenodetic system established 

by the U.S. Geological Survey and National Geodetic 

Survey (Doyle and others, 1976). Four categories of experimental photogrammetric studies are reported below: (1) the effect of illumination conditions on precision of measurements, (2) experimental topographic 

maps prepared to support specific topical studies and to 

demonstrate the capabilities of the photogrammetric 

method, (3) detailed profiling to be used in connection 

with specific topical studies, and (4) terrain analyses in 

support of the Apollo bistatic-radar experiment. These 

experimental photogrammetric studies demonstrate 

the value of the photogrammetric techniques in 

planetary exploration when suitable maps and photographs of the planetary surface are part of the exploration program.

Acknowledgments.—Results reported in this paper 

are based on work performed by the U.S. Geological 

Survey as part of NASA Experiment S-222 

(Photogeology—Apollo 15-17; NASA contract 

T-1167B) on behalf of the National Aeronautics and 

Space Administration. The authors wish to express 

their appreciation to S. N. Hardee and J. Dixon of the 

Johnson Spacecraft Center, Houston, Tex. for their 

support and assistance in the experiment. Results reported in this paper were made possible because of the 

diligent and skillful efforts of Raymond Jordan, Francis J. Schafer, Bobby C. Philpott, and Gary M. Nakata 

of the U.S. Geological Survey. G. L. Tyler of Stanford 

University kindly furnished the results from the 

Apollo Bistatic-Radar Experiment.

CAMERAS AND PHOTOGRAPHY

Apollo cameras and photography used for photogrammetric purposes evolved from simple hand-held 

and bracket-mounted cameras in the Command 

Module and photographs taken through the spacecraft 

windows (Norman and others, 1969) to a sophisticated 

mapping camera system mounted in a scientific instrument module (Light, 1972). Photographs taken 

with Hasselblad cameras during the early Apollo 

missions were used to demonstrate the applicability of 

photogrammetry to mensuration and topographic

mapping of the lunar surface (Norman and others, 

1969; Wu, 1969, 1971). Apollo 14 was the first mission 

to obtain high-quality photographs suitable for photogrammetric purposes. The lunar topographic camera 

on board the Apollo 14 Command Module (Dietrich, 

1971) was used to obtain data on fine-scale lunar 

roughness (Moore and others, 1975,1976,1980). Apollo 

missions 15, 16, and 17 carried the sophisticated mapping camera system in orbit (Dietrich and Clanton, 

1972a, 1972b; McEwen and Clanton, 1973). In the 

mapping camera system, a 3-inch stellar camera was 

mounted at a 96° angle to the axis of a 3-inch mapping 

camera, and a laser altimeter capable of measuring 

slant range withirtt 2 m was alined with the mapping 

camera. This system has been used for establishing a 

selenodetic control network as well as topographic 

mapping (Doyle and others, 1976; Cannell and Ross, 

1976; Kopal and Carder, 1974). A panoramic camera, 

carried on Apollo missions 15-17, obtained highresolution stereophotographs that are useful for detailed studies. The cameras and photographs used to 

collect data in this report are discussed briefly below 

and listed in table 1.

LUNAR TOPOGRAPHIC CAMERA

The lunar topographic camera (45.5-cm focal length) 

(also called the Hycon camera) was carried aboard the 

orbiting Command Module of Apollo 14 to obtain 

high-resolution topographic data of the Apollo 16 landing site and the Apollo 14 landing site. A camera malfunction prevented acquisition of these data and resulted in the recovery of only 193 frames from altitudes 

of approximately 18 km extending from the east rim of 

the crater Theophilus to a point northwest of the crater 

Kant (El-Baz and Head, 1971). At a nominal spacecraft 

altitude of 20 km, each photograph, which has an 11.43 

x 11.43-cm format, covers an area about 5.0 km on an 

edge. Photoscale is about 1:44,000. Stereoscopic coverage was achieved by overlapping consecutive frames by 

60 percent, producing a base-height ratio of 0.095. Use 

of alternate pictures gives a base-height ratio near 

0.19.

Photography taken with this camera had the highest 

resolution of all the Apollo missions flown previously, 

but higher resolutions were achieved by subsequent 

missions. Resolutions achieved by the lunar topographic camera are 62 optical pairs per millimeter at a 

tribar contrast of 2:1 with 3400 type film, which corresponds to a ground resolution of 0.7 m (H. W. Radin, 

memorandum for Bellcomm Inc., August 31, 1970).

The high resolution required image motion compensation, which was accomplished by rocking the camera 

in the direction of flight. Calibration of the camera 

using stellar methods yields a calibrated focal length of
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D3 

TABLE 1.—General features, films, and remarks for Apollo cameras used in experimental photogrammetric studies

[After Dietrich (1971) and Dietrich and Clanton (1972a)]

Cameras Features Film size and type Remarks

Lunar Topographic CameraMapping Camera

45.5-cm lens, vacuum platen, 127 mm; type SO 349 highimage-motion compensator definition aerial film, AEI 6;

3400 Panatomic-X blackand-white film, ASA 80.

-Electric; controls in CSM1 ; 457.2 m of 127-mm film type 

7.62-cm-focal-length lens; 3400 Panatomic-X, ASA 80. 

74° by 74° field of view; a 

square array of 121 reseau

fiducial marks,

camera serial

Panoramic Gamer a _

crosses, a 

and the 

number recorded on each 

frame with auxiliary data of 

time, altitude, shutter speed, 

and forward-motion control 

setting.

-Electric; controls in CSM; 

60.96-cm lens; 10°46' by 108° 

field of view; fiducial marks 

printed along both edges; 

IRIG B time code printed 

along forward edge; data 

block includes frame 

number, time, mission data, 

V/h, and camera-pointing attitude.

1981.2 m of 127-mm film EK 

3414.

Used to obtain high-resolution photographs of lunar surface near candidate 

Descartes crater landing site. Operating 

difficulties prevented scheduled convergent stereoscopic photography of the approach to the Descartes landing site, of 

the landed Lunar Module near Fra 

Mauro crater, and of the impact points of 

the Apollo 14 SIVB booster rocket stage 

and Lunar Module.

The 11.43 by 11.43-cm frames with 78 percent forward overlap provide the first 

Apollo photographs of mapping quality. 

Data recorded on the film and telemetered to Earth will permit reconstruction of lunar-surface geometry with an 

accuracy not available with earlier systems.

11.43 by 114.8-cm images were taken looking alternately forward 12.5° then 12.5° 

aftward for stereopairs. Consecutive 

frames of similar tilt have 10 percent 

overlap; stereopairs, 100 percent overlap. Panoramic photographs provide 

high-resolution stereoscopic coverage of 

a strip approximately 330 km wide, centered on the ground track.

'Command and Service Module.

455.677±0.013 mm. A maximum radial distortion of 26 

/xm occurs at a radial distance of 72 mm and less than 

10 /xm within a distance of 40 mm for a standard format (Malhotra, 1970). Tangential distortions are 1.2 

and 0.4 /xm at distances of 72 and 40 mm, respectively.

MAPPING CAMERA

Mapping cameras (7.62-cm focal length) (also called 

metric or terrain cameras) were carried in the scientific 

instrument modules of the orbital spacecraft in Apollos 

15, 16, and 17. Among the scientific objectives of the 

cameras were the development of a coordinate network 

of control points on the lunar surface with an accuracy 

of 10 to 15 m (Light, 1972) and the preparation of topographic maps (for example, Defense Mapping 

Agency, 1974a). Photographic coverage of the Moon by 

these cameras is extensive but constrained by the 

spacecraft orbits and illumination conditions of the 

Moon during the missions (Aeronautical Chart and Information Center, 1971; Defense Mapping Agency, 

1972, 1973a). Importantly, some coverage was taken at 

oblique angles by rolling the spacecraft. At the nominal spacecraft altitude of 110 km, each photograph, 

which has an 11.43x 11.43-cm format, covers an area 

about 165 km on an edge. Photoscale is near 1:1.45 

million. Stereoscopic coverage was obtained by overlapping consecutive frames 78 percent, producing 

base-height ratios near 0.33. Use of alternate frames 

increases the base-height ratio to 0.66.

Resolution of the cameras was 200 lines/mm at 1,000 

to 1 contrast with film type 3400. Line-pair resolution 

of the ground is near 15 to 20 m at nominal altitude 

(National Space Science Data Center, 1972, 1973, 

1974). Lens distortions are nominally less than 50 /xm 

(Light, 1972). Film position and distortion can be controlled using images of 8 fiducial marks and a square 

array of 121 reseau marks engraved on the glass 

focal-plane plates used in each camera (Itek Corp., 

1972). Calibration data for each camera are listed below.

Mission

Camera 

serial No.

Apollo 15 ____003

Apollo 16 ____005

Apollo 17 ____203

Calibrated focal 

length <mm>

76.080 ± 0.002 

75.936 ±0.003 

75.842 ± 0.003

Offset of principal point

(mm)

x,, = -0.006, v,, = -0.002 

*„ = -0.010, >„ = -0.004 

xp = -0.005, ?„ = -0.007

PANORAMIC CAMERA

The panoramic camera (60.96-cm focal length) is the 

highest resolution orbital camera employed by Apollo 

and combines high resolution with overlapping convergent photographs so that fine-scale measurements 

and detailed topographic maps may be made from photographs taken by the camera. In contrast with the
D4 APOLLO 15-17 ORBITAL INVESTIGATIONS

other Apollo cameras, the Itek optical bar panoramic 

camera is a fixed-focal-length direct-scanning camera 

producing cylindrical camera geometry. Scanning is 

accomplished mechanically with the scanning slit and 

center field of the lens operating as a unit. Use of the 

center field of the lens permits projection of the 

sharpest possible image onto the film. Photographic 

coverage of the Moon is extensive but constrained by 

the spacecraft orbits and illumination conditions of the 

Moon during the missions (Aeronautical Chart and Information Center, 1971; Defense., Mapping Agency, 

1972, 1973a). The frame format is 11.43 x 11.43 cm. 

Because of the cylindrical camera geometry, highest 

resolution is achieved along the ground track traced by 

the camera optical axis with minimum distance to the 

surface. At the nominal spacecraft altitude and 12.5° 

tilt in the direction of flight, the 11.43-cm film width 

corresponds to about 21 km along the ground track. 

Coverage in the crosstrack direction is about 330 km 

wide. Resolution decreases and coverage increases in 

the cross-track direction as tilts due to scanning increase symmetrically about the ground track. Photoscale along the track is near 1:185,000 for the nominal 

altitude. Stereoscopic coverage was obtained by alternately tilting the camera 12.5° forward along the track 

and 12.5° aftward along the track at 5-second intervals 

so that overlaps were 90 to 100 percent (National Space 

Science Data Center, 1972, 1973, 1974). Base-height 

ratios for nominal conditions were near 0.44, producing 

strong stereo-model geometry.

Resolution of the camera is 135 lines/mm at a contrast ratio of 2 : 1,180 lines/mm with medium-contrast 

targets, and 150 lines/mm with low-contrast targets 

(Itek Corp., 1967). Line-pair resolutions correspond to 

ground resolutions of 3.0, 2.0, and 2.5 m respectively at 

the center of scan. Because of the mechanical scanning, 

cylindrical geometry, and convergent stereopairs, distortions are complicated and more difficult to correct 

than those of frame cameras, and stereoscopic models 

are difficult. For these reasons, specially designed 

equipment such as the AS-11A stereoplotter (Ottico 

Meccanica Italiana, 1964) was required for mapping 

purposes. Some mensuration data such as profiling 

may be obtained with little or no error in directions 

parallel to the ground track using the AP/C plotter 

(Ottico Meccanica Italiana, 1966). The panoramic 

cameras used during each of the Apollo missions were 

completely calibrated (Itek Corp., 1967), and calibrated 

focal lengths are listed below.

Mission

Lens 

serial No.

Apollo 15 __________N-54

Apollo 16 ____________N-45

Apollo 17 -----___-N-53

Camera 

No.

003

005

9

Calibrated focal length 

(mm)

609.752 ± 0.025 

609.524 ± 0.025 

609.676 ± 0.025

Some of the panoramic camera photographs of the 

Apollo 17 mission near the area of the lunar crater 

Euler were obtained without rocking the camera to 

produce the 25.0° convergence angle. For this photography a 10 percent overlap of consecutive frames was 

obtained, giving base-to-height ratios less than or close 

to 0.1. Here stereomodel geometry is weak, and mensuration is substantially poorer than for the nominal 

panoramic photographs.

METHODS AND PROCEDURES 

EQUIPMENT AND MATERIALS

Photogrammetric equipment used in the mensuration and topographic mapping in this report were the 

AP/C (Ottico Meccanica Italiana, 1966) and the 

AS-11A (Ottico Meccanica Italiana, 1964) analytical 

stereoplotters. Both plotters are controlled by computers. The plotters are very flexible in accommodating 

a wide range of photographic geometries, principal distances, and base-height ratios, and lens distortion and 

lunar curvature can be corrected by the computers. 

Topographic maps prepared from panoramic camera 

photographs require the AS-11A plotter, but the AP/C 

can be used with panoramic camera photographs for 

profiles parallel to and measurements near to the 

groundtrack. Cross-track profiles from panoramic 

camera photographs prepared using the AP/C are 

curved because of the cylindrical geometry described 

above. Both plotters have a least significant reading 

capability of 1 ^tm, and repeated measurements have a 

precision near ±2 /um. When combined with the scale 

and base-height ratios of the mapping camera photographs, this precision translates to ±7.5-10 m for a 

variety of mapping camera photographs (Wu, 1976). 

Nominal values for each camera are listed in table 2.

In the studies, second-generation master positive 

transparencies prepared from the original negative 

were used in the plotters. These transparent positives 

are the best quality reproductions available in original 

format size and provide photographs with minimal loss 

of the original resolution. Probable errors in elevation 

measurements are interpreted in terms of nominal 

photograph resolution (Gardner, 1932) in table 2.

CONTROL AND LEVELING

Because the selenodetic control points were not 

available at the time of part of the photogrammetric 

processing, stereomodels of mapping camera photographs were oriented and leveled using photosupport 

data and existing small-scale topographic maps. For 

setting up models of panoramic camera photographs, 

control information was obtained from stereomodels of
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES 

TABLE 2—Nominal errors in elevation related to Apollo photographs and analytical stereoplotters

D5

Cameras

Lunar topographic

Panoramic

Mapping

Scale (xlO-6 )

. ___ 0.044

______ .185

___ 1.45

Resolution

(lines/mm )

62

180

200

Baseheight

ratio

0.19

.44

.33

Plotter

precision

(^ml

+2

+2

Plotter

precision

in elevation

(m)

0.15

.64

8.6

Photograph

probable

error

(fan}

3.2-4.0

1.1-1.3

1.0-1.2

Probable

error in

elevation

(m)

0.71-0.88

.47- .56

4.3 -5.4

mapping photographs covering the same area. In the 

case of the lunar topographic camera photographs, 

model orientation information was sometimes obtained 

from Lunar Orbiter pictures and data (National Space 

Science Data Center, 1969). In some cases, where the 

geology of a local area was of interest and where no 

information was available, such techniques as assuming a mare surface to be level or the rim of a large 

crater to be level were used.

METHODS OF MEASUREMENTS

For map compilation or profile plotting, after a 

stereomodel is obtained, regular photogrammetric procedures are followed to plot measurements. However, 

for the support of terrain analysis, specifically for the 

study of slope-probability distributions of the lunar 

surface, which will be described in detail in this report, 

statistical profiles are measured in a model along 

linear traverses using a constant horizontal distance 

between consecutive points. Each profile contains at 

least 500 points. At each point three to five readings 

were taken. A sample area was chosen that is representative of a surface geologic unit. The slopeprobability statistics then provide a quantifier for that 

ftype surface or that geologic unit.

PRECISION OF MEASUREMENT

The level of detail that can be achieved in preparing 

profiles and topographic maps from Apollo 

stereophotographs depends on the standard error in 

elevation measurements (a*), 1 which is the product of 

photograph scale or its reciprocal-scale factor (Sp ), the 

height-base ratio (H/B), and the standard error of 

parallax measurement (ov) (Doyle, 1963; Light, 1972). 

Scale factors and height-base ratios using Apollo photographs with suitable plotters are generally ideal to 

very good. The standard error of parallax measurement is related to a number of factors such as lens 

distortions, photograph quality, scene contrast, and the 

person who measures parallax. Scene contrast is re-

'When experimentally determined, the standard error in elevation measurement is designated SE .

lated to surface roughness or patterns and illumination 

conditions. The wide variety of illumination conditions 

of Apollo photography combined with the reflective 

properties of the lunar surface offered an opportunity 

to discover the relation between illumination and the 

standard error in measurement. Extensive studies 

using mapping camera photographs have been made 

relating standard error in measurements with variable 

illumination conditions and, to some extent, with 

slopes (Wu, 1976). Data on standard errors in measurement for the lunar topographic camera and 

panoramic camera photographs are limited, but some 

results are reported here (see also Wu and others, 

1973).

MAPPING CAMERA PHOTOGRAPHY

Standard errors in measurement for Apollo mapping 

camera photographs correlate strongly with the illumination conditions (Wu, 1976). When sun elevation 

angles are less than about 10°, large areas of the rugged parts of the Moon are covered by shadow. This 

condition precludes measurements in deep shadows, 

and standard errors in diffuse shadows tend to be large. 

Photographs taken with sun elevation angles larger 

than 30° show increasing average standard errors in 

measurements because scene contrast is reduced by the 

large relative increase in reflected sunlight or 

heiligenschein at large incidence angles (Wildey, 

1972).

Regression fits were made to the data in the form

Y = a + (3X + yX2 ,

Where Y is the standard error in measurement, X is 

sun elevation angle, and a, (3, and y are coefficients 

listed in table 3 for each mission and the combined 

missions. The regressions, exclusive of Apollo 16, show

TABLE 3.—Coefficients of regression curves determined from all standard errors and local sun elevation angles for each measured point

Coefficients of 

regression curve Apollo 15 Apollo 16 Apollo 17

Combined 

Apollo 15-17

a ____________7.70 6.91 10.84 8.48

(3 - ___ .0361 .0938 -.206 -.561

7 _ _ .00149 .000194 .00348 .00181
D6 APOLLO 15-17 ORBITAL INVESTIGATIONS

a tendency for the minimum standard error in elevation measurement to occur near a sun elevation angle 

of 30° (fig. 1). Similar results are obtained where local 

slope is taken into account (fig. 1). Results in detail are 

described in an investigation on illumination and 

measurement precision for lunar photography (Wu, 

1976).

Although these studies clearly show that sun elevation angles near 30° are optimal for stereophotogrammetry, the effects of the photometric function, surface 

albedo, and height-base ratio have not been carefully 

studied.

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UJ

UJ 4

oc

D

(f) 2

UJ

2 n

-

-

/

: /

~ /

.

- /

/

~ /

_ X

-

_

_

—

A

I I I I t I I I I I I I I I I I I i

30 60 90 30 60 90

20

18

O

OC 16

O

OC

CC 14

UJ

10

M 8

I I I I I I I I I

D

I I I I I I I I I

30 60 90 30 60 90

SUN ANGLE,IN DEGREES

FIGURE 1.—Regression curves determined from standard error in 

elevation measurement (SE ) and local sun elevation angles 

(dashed lines); standard error in elevation measurement and 

local sun elevation angles corrected for surface tilt (solid lines): 

(A) Apollo 15, (B) Apollo 16, (C) Apollo 17, and (D) combined 

data.

PANORAMIC AND LUNAR TOPOGRAPHIC CAMERA 

PHOTOGRAPHY

As part of the measurements for surface roughness 

and slope-probability distributions at the fine scale, 

average standard errors in measurement were computed for 500 to 1,000 points on lunar topographic and 

panoramic camera photographs. Standard errors in 

elevation measurements (SE ) for each point were estimated from the readings. Averages of the standard 

error in measurement, tabulated below, represent an 

estimate for those photographs.

Camera

Average of standard error

of average 

of measurements

Lunar topographic_------_0.7 ± 0.4 m

Panoramic ____________ .9 ± .2m

Number of standard errors 

in average

9

15

TOPOGRAPHIC MAPS

Apollo mapping and panoramic camera photographs 

provide accurate data on the morphology of lunar craters and other features with subtle relief. Topographic 

mapping of the Moon at 1 : 250,000 scale with mapping 

camera photographs has been extensive (Kinsler, 

1975). Contour intervals of 100 m are standard for 

these maps, and in some cases supplementary contours 

with a 50-m interval are given (see for example Defense Mapping Agency, 1975). Scales and contour 

intervals of maps prepared from panoramic camera 

photographs vary depending on the features portrayed. 

The largest scale maps are 1 : 10,000 with a 10-m contour interval and 5-m supplementary contours (see for 

example Defense Mapping Agency, 1974d). These contour intervals are entirely consistent with the 

capabilities of the cameras and the quality of the photographs. Acceptable contour intervals are three or 

more times the standard error in elevation (3 ay,) and 

fall within or close to the combined errors of resolution, 

instrument errors, and errors measured experimentally.

Some experimental topographic maps were prepared 

by the U.S. Geological Survey to test the capability of 

the photography and to obtain scientific data on a 

timely basis and with sufficient detail. Purposes of the 

maps included support of the bistatic-radar studies, 

dimensions of craters, and miscellaneous geologic 

studies. Table 4 summarizes the maps prepared and 

their use. Although not considered in detail here, two 

maps prepared from Apollo 12 Hasselblad photographs 

are included in the table.

VERTICAL MAPPING CAMERA PHOTOGRAPHY

A topographic contour map of the scablands region 

north of the Aristarchus Plateau was compiled from
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D7

vertical mapping camera photographs (fig. 2). The 

photographs were taken under a number of favorable 

conditions such as (1) vertical optic axes, (2) a large

base-height ratio (0.4), and (3) good sun illumination 

conditions (sun elevation angle of 12°). In addition, 

horizontal and vertical control was available from the

TABLE 4.—Experimental topographic maps prepared in support of Photogeology-Apollo 15-17 (NASA Experiment S-222)

Map name 

or title

Scablands north of

Do _ ____ _ __ _ _______

Location

Long.

2° W.

27° W.

_ -___53° W.

___ _53° W.

______2° W.

Lat.

6°S. 

2°S.

28° N. 

28° N. 

12° S.

Scale

1:200,000 

1:200,000

1:100,000 

1:50,000 

1:250,000

Contour 

interval

(m)

200 

200

50 

10 

200

Photographs used

AS12 8069, 8070

80-mm Hasselblad 

AS12 8093, 8094

80-mm Hasselblad 

AS15-Map- 2483,- 2484

AS15- Part- 2344, -2349 

AS16- Map-2477,- 2478

Plotter 

used

AP/C 

AP/C

AP/C 

AS-11A 

AP/C

Map 

compiler

R. Jordan 

____do - _ _

_ _ do ___ ___

_ _ do_ ___ _

G. Nakata 

R. Jordan

Use

Support Bistatic-Radar Experiment, study of large-scale lunar 

roughness. 

Do.

Geologic study of Aristarchus region. 

Do.

Demonstration of use of oblique 

mapping camera photographs in

Southeast Krieger area ______45° W. 28° S. 1:10,000 

Mare dome northeast

AS15-Pan-0320,-0325

preparation of topographic 

maps.

AS-HA R.Jordan Study of morphology of secondaryimpact craters from Aristarchus.

49° W

34° W

Domed crater in crater Aitkin _ 168° 

W. 

Lee-Lincoln Scarp (strip map) __ 30° W.

31° N.

28° N.

15° S. 

20° N.

1:15,000 

1:50,000

1:15,000 

1:25,000

10 

20

10 

10

AS15-Pan-0332,-0337

AS15- Pan- 1915,- 1920

AQ17 Pan 97fV9 97^7

AS-11A 

AS- HA

AS- HA 

AS-11A

do ___

__ do _ __

_ _do ___

_ _ do _ __

Study of morphology of lunar

domes. 

Study of crater morphology. Provides data on dimensions of 

smallest craters photographed 

by Apollo from orbit.

domes.

lunar surface.

FIGURE 2.—Vertical Apollo 15 mapping camera photograph 2483 of scabland region 

north of Aristarchus plateau. Photograph is one of a stereoscopic pair used to make 

topographic map in plate 1.
APOLLO 15-17 ORBITAL INVESTIGATIONS D8

1: 250,000-scale maps "Nielsen" and "Freud" (Defense 

Mapping Agency, 1974e, f). For these reasons it was a 

good model to use to determine the smallest contour 

interval that could be obtained with this type of photograph. As shown in plate 1, a 50-m contour interval can 

be obtained from the Apollo mapping camera photographs. This map, combined with one prepared from 

panoramic camera photographs, was used to detect 

warping of the lunar surface that occurred after the 

formation of the rilles. Figure 2 is one of the mapping 

camera photographs used in compiling the topographic 

map in plate 1.

OBLIQUE MAPPING CAMERA PHOTOGRAPHY

An experiment has demonstrated that valuable topographic data can be obtained from high oblique photographs (Wu and others, 1972). As shown in figure 3, 

the crater Alphonsus was covered by Apollo 16 mapping camera photographs 2477 and 2478. The high tilt 

(40°) of these photographs was enough to include the 

horizon. A topographic form-line map was compiled 

from this model in the AP/C plotter (fig. 4). In spite of

the large tilt angles, this model has a 0.35 base-height 

ratio. The average standard error of repeatability of 

elevation measurements within the mapped area was 

near llm. Thus it is possible to attain a contour interval of 50 m. Because the photographic support data for 

the Apollo 16 photographs were not available at the 

time this test was made, the model was scaled using 

Lunar Orbiter support data (LO IV H- 108) and leveled 

assuming that the floor of Alphonsus was level.

PANORAMIC CAMERA PHOTOGRAPHY

Very detailed topographic information of subtle 

landforms and small craters can be obtained from the 

panoramic camera photographs. Several experimental 

topographic maps were compiled of geologically 

significant features on the lunar surface. Some of these 

topographic maps are described in the following sections. All of the model geometries from which these 

maps were compiled are similar in that they all have a 

25° convergent angle, which gives a strong base-height 

ratio of 0.44, and they all have from 90 to 100 percent 

overlap. The model scales range from 1 : 150,000 to

FIGURE 3.-Apollo 16 mapping camera photograph 2477 is one of the photographs used 

in compiling the topographic map shown in figure 4. Outline shows location of boundaries of map in figure 4.
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D9

1 : 200,000, from which a 1 : 10,000 map scale is quite 

easily obtainable on an analytical plotter.

One experimental topographic map of an area southeast of Krieger was compiled from Apollo 15 panoramic

photographs (pi. 2). This map demonstrates that a scale 

as large as 1 : 10,000 with a 5-m form-line interval can 

be obtained from a model of panoramic photography. 

To obtain control information to orient this model, a

-5 13' -0°36'

-11 08'

-16 12'

-10° 50'

-15 55'

-5 00' 10 20 30 40 50 KILOMETERS -0 05'

CONTOUR INTERVAL 200 METERS

(Approximate)

FIGURE 4.—Contour map of Alphonsus compiled from oblique Apollo 16 mapping camera photographs 2477 (see fig. 3) and 2478. Map

prepared under NASA contract T5874A.
DIG APOLLO 15-17 ORBITAL INVESTIGATIONS

model from Apollo 15 mapping camera photographs 

(numbers 2478 and 2479) was set up on the AP/C 

analytical plotter. The scaling information for this 

mapping camera model was obtained from the photographic support data, and the leveling was accomplished by selecting elevations from Lunar Topographic Orthophotomap LTO 39A1, Kreiger (Defense 

Mapping Agency, 1973b). Secondary craters portrayed 

on this map were produced by Aristarchus some 150 

km south and form part of the data set on lunar crater 

geometry (Pike, 1974, 1980). Secondary crater diameters, depths, rim heights, circularity, and ejecta symmetry can be measured on the map.

Another topographic map (pi. 3) illustrates that subtle features such as lunar domes can be accurately 

portrayed using panoramic camera photographs. The 

dome has a mere 60 m of relief and is seen with vivid 

clarity on low-sun photographs. On the 1 : 250,000- 

scale Lunar Topographic Orthophotomap (LTO) 

Krieger (Defense Mapping Agency, 1973b), only one 

contour is present around the dome because of the 50-m 

contour interval. Thus, subtle features barely detectable in topographic maps prepared from mapping camera photographs can only be portrayed in detail by 

stereophotogrammetry from panoramic camera photographs.

A topographic map of the Delisle-Diophantus area 

compiled on the AS-HA plotter is included on the area 

covered by LTO Delisle (Defense Mapping Agency, 

1974a) (pi. 4). Dimensions of small craters derived from 

this map represent the best data in the sample on very 

small lunar craters used in establishing the geometry 

of lunar craters (Pike, 1974). The nature and amount of 

filling of Rima Brahms (the sinuous rille that transects 

the map) by ejecta from two larger craters to the north 

and south (Delisle and Diophantus) can be measured. 

Some data on the morphology of ejecta blankets can be 

obtained from this map.

PROFILES

Some topical studies of the Moon require carefully 

and specially prepared profiles in order to achieve the 

objectives of the study, and close coordination between 

the user and photogrammetrist is required. Pioneering 

efforts were conducted with Apollo 10 Hasselblad photographs to compare profiles derived with photogrammetric and photoclinometric techniques (Lucchitta, 

1971), to study mass wasting (Pike, 197Ib), and to 

demonstrate the photogrammetric method for lunar 

research (Wu, 1969, 1971). Subsequently, photographs 

taken with the photogrammetric quality cameras of 

Apollo 15, 16, and 17 were used to make profiles for 

specific studies. Two such examples are the quantitative studies of crater dimensions and lunar flows.

CRATER GEOMETRY

Profiles of craters were very important in the early 

phases of studies employing Apollo mapping camera 

photographs when carefully controlled maps prepared 

with them were not yet available. Profile data along 

with geologic interpretation resolved the controversy 

of the origin of the previously enigmatic crater Linne 

(fig. 5), which turned out to be an ordinary albeit very 

fresh impact crater (Pike, 1973b, 1980). Topographic 

analyses of 25 farside craters (table 5) 1.6 to 275 km 

across showed that the craters do not differ in shape 

from nearside craters and their shapes were more consistent with an impact origin than a volcanic origin 

(Pike, 1973a, 1980). It was also shown that shapes of 

farside craters measured with stereophotogrammetry 

were more consistent with lunar nearside craters than 

those measured using photometry. Because carefully 

controlled maps were not available for these early 

studies, orientations of stereomodels were accomplished with sufficient accuracy in a variety of ways: 

(1) For craters superposed on maria, surrounding surfaces were assumed to be level, (2) for large craters, 

their flat floors were taken as level, and (3) for some 

craters, Lunar Orbiter data were used (National Space 

Science Data Center, 1969). Stereophotogrammetric 

profiles prepared by the U.S. Geological Survey and 

measurements obtained from Lunar Topographic Orthophotomaps (for example Defense Mapping Agency, 

1974a) prepared from Apollo mapping and panoramic 

camera photographs have resulted in a revision of 

depth-diameter relations of lunar craters (Pike, 1974) 

and have revealed discrepancies of some pre-Apollo 

data (Pike, 1972).

LUNAR FLOWS

Detailed profiles of a flow lobe (figs. 6 and 7) in Mare 

Imbrium were a necessary part of a study of the 

rheological properties of the flow and tectonic deformation in the general area (Moore and Schaber, 1975). In 

this study it was shown that the yield strength of the 

lunar flow was comparable to measured values of 

molten lava in Hawaii and that little or no post-flow 

regional tectonic tilt had occurred, although there was 

evidence for local warping. Both carefully controlled 

maps and high-resolution Apollo panoramic camera 

stereophotographs were required for the study. Relief 

of the flows is 7-20 m, comparable to the standard 

error of elevation measurement of the mapping camera 

photographs. In contrast, panoramic camera photographs have a standard error of measurement near 1.0 

m (Wu and others, 1973). Profiles were measured using 

the AP/C stereoplotter because the desired profiles 

were very nearly parallel to the ground track. Cross-
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES Dll

1418 N 

1392\

1435-' 

1440/

1458.'

1435 :

144O 

1436 \1413

1436

1448\

LINNE 1451

1453

1443

3 KILOMETERS

FIGURE 5.—Profiles and rim-crest elevations of Linne; dashed lines indicate areas in shadow; horizontal and vertical scales are equal. 

Numbers to right indicate altitudes in meters above an arbitrary datum. Linne was a famous "problem" crater which Apollo 15 

photographs revealed to be an extremely fresh impact crater (Pike, 1973b, 1980). Profiles and rim-crest elevations prepared by R. Jordan, 

U.S. Geological Survey, Flagstaff, Ariz. from Apollo 15 mapping camera frames 0408 and 0407.

TABLE 5.—Profiles prepared for studies of crater dimensions

[From Pike, 1972, 1973a, 1980]

Name or 

location

Rim 

diameter 

(km)

Depth 

(m)

Outer rim 

height 

(m)

Farside craters-Apollo

In Sklodowska 

Do __________

Do __________

In Tsiolkovsky 

Do __________

In Hilbert

Do __________

Do __________

In Pasteur

In Saha

In Gagarin

In Gagarin

On western rim 

of Gagarin

In Gagarin

__ 1.6

__ _ 2.8

__ 128.0

__ 3.5

____ 4.9 

___190.0

_ 6.0

_ 17.0

___ 178.0

— _ 9.9

____ 15.7

__ _ 16.0

__ 17.0

_ _ 26.0

_ _ 275.0

300

550 

4,500 

500 

950 

4,700

950

1,800 

4,100 

1,100 

880 

1,350

1,700

2,600 

5,375

95

125 

1,850 

175 

100 

1,750

150

400 

1,500 

105 

280 

650

450

725 

(3,350?)

Mapping camera 

frames AS- 15 

metric

15

1875 & 

1968 & 

1970 & 

1966 & 

____do_

____do

0919 & 

0480 & 

0482 & 

1569 & 

1571 & 

1573 & 

1575 & 

1576 & 

1714 & 

1589 & 

1727 & 

1729 & 

1732 & 

1867 &

0910 & 

0333 & 

0293 & 

0295 & 

0098 & 

0289 & 

0291 & 

0297 & 

0299 & 

0300 & 

0102 & 

____do_

____do_

____do_

1874, 

1967, 

1969, 

1965

0917 

0479 

0481, 

1568, 

1569, 

1571, 

1573, 

1575, 

1713 

1588, 

1726, 

1728, 

1731, 

1866 

do. 

do. 

0908 

0332 

0291, 

0293, 

0097, 

0288, 

0289, 

0295, 

0297, 

0297, 

0101

Number 

of 

profiles

2

4 

1 

2

2

4 

2 

4

____ 4

____ 5

Name or 

location

Rim 

diameter 

(km)

Outer rim 

Depth height

(m) (m)

Mapping camera 

frames AS- 15 

metric

Number 

of 

profiles

Farside craters- Apollo 15 — Continued

Izsak

Gilbert M ___

South of Saha

Schorr

Ritz ___ ___

In King

In Langema-K 

In Curie

_____ 33.2

__ __ 34.0

___ 44.0

_____ 50.5

_ __ 53.5

_ __ 59.0

_ __ 71.0

__ 110.0 

_____158.0

3,400 1,025 

3,100 850 

3,550 950 

3,640 1,380 

3,700 730 

3,750 1,800 

3,830 1,690 

4,370 880

3,850 1,500

Mare craters-Apollo

Langrenus

9 ^

38

_____135

600 130 

3,000 850 

4,500 1,500

Mare craters-Apollo

Ma'dler 27.0

Langrenus B_ ____ 32.0 

Isidorus 36.8

Capella

King _

_ __ 38.8

_____ 71.0

2,830 885 

1,865 470 

2,110 830 

2,800 895 

3,830 1,690

Mare craters-Apollo

Pierce B

Pierce

__ __11

__ _20

______28

2,040 460 

2,160 640 

4,040 1,790

1859 & 1858 

1072 & 1071 

1057 & 1055 

0333 & 0332 

2230 & 2229 

1879 & 1878 

1557 & 1558 

0123 & 0122, 

0122 & 0121 

2368 & 2369, 

2366 & 2367, 

2365 & 2364

15

0407 & 0408 

1830 & 1831 

2108 & 2109, 

2390 & 2391, 

2390 & 2389, 

0121 & 0122, 

2261 & 2662

16

2 

2 

2 

2 

2 

2 

2 

2

2

2 

2

4

0123,

2971, 2972 1 

Pan 5000 & 5005 8

17

0287-0291 

____do______^

0293-0296

3

3
D12 APOLLO 15-17 ORBITAL INVESTIGATIONS

FIGURE 6.—Lava flows in Mare Imbrium. Flow lobe in figure 7 indicated by arrow at lower left. Relief of flows is generally small (7-20 m), 

requiring careful techniques and Apollo panoramic camera photographs to obtain detailed profiles. Rectified oblique photograph; sun is 

to right. (Apollo mapping camera frame 1556.)

track profiles showed the curvature expected from 

camera geometry and were not used. Approximate 

leveling was achieved using an existing base map (Defense Mapping Agency, 1974b). The profiles appear to 

be tilted a large amount (fig. 7) because of the large 

vertical exaggeration, but tilts are in reality very 

small, less than 0.4° in every case. In an independently 

measured profile (not shown in fig. 7) along C-C", the 

tilt was in the opposite direction. Thickness estimates 

remained the same. Because of the artificial tilts and 

obvious curvature in the cross-track profiles, gradients 

in the direction of flow for the rheological and tectonic 

study were obtained from a map at a scale of 

1 : 250,000 prepared from mapping camera photographs (Defense Mapping Agency, 1974b). The 100-m 

contour interval of the map was much too large for 

estimating the thickness of the flow.

Profiles of a flow lobe in the basin just north of the 

crater King (fig. 8) were also analyzed in conjunction 

with a quality 1 : 250,000-scale map (Defense Mapping 

Agency, 1974c) to study the rheology of flows in the 

lunar highlands (Moore and Schaber, 1975). Yield 

strengths for this highland flow were much larger than 

those of the Imbrium volcanic flow and consistent with 

a higher silica content of the highland flow. Additionally, topographic data showed that frictional sliding could not account for the movement of the flow 

mass.
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D13

FIGURE 7.—Map and profiles of Imbrium flow lobe. Solid lines on map are contours of elevation taken from Lunar Topographic Orthophotomap, La Hire; LTO 40A 4 (250) (Defense Mapping Agency, 1974a); dashed lines delineate flow base; stipples indicate flow that 

was the subject of a topical study (Moore and Schaber, 1975). Solid lines of profiles delineate present surface; short dashes indicate 

apparent base of flow and approximate top of flow in some profiles; craters disrupt centers on profiles D-D' andB-B'; vertical exaggeration of profile is lOOx. Profiles prepared by R. Jordan and B. C. Philpott, U.S. Geological Survey, Flagstaff, Ariz., from Apollo 15 

panoramic camera frames 0270, 0275, 0272, and 0277.

LUNAR SURFACE ROUGHNESS

The Apollo orbital missions provided two independent methods of estimating surface roughness: radar 

and photogrammetry. Command and Service Modules 

of Apollo 14, 15, and 16 conducted bistatic-radar experiments which resulted in estimates of surface roughness from areas 10 to 20 km across along the gound 

tracks (Howard and Tyler, 1971). Slope-probability 

distributions are also obtained at two wavelengths by 

summing the echoes over 2° intervals (Parker and 

Tyler, 1973). Roughness and slope-probability distributions measured on positive transparencies of 

stereoscopic photographs taken by the lunar topographic, mapping, and panoramic cameras provide a 

basis for comparison of the radar and photogrammetric 

methods. Earlier studies compared the results of the 

Explorer 35 bistatic-radar experiment with 220-cm 

wavelength radio transmissions (Tyler and Simpson, 

1970) and photoclinometric studies on Earth-based 

photographs (Tyler and others, 1971). Preliminary 

studies of lunar surface roughness using stereophotogrammetry began during Apollo 10 and employed Has-
D14

APOLLO 15-17 ORBITAL INVESTIGATIONS

FIGURE 8.—Flow lobe in basin north of King for which profiles were measured to obtain thickness 

of flow. Sun is to left (enlargement of Apollo 16 panoramic camera frame 5000).

selblad photographs (Pike, 197la). Such studies continued through Apollo 17 using the newer photographs 

(Wu and Moore, 1972; Moore and Tyler, 1973; Moore 

and Wu, 1973). Slope-probability distributions measured with the radar and photogrammetry were compared for the first time after Apollo 17 (Moore and 

Tyler, 1973). As a result of these studies, certain aspects of the slope-probability distributions were found 

to be similar and others different (Moore and others, 

1980).

BISTATIC-RADAR METHOD

In the Apollo radar experiments, radio signals with 

wavelengths of 13 cm and 116 cm transmitted by the 

orbiting spacecraft were reflected from the lunar surface and their echoes received on Earth (Tyler and 

Howard, 1973). The echoes were broadened in doppler 

according to the roughness of the reflecting area or

subspecular area. The area is assumed to be statistically homogeneous in the analysis because echoes near 

the center of the area are produced exclusively by surfaces with small tilts and echoes from progressively 

larger distances are produced by surfaces with progressively larger tilts. Thus large tilts from the center are 

not detected and small tilts at the periphery are not 

detected. Very large tilts tend to be mixed with and 

attributed to noise and are not taken into account. 

These tilts are about 20° and larger so that omission of 

them in the analyses is not serious for smooth surfaces, 

but significant errors may occur in very rough lunar 

highlands. Roughness, expressed as root-mean-square 

(rms) slopes,2 is estimated from echo broadening by

'Slope and slope-probability distributions used here are unidirectional or traverse slopes. 

Thus, they are components of slope measured in a vertical plane and differ from adirectional 

or landing slopes, which are the maximum component of slope at a given point. Slope angles 

are measured from the local horizontal to the tilted surface.
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D15

hand calculations and machine-calculated algorithms 

(Tyler and Howard, 1973). These two estimates are not 

necessarily equal (Moore and others, 1976, p. 46). 

Slope-probability distributions are determined by 

analyses of the doppler shift of the echo spectra (Parker 

and Tyler, 1973) summed over 2° of lunar longitude 

and limited to slope angles less than 20°. Algebraic 

standard deviations estimated from the slopeprobability distributions are normally larger than 

hand- and machine-calculated rms slopes (Moore and 

others, 1976, p. 80, 1980). The scale length sampled by 

the radar is a function of the wavelength of the 

transmitted signal and surface roughness characteristics (Tyler, 1976). The mean horizontal distance of the 

scale length for the radar from empirical determinations is about 100 to 300 radio wavelengths (Tyler and 

others, 1971; Moore and others, 1975).

PHOTOGRAMMETRIC METHOD

In the stereophotogrammetric method, slopeprobability distributions are obtained using stereoscopic pairs of lunar topographic, metric, and 

panoramic camera positive transparencies in the AP/C 

plotter. Stereomodels were leveled and scaled from 

auxiliary data derived from orbital support data (National Space Science Data Center, 1972, 1973, 1974). 

Three elevation measurements are averaged for each 

of a number of points separated by a fixed horizontal 

distance along a linear traverse. The fixed horizontal 

interval will be referred to as slope length (AL) in the 

following discussion; it is roughly equivalent to the 

scale length of the radar. Use of a fixed horizontal 

interval is compatible with previous terrain analysis 

procedures (Pike, 197la; Rowan and others, 1971; Pike 

and Rozema, 1975). Repeated elevation measurements 

are used to estimate the standard error of measurement (SE ), which can substantially affect results under 

certain circumstances. More than 400 slopes are determined for each slope-probability distribution. Two 

statistical descriptors commonly used are mean absolute slope (X) and algebraic standard deviation (or). 

Mean absolute slope is the average of all values of absolute slope angle. Algebraic standard deviations are 

estimated from the cumulative absolute slopeprobability distributions and taken as the slope angle 

corresponding to a cumulative fraction of 0.32 

(—0.3174) when slope lengths are near 25 m. For large 

slope lengths, mean absolute slopes and algebraic 

standard deviations are calculated by the U.S. Geological Survey's terrain analysis computer program.

Radar and photogrammetric roughness estimations 

differ in several ways: (1) Radio waves penetrate the 

surface during reflections so that the actual surface is

not necessarily measured, whereas stereophotogrammetry is beset with measurement errors related to the 

instrument, operating personnel, illumination conditions, and photographic quality so that measurement 

of the surface is approximate, (2) the scale length of 

sampling by the radar is 100 to 300 wavelengths but 

varies in relation to location in the sample area and 

surface roughness, whereas the slope length of sampling by stereophotogrammetry is a fixed horizontal 

interval, (3) the radar selectively samples surface tilts 

by magnitude according to location in the sampled 

area, whereas stereophotogrammetry samples surface 

tilts as they occur along the traverse, (4) regional tilts 

of the surface at right angles to the flight path may go 

unrecognized in radar doppler analyses whereas artificial tilts may be introduced in the photogrammetric 

method by improper leveling, (5) both methods may 

encounter sampling problems when the scale of roughness is larger than the size of the samples. Despite 

these differences and problems, the forms of the slopeprobability distributions obtained and variation with 

horizontal scale are in general agreement.

READING ERROR PROBLEM

As an initial test case, slope-probability distributions for Mare Fecunditatis and the Censorinus 

Highlands were measured using the stereophotogrammetric method and Apollo 16 mapping camera photographs (Wu and Moore, 1972) at a slope length of 500 

m. Estimated algebraic standard deviations from the 

distributions were compared with rms slopes from the 

Explorer 35 bistatic-radar experiment (Tyler and 

Simpson, 1970) for which a scale length between 220 m 

and 660 m should be expected. The results showed that 

the roughness determined by the photogrammetric 

method was higher than the radar method by a 

significant factor of 1.5 but that both methods found 

the highland area rougher than the maria by a factor of 

2.5 (see table below). This difference prompted an investigation of the effect of reading error on stereophotogrammetrically determined slope-probability 

distributions (Moore and Wu, 1973).

Location Radar slope 

(degrees I

Censorinus Highlands ____________6

Mare Fecunditatis_______-__-2.4

Photogrammetry slope 

t degrees)

9.1

3.8

In the photogrammetric method, a fictitious roughness of sizeable magnitude can be introduced (Moore 

and Wu, 1973). Repeated elevation measurements are 

normally distributed about the true value under ideal 

conditions that include a large sample size. These normally distributed elevation errors introduce "noise" in
DIG APOLLO 15-17 ORBITAL INVESTIGATIONS

0.2

0.1

0.01

-3/16 -1/8 -1/16 0 1/16 

SLOPE(S)

1/8 3/16 -3/16 -1/8 -1/16 0 1/16 

SLOPE(S)

1/8 3/16

1.0

Q 

CO UJ < t

CO <

O O

"• oc 

!" o

-> UJ

H Q

< DC 

J UJ

3 Q. 5

3 

O

0.1

0.01

1.0

0 5 10 15 20 

SLOPE ANGLE, IN DEGREES

Q 

CO 111

0.1

0.01

10 15 20

SLOPE ANGLE, IN DEGREES

FIGURE 9.—Effect of reading error on semilogarithmic slope-probability distributions. Figure 9A shows starting 

hypothetical distribution. Mean absolute slope is tan 4°. Figure 9B shows apparent distribution produced by 

reading error. Mean absolute slope is tan 4.4°. Notice difference in peakedness of the two distributions. Figure 

9C shows apparent or measured slope-probability distribution of Cayley plains in lunar highlands. Figure 9D 

shows absolute slope-probability distribution corrected for reading error using practical method of Moore and 

Wu (1973). Corrected distribution is smoother and more peaked than measured distribution.

the resulting slope probability distribution making the 

surface appear rougher than it actually is. The general 

effect is illustrated in figure 9.

Reading errors may produce more pronounced or less 

pronounced effects on slope-probability distributions 

depending on the ratio of the slope length and the

standard error of elevation difference,3 (AL/CTjg). For 

small slope lengths and large standard errors of eleva3The standard error of the elevation difference (o^g) is equal to the square root of the sum 

of the squares of the standard error of the estimate of the mean elevation for each point (Sgl, 

and the standard error of the estimate of the mean elevation is equal to the standard error of 

measurement (S^ ) divided by the square root of the number of measurements in the sample
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D17

tion differences, changes are pronounced, whereas for 

very large lengths and small errors changes are trivial 

(fig. 10). Application of the general analyses to the 

Censorinus Highlands and Mare Fecunditatis for reading errors near 10 m and slope-lengths near 500 m 

places the ratio of AL/^ near 50, and so the differences 

between the radar and photogrammetry (1.4° and 3°) 

are too large to be accounted for by reading error.

Most mare surfaces have algebraic standard deviations of 3° to 5° depending on slope length. Thus, 

slope lengths employed for traverses were guided by

0.4

0.3

0.2

0.1

o

0.4

o

I- 0.3

0.2

0.1

•16-

12.

•16-

10 20 40 80 160 320

reading error. Individual slope-probability distributions at the smallest slope lengths were corrected 

using the practical method outlined in Moore and Wu 

(1973). Table 6 summarizes the results of slope probability distributions and their corrections.

RESULTS OF COMPARISON

The radar and photogrammetry methods generally 

agree on four major points: (1) Maria are smoother 

than uplands, (2) the magnitude of the algebraic standard deviations derived from the two methods are comparable for the maria, (3) maria appear rougher at 

small scale lengths than at large scale lengths, and (4) 

slope-probability distributions are typically semilogarithmic, but they vary and may be gaussian or 

complex. They disagree on two major points: (1) The 

roughness of the upland surfaces may appear smaller 

to the radar at small scale lengths than at large scale 

lengths, whereas the photogrammetric method shows a 

larger roughness at a small scale length than at a large 

scale length, and (2) the magnitude of the radar roughness of the uplands at the small scale length (13-cm 

wavelength) is low compared to the roughness measured by photogrammetry. Although these results have 

been discussed previously (Moore and others, 1975, 

1976, 1980; Moore and Tyler, 1973), several examples 

are discussed below.

Comparison of slope-probability distributions of typical maria and the uplands of the Kant Plateau determined by photogrammetry and the radar illustrate the 

agreement in relative roughness, magnitude of the 

roughness (algebraic standard deviation), and general 

agreement in the forms of the distributions (figs. 10, 

11, and 12). Perhaps the most important finding by

•*- FIGURE 10.—Effect of photogrammetric reading error on 

statistical descriptions of slope-probability distribution as a 

function of slope length (AD, standard deviation of elevation difference (cr^), and surface roughness. A, Mean absolute slopes of apparent slope-probability distributions as a 

function of standard error of slopes resulting from elevation 

reading errors for semilogarithmic hypothetical slopeprobability distributions. Mean absolute slopes for the 

hypothetical slope-probability distributions are indicated 

near right ordinate as slope angles. Solid lines indicate apparent mean absolute slopes for various ratios of slope 

length and standard deviation of elevation differences for 

adjacent points (AL cr^). B, Algebraic standard deviations 

of apparent slope-probability distributions as a function of 

standard error of slopes resulting from elevation reading 

errors for normal or gaussian hypothetical slope-probability 

distributions. Algebraic standard deviations for the 

hypothetical slope-probability distributions are indicated 

near right ordinate as slope angles. Solid lines indicate apparent algebraic standard deviations for various values of 

the ratio of slope length and standard deviation of elevation 

differences for adjacent points
TABLE 6.—Statistical parameters of slope-probability distributions using Apollo photographs and stereophotogrammetry

[cr, algebraic standard deviation; St , standard error of measurement; AL, slope length]

Stereophotogrammetric measurements

Location

Location and terrain

Apollo 14 (Lunar Topographic Camera): 

Theophilus, flank near rim __- ------

Rugged upland (Kant Plateau) __________ 

Rugged upland (Kant Plateau) __________ 

Rugged upland (Kant Plateau) __ _ _____

Apollo 15 (Panoramic Camera):

Rugged upland (Crisium flank) __ _ _____ 

Apollo 16 (Panoramic Camera):

Cratered plain (in Ptolemaeus) __„____-__

Cratered upland plain

Uplands (Imbrium sculpture) _ „ ___ 

Apollo 17 (Panoramic Camera):

Lunar Orbiter:

Apollo 16 and 17 (Mapping Cameras):

Mixed mare-uplands (Littrow) - _ _ __ _ - 

Mixed mare-uplands (Littrow) ______„_-_ 

Mixed mare-uplands (Littrow)

Long.

24.9 E 

24 .4E 

22. 5 E 

22.4 E 

20.5 E 

20.3 E 

20.1 E 

18.4 E 

18.2 E

28. IE 

27.5 E 

3.7 E 

44.4 E 

31.3E 

51. 2E

24.4 W 

0.7 W 

35.4 E

15. 5 E 

2.1 E 

16.7 E 

6.0 W

30.7 E 

30.7 E 

29.0 W

44. 1W

31.6 E 

43.5 E 

30. IE 

30. IE 

30. IE

Lat.

10.7 S 

10.7 S 

10.3 S 

10.3 S 

9.9 S 

9.9 S 

9.9 S 

9.5 S 

9.5 S

20.0 N 

20.2 N 

26. IN 

14.4 N 

19.2 N 

11. 7N

10.3 S 

9.2 S 

9.0 S

8.9 S 

9.2 S 

9.1 S 

9.2 S

20.2 N 

20.2 N 

23.5 N

2.6 S

4.7 S 

3.2 N 

20.8 N 

20.8 N 

20.8 N

Absolute mean, 

X (degree)

Corrected

8.75 

6.28 

6.20 

7.30 

8.37 

9.74 

8.06 

4.71 

5.74

470 

4.78 

5.64 

5.30 

6.17 

8.24

3.12 

3.29

3.81

5.26

5.77 

6.33

7.14

3.76

3.88 

14.82

3.45

7.63 

3.10 

5.66 

5.63 

4.90

Measured

8.88 

6.45 

6.28 

7.40 

8.46 

9.80 

8.22 

4.75 

5.82

4.90 

4.97 

5.81 

5.51 

6.32 

8.38

3.54 

3.45 

4.08

5.53 

5.81 

6.71 

7.39

4.05 

4.19 

15.38

3.59

7.73 

3.16 

5.86 

5.70 

5.06

AL

(m)

25.0 

24.9 

24.5 

23.0 

17.1 

17.6 

16.3 

24.8 

16.8

25.0 

24.9 

25.0 

25.1 

25.2 

25.2

25.0 

26.0 

25.0

25.1 

26.1 

24.0 

25.1

25.1 

25.1 

24.1

17.3

505 

500 

500 

501 

502

Estimated 

a 

(degree)

10.8 

7.8 

7.8 

9.0 

10.9 

12.2 

10.3 

6.3 

6.8

5.9 

7.0 

7.0 

6.1 

7.6 

10.5

3.9

3.8 

4.7

6.2

7.5 

8.0 

8.5

4.5 

4.6 

18.3

4.1

9.0 

3.7 

6.4 

6.3 

5.5

Algebraic 

mean and 

type'

0.16 G 

.168 

.15G 

.22G 

1.9G 

1.8 G 

.15C 

.03C 

.08 S

.51 S 

.42 S 

.04 G 

1.3 S 

1.5C 

2.8 C

.148 

.058 

.398

.118 

1.04 C 

1.31G 

1.46 S

.088 

.048 

2.49 G

.698

.028 

.01 S 

.13 S 

.01 S 

.038

SK

(m)

1.10 

.90 

.54 

1.00 

.59 

.73 

.60 

.34 

.61

.63 

.56 

.54 

.66 

.95 

1.14

1.10 

.86 

.94

.67 

.94 

1.07 

1.12

.98 

1.03

.41

8.39 

6.40 

8.51 

9.23

8.87

Standard 

error, one 

slope, S,, 

(degree)

1.88 

2.22 

1.22 

1.63 

1.36 

1.62 

3.07 

.75 

1.47

2.02 

1.79 

1.73 

2.00 

2.08 

2.00

2.35 

1.79 

2.08

2.12 

1.93 

2.15 

2.31

2.10 

2.18

1.29

1.30 

1.03 

.92 

.98 

.95

Number 

of 

slopes

505 

526 

517 

510 

503 

498 

513 

528 

507

636 

581 

996 

666 

622 

595

654 

631 

647

999 

632 

656 

609

624 

639 

673

513

1001 

1031

571 

584 

724

a 

(degree)

5.80 

4.3 

5.0 

4.0 

7.6 

9.5 

7.5 

3.9 

2.3

2.3 

2.5 

1.5 

4.3 

5.5 

7.8

1.8 

2.5 

3.6

4.9 

6.1 

7.3 

8.2

2.2 

2.7 

15.3

1.3

Photogr

AL 

(m)

196 

198 

196 

184 

137 

141 

130 

198 

135

200 

199 

200 

201 

202 

202

200 

208 

200

201 

209 

192 

201

200 

201 

193

138

(

'C—complex

G—gaussian distributions 

S—semilogarithmic distributions
. i

C 2 03

2-0 5-

r•

H"< <

CUMULATIVE PROBABILITY AND PROBABILITY 

PER DEGREE IN INTERVAL INDICATED

O o

CUMULATIVE PROBABILITY AN

PER DEGREE IN INTERVAL 

z _,

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CUMULATIVE PROBABILITY AND PROBABILITY 

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CUMULATIVE PROBABILITY AND PROBABILITY 

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CUMULATIVE PROBABILITY AN

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o 

'_» 

"IIIIT
EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D21

both methods is the widespread occurrence of semilogarithmic distributions for cratered mare and upland 

plains (Moore and others, 1975, 1976, 1980). Such distributions had previously been recognized for cratered 

lunar plains at smaller scale lengths and found to 

characterize cratered plains produced by experimental 

impacts (Moore and others, 1974, and unpublished 

data). Both methods find distributions different from 

semilogarithmic in some uplands. These may approach 

a gaussian distribution or be complex with several 

modes (fig. 12). Slope-length dependence on roughness 

as measured by the algebraic standard deviation for 

single photogrammetric traverses is illustrated in 

figure 13 (see also table 6), where it may be seen that 

roughness increases with decreasing slope length 

(scale length). For the radar, the magnitude of algebraic standard deviation estimated from the distributions may be smaller for the shorter wavelength 

radar echoes (smaller scale length) than for the large 

wavelength ones (Moore and others, 1975, p. 83). 

Root-mean-square slopes of uplands measured by the

20

w

"J 18 UJ 1B

cc

CD

Q 16

z

0 14

o

12

10

10 100 

SLOPE LENGTH, AL, IN METERS

1000

FIGURE 13.—Generalized relations between algebraic standard 

deviation and slope length as determined using photogrammetric method. Lunar surfaces can be divided into groups: 

crater interiors, rough uplands, smooth uplands, and maria. 

Numbers indicate (1) single traverse in interior of Euler from 

rim to floor to top of central peak (table 6), (2) algebraic standard deviation for Censorinus uplands, from mapping camera 

photograph (table 6), (3) upland surface (Imbrium sculpture) 

that deviates from general trend (table 6), (4) algebraic standard deviation for Mare Fecunditatis from mapping camera 

photographs (table 6), and (5) mare surface that deviates from 

general trend (Apollo 15 landing site, table 6).

radar are commonly larger at the large wavelength 

than at the small wavelength (Moore and others, 1975, 

1976). Differences between roughness estimates based 

on radar and photogrammetry are significant for some 

uplands such as the Kant Plateau (fig. 12), where 

photogrammetry estimated the algebraic standard deviation to be 11° and the radar method obtained 7.4° for 

the smaller scale lengths. In some uplands such as near 

Vitruvius the two methods agree (Moore and others, 

1976, p. 83).

Unresolved problems remain for both methods. In 

some lunar areas such as the Censorinus Highlands 

and the south flank of Crisium, the scale length of 

roughness may exceed the "spot-size" of the radar and 

the length of the photogrammetric traverses. In these 

areas as well as the Kant Plateau, many slopes exceed 

20° and are not measured by the radar. Although 

photogrammetry measures slopes greater than 20° 

along the traverse, very steep slopes are avoided in the 

selection of a sampling area. These factors may account 

for the difference in roughness for the Censorinus 

Highlands measured with the mapping camera and 

that measured with panoramic camera in the Censorinus Highlands near Capella (table 6). Despite these 

unresolved problems, current comparisons between the 

radar and photogrammetry have yielded encouraging 

results, particularly for the cratered plains, and recognition of the complexity of some upland areas.

CONCLUSION

Apollo orbital photography progressed from unsophisticated systems with valuable but limited measurement capabilities to a sophisticated system with 

high-quality measurement capabilities. The sophisticated mapping camera system has provided the ingredients for lunar selenodetic control and topographic 

mapping at scales of 1 : 10,000 to 1: 250,000. The metric quality of the photographs obtained with the Apollo 

14 lunar topographic camera and Apollo 15-17 mapping cameras and panoramic cameras have been 

profitably used to achieve experimental and scientific 

objectives. Stereophotogrammetric measurements 

have been found to be most accurate at sun illumination angles of about 30°. The fine-scale morphology of 

lunar landforms and structural deformation of the 

lunar surface can be quantified using topographic 

maps prepared from the photographs. Equations describing the geometry of lunar craters have been revised because of the topographic maps and profiles prepared from the photographs. Rheological properties of 

some lunar lava flows have been determined using 

theory and measurements made from the photographs. 

Data on lunar surface roughness measured by
D22 APOLLO 15-17 ORBITAL INVESTIGATIONS

stereophotogrammetry form a basis for comparison 

with results obtained independently by the bistaticradar experiments.

Full use of the metric quality photographs for some 

scientific purposes has not been realized. Close coordination between the operator and investigator are required for the purpose. Among the investigations that 

are incomplete are:

1. A careful study relating stereophotogrammetric 

measurement with local slopes, the photometric function, and surface albedo.

2. Collection of additional data on crater geometry 

at the fine scale.

3. Measurements of additional lunar flows.

4. Collection of additional data on lunar surface 

roughness using a random sampling grid covering a 

large area comparable to that of the bistatic-radar 

work.

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EXPERIMENTAL PHOTOGRAMMETRY OF LUNAR IMAGES D23

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