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GEOLOGICAL SURVEY CIRCULAR 164 

BOOK 3 TOPOGRAPHIC INSTRUCTIONS 

Part 3 C — Photogrammetric Mapping 

Chapter 3 C 7 a-e MULTIPLEX PROCEDURE 

By Edward I. Loud, Jr. 
UNITED STATES DEPARTMENT OF THE INTERIOR 

Oscar L. Chapman, Secretary 

GEOLOGICAL SURVEY 

W. E. Wrather; Director 

GEOLOGICAL SURVEY CIRCULAR 164 

TOPOGRAPHIC INSTRUCTIONS 

BOOK 3 

Part 3 C 

Photogrammetric Mapping 

Chapter 3C 7 a-e 

MULTIPLEX PROCEDURE 

By Edward I. Loud, Jr. 

This circular has been prepared as a part 

of the manual of Topographic Instructions. The 

original text was written in the Atlantic Region 

office and prepared for publication by the Research and Technical Control staff of the Topographic Division. 

Washington, D. C., 1952 

Free on application to the Geological Survey, Washington 25, D. C. 
CONTENTS 

Chapter 3 C 7-a. Introduction to the multiplex 

3C 7-b. Multiplex equipment 

3 C 7-c. Multiplex orientation 

3C 7-d. Multiplex stereotriangulation 

3C 7-e. Map compilation by multiplex 

(Each chapter is separately paged. ) 
GEOLOGICAL SURVEY 

TOPOGRAPHIC INSTRUCTIONS 

Chapter 3C 7-a 

INTRODUCTION TO THE MULTIPLEX 

Contents 

Page 

Abstract 5 

The multiplex method 5 

1. General principles of multiplex . 5 

2. Applicability of the multiplex. . . 8 

Steps in multiplex procedure 8 

3. The major phases 8 

Page 

Steps in multiplex procedure, continued 

4. Orientation 8 

a. Interior orientation. .. .. 8 

b. Relative orientation 9 

c. Absolute orientation 9 

5. Stereotriangulation 9 

6. Compilation of detail 10 

Illustrations 

Figure 1.-- Geometric parallelism between aerial photography and multiplex reconstruction . . 6 

2.-- Principle of the multiplex 7 

Chapter 3 C 7-a l 

INTRODUCTION TO THE MULTIPLEX 

ABSTRACT 

By direct projection of overlapping photographs, printed on glass 

plates, the multiplex produces an exact optical model, in miniature, of 

the terrain to be mapped. To create the model, the multiplex projectors 

must be properly positioned and oriented so that they duplicate the orientation of the aerial camera at the instant of each exposure. By means of 

a floating mark, horizontal and vertical measurements can be made in 

the model, and planimetry and contours can be drawn. The applicability 

of the multiplex to a given mapping project depends largely on the contour 

interval and compilation scale required, and also depends, to a lesser 

extent, on the vegetation and terrain cover as it may affect accuracy requirements. The steps in multiplex procedure are orientation, stereotriangulation, and compilation of detail. In orientation, the projectors 

are arranged so that the projected images form a stereoscopic model 

which can be adjusted to fit horizontal and vertical control points. In 

stereotriangulation, three or more multiplex projectors are oriented so 

that the consecutive models fit existing control, permitting the establishment of additional or intermediate control. In compilation, the features 

appearing in the model are delineated on the map manuscript. 

THE MULTIPLEX METHOD 

1. General principles of multiplex 

In the multiplex method of mapping, the 

natural terrain features are re-created at a miniature scale by the optical projection of overlapping aerial photographs properly oriented to each 

other and to the datum. Each photograph, in the 

form of a miniature print on a glass plate (called 

the diapositive), is positioned on the focal plane 

stage of a projector. Light from the projector 

light source passes through the diapositive and 

the optical system of the projector so as to project the image of the terrain in a manner which 

1The number 3 C 7-a signifies Book 3, Part C, 

Chapter 7-a of the Geological Survey loose-leaf 

manual of Topographic Instructions. For a table 

of contents, see Chapter 1 A 2 (Circular 92). 

is geometrically similar to the original photographic process but opposite in direction. The 

parallelism that exists between the geometry of 

the aerial photography and the geometry of the 

multiplex reconstruction, or "model" 2 , is suggested in figure 1. 

In order that the model may be an exact 

duplicate, in miniature, of the actual terrain, 

the projected photographs must be accurately 

positioned and oriented so as to reproduce exactly the conditions existing at the instant each 

photograph was taken. It is therefore necessary 

to recover the space coordinates of the exposure 

stations, at the model scale, and the angular 

2

That portion of the reconstructed terrain 

formed by a single pair of overlapping photographs 

constitutes one "model". The several successive 

models formed by consecutive photographs in the 

line of flight constitute a multiplex "strip". 

5 
MULTIPLEX MODEL 

6 (Ch. 30 7-a) TOPOGRAPHIC INSTRUCTIONS 

TERRAIN IN NATURE 

Figure 1. --Geometric parallelism between aerial photography and multiplex reconstruction. 

orientation of the camera at each station. This 

is accomplished by adjustment of the multiplex 

projectors which have translational motions along 

three mutually perpendicular axes, and rotational 

motions about each of these axes. When the projectors are properly oriented, all corresponding 

image rays from a pair of projectors intersect 

in space. The integration of all such points represents an optical model similar in all respects 

to the actual terrain. 

In order that the observer may see the 

model in three dimensions it is necessary that 

he view one of the photographs with one eye, and 

the second photograph with the other eye. This 

is accomplished by projecting the images in 

complementary colors and observing them through 

correspondingly colored spectacles. By means of 

a floating mark, accurate horizontal and vertical 

measurements can be made in the model. The 

floating mark is contained in the surface of a 

viewing screen, or platen, mounted on a tracing 

table. To examine any portion of a model, the 

tracing table is moved into such position that the 

projected images of that portion fall on the platen. 

Vertical motion of the floating mark is obtained by raising or lowering the platen by means 

of an elevating wheel and screw forming a part 

of the tracing table. This motion can be measured 

by means of a height-indicating scale. Horizontal motion of the floating mark is obtained by 

sliding the tracing table over the map surface. 

A pencil is mounted vertically below the floating 

mark so that map detail observed in the model 

can be drawn on the map sheet. 

The multiplex is simple in principle and 

construction. Because of this simplicity, it is 

especially well adapted to the teaching of the 

basic principles of photogrammetry and to the 

training of personnel in the basic methods of 

stereoscopic mapping. Experience has shown 

that persons trained in the operation of the 

multiplex are able to comprehend the operation 

of other stereoscopic instruments more easily 

and rapidly than would otherwise be possible. 

A feature which makes the multiplex unique 

among instruments is the manner in which multiplex stereotriangulation is performed. Several 

successive photographs can be placed in simultaneous orientation to form a continuous, bridgelike strip of models for the purpose of spanning 

areas having little or no control. The inadequately controlled models, being members of the bridge, 

are consequently fully oriented when the bridge 

as a whole is oriented. Further supplemental 

procedures are required only to the extent that 

errors, which are present to some degree in 
INTRODUCTION TO THE MULTIPLEX (Ch. 307-a) 7 

Figure 2. --Principle of the multiplex. 

MULTIPLEX 

PROJECTORS 
8 (Ch. 3C 7-a) TOPOGRAPHIC INSTRUCTIONS 

any plotting system, may make the strip deviate 

slightly from this ideal condition. Some simple 

analytical correction may then be advisable. 

Both positions and elevations can be established 

by multiplex stereotriangulation, but the vertical 

accuracy requirements, being generally more 

rigid than the horizontal accuracy requirements, 

may limit and often preclude the practice of vertical stereotriangulation. Supplemental horizontal positions, however, are regularly established 

by multiplex stereotriangulation, using from 2 to 

11 or 12 models, although as many as 19 or 20 

models may be set up. Insofar as the accuracy 

requirements permit, the limit depends on the 

projector capacity of the particular multiplex 

supporting frame being used. 

2. Applicability of the multiplex 

The mapping assignments of which the multiplex is capable—as expressed by the scales, flight 

heights, and contour intervals that are suitable 

for multiplex compilation--are determined by the 

more or less fixed relationship that must be maintained among these three factors3 . Thus the contour interval, which is often the controlling factor, 

roughly determines the necessary flight height, 

and this in turn rather closely determines the 

model scale (which is the same as the compilation 

scale, except when a pantograph or other device 

is used for scale conversion). 

When referring to the flight height-contour 

interval relationship, the term "C-factor" is often 

used. By definition, this is the ratio of the flight 

height to the smallest contour interval that can be 

obtained from the instrument within the generally 

accepted standard of accuracy for topographic 

maps. In theory it should be possible to calculate the maximum C-factor for any stereoscopic 

plotting instrument when its various characteristics are known. However, in practice the maximum C -factor cannot easily be determined because 

it is affected to such a large extent by other factors that have no particular connection with the 

plotting instrument itself. Some of these are: 

the amount and type of control; the accuracy standard to be complied with; the type of terrain; 

3See Chapter 3 B 3, Planning vertical photography, for a detailed discussion of this relationship. 

atmospheric conditions; quality of photography; 

and the likelihood of errors in other phases of 

the process. The actual C-factors used for 

compilation vary over wide limits for the same 

reason, and for other reasons such as the necessity of planning flights within prescribed boundaries, or the necessity of utilizing photography 

not specifically planned for a project. As a result of Geological Survey experience, a value of 

600 is usually considered to be a safe limiting 

value for the multiplex C -factor, under average 

conditions. Once the flight height is established, 

the multiplex model scale is governed solely by 

the projection distance of the multiplex projector 

which distance can be varied only insofar as the 

depth of focus of the lens permits. 

STEPS IN MULTIPLEX PROCEDURE 

3. The major phases 

The steps in the compilation of a map by 

the multiplex are grouped into two or, in some 

instances, three major phases. The basic phase 

is orientation, or the process by which the model 

is brought into being and made to conform to a 

datum. When stereotriangulation is required, 

orientation becomes both an initial part of the 

stereotriangulation phase and, usually, an intermediate phase between stereotriangulation and 

compilation. Compilation is the final phase, 

which covers the delineation on the manuscript 

of the features seen in the model. When stereotriangulation is not required, the initial orientation is followed directly by compilation. 

4. Orientation 

The orientation phase can be divided into 

interior orientation and exterior orientation. 

Exterior orientation can be further subdivided 

into relative orientation and absolute orientation. 

a. Interior orientation. --The purpose of 

interior orientation is to recover, insofar as 

possible, a projected cone of rays geometrically 

identical with the cone of rays that entered the 

camera lens to make the original exposure. Interior orientation imposes two requirements: 

(1) The diapositive must represent a reduction 

from the original aerial negative in the ratio of 
INTRODUCTION TO THE MULTIPLEX (Ch. 3C 7-a) 9 

the focal length of the aerial camera to the principal distance4of the projector, the principal 

distance being the length of the perpendicular 

from the interior perspective center of the projection lens to the plane of the diapositive; and 

(2) this perpendicular must intersect the plane 

of the diapositive at the principal point of the 

photograph. The first requirement is satisfied 

in the diapositive printing operation by proper 

setting of the reduction ratio of the printer. Interior orientation, to the stereocompiler, means 

only satisfying the second requirement. This is 

accomplished in the operation known as "centering" 

the diapositive. 

b. Relative orientation. --The purpose of 

relative orientation is to reconstruct the same 

perspective conditions between a pair of photographs that existed when the photographs were 

taken. As it is not ordinarily known just what 

these conditions were, the multiplex procedure 

of relative orientation is founded on the fact that 

each point on the ground was the origin (and hence 

an intersection) of a pair of conjugate rays, one 

to each exposure station. Therefore, their reprojected counterparts in the multiplex must also 

be made to intersect, pair by pair. Following 

interior orientation, relative orientation is accomplished by a systematic procedure of applying rotational and translational movements to the 

projectors, at the same time observing the images 

on the platen of the tracing table, until conjugate 

images are made to coincide over the entire model 

area. This procedure of relative orientation is 

familiarly referred to as "clearing y-parallax." 

c. Absolute orientation. --As a final step, 

the model which has been created as a result of 

interior and relative orientations must now be 

'' absolutely" oriented with reference to a vertical 

and a horizontal datum, if map-making measurements are to be readily obtained from it. The 

vertical datum is provided by the top surface of 

the multiplex supporting table. The slight difference between this surface, which is plane, and 

the datum in nature, which conforms to the curvature of the earth, is not significant within the area 

usually covered by a single model. The horizontal datum is provided by the control points plotted 

with reference to the map projection on the base 

4

See figure 6, Multiplex projector optical 

system, in Chapter 3 C 7—b. 

sheet. This base sheet is laid flat upon the 

multiplex table top, where the tracing table can 

slide upon it. 

Absolute orientation procedure comprises 

three operations: bringing the model to the 

proper size, or "scaling" the model; bringing 

the model datum parallel to the table top, called 

either "leveling" or "horizontalizing" the model; 

and "positioning" the model with reference to 

the horizontal datum. 

The multiplex model is spatial in concept, 

embracing not only the visible surface of the 

terrain but also the space above and below this 

surface. In addition to the terrain surface, 

therefore, another surface can be conceived as 

having been reconstructed as part of the model, 

a surface representing the sea-level datum of 

nature. This surface is called the "model datum." 

When the interior and relative orientations of 

the photographs have been correctly recovered, 

the model datum is, for all practical purposes, 

a plane or flat surface over the extent of one 

model. When absolute orientation is also recovered, the model datum becomes parallel to 

the table top, or "level." If photographic distortions or orientation errors cause this model 

datum to be deformed, or "warped," the datum 

cannot be leveled. In speaking of the model 

datum, the word "datum" is often omitted, hence 

it is customary to refer to the model as being 

either "warped, " or "flat but not level," or 

"level, " as the case may be. Although the terrain surface of the model may also be referred 

to as flat, or level, the context will always make 

the reference clear. 

5. Stereotriangulation 

A stereotriangulated strip that is supported 

by control at both ends is called a "bridge;" a 

strip that is supported at only one end is called 

an "extension. Bridging is the more usual type 

of stereotriangulation, because an extension will 

not provide the accuracy needed in most domestic 

mapping. Bridging and extending procedures are 

further qualified as "horizontal" or "vertical" 

according to their primary purpose, which may 

be either to establish supplemental positions 

(horizontal pass points) or to establish supplemental elevations (vertical pass points). In the 

absence of ground control, these pass points are 
10 (Ch. 30 7-a) TOPOGRAPHIC INSTRUCTIONS 

needed to control each individual model during 

the compilation of detail; pass points also afford 

a means of foreseeing and adjusting differences 

between adjacent strips. 

It was mentioned previously that certain 

small errors--arising particularly in the various 

lenses through which the image must pass--are 

responsible for a difference between the theory 

and the practice of stereotriangulation. Disregarding these errors for the moment, the basic 

procedure of stereotriangulation is as follows. 

After the absolute orientation of the first 

and second of a series of projectors has been 

attained, forming a model also in absolute orientation, it is possible to orient a third projector 

relative to the second, forming a new model; it 

is further possible to bring the new model to the 

same scale as the original--both operations utilizing motions of the third projector alone, without 

disturbing the first two projectors or the original 

model. When this procedure is carried out, the 

third projector will perforce become absolutely 

oriented like the others, and both models will 

exist simultaneously in a state of absolute orientation. This process of attaching additional 

models to previously oriented models can be 

continued up to the limit imposed by the length 

of the multiplex frame. In effect, the several 

models then constitute one continuous strip 

model, which is all in absolute orientation inasmuch as the initial model was in absolute orientation. If stereotriangulation practice were 

like stereotriangulation theory, the compilation 

of detail could now proceed without further delay. 

In actual stereotriangulation, however, 

progressive discrepancies within the length of 

the strip will be encountered, owing to the cumulative effects of, the aforementioned small errors. 

In practice, therefore, stereotriangulation procedure must include steps for minimizing these 

discrepancies. 

6. Compilation of detail 

When the model is in absolute orientation 

(or reorientation, as the case may be) it is ready 

for the compilation of detail. In compilations, 

the planimetric features are almost always compiled first. These are then inked, to be followed 

finally by the compilation and inking of the contours. 
GEOLOGICAL SURVEY 

TOPOGRAPHIC INSTRUCTIONS 

Chapter 3C 7-b 

MULTIPLEX EQUIPMENT 

Contents 

Abstract 

Page 

5 Multiplex plotting equipment, continued 

Page 

Types of multiplex equipment 5 14. Filter spectacles 18 

1. Different makes 5 15. The electrical system 18 

2. Degree of tilt accommodated. 5 16. The cooling system 19 

3. Angular field 5 Calibration and adjustment of multiplex 

4. Principal distance 6 equipment 19 

Multiplex diapositive printer 6 17. Distinction between routine and 

5. Functions of diapositive printer 6 laboratory procedures 19 

6. Reduction of negative size 6 18. Adjusting the floating mark bulb 19 

7. Distortion compensation 9 19. Checking the verticality of the 

8. Addition of the principal point mark 9 tracing table columns 20 

Multiplex plotting equipment 9 20: Centering the plotting pencil 20 

9. Main components 9 21. Focusing the principal-point 

10. The projector 9 microscope 20 

a. 12,ssential parts 9 a. Eyepiece 20 

b. The projection lens 

c. The diapositive stage and 

10 b. Objective 

22. Checking the collimation of the 

21 

centering mechanism 

d. The principal-point indicating 

10 principal-point microscope . . 

23. Orienting the axis of the filament 

21 

device 12 coil of the projector bulb . . . 21 

e. The projector supporting bracket 14 • 24. Positioning the projector bulb . 21 

f. The lamp house 14 25. Checking the adjustment of the 

11. The tracing table 14 reflector 22 

a. Function 14 26. Checking the principal distance 

b. The screen and floating mark . 16 of the projector 22 

c. The height-indicating scale . . 16 a. Suggested procedure 23 

d. The plotting pencil and base . 16 b. Alternative procedure 23 

12. The supporting frame 16 27. Checking the principal point of 

a. Function 16 the projector 24 

b. Bar 17 a. Suggested procedure 24 

c. Uprights 17 b. Alternative procedure 24 

13. The supporting table 17 

a. The table top 17 

b. The table frame 18 

3 
Illustrations 

Page 

Figure 1. Multiplex diapositive printer 7 

2. Multiplex plotting equipment 8 

3. Relationship of camera, printer, and projector in the multiplex system 9 

4. Multiplex projector optical system 10 

5. Multiplex projector 11 

6. Multiplex projector camera body 12 

7. Principal-point microscope and testing equipment 13 

8. Multiplex tracing table 15 

9. Checking principal distance by projected grid 23 

4 
Chapter 3C 7-b1- 

MULTIPLEX EQUIPMENT 

ABSTRACT 

• 

The several types of multiplex equipment may be classified according to make, degree of tilt that can be accommodated, angular field, and 

principal distance. The main components of multiplex plotting equipment 

are the projector, the tracing table, the supporting frame, the supporting 

table, the filter spectacles, the electrical system, and the cooling system. 

The diapositive printer is a necessary complement of multiplex equipment, 

although it is not a part of the plotting instrument itself. All of these are 

described in detail. Procedures for the calibration and adjustment of 

multiplex equipment are divided into routine procedures performed by the 

stereocompiler and laboratory procedures performed by skilled technicians with special tools, but laboratory procedures are beyond the scope 

of this chapter. Routine procedures, and methods of roughly checking 

laboratory calibration are described in detail. 

TYPES OF MULTIPLEX EQUIPMENT 2. Degree of tilt accommodated 

1. Different makes 

The multiplex is manufactured in the United 

States by the .pausch and Lomb Optical Company. 

Among the foieign-made multiplex instruments 

are the Williamson and Ross type (England); the 

Zeiss type (Germany); and the Nistri type (Italy). 

In addition, different models of the same manufacture increase the total number of different designs of multiplex equipment. Although these differences alter the superficial appearance of the 

equipment, they do not change the fundamental 

principles; and although these differences may 

have an important bearing on the operational accuracy of the instrument, they have relatively 

little effect on operational procedures. The discussion of multiplex equipment in this chapter 

applies particularly to the Bausch and Lomb instrument of U. S. Geological Survey design. 

1The number 3 C 7-b signifies Book 3, Part C, 

Chapter 7-b of the .Geological Survey loose-leaf 

manual of Topographic Instructions. For a table 

of contents, see Chapter 1 A 2 (Circular 92). 

The multiplex is primarily adapted for 

use with vertical photography. Small tilts can 

readily be accommodated (the mechanical limit 

of the tilt of a multiplex projector ranges from 

10°about the x-axis to approximately 20°about 

the y-axis). During the war, some multiplex 

projectors were converted to utilize the highoblique photography of the trimetrogon cameras. 

by a simple change in their supporting brackets 

that gave them an initial tilt of 60°from the vertical. Subsequently, a limited number of projectors have been manufactured specifically for 

use with oblique photography. These projectors 

embody changes in their optical design to provide a better image, and other minor modifications. Except for these minor changes, oblique 

equipment is similar to vertical multiplex equipment. This chapter, however, deals specifically with the vertical multiplex. 

3. Angular field 

The earlier multiplex projectors had an 

angular field of about 70°which matched the 

5 
6 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 

maximum angular coverage afforded by singlelens aerial cameras at the time. This type of 

projector, called the "normal-angle" projector, 

is obsolete, having been replaced by the wide 

angle type which projects a cone slightly in excess of 90° . This wider angular coverage permits the use of more favorable base-height ratios, thus increasing the accuracy of the instrument despite the possibility of some slight loss 

in the definition of the projected image. The 

wider angular coverage also increases the model 

area, thus decreasing the amount of control required. Although the procedures employed in 

operating either type of projector are almost 

identical, the wide-angle type is specifically 

assumed in the present discussion. 

4. Principal distance 

An important geometrical property of a 

multiplex projector is its principal distance (the 

perpendicular distance from the internal perspective center of the projector lens to the plane of 

the emulsion side of the diapositive). This dis 

tance has a direct bearing on the ratio of reduction from negative to diapositive scale and on the 

ratio of enlargement from diapositive to model 

scale. 

The nominal principal distances of the different types of multiplex projectors used in this 

country are: 

B&L wide angle--USGS type . . . . 30 mm 

B&L wide angle--US Army type . 28 mm 

B&L normal angle 46 mm 

Zeiss wide angle 22 mm 

Zeiss normal angle 46 mm 

MULTIPLEX DIAPOSITIVE PRINTER 

5. Functions of diapositive printer 

A prerequisite to any understanding of the 

multiplex is an understanding of the functions of 

the multiplex diapositive printer. This printer 

(fig. 1) is essentially a reducing camera of the 

highest precision, which is used to prepare the 

diapositives (positive transparencies of the aerial 

photographs on glass plates) required by the multiplex projectors. Although the printer is necessarily considered an item of multiplex equipment, 

the operation of diapositive printing is not regarded as a multiplex operation--the latter begins with the orientation of the completed diapositives in the multiplex projector2 . 

The multiplex printer has three important 

functions: reduction of negative size; distortion 

compensation; and addition of the principal point 

mark. These functions are particularly important in enabling the multiplex projectors to 

achieve the geometrically parallel reproduction 

of nature which is an essential principle of the 

multiplex. 

6. Reduction of negative size 

The diapositive printer reduces the aerial 

photograph approximately according to the ratio: 

focal length of camera 

principal distance of projectors 

More precisely, the reduction setting of the 

printer is based on the principal distance 3of 

the aerial negative, rather than on the focal 

length of the aerial camera. Thus the effect of 

film shrinkage is taken into account. 

If the cone of rays emanating from a projector is to be similar to the original cone that 

entered the camera at the instant of exposure, 

the principal distance of the diapositive must be 

equal to the principal distance of the projectors. 

Therefore, provision is made for setting the reduction ratio precisely. If the reduction ratio 

were not accurately set, the projected cone of 

rays would be either slightly elongated or slightly 

flattened, with the result that the vertical scale 

2

A full description of the diapositive printer 

and its operation is contained in Chapter 3 C 6, 

Diapositive preparation. 

3Principal distance is the perpendicular distance from the internal perspective center to the 

plane of a particular finished negative or print. 

This distance is equal to the calibrated focal 

length corrected for both the enlargement or reduction ratio and the film or paper shrinkage or 

expansion and maintains the same perspective angles 

at the internal perspective center to points on 

the finished negative or print, as existed in 

the taking camera at the moment of exposure. 

This is a geometrical property of each particular 

finished negative or print. 
MULTIPLEX EQUIPMENT (Ch. 3C 7-b) 7 

Figure 1. --Multiplex diapositive printer. 
Figure 2. --Multiplexplottingeq

uip

ment. 

8 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 
MODEL 

PROJECTOR 

DIAPOSITIVE 

A _ F. L. 

B - P.D. 

\ ACTUAL RAY PATH 

PATH OF RAY IF THERE 

WERE NO DISTORTION 

AERIAL NEGATIVE 

cr 

z 

rr 

F. L. \ 

= ANGULAR 

DISTORTION 

= DISTORTION 

COMPENSATION 

TERRAIN 

cr 

MULTIPLEX EQUIPMENT (Ch. 30 7-b) 9 

of the model would be slightly in error with respect to the horizontal scale. With the proper 

reduction ratio, the vertical and horizontal scales 

will be equal. 

7. Distortion compensation 

Another function of the multiplex diapositive 

printer is distortion compensation. The optical 

system of the printer introduces a calculated distortion such that the resultant distortion of camera, 

printer, and projector combined is as near zero 

as possible. Figure 3 illustrates the functions 

of distortion compensation and reduction of negative size in recovering the same angle between 

two projected rays as existed between the corresponding rays in nature. 

8. Addition of the principal-point mark 

The multiplex printer is the source of the 

small cross (or circle), printed on the diapositive, 

that marks the principal point of the photograph. 

The original of this mark is etched on a glass 

plate in the negative plane of the printer. It is 

the responsibility of the printer operator to position the negative before a diapositive is exposed, 

by alining the fiducial marks on the negative with 

certain collimating lines on the glass plate. 

MULTIPLEX PLOTTING EQUIPMENT 

9. Main components 

The multiplex in readiness for operation is 

shown in figure 2. The principal items that may 

be seen in the illustration are: the projectors 

(1 and 2)--two different designs are shown; the 

tracing table (3); the supporting frame (4); the 

supporting table (5); the filter spectacles (6); the 

electrical control box (7); and the principal point 

microscope (8). 

10. The projector 

a. Essential parts. --Of the two designs of 

the Geological Survey-type multiplex projector 

that are illustrated in figure 2, projector 1 is at 

present the more widely used, while projector 2 

is of more recent design. Projector 2, which is 

shown in more detail in figures 5 and 6, is used 

as a basis for this description, although the 

Figure 3. --Relationship of camera, printer, 

and projector in the multiplex system. 
d

co

° i

J 

a_ 

0 

z 

MODEL 

D c.) 0 

LI0 

REFLECTOR 

LIGHT SOURCE 

COLOR FILTER 

CONDENSER 

LENSES 

DIAPOSITIVE 

PROJECTION LENS 

10 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 

significant differences between the two designs 

will be mentioned. The description of the multiplex projector will also be aided by reference to 

figure 4, which shows diagrammatically the path 

of a light ray through the optical system. 

Figure 4. --Multiplex projector optical system. 

The essential parts of the multiplex projector are: the light source (1, fig. 5); the color 

filter (2, fig. 5); the condensing system in the 

condenser housing (3, fig. 5); the projector supporting bracket (4, fig. 5); and the camera body 

(fig. 6) containing the projection lens (1) and the 

diapositive stage (2). The camera body is sometimes called "projector cone" or "lens cone." 

In a discussion of multiplex operation it is convenient to distinguish between the two main assemblies: the lamp-filter-condenser assembly (5, 

fig. 5), which is quite generally termed the 

'' lamp house;" and the camera body-supporting 

bracket assembly (6, fig. 5), which is variously 

referred to as the "base, " the "projector body," 

or simply as the "projector." The components 

of this base portion of the projector will be described first. 

b. The projection lens. --The multiplex 

projection lens is small and essentially distortion-free. Its focal length and aperture opening 

have been selected so as to bring the image of 

the diapositive to optimum focus in a plane 360 

millimeters below the projector, with an approximate range from 290 to 460 millimeters within 

which the loss of definition is hardly perceptible. 

This depth of focus is necessary because the 

tracing table platen on which the projected image 

is viewed must be raised and lowered in accordance with the relief of the stereoscopic model. 

c. The diapositive stage and centering 

mechanism. --The diapositive is supported in 

the projector at a fixed distance above the projection lens. In the Geological Survey-type projector, the diapositive is supported upon four 

bosses, one under each corner, which duplicate 

those used to support the diapositive in the multiplex diapositive printer. In the later-model 

projectors these bosses are mounted in a frame 

(2, fig 6) which surrounds the diapositive and in 

which the diapositive can be securely fastened. 

Centering adjustment screws (3, fig. 6) slide 

this frame in its own plane (perpendicular to the 

lens axis) for the purpose of alining the principal 

point of the diapositive with the principal point 

of the projector ("centering" the diapositive). 
' ''.mow 

MULTIPLEX EQUIPMENT (Ch. 3C 7-b) 11 

Figure 5. --Multiplex projector. 
12 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 

Figure 6. --Multiplex projector camera body. 

d. The principal-point indicating device. --

One of the great differences to be found among 

recent designs of the multiplex projector is in 

the device employed to indicate the principal 

point. Three different indicating devices are 

briefly described. 

(1) Centering arm. --The centering arm 

device may be seen in figure 6. The principal 

point of this projector is indicated by a small 

dot etched on a glass reticle mounted on a 

movable arm (4). Normally out of the field of 

view, this arm is pivoted at one end so that it 

may be swung out beneath the diapositive by an 

external release screw (5). Releasing the arm 

until it hits a stop automatically places the dot 

at the principal point of the projector. 

(2) Principal-point microscgpe. --The earlier and more widely-used model of the Geological Survey-type projector (1, fig. 2) requires 

the use of an accessory instrument known as a 

principal point microscope. Figure 7 shows 

this instrument (1) together with the testing fixture (4) and gauge (3) required in its calibration. 

A point on the line of collimation is defined in 

the microscope by cross lines etched on a glass 

reticle. To center a diapositive, the microscope 
MULTIPLEX EQUIPMENT (Ch. 30 7-13) 13 

Figure 7. --Principal-point microscope and testing equipment. 

must be placed on the camera body as shown. 

Three foot pads are located beyond the diapositive 

frame just inside the rim of the camera body to 

receive the feet of the microscope. One of these 

foot pads is conical, one is V-shaped, and one 

is flat, to insure a positive position of the microscope such that its line of collimation accurately 

indicates the principal point of the projector. 

The use of the testing equipment is described 

below in article 22. 

(3) Stage plate. --Both in the Zeiss-Geological Survey and in the Bausch and Lomb-U. S. 

Army types of projectors, the diapositive is supported, not upon bosses, but upon a glass plate 

called a stage plate. Spring clamps force the 

diapositive down against this plate; the centering 

mechanism moves only the diapositive itself. 

A disadvantage of this arrangement is that in 

time the stage glass may become scratched from 

the diapositive sliding upon it. The advantage 
14 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 

of the stage plate, however, is in the marking 

of the principal point. A small dot on the upper 

side of the stage glass indicates the principal 

point of this type projector simply and continuously. 

e. The projector importing bracket. --In 

addition to supporting the projector on the multiplex frame, the bracket provides the camera body 

with six freedoms of motion (three of translation 

and three of rotation), which are essential to the 

complete recovery of the photograph orientation. 

The supporting bracket provides translational motions through an L-shaped arrangement 

of two sliding members: a horizontal arm or 

y-slide (7, fig. 5) and a vertical arm, or z-slide 

(8, fig. 5). The whole assembly is designed to 

be hung on the x-slide of the multiplex bar (9, 

fig. 2) along which it can be moved in the x-direction. Although the orientation of these three 

slides with reference to some fixed part of the 

multiplex supporting table changes slightly with 

tilt of the supporting frame, the orientation of 

the slides serves to designate the x-, y-, and 

z-directions sufficiently well for descriptive 

purposes. In certain instances, it may be convenient to assume an explicit orientation of one 

or more axes with reference to the supporting 

table, or to the model air base, or to some 

other designated element.. The knobs that control the translational motions are grouped at 

the rear of the projector: Knob 9 (fig. 5) drives 

the projector in x; knob 10 (fire. 5) drives it in y; 

and knob 11 (fig. 5) drives it in z. 

The camera body is mounted in a gimbal 

affixed to the front end of the y-slide. This 

mount permits the camera body to be rotated 

about three axes that normally are perpendicular 

to one another. Rotation of the camera body 

within the inner ring of the gimbal is about a 

z-axis and is called swing. Rotation of the inner 

ring is about an x-axis (secondary axis) and is 

called x-tilt. Rotation of the outer ring is about 

a y-axis (primary axis) and is called y-tilt. The 

x-tilt and the y-tilt are controlled by tangent 

screws (12, fig. 5; and 13, fig. 5, respectively) 

which permit the camera body to be tilted from 

its normal position approximately 10°crosswise 

to the line of flight and almost double that amount 

parallel to the flight direction. A third tangent 

screw (14, fig. 5) is used for the finer adjustments of swing; for the larger adjustments the 

swing clamp screw (15, fig. 5) is loosened, 

permitting the camera body to be rotated manually through a full circle. 

f. The lamp house. --The earlier design 

of multiplex lamp house (1, fig. 2) places the 

bulb socket at the very top, in which a T-8 bulb 

is mounted base up. The condensing system 

does not include the reflector indicated in figure 4. In the newer style projector (fig. 5) a 

prefocused G-162 bulb is mounted horizontally. 

This change not only permits a reflector to be 

used for added concentration of light, but also 

provides a better ventilation of the bulb. A fitting (16, fig. 5) to which an air hose can be 

attached is provided on both types of lamp houses, 

although forced air cooling is not required by the 

newer type lamp house. 

Adjustments are provided on the bulb mount 

for focusing the maximum light upon the aperture 

of the projection lens, as light that does not pass 

through this opening does not help to illuminate 

the model. (Instructions for making these adjustments are given in article 24.) The small size 

of the aperture opening limits the size of the 

filament of the bulb, and indirectly limits the 

filament voltage rating. Twenty-volt bulbs are 

now commonly used, although some of the older 

multiplex projectors were designed to use a 

6-volt and some a 12-volt bulb. 

The color filter (2, fig. 5) is inserted in a 

slot below the bulb and above the condenser lenses. 

Filters of red glass are interchangeable with filters of blue glass, so that complementary colors 

for the projection of the stereoscopic pair of 

photographs can always be provided. 

11. The tracing table 

a. Function. --The multiplex tracing table 

shown in figure 8, provides the means of relating 

the stereoscopic model and the manuscript. It 

forms the connecting link between these two. 

Essentially, the tracing table provides a screen (1) 

on which the projected model can be viewed; a 

floating mark (2); a height indicating scale (3); 

a plotting pencil (4); and a horseshoe-shaped 

base to support the whole. 
MULTIPLEX EQUIPMENT (Ch. 3C 7-b) 15 

Figure 8. --Multiplex tracing table. 
16 (Ch. 30 7-b) TOPOGRAPHIC INSTRUCTIONS 

b. The screen and floating mark. --The 

viewing screen is a circular platen about 

inches in diameter. If desired, its white surface 

can be made even whiter by igniting a small ribbon of magnesium and holding the platen, which 

is removed from the tracing table, above the 

flame so that a smooth coating of the powdery 

white magnesium oxide is deposited on the viewing surface. 

A feature of some tracing tables is a platen 

that can be tilted as much as 30°toward the observer as an aid to viewing the more distant parts 

of the model. This tilt of the platen in no way 

affects the plotting geometry since the axis of 

tilt is designed to pass through the floating mark. 

The floating mark is a single, luminous dot, 

formed by light from a small bulb beneath the 

platen shining through a hole in the center of the 

platen approximately 0.004 inch in diameter. 

Recently, an improved floating mark has been 

developed by mounting a small sapphire in this 

hole to disperse the light through a wider angle. 

The intensity of the luminous mark can be varied 

by a control (5) mounted on the base. 

c. The height-indicating scale. --When the 

lock screw (6, fig. 8) is loosened, the height of 

the floating mark can be varied by turning the 

elevating wheel (7, fig. 8), which drives the platen carriage up or down the two vertical columns. 

The vertical movement is indicated by a scale, 

several types of which have been developed. One 

simple device (not shown) is a millimeter scale 

engraved directly on one of the columns. A vernier affixed to the platen carriage affords a minimum reading of 0.1 millimeter. The vernier can 

be adjusted through a range of about 10 millimeters 

for the purpose of "indexing" or setting the zero 

reading at a convenient value. Conversions between metric and English units are readily made 

from tables, prepared in advance, that list for 

each foot the equivalent millimeter values at 

each of the commonly used model scales. 

Another type of scale is a "Veeder" counter 

(3, fig. 8) geared to the elevating thread. Three 

drums record the vertical motion in tens, units, 

and tenths of millimeters. This counter can 

easily be set to any index reading by lifting the 

gear box cover (8, fig. 8) and loosening a lock 

nut to disengage the gears. 

A recent development of the counter type 

scale is a gear box equipped with interchangeable gears, so as to provide for readings directly in feet at a variety of model scales. 

Another recent development is the Williamson tracing table of British manufacture. 

Differing in many details, this tracing table has 

as its most outstanding feature a scale engraved 

on a glass bar, magnified by optical projection 

onto a glass screen at the rear of the platen. 

No vernier is employed. A number of interchangeable glass scales enable this table to read 

elevations in the stereoscopic model not only in 

millimeters, but also in feet at many different 

model scales. 

d. The plotting pencil and base. --The 

plotting pencil is supported directly below the 

floating mark so that it will mark upon the manuscript the orthographic projection of any point 

in the model at which the floating mark is placed. 

The pencil can be lifted from or lowered to the 

manuscript by means of the ring (9, fig. 8) at 

the rear of the base. A thumb bar (10, fig. 8) 

helps to steady the lowering motion. The weight 

(11, fig. 8) can be placed on the pencil chuck to 

increase the pressure as the point of the pencil 

wears. 

A 6-8 volt bulb in each side of the base 

(12, fig. 8) lights a small area of manuscript 

around the plotting pencil. A switch (13, fig. 8) 

controls these lights and the light provided to 

illuminate the height scale. These three lights 

are usually wired in series to operate from the 

20-volt supply. 

The tracing table slides easily over the 

manuscript sheet on small agate feet. Provision is made for adjusting these feet, together 

with the plotting pencil, to insure that the pencil 

is perpendicular to the table and centered below 

the floating mark at all times. These adjustments are described in articles 19 and 20. 

12. The supporting frame 

a. Function. --The multiplex supporting 

frame consists of a horizontal bar (10, fig. 2) 

and one or more uprights (11, fig. 2) that support this bar over the multiplex table. In addition to supporting the projectors, one of the usual 
MULTIPLEX EQUIPMENT (Ch. 30 7-b) 17 

functions of the frame is to tilt all the projectors 

as a unit, thereby providing a simple means of 

leveling either a model or a strip. 

Inasmuch as the top surface of the multiplex supporting table is the vertical datum of the 

instrument, the term "level" is used with reference to the model and to all parts of the multiplex except the table top itself to designate parallelism with the table top, which may or may not 

be truly horizontal 4 . 

b. Bar, --The multiplex bar spans the table 

lengthwise. Attached to and extending the full 

length of the bar is a smooch track (9, fig. 2) upon which the projectors can be hung and along 

which they may be slid in an x-direction. A rack 

running the full length of this x-slide engages a 

pinion gear on each projector to provide a means 

of driving the projectors along the slide. 

The length of multiplex bars ranges from 

3 to 14 feet, but 6 feet and 7 feet are the most 

common lengths. The multiplex unit pictured in 

figure 2 has a 7-foot bar. Some 7-foot bars are 

so made that two can be joined together to form 

a longer bar. When this i s done, a cantilever 

upright is needed to give additional support to the 

bar at the junction of the sections. Such a frame 

is more easily transported than one with a single 

14-foot section, but it has an operational disadvantage in that the center support makes leveling 

by means of the frame more difficult. 

c. Uprights. --Because the space beneath 

the projectors must be unobstructed, the multiplex bar is supported either by uprights at its 

ends or in cantilever fashion by one or more uprights at the back of the table. Three types of 

uprights are described, the inverted T-frame, 

the A-frame, and the nontilting frame. 

The "Inverted-T" frame is the type of upright shown in figure 2. Each end of the bar is 

supported on a vertical, threaded post. This bar 

can be inclined lengthwise by handwheels (12) 

which regulate the height of each end independently. 

The base of each upright is supported on foot 

screws (13) by which the entire frame can be 

tilted in any direction. One of the posts is usually 

pivoted at its junction with the base; otherwise the 

4 See article 3, Chapter 3 C 7-a. 

four-point support of the frame would make it 

possible to put an undesirable twisting stress 

on the bar. The handwheels, foot screws, and 

pivot can all be securely locked when the orientation of the model is completed. 

The "A" frame uprights are the simplest 

and most rigid type. They have no handwheels, 

all the tilting being done by means of the four 

foot screws. One of the uprights is usually pivoted at its junction with the bar. Without a pivot 

to release any twisting stress, extra care must 

be taken in co-ordinating the adjustments of the 

foot screws. 

The nontilting frame is suitable for those 

multiplex users who never set up more than one 

or two models at a time. This is a small multiplex frame and table in one integral unit, having 

a 3-foot bar supported in cantilever fashion by 

a rigid framework that extends up from the rear 

of the table. Although this frame cannot be 

tilted, the slab forming the table top rests upon 

an adjustable support so that it can be tilted instead. As explained in Chapter 3C 7-c, however, 

it is always possible to level a model entirely 

with the projector motions, without ever using 

these adjustments of the slab or frame. 

13. The supporting table 

a. The table top. --Multiplex table tops 

are uniformly about 3 feet wide (measuring from 

front to back) but come in lengths ranging from 

3 to 7 feet to suit the various lengths of supporting frames. Longer supporting frames can be 

placed on two tables that have been placed end 

to end and carefully alined. The primary requirement of the table top is that its upper surface be flat within a few thousandths of an inch, 

as this surface is the datum plane of the instrument. The material of which the table top is 

made is therefore important; slate, aluminum, 

and glass have been used. Of these, slate is by 

far the best. 

Slate tops, in addition to being the sturdiest and most stable of the three materials, are 

also the most easily surfaced, the most consistently available, and the least expensive. A 3-

by 7-foot slate top having a thickness of 3 inches 

is sufficiently rigid to remain flat without critical dependence upon its supports. Such a slab, 
18 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 

however, weighs about 1,100 pounds; therefore, 

when portability of the equipment is a factor, the 

purchaser turns to aluminum or glass. 

Aluminum table tops are much thinner than 

those of slate, being reinforced by heavy ribs 

cast on the underside. No separate frame is 

needed, as the legs can be fastened directly to 

the top casting. The aluminum top is not as rigid 

as the slate, however, and each leg (of which 

there are five) must be carefully adjusted after 

the table is set up to eliminate any warp or bending of the top surface. Aluminum tops have been 

preferred for setting up long tables because of 

the ease with which they can be clamped and 

splined together to form a continuous flat surface. 

Glass tops are the least desirable and the 

least used. Large glass plates would require 

several intermediate adjustable supports. The 

use of glass is best limited to small multiplex 

tables (for one or two models only). 

b. The table frame. - -A slate top or a glass 

top must be supported on a frame, preferably one 

of steel, as the weight of the table top plus the 

weight of the multiplex bar and projectors is considerable. The multiplex table frame is provided 

with adjustable feet, so that all the legs can be 

brought to bear equally upon the floor. If desired, 

the plane of the table top can be established as a 

truly horizontal plane by means of these foot adjustments. It is not necessary, however, to have 

the table top exactly leveled except in unusual instances when some gravity-dependent device such 

as a plumb bob or a spirit level is to be used in 

connection with the orientation of the projectors 

or model. 

14. Filter spectacles 

The filter spectacles (6, fig. 2) which the 

observer must wear in order to see the stereoscopic model have one red lens and one blue lens. 

As a rule, the greater the observer's stereoscopic 

ability, the greater is his preference for densities and shades of these colors that subdue rather 

than completely obscure the alternate image. 

Beginners, however, will benefit by the darker 

shades which provide a more solid though less 

brilliant model. The red lens is always plane; 

the blue lens is now made with a slight negative 

correction to balance the refraction of the two 

colors. For the observer's convenience in viewing consecutive models without having to exchange 

the projector filters, the spectacles either are 

made reversible or are supplied in sets of two, 

one with the red lens on the left and one with the 

blue lens on the left. 

Experiments have been made using polarized light to project the model and polarizing 

eye filters to obtain stereoscopic perception. 

A special surface for the tracing-table platen is 

required to provide a diffused but still polarized 

reflection, but such a surface has been difficult 

to obtain. The usual result is that either the 

back of the model appears too dim, or the texture 

of the platen surface is too evident. Although the 

method is workable it is not, at least at the present time, as satisfactory as the complementary 

colors. 

15. The electrical system 

The multiplex electrical system usually 

consists of a transformer, a control box (7, fig. 2) 

containing two or more selector switches and 

two or more rheostats, a multiple-outlet strip 

along the top or back of the horizontal bar, and 

the interconnecting wiring. 

The function of the transformer is to reduce the line voltage to the maximum required 

by the various light bulbs (commonly 20-volt, 

although both 6-volt and 12-volt multiplex projectors were once used). The selector switches 

are wired to the multiplex outlets--except one 

or two constant voltage outlets reserved for the 

tracing table connection--so that any desired 

pair of projectors can be lighted. The rheostats 

regulate the brightness of each irrage independently. (For good stereoscopic perception, each 

image must be about equally bright at the part 

of the model being viewed. ) 

A slightly different method of voltage control is employed in the case of the 3-foot multiplex frame and table mentioned above. This unit 

is equipped with two "Variac" controls, which 

combine the function of transformer and rheostat 

in each control. 
MULTIPLEX EQUIPMENT (Ch. 3C 7-b) 19 

16. The cooling system 

Forced air cooling for the multiplex projectors of newer design (2, fig. 2) is optional, 

but the projectors of older design (1, fig. 2) are 

operated without cooling only at the expense of 

shorter bulb life and at the risk of damaging the 

condenser lens. A fitting (16, fig. 5) for an air 

hose is provided on both types of lamp house, 

and the supporting frame carries a header (14, 

fig. 2) to which several air hoses can be connected. 

A large hose connects the header either to an individual fan or, in laboratories having several 

multiplex units, to an air duct connecting all the 

units to a central fan. 

The cooling system car be either a blower 

or an exhaust system. An advantage of a system 

that blows air into the projector is that a filter 

can be used on the air intake to catch the dust 

that otherwise would be sucked into the lamp house, 

where it would accumulate on the filter and upper 

condenser lens, and rapidly decrease the efficiency of the lighting system. 

CALIBRATION AND ADJUSTMENT OF 

MULTIPLEX EQUIPMENT 

17. Distinction between routine and laboratory 

procedures 

For the purpose of this discussion, the procedures involved in calibrating and adjusting multiplex equipment will be divided into two classes: 

routine procedures, or those which are the responsibility of the stereocompiler and, hence, a 

routine part of operation; and laboratory procedures, or those requiring the use of special tools 

and equipment in the hands of skilled technicians. 

The procedures in the routine class will be described in detail, but a discussion of the laboratory procedure is beyond the scope of this chapter--instead, there will be described methods 

that are available to the stereocompiler for 

roughly checking the calibration performed in the 

laboratory. 

The stereocompiler will make thel

adjustments or perform the checking operations listed 

below, either at such times as are suggested, 

or whenever the need is apparent. When a complete adjustment and check of equipment is made, 

however, it is important that the order in which 

the operations are listed be followed rather 

closely. 

(1) Adjust the floating mark bulb. 

(2) Check the verticality of the tracing table 

columns. 

(3) Center the plotting pencil. 

(4) Focus the principal-point microscope 

(when this instrument is used). 

(5) Check the collimation of the principalpoint microscope (when this instrument is used). 

(6) Orient the axis of the filament coil (in the 

newer type lamp house only). 

(7), Position the projector bulb. 

(8) Check the adjustment of the reflector (in 

the newer type lamp house only). 

(9) Check the principal distance of the projector. 

(10) Check the principal point of the projector. 

Of these operations, (2), (3), (5), (9), and 

(10) are,related to the calibration of multiplex 

equipment, inasmuch as they involve adjustments 

made to fixed standards upon which the proper 

geometric functioning of the instrument depends. 

The remaining operations pertain to adjustments 

that are not highly critical, but that primarily 

affect the convenience with which the visual observations can be made. Indirectly, anything 

hindering the stereocompiler's observations 

may result in errors in the map compilation 

fully as serious as errors due to faulty calibration of the equipment. 

18. Adjusting the floating mark bulb 

The position of the bulb beneath the hole 

in the platen of the trcing table affects the visibility of the floating mark, especially at the far 

edge of the model. Whenever this bulb is replaced, therefore, it should be repositioned as 

follows: 
20 (Ch. 30 7-b) TOPOGRAPHIC INSTRUCTIONS 

Loosen the screw (14, fig. 8) on the underside 

of the platen carriage. Move the bulb 

back and forth by sliding this screw in 

its slot, at the same time viewing the 

floating mark at a low angle. 

When the position of the bulb affording the 

brightest light is found, lock the bulb 

in position by retightening the screw. 

19. Checking the verticality of the tracing table 

columns 

To insure that the vertical movement of the 

floating mark is perpendicular to the supporting 

table top, the three agate feet of the tracing table 

are so mounted that each one can be adjusted up 

or down independently, until the columns on which 

the platen carriage rides are perpendicular to the 

plane of the feet. This is a laboratory adjustment, 

which the stereocompiler can check as follows: 

Lower the platen as far as it will go. Illuminating one projector, place the floating 

mark on any well-defined image point 

and plot this position with the tracing 

table pencil, first making sure that the 

pencil lead is sharpened to a carefully 

centered point. 

Without disturbing the elevation of the platen, 

turn the tracing table 180°and replot 

the same image point. If there is a discrepancy between the two plotted positions, tentatively adjust the pencil point 

to a mid-point position as described in 

step (3) of article 20. 

Raising the platen to its highest point, repeat 

the above procedure of plotting and 

checking a point, which may be either 

the same or some other well-defined 

image point. If a discrepancy is now 

apparent at this elevation, it indicates 

that the columns are not plumb. This 

adjustment needs to be checked only 

occasionally. 

20. Centering the plotting pencil 

This adjustment of the tracing table is the 

only adjustment affecting the calibration of 

multiplex equipment that the stereocompiler is 

charged with as a routine part of multiplex 

operation. The purpose of the adjustment is to 

center the pencil directly beneath the floating 

mark. The pencil lead should at all times be 

sharpened to a carefully centered point. This 

adjustment presupposes that the columns of the 

tracing table are perpendicular to the plane of 

the feet of the tracing table. 

Lock the platen at a fixed height (preferably 

at about the average plane of a model). 

Illuminating one projector, place the 

floating mark on any well-defined image 

point and plot this position with the 

tracing table pencil. 

Turn the tracing table 180°and replot the 

same image point. If there is a discrepancy between the two plotted positions, mark a mid-point between the 

two. 

Keeping the floating mark on the same image 

point, loosen the two adjusting screws 

(15, fig. 8) at the sides of the pencil 

chuck. Shift the chuck by means of 

these screws and the one behind the 

chuck (16, fig. 8) until the pencil point 

moves to the mid-point position. Tighten the side screws to lock the chuck in 

position. 

Check the adjustment by repeating the procedure. 

The stereocompiler should check this 

adjustment at least once a day until he is confident that the pencil will hold its adjustment for 

a longer period. 

21. Focusing the principal-point microscope 

a. Eyepiece. --Each stereocompiler who 

uses the principal-point microscope should refocus the eyepiece (2, fig. 7) if necessary, to 

suit his own vision. The eyepiece, which is 

threaded into the microscope tube, should be 

turned until the cross lines on the reticle appear 

sharp. Focusing the eyepiece does not disturb 

the collimation of the microscope. 
MULTIPLEX EQUIPMENT (Ch. 3C 7-b) 21 

b. Objective. --The objective lens of the 

principal-point microscope is properly focused 

upon the plane of the diapositive at the factory, 

and should not need refocusing. The stereocompiler can check the focus of this lens while using 

the microscope to center a diapositive, by moving 

his eye from side to side across the diameter of 

the eyepiece lens. If the cross lines on the microscope reticle appear to move relative to the diapositive image, the objective is not properly focused. Correcting the focus of the objective lens 

shouldbe done in the instrument laboratory, since 

it is almost certain to necessitate the readjustment of the instrument's line of collimation. 

22. Checking the collimation of the principalpoint microscope 

The test equipment shown in figure 7 is 

used in the laboratory adjustment of the line of 

collimation of the principal-point microscope. 

Two requirements have to be met: First, the 

feet of the microscope must define an equilateral 

triangle of a certain size; second, the cross lines 

of the reticle must define a line of sight that 

passes through the exact center of this triangle. 

The gauge plate (3, fig. 7) is used first to set 

the feet in the proper triangle, after which the 

illuminated testing fixture (4, fig. 7) is used to 

adjust the line of sight. Once the target on the 

testing fixture has been properly set, subsequent 

collimations of the principal-point microscope 

can be made on this fixture alone. 

The following procedure of checking the 

adjustment of the line of collimation will be used 

by the stereocompiler each time he centers a 

diapositive in a projector. 

With the microscope placed on the projector 

in one of the three alternative positions, 

center the diapositive as described in 

article 4 (b), chapter 3 C 7-c. 

Check this centering by successively placing 

the microscope in each of the other 

positions. A need for recollimation 

of the microscope is indicated if a discrepancy in one or both of the check 

positions is noted. (A tolerance of 

0.001 inch or about the width of one of 

the lines forming the principal-point 

mark is permissible. ) 

23. Orienting the axis of the filament coil of 

the projector bulb 

This adjustment applies only to lamp 

houses such as the one shown in figure 5, in 

which the bulb is mounted horizontally. With 

this orientation of the bulb, the axis of the filament coil revolves in a vertical plane when the 

socket mount is rotated. The best illumination 

is obtained when the filament coil axis is vertical, or parallel to the axis of the optical system. 

To adjust the axis of the filament coil: 

Hold an auxiliary lens of short focal length, 

such as a pocket magnifier, below the 

projector, and move this lens up or 

down until it forms an image of the 

lighted filament upon the table top. 

(If an auxiliary lens is not available, 

the projector lens itself can be made 

to focus the filament image by carefully lifting the lamp house from the 

base a distance approximately equal to 

the principal distance of the projector. 

The auxiliary lens method is preferred, 

however.) 

Rotate the bulb by the knurled ring (18, fig. 5) 

at the back of the bulb socket until the 

filament image appears doughnut-shaped. 

Whenever a bulb is replaced after this 

adjustment is once made, the filament coil axis 

will always come to a vertical position if .the 

three-holed flange on the socket assembly is 

always replaced with the same hole at the top. 

Therefore, the stereocompiler needs to check 

this adjustment only when he suspects that it 

may have been disturbed. 

24. Positioning the projector bulb 

Before this adjustment can be made, 

either a diapositive or a clear glass plate of 

equal thickness must be in place in the projector. 

With the lamp house in place, turn on the light 

to maximum intensity. Remove the 

color filter. Hold a white screen (the 

back of a contact print will do) close 

beneath the projector lens so that the 

whole field of illumination can be 

viewed. 
22 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 

Using the two lateral adjusting screws on the 

bulb mount (17, fig. 5), center the filament so that any color appearing in the 

illuminated area is symmetrically disposed. (This color is caused by chromatic aberrations of the condensing 

system.) If the filament were now to 

be viewed by the method described 

above of holding a small auxiliary lens 

beneath the projector, the filament 

should appear well centered in the aperture opening, which appears as a faint 

circle surrounding the filament image. 

Using the knurled ring (20, fig. 5) at the top 

of the lamp house, adjust the bulb vertically until the illuminated field is as 

color-free as possible. In particular, 

any bluish cast should be avoided--a 

tinge of yellow, on the other hand, is 

not undesirable, and a residual ring of 

light yellow around the outer edge of the 

field may often have to be accepted. 

25. Checking the adjustment of the reflector 

The reflector in the newer-style lamp 

house (fig. 5) is properly adjusted at the factory 

and should seldom need readjusting. Its adjustment is a laboratory procedure. The adjusting 

screws (19, fig. 5) should not be disturbed by 

the stereocompiler. The stereocompiler can 

check the adjustment of the reflector as follows: 

Position the bulb carefully by the procedure 

given in article 24. 

Grasping the lamp house firmly with both 

hands, raise it from the projector base 

until the image of the filament is seen 

on the table. (When this test is made 

in the laboratory, a special jig is used, 

which fits upon the projector base and 

provides a platform to support the lamp 

house at the proper height above the 

projector lens. ) 

Displace the lamp house horizontally to include 

the image formed by the reflector. (Because of the hole in its center, the reflector images only the oblique rays. ) 

If the reflector is properly adjusted, the 

reflected image should be of the same 

size as the direct (and brighter) one 

formed by the condenser lenses alone, 

and the two images should be in superposition. Adjust ent of the reflector 

is therefore needed if one image is 

readily distinguishable from the other. 

As an improperly positioned bulb could 

also be the source of a displacement between the 

direct and the reflected images of the filament, 

it is suggested that the bulb be repositioned by 

trial, when a displacement is noted, until the 

two images are brought together. With the lamp 

house then replaced on the base, if the illuminated field shows an undesirable amount of color, 

the lamp house should be sent to the optical laboratory for readjustment of the reflector. 

26. Checking the principal distance of the 

projector 

The two procedures that are here given 

for checking the principal distance will afford 

only a rough check, for the purpose of discovering a relatively large error, as they are capable 

of but one-fifth to one-tenth the accuracy required 

in the laboratory calibration of the principal 

distance. (In the laboratory calibration, it is 

attempted to set the principal distance to its 

nominal value with a precision of approximately 

1 part in 3,000. ) 

The principal distance is accurately calibrated before the projector leaves the factory, 

and seldom needs recalibration. The stereocompiler will, therefore, check the principal 

distance only when there are consistent indications that it may be in error. The indication of 

an error of principal distance is basically an 

inequality between the horizontal and vertical 

scale of the models. 

If the stereocompiler should find it necessary to check a principal distance, he will need 

one accessory that is not required in the everyday operation of the multiplex, a diapositive 

having calibrated graduations as indicated in 

figure 9. A glass plate etched with a precise 

grid is commonly used in the laboratory 

5See article 5, Chapter 3 C 7-c. 
MULTIPLEX EQUIPMENT (Ch. 3C 7-b) 23 

b1 4) I a 

Figure 9. --Checking principal distance 

by projected grid. 

calibration of the principal distance, and carefully made photographic copies of such a grid can 

be used in the following procedures. 

a. Suggested procedure. --The preferred 

procedure for checking principal distance is as 

follows: 

Place the grid plate in the projector and center one of the grid intersections. Swing 

the camera body until the grid lines are 

roughly parallel to the x- and y-axes of 

the projector. 

Viewing the projected grid on the table top, 

tilt the projector (x- and y_-tilt) until the 

pattern is precisely rectangular. Triangle OAB (figure 9) is now similar to 

triangle Oab. The grid plate is also 

parallel to the table top provided the 

optical axis of the projection lens is a 

straight line. 

On the grid line passing through the principal 

point in the x-direction, select two grid 

intersections, one on each side of the 

principal point and each approximately 

20 millimeters from the principal point. 

Using a needle in place of the tracing 

table pencil, and having checked the 

calibration of the tracing table with the 

needle in place, plot the positions of 

the selected grid intersections, once 

with the platen at its lowest possible 

elevation and again with the platen at 

its maximum height. Calculate the 

sum of the two displacements, d1 + d2. 

Compute the principal distance (P. D. ) according to the relationship 

h P. D. = x ab (1) d1 + d2 

where h is the vertical range of the 

platen and ab is the distance on the grid 

plate between the two grid intersections. 

b. Alternative procedure. --On the front 

of the outer gimbal ring is a conical boss (6, fig. 6). 

The following procedure makes the assumption 

that the center of this boss is exactly at the height 

of the exterior perspective center when the yslide of the projector is supported in a level position. The assumption of this condition is warranted, for it is a condition which the manufacturer attempts to attain very closely. (Subsequent adjustments of the principal distance will 

disturb this relationship slightly, as the principal 

distance is altered physically by a movement of 

the lens in relation to the rest of the camera body 

while the diapositive plane remains fixed.) 

Tilt the supporting frame until the y-slide of 

the projector is parallel to the top of 

the multiplex supporting table. The yslide may be leveled by means of a 

bubble, provided the table top has also 

been leveled. 

Place the grid plate in the projector and center one of the grid intersections. 

Viewing the projected grid on the table top, 

tilt the projector as described in the 

second step of the procedure described 

under a, until the pattern is precisely 

rectangular. 
24 (Ch. 3C 7-b) TOPOGRAPHIC INSTRUCTIONS 

Measure the distance AB (fig. 9) on the table 

between two grid intersections in line 

with the principal point and approximately 20 millimeters either side of the 

principal point. The distance ab between 

the same two points on the grid plate 

should also be measured, if not known. 

Measure the height H of the center of the conical boss above the multiplex table. 

Compute the principal distance (P. D. ) from 

the relationship 

H x ab 

P• —• AB 

27. Checking the position of the principal point 

of the projector 

The two procedures that are given here for 

checking the principal point will afford only a rough 

check, for the purpose of discovering a relatively 

large error, as they are capable of approximately 

one-fifth to one-tenth the accuracy required in the 

laboratory calibration of the principal point. (In 

the laboratory calibration it is attempted to set 

the principal point mark to define a perpendicular 

from the interior perspective center to the diapositive plane with an angular error no greater 

than 15 seconds.) 

The principal pc int is accurately calibrated 

before the projector leaves the factory, and seldom needs recalibration. The stereocompiler 

will therefore check the principal point only when 

there are consistent indications that its position 

may be in error. A position error of the principal point is often indicated by its effect on y-parallax, and sometimes by its effect on elevations in 

the model. Like a principal distance error, the 

effect of a given error increases in proportion to 

the relief in the models. 

a. Suggested procedure. --This procedure 

requires the use of the precise grid plate described in article 26. 

6

See article 5, Chapter 3 C 7-c. 

Place the grid plate in the projector and carefully center one of the grid intersections. 

(If the centering is done by means of a 

principal-point microscope, the adjustment of this instrument must have been 

previously checked. ) 

Viewing the projected grid on the table top, 

tilt the projector (x- and y-tilt) until 

the pattern is precisely rectangular. 

Using a tracing table that has been carefully 

calibrated with respect to the verticality of its columns, place the floating 

mark on the principal-point image. 

Without moving the base of the tracing 

table, move the platen up and down 

through its full range. If the floating 

mark and the principal-point image 

do not remain coincident, that is, if 

the principal-point ray is not plumb, 

the principal point is in error. 

b. Alternative procedure. --This procedure does not require the use of a grid plate, 

but it does make the assumption that the optical 

axis of the projector lens is a straight line and 

that the diapositive plane is perpendicular to 

the mechanical axis of swing. 

Carefully center a diapositive in the projector. If a principal-point microscope 

is used, it should be in accurate adjustment. 

Observing the principal-point mark on either 

the multiplex table or the platen, slowly rotate the projector by the swing 

motion through 180°, being careful not 

to disturb any of the other motions. If 

the principal-point mark does not remain 

stationary, an error in the position of 

the principal point is indicated. 

(2) 

INT.-DUP. SEC . , WASH., D . C .1 3 4 9 7 
GEOLOGICAL SURVEY 

TOPOGRAPHIC INSTRUCTIONS 

Chapter 3C 7-c 

MULTIPLEX ORIENTATION 

Contents 

Page 

Abstract 5 

Scope of multiplex orientation 5 

1. Procedures and objectives 5 

Interior orientation procedure 6 

2. Preliminary steps 6 

3. Inserting the diapositive 6 

4. Centering the diapositive 

a. Centering arm 

b. Principal-point microscope . 6 

c. Stage plate 7 

5. Effects of errors of interior 

orientation 7 

a. Principal-distance errors 8 

b. Principal-point errors 8 

Relative orientation procedure 8 

6. Preliminary steps 8 

a. Adjusting the lighting 8 

b. Preliminary orientation 8 

7. The perception of y-parallax 8 

8. Suggested procedures for clearing 

parallax 9 

a. "One-projector" method 9 

b. "Swing-swing" method 10 

9. When to use each method 11 

10. Possible use of positions outside 

the neat model 11 

11. Effects of errors of relative 

orientation 11 

12. Relative orientation problems • 13 

a. Rugged terrain 13 

b. Excessively tilted photographs . • 14 

c. Unequal settings of the y-slides. 14 

d. Extensive water areas 14 

Page 

Absolute orientation procedure 15 

13. Preliminary steps 15 

a. Identification of horizontal 

control 15 

b. Identification of vertical 

control 16 

c. Conversion of elevations . . 16 

14. Establishing scale and horizontal 

position 16 

a. Base sheet not moved 16 

b. Base sheet moved 17 

c. When to use each method . . 17 

15. Difficulty in positioning a model 17 

16. Leveling the model 17 

a. Leveling in the y-direction, 

using the projectors 18 

b. Leveling in the x-direction, 

using the projectors 18 

c. Alternative procedure of 

leveling in the x-direction, 

using projectors 18 

d. Leveling with the frame . . . 19 

e. Leveling with the projectors 

vs. leveling with the frame. . 19 

17. Effect of leveling on the position 

of the model 19 

18. Warped models 20 

19. Difficulty in leveling a model . 20 

Progressive achievement of exterior 

orientation 21 

20. Effect of repetition of orientation 

procedures on degree of 

refinement 21 

3 
Illustrations 

Page 

Figure 1. Effects of interior orientation errors 7 

2. Locations in the model at which to observe y-parallax 9 

3. Effects of the six projector motions 10 

4. Effects of relative orientation errors 12 

5. Examples of the effect of relief 13 

6. Examples of extensive water areas 15 

4 
Chapter 3 C 7-c 

MULTIPLEX ORIENTATION 

ABSTRACT 

Orientation procedure is divided into interior orientation and exterior orientation. The latter is subdivided into relative orientation and 

absolute orientation. Alternative methods are available for each phase 

of orientation; once the method is selected, a fixed routine is followed. 

Where alternative methods are given, the exposition is accompanied by 

a discussion of when to use each method. Interior orientation procedure 

varies according to the means provided for centering the diapositive; the 

means may be a centering arm, principal-point microscope, or stage 

plate. Relative orientation can be accomplished either by the "one projector" method or the "swing-swing" method, depending on whether it is 

desired to limit the adjustments to one projector or apply them to both 

projectors. In absolute orientation procedure, positioning of the model 

can be effected with the base sheet either fixed or movable, and leveling 

of the model can be accomplished by adjusting either the projectors or 

the frame. Difficulties arising from special problems and the effects of 

errors are treated in connection with each phase of orientation. Minor 

variations from the described procedures are permissible, but are not 

given in detail. 

SCOPE OF MULTIPLEX ORIENTATION 

1. Procedures and objectives 

The broad steps of multiplex orientation, 

and the relation of orientation to the complete 

chain of multiplex mapping operations, are indicated in a preceding chapter 2 . The objects of 

the various orientation procedures may be briefly 

restated as follows: 

a. Interior orientation. --To recover a projected cone of rays geometrically identical with 

the cone of rays making the original exposure. 

1The number 3 C 7=c signifies Book 3, Part C, 

Chapter 7-c of the Geological Survey loose-leaf 

manual of Topographic Instructions. For a table 

of contents, see Chapter 1 A 2 (Circular 92). 

2 Chapter 3 C 7-a, Introduction to the multiplex. 

b. Exterior orientation. --To recover the 

position of each camera station and the angular 

orientation of each photograph. Exterior orientation is divided into two parts: 

(1) Relative orientation--To reconstruct 

the same perspective conditions between a pair 

of photographs that existed when the photographs 

were taken, thus establishing a model. 

(2) Absolute orientation—To orient the 

model with reference to a horizontal and vertical datum. 

This chapter is devoted to, detailed instructions for effecting each orientation procedure. 

5 
8 (Ch. 3C 7-c) TOPOGRAPHIC INSTRUCTIONS 

INTERIOR ORIENTATION PROCEDURE 

2. Preliminary steps 

Remove the lamp houses from all the projectors. As the bottom rims of the lamp houses 

are likely to leave black marks wherever they 

are set down, care should be taken never to set 

the lamp houses directly on the compilation sheet. 

Loosen each swing lock screw and rotate 

the projectors until all the diapositive centering 

mechanisms are similarly oriented. When the 

projectors being used are of the types having external screws for the centering of the diapositive, 

it is essential that the projectors all be turned 

with these screws to the front. When the centering screws are internal (i. e. , in the type projector employing a principal-point microscope), 

this step is not essential, but is a matter of convenience. 

Before inserting any diapositives, carefully 

blow or brush any dust or chips of glass from the 

projector lens. (In the Bausch and Lomb-U. S. 

Army type projector, dust is kept from the lens 

by the stage plate. Dusting the stage plate is 

especially important as dust or glass chips here 

may make a permanent scratch upon the glass, 

as well as being a potential source of error by 

preventing the diapositive from lying in its proper 

plane.) 

3. Inserting the diapositive 

For convenience, it is suggested that all 

the diapositives be placed in the projectors in 

such order and orientation that it will not be necessary to shift the order of the projectors on the bar 

or to rotate any projector 90°or 180° . One way 

to do this is to lay out the contact prints in the 

desired order and with the overlapping portions 

of the photographs adjoining each other. Lay out 

the diapositives, emulsion side down, in the same 

order and with the same orientation. Then simply 

rotate each diapositive 180°when placing in the 

projector to allow for the fact that in projection 

the image is reversed left for right and top for 

bottom. 

Having placed each diapositive in its projector, emulsion side down, clamp it securely. 

Whatever manner of stops or springs is used 

to hold the diapositive in place, care should be 

taken to see that the diapositive is secure but 

not subject to any undue pressure that might 

bend or break the glass between the supporting 

bosses. 

Check the diapositive for contact with the 

bosses by tapping it lightly on each corner. If 

the contact is good, no clicking of the glass 

against the boss will be heard. Checking the 

diapositive for contact with a glass stage plate 

(as is required in the U. S. Army type projector) 

is best done by looking for the interference patterns, or "Newton's rings," in the light reflected 

from the two surfaces in contact. The presence 

of these "rings" is an indication of sufficient 

contact. 

If the projector is one of the newer Geological Survey types in which the diapositive is 

fastened in a surrounding frame, it is well to 

tap this frame lightly to see that it in turn rests 

securely on its supporting bosses. 

4. Centering the diapositive 

The diapositive centering procedure will 

depend on which of the three previously described 

devices is used for indicating the principal point 

of the projector. 

a. Centering arm. --Replace the lamp house 

and release the centering arm until it comes up 

against its stop. Either on the platen or on the 

table, observe the image of the black dot on the 

reticle of the centering arm, and the image of 

the white cross or circle marking the principal 

point of the diapositive. Bring these marks into 

concentric alinement by means of the centering 

screws, being careful to make the final twist of 

the screws a positive motion, against their opposing springs. 

b. Principal-point microscope. --Do not 

replace the lamp house, but place the microscope 

in position on the projector by first placing one 
MULTIPLEX ORIENTATION (Ch. 30 7-c) 7 

foot (any one of the three may be used) in the 

cone-shaped foot pad, then revolving the second 

foot into the V-shaped pad, and finally lowering 

the third foot onto the flat pad. Place a light 

source or a light-colored surface below the projector lens for a background. Observing the principal-point mark of the diapositive through the 

microscope, aline it with the cross lines of the 

microscope reticle, always being careful to 

make the final adjustment against the spring. 

Check this alinement with the microscope successively placed in all three possible orientations. 

If the centering checks, remove the microscope 

and replace the lamp house. 

c. Stage plate.--Replace the lamp house. 

Observing the projected images of the principalpoint marks, the one on the stage plate and the 

one on the diapositive, aline them by means of 

the centering screws, being careful to make the 

final movement of the diapositive against the two 

springs. 

5. Effects of interior orientation errors 

Figure 1 shows the deformations of a model 

caused by small errors of principal distance and 

of principal-point location. Principal-distance 

and principal-point errors have no effect upon a 

model that is a flat surface, but their effects increase in proportion to the relief in the model. 

Only the vertical effects are important; the horizontal displacements are seldom large enough to 

be significant. In figure 1, the dashed lines indicate the normal shape of a model which, in this 

illustration, is assumed to be a block with rectangular faces. The solid lines then picture the 

nature of each particular deformation. The magnitudes of the deformations shown are greatly 

exaggerated in proportion to those that would 

likely occur in practice. 

PRINCIPAL DISTANCE - ONE ONLY PRINCIPAL DISTANCE -BOTH EQUAL 

PRINCIPAL POINT -EQUAL IN X PRINCIPAL POINT - OPPOSITE IN X 

PRINCIPAL POINT-OPPOSITE IN Y PRINCIPAL POINT EQUAL IN Y 

Both principal-distance error and principalpoint error can result from improper calibration 

of either the aerial camera, the multiplex printer, 

or the multiplex projector. Principal-point error 

can also result from a failure on the part of the 

diapositive maker to aline each negative properly 

in the printer, or from a failure on the part of the 

stereocompiler to center each diapositive correctly in its projector. 

Figure 1. --Effects of interior orientation 

errors. 

Those errors having their source in the 

optical or mechanical performance of the aerial 

camera or diapositive printer are very likely 

to be duplicated in each projection. The errors 

of negligent operation are more likely to occur 

in one projection only. 
8 (Ch. 3C 7-c) TOPOGRAPHIC INSTRUCTIONS 

a. Principal-distance error. --The essential effect of principal-distance error is to alter 

the vertical scale of the model with respect to 

the horizontal scale of the model. An error in 

the principal distance of one projector bears the 

same proportion to the total principal distance 

as the resultant error in the vertical dimension 

of the edge of the block under the opposite projector bears to the total height of the block. Thus, 

when both principal distances are equally in error, 

the vertical dimension of the whole block is uniformly in error; if the principal-distance error 

is, say 1 millimeter in a principal distance of 

30 millimeters, the vertical error would amount 

to 1 foot in 30 feet, 10 feet in 300 feet, etc. 

b. Principal-point error. --When the principal points are displaced so as to have unequal 

x-components, errors of vertical scale occur. 

In this case, the vertical scale is uniformly affected over the entire model. When both principal points are displaced equally in any direction, 

a condition is obtained wherein there is no scale 

error and no y-parallax error. The block simply 

leans slightly- in the direction of the error. When 

the principal points are displaced so as to have 

unequal y-components, y-parallax will be evident 

in the model at all elevations above and below the 

plane of the points used for clearing y-parallax 

in the relative orientation procedure. 

RELATIVE ORIENTATION PROCEDURE 

O. Preliminary steps 

a. Adjusting the lighting. --When the diapositives are in place and the lamp houses have 

been replaced, it is well to check the adjustment 

of each light bulb to see that it gives the best possible illumination3 . 

b. Preliminary orientation. --The time required to perform orientation (both relative and 

absolute) may often be decreased if at the start 

the projectors are roughly oriented according to 

the best estimate of what their ultimate orientations will be. If nothing else is known, it may 

at least be assumed that the flight line is level, 

stra- ght, and parallel with the multiplex bar and 

that each photograph is truly vertical. Accordingly, it is good practice to commence by leveling the multiplex frame and each projector, not 

3This adjustment is described in article 24, 

Chapter 3 C 7-b, Multiplex equipment. 

necessarily measuring these adjustments, but 

at least estimating them with care. Set all the 

y-slides to a uniform value, likewise the z-slides. 

Space the projectors apart an average amount 

(200 to 240 millimeters). 

7. The perception of y-parallax 

When corresponding images from a pair 

of projectors not in relative orientation are observed on the tracing table platen, components 

of separation in both the x- and y-directions 

will ordinarily be seen. (For the purpose of 

this discussion of relative orientation, the model 

air base will be considered to be parallel to the 

x-direction unless otherwise stated.) The xcomponent at any one point can be eliminated 

either by altering the air base (x-motion of the 

projectors) or by changing the height of the platen. The separation then remaining at the point 

is strictly y-parallax (often referred to among 

multiplex photogrammetrists simply as parallax), 

which can be eliminated only by some motion of 

the projectors other than x-motion. 

When relative orientation is first begun, 

y-parallax will be observed without the filter 

spectacles and will appear as a distinct separation between corresponding images. The color 

filters should be in place but only as an aid in 

distinguishing one image from the other. Images 

affording good contrast and ready identification 

should be selected, such as cleared fields surrounded by woods, or prominent roads or fence 

patterns. 

As relative orientation progresses and the 

y-parallax separation diminishes to something 

less than a millimeter it becomes preferable to 

view the parallax stereoscopically, using the 

filter spectacles. Viewed in this way, y-parallax 

appears no longer as a separation of the two 

images, for they are fused into one three-dimensional model, but as a y-direction split in the 

floating mark, the apparent separation between 

the two dots being equal to the disagreement of 

the actual images on the platen. The smallest 

y-parallax appears finally as a slight fuzziness 

of the dot or perhaps as a slight fringe of colors 

upon its upper and lower edges. Moving the 

mark about a small area to obtain different backgrounds, an experienced observer can detect a 

y-parallax of 0.1 millimeter or even less. 
6 -INCH COVERAGE 

5' 

NEAT MODEL 

/ 

/ I 

I 

/ I 

I I --I- 7 

I 

I 

I 

/ / 

MULTIPLEX ORIENTATION (Ch. 3C 7-c) 9 

8. Suggested procedures of clearing y-parallax 

The many alternative procedures of clearing y-parallax are but slight variations of one 

fundamental procedure of relative orientation. 

The procedures given in this article are two of 

the standard variations which the multiplex beginner should memorize, practising them at first 

using a pair of specially made diapositives having 

lines or dots to mark the positions numbered 1 to 

6 in figure 2. 

FOR 9X9-INCH FORMAT. 

LIMIT OF 4-INCH STEREO COVERAGE 

LIMIT OF 5.2-INCH COVERAGE 

- - 

II 

Figure 2. --Locations in the model at which 

to observe y-parallax. 

The possible variations of procedure can 

more readily be appreciated if the six motions 

of the multiplex projector are examined, as the 

effects of these motions dictate the general procedure of relative orientation. Figure 3 shows 

how these motions would appear to distort the 

projected image of a grid. The plane of projection is assumed originally to be parallel to the 

diapositive grid plate, and the projected grid in 

this position is represented by dashed lines. 

The numbers locate the critical positions in a 

model at which y-parallax will be observed and 

cleared, as indicated in figure 2. 

Clear y-parallax at 2 with y-motion. 

Clear y-parallax at 1 with swing. 

Clear y-parallax at 4 with z-motion. 

Clear y-parallax at 3 with y-tilt. If the 

amount of tilt is large it is ofttimes convenient, although never necessary, to 

restore the model approximately to its 

original projection distance by a suitable x-motion. 

Overcorrect approximately q times the yparallax at 6 with x-tilt. 

Repeat the procedure until no y-parallax remains at any of the five positions. 

Check position 5. The y-parallax here indicates that some of the previous positions 

have not been completely cleared of 

y-parallax. 

If projector I had been used, the requirement obviously would have been to reverse positions 1, 3, and 5 with positions 2, 4, and 6 

respectively. Positions 3 and 4 may be reversed 

with positions 5 and 6 respectively in any procedure. This is a matter of choice. 

a. "One-projector" method of relative 

orientation (sometimes called "y-swing" method).—

Refer to the numbered positions given in figure 2. 

All the motions are applied to projector II: 
5 6 

2 

3 ,4 

2 

4 

X - MOTION 

5 6 

H 2 

3 4 

5 

Z-MOTION 

6 

10 (Ch. 30 7-c) TOPOGRAPHIC INSTRUCTIONS 

5 6 

1 

4' 2 

,3 

Y-MOTION 

5 6 

,2 

X-TI LT 

5 6 

In addition to these possible substitutions of positions, the order in which the 

motions are adjusted may also be ,varied 

to some extent. From the different combinations of these factors that are possible, 

the stereocompiler can perhaps choose an 

alternative procedure that he will prefer 

to the one given above. For example, an 

alternative that is preferred by some stereocompilers consists of adjusting the zmotion in the third step of the foregoing 

procedure so as to distribute y-parallax 

equally between positions 4 and 6. The xtilt is next adjusted, overcorrecting the 

y-parallax at either 4 or 6 approximately 

4 times. If these adjustments are suitably 

made, positions 2, 4, and 6 can be cleared 

of y-parallax by a readjustment of the ymotion alone. Finally, y-tilt is adjusted 

at position 3. 

b. "Swing-swing" method of relative 

orientation. --Insofar as relative orientation is concerned, it is evident that identical swings applied to both projectors have 

the same effect as y-motion applied to one 

alone. Also, identical y-tilts applied to 

both projectors have the same effect as zmotion applied to one alone. If these substitutions are made in the foregoing procedure, a method of achieving relative 

orientation without the use of translational 

motions is obtained: 

Clear y-parallax at 1 with swing of 

projector II. 

Clear y-parallax at 2 with swing of 

projector I. 

Y-TI LT SWING 

Figure 3. --Effects of the six projector motions. 

Clear y-parallax at 3 with y-tilt of 

projector II. (Follow with 

x-motion if desired. See step 4, 

one-projector method. ) 

Clear y-parallax at 4 with y-tilt of 

projector I. (Follow with 

x-motion if desired. ) 
MULTIPLEX ORIENTATION (Ch. 3C 7-c) 11 

Overcorrect times) the y-parallax at either 

5 or 6 with x-tilt of either projector. 

Repeat the procedure until all positions have 

been cleared of y-parallax. 

9. When to use each method 

When one model is being added to another 

already in relative orientation, as when a strip 

of models is being oriented in the process of 

stereotriangulation, it is necessary to use the 

"one-projector" method to orient the added projector. Otherwise it is always possible to use 

either method. 

As the "swing-swing" method does not 

make use of the translational motions, the y- and 

z-settings of the projectors will remain unchanged 

during the process of relative orientation by this 

method. If some particular setting of these elements is desired in the ultimate model, the 

"swing-swing" method makes it possible to preset these values and then accomplish relative 

orientation without disturbing them. The common 

application of the "swing-swing" method is in the 

relative orientation of the initial model of a strip, 

or of any single model, wherein the projectors 

should be preset so that the air base is parallel 

to the bar. The subsequent leveling of the model 

will be simplified by maintaining the air base 

approximately level during relative orientation. 

The adjustments of both relative and absolute 

orientation are simplified by maintaining the xtilt axes of the two projectors as nearly as possible in line with each other. 

When it is permissible to use either method, 

the stereocompiler may, if he desires, combine 

parts of both methods. Thus, for example, he 

might use the y-motion of one projector but not 

the z-motion; o-r the z-motion but not the y-motion. 

This intermixing of methods is often practiced, 

especially when the adjustments to be made are 

small. 

10. Possible use of positions outside the neat 

model 

There are times when it is advantageous to 

observe y-parallax at positions outside the neat 

model, after the best solution has been obtained 

using the positions 1 through 6 (which have been 

assumed to lie on the edges of the neat model). 

Positions 7 and 8 obviously offer the largest possible base for determining the swing settings. These settings can be checked most accurately by looking for y-parallax here. Positions 9, 10, and 11 offer the largest possible 

base for determining the relative x-tilt setting. 

A small error in this setting may be noticed by 

careful observations at these three positions. 

The strongest determination of the relative y-tilt setting would seem to be made at positions outside of 3, 4, 5, and 6, but as various 

residual image distortions are likely to have 

their greatest effect in these areas it is actually 

necessary to take care not to observe y-parallax 

beyond the limits of the neat model in the corners. (Although distortion might exist at positions 7, 8, 9, 10, and 11, it would not create 

y-parallax. Distortion would not create y-parallax at positions 7, 8, and 10 because its direction at these positions would have no y-component. At positions 9 and 11 any distortions 

would be symmetrical, hence their y-components 

would be equal and would cancel each other in 

effect. ) 

11. Effects of errors of relative orientation 

The effects on the model datum of a small 

error in the setting of each motion of the multiplex projector are pictured in figure 4. (These 

effects, as indicated by the differences between 

the dashed and the solid outlines, are greatly 

exaggerated for illustrative purposes. Assuming 

a maximum residual y-parallax of 0.1 millimeter, 

the magnitude of any effect is but a few tenths of 

a millimeter, excepting, of course, the effect 

of x-motion, which involves no y-parallax. ) 

These errors affect elevations in the model more 

seriously than they do horizontal positions. The 

horizontal deformation resulting from a residual 

y-parallax o' 0. 1 or 0.2 millimeter is not significant in a single model. 

As indicated in figure 4, errors of relative orientation affect the vertical datum of the 

model essentially as follows: 
12 (Ch. 30 7-c) 

Y-MOTION 

X-MOTION 

Z-MOTION 

X- TILT 

TOPOGRAPHIC INSTRUCTIONS 

uniform raising or lowering of the model datum 

with respect to the table top, or instrument datum, is offset by re-indexing the scale of the 

tracing table. 

Error from z-motion. --The principal effect of this error is to tilt the model datum about 

a y-axis. As the datum remains flat, this effect 

is offset by the subsequent leveling of the model 

when absolute orientation is performed. The 

maximum tilt of the neat model permitted by 

0.1-millimeter y-parallax in the neat model is 

0.2 millimeter 4 . 

Error from x-tilt. --The principal effect 

of this error is to produce a hyperboloidal warping of the model datum. The maximum curvature 

of the datum occurs along the diagonals of the 

model. In the x- and in the y-directions the datum remains uncurved; that is, any xz- or yzsection is a straight line. Maximum warp permitted by 0.1-millimeter y-parallax in the neat 

model (deviation of one corner above or below 

a plane passing through the other three corners) 

is 0. 8 millimeter. (See footnote 4). 

Y-TILT 

Error from y-tilt. --The principal effect 

of this error is to produce a cylindrical warping 

of the model datum. The maximum curvature of 

the datum occurs in the x-direction, the datum 

remaining uncurved in the y-direction. Convergent y-tilt lowers the y-direction center-line of 

the model with respect to the left and right edges, 

as shown in figure 4; divergent y-tilt causes this 

center-line of the model to be raised. Maximum 

warp permitted by 0. 1-millimeter y-parallax in 

the neat model (deviation of the center of the 

model above or below a plane passing through the 

four corners) is 0.1 millimeter. (See footnote 4). 

SWING 

Swing error. --The principal effect of this 

error is to tilt the model datum about an x-axis. 

As the datum remains flat, this effect is offset 

by the subsequent leveling of the model when 

absolute orientation is performed. Maximum 

tilt permitted by 0.1-millimeter y-parallax in 

the neat model is 0.44 millimeter. (See footnote 4). 

Figure 4. --Effects of relative orientation 

errors. 

Error from y-motion. --The error has no 

effect upon the model datum. 

Error from x-motion. --The effect of this 

error is to change the scale of the model. The 

4

Approximate values. Computed for a baseheight-width ratio of 2:3:3. 
A 

Figure 5. --Examples of the effect of relief. 

MULTIPLEX ORIENTATION (Ch. 30 7-c) 13 

To summarize, it is seen that of the six 

errors only two, namely x-tilt error and y-tilt 

error, have a significant effect. Each of these 

warps the model datum in a characteristic manner, by which the error may be identified. It is 

also to be noted that no relative orientation error 

permits of any curvature of the model datum in 

the y-direction. 

Errors of relative orientation can result 

not only from failure of the stereocompiler to 

clear y-parallax completely, but also from a 

photographic distortion. As the y-components 

of distortion at each of the four corner locations 

where y-parallax is observed usually differ between the two photographs of the overlapping pair, 

erroneous projector settings will undoubtedly result from clearing y-parallax completely at these 

positions. Fortunately, however, the effect of 

distortion in present-day multiplex projectorprinter-camera systems is not appreciable in a 

single model. 

As relative orientation is but a means to 

an end, the ultimate objective of all the orientation processes being absolute orientation, it is 

permissible to use the flatness of the model datum instead of y-parallax as a means of adjusting 

the x-tilt and the y-tilt settings. In fact, the ultimate settings of these two motions usually must 

depend on their effect on model flatness as revealed during the course of leveling. The x-tilt 

motion especially creates a warp of the model 

datum more critical than its y-parallax effect 

(see article 18). 

12. Relative orientation problems 

The terrain model is never a perfectly 

rectangular, plane surface, as has been assumed, 

and the projector axes are not often truly parallel 

to the x-, y-, and z-directions respectively. Yet 

in most cases, the actual model is regular enough 

to respond normally to the standard procedures 

of clearing y-parallax. 

The attainment of a parallax-free model 

becomes more difficult, however, when the model 

presents any of the following to an extreme degree.: 

rugged terrain, tilt of the photographs, unequal 

settings of the projector y-slides, or water areas. 

The nature of the problem presented by 

each of these conditions is outlined below and 

a course of action suggested, but the stereocompiler must deduce the exact steps to be taken 

in any particular situation. 

a. Rugged terrain. --The effect of topographic relief upon relative orientation procedure depends both on the magnitude of the relief 

and on the distribution of the areas of high and 

low relief within the model. As an example of 

this, two extreme cases are illustrated in figure 5. 

Figure 5A illustrates a hypothetical model 

in which the terrain surface has the shape of a 

cylinder whose axis is parallel to the air base 

and is at such a distance from it that the extension of the cylindrical surface would include the 

air base. The dashed lines show how a projector 

can assume various orientations and still permit 

all pairs of conjugate image rays to intersect. 

Thus, relative orientation cannot be determined 

solely by the usual y-parallax effects. Unless 

the relative x-tilt is properly set, however, the 

model datum will be warped, as indicated in 

figure 4. In lieu of y-parallax observations, 

therefore, the x-tilt setting must be determined 

by adjusting the motions until elevations in each 

of the four corners of the model read correctly. 
14 (Ch. 30 7-c) TOPOGRAPHIC INSTRUCTIONS 

Figure 5B illustrates the opposite condition 

in which the terrain is at a much higher elevation 

directly under the flight line than it is along the 

front and back edges of the model. This condition 

increases the accuracy of the x-tilt setting as determined by y-parallax, because for a given increment of x-tilt it creates a greater than normal 

y-parallax differential between AB and BC. For 

the condition shown in figure 5B the required 

overcorrection of x-tilt in the routine procedure 

would be but one-half, approximately, of the 

amount of y-parallax, Py. 

b. Excessively tilted photographs. --If excessive tilts of the aerial photographs decrease 

the area of stereoscopic overlap so that it is not 

possible to make y-parallax observations at the 

ideal positions, the difficulty of relative orientation will be increased accordingly. The strength 

of the resultant orientation will also be diminished. 

But the principal difficulty caused by excessive 

tilts is due to the displacement of the rotational 

axes of the projectors from their rectilinear 

orientation with respect to the air base and/or 

with respect to each other, conditions on which 

the procedures of relative orientation were postulated. 

The one axis of a multiplex projector that 

is not disturbed by rotation of the projector about 

the other axes is the y-axis (primary axis). The 

y-tilt adjustments are therefore always observed 

in the model at the same positions relative to the 

y-axes. 

The x-tilt axis can become displaced so that 

components of swing are introduced by the x-tilt 

motion and the apparent overcorrection of y-parallax by this motion must be varied to allow for this. 

Trial and error will soon reveal whether more or 

less correction is required. 

The swing axis can become displaced in both 

the x- and the y-directions, but as the swing adjustments are made prior to any other, this is 

not of particular consequence. If it is desired 

that the y-parallax cleared by the swing motions 

should not be reintroduced by the succeeding 

y-tilt adjustments, swing parallax must be cleared 

primarily at each nadir point rather than at the 

principal points. However, the swing motions 

(or y-motion and swing) undoubtedly will be 

slightly interaffecting at the nadir positions and 

successive trials of slight over- or under-corrections of the swing settings probably will be 

required. 

c. Unequal settings of the y-slides. --Though 

it is not attributable to tilts of the aerial photographs, an excessive difference in the settings 

of the projector y-slides also violates the rectilinear orientation of the rotational axes with respect to the air base. The y-tilt in effect introduces components of x-tilt, and conversely, xtilt introduces components of y-tilt. Relative 

orientation procedure is complicated by this 

condition which should be avoided whenever possible. If the air base must be set at an excessive 

angle to the bar, however, the logical procedure 

is to use, in place of x-tilt alone or y-tilt alone, 

a combination of the two motions calculated to 

produce a resultant tilt in the desired direction. 

Simple estimation of the proportions of each tilt 

motion together with a few extra runs through the 

procedure willbe all that ordinarily is required. 

d. Extensive water areas. --The orientation of photography over coastal areas often is 

difficult because it is not possible to see y-parallax in the water portions of the model. The least 

that can be done, of course, is to clear the yparallax over the extent of the land area, but 

such a solution will obviously not be as strong 

as it would have been if images had been available over the full model for y-parallax observation. Limited lana areas for y-parallax observation will thus lessen the accuracy of stereotriangulation, although they will not, as a rule, 

lessen the accuracy obtainable from the individual model, inasmuch as the area of the model 

from which detail can be compiled is limited to 

exactly the same extent. 

Nevertheless, advantage should be taken 

whenever possible of any effects that erroneous 

relative orientation has upon the flatness of the 

model datum. These effects are illustrated in 

figure 4. If water-level readings can be taken 

along shore lines at certain critical positions in 

the model, they provide a means of readily detecting warping of the model datum. 
MULTIPLEX ORIENTATION (Ch. 3C 7-c) 15 

As examples of the use of elevation readings 

in achieving relative orientation, figure 6 represents models wherein excessive water areas preclude the making of y-parallax observations at 

one or more critical positions. 

A 

Figure 6. --Examples of extensive water areas. 

Missing in the model in figure 6A is a position at which to observe the y-tilt adjustment of 

projector I (step 4 of the "swing-swing" method). 

In place of step 4, therefore, projector I should 

be y-tilted until shore-line readings at positions 

1, 10, and 2 indicate no curvature of the model 

datum in this direction. (These elevations may 

not necessarily indicate a level datum, however. ) 

If projector II were to be used alone, its 

y-tilt adjustment would precede rather than follow the adjustment of the z-motion. Step 3 of 

the "one-projector" method would then be the 

adjustment of the y-tilt of projector II using the 

three shore-line readings across the width of the 

model as described above. Step 4 would be the 

z-motion adjustment, observing y-parallax at 

position 3 (or 5) instead of position 4 (or 6). 

Missing in the model in figure 6B are positions at which to observe the swing adjustments. 

A procedure similar to this might be used: 

Swing projector II until the y-parallaxes at 5 

and 3 are symmetrical with respect to 

the x-axis of the model. 

Swing projector I until the y-parallaxes at 4 

and 6 are symmetrical. 

Clear y-parallax at 3 by y-tilt of projector II. 

This should simultaneously clear y-parallax at 5. 

Clear y-parallax at 4 by y-tilt of projector I. 

This should simultaneously clear y-parallax at 6. 

Then x-tilt either projector until shore-line 

readings at positions 3, 4, 5, and 6 

indicate no warping of the model datum 

(elevation difference between 3 and 5 

equals elevation difference between 4 

and 6). 

Repeat the procedure until the model datum 

is flat and until at the same time no 

y-parallax remains at any position. 

ABSOLUTE ORIENTATION PROCEDURE 

13. Preliminary steps 

a. Identification of horizontal control. --

The horizontal control to which the model will 

be positioned may have been identified in various 

ways

5

. Positions that have been established by 

ground surveys either are marked on the faces 

of the contact prints, or are identified solely by 

descriptions of the points. In the latter case, 

the identification of several points in a group 

(as, for example, stations along a traverse line) 

can often be verified by the way in which, as a 

group, they correlate with their plotted positions. 

Horizontal pass points, or supplemental 

positions established by stereotriangulation6for 

controlling individual models, will have been 

plotted on the base sheet either as actual points 

or as lines delineating small portions of planimetric features. When the stereotriangulator 

has used points, he will have marked the images 

on the faces of the contact prints; when he has 

used lines, identification of the images will 

usually be self-evident once the general locations 

of the features are known. The stereotriangulator 

5

See Chapter 2 F 1, Supplemental control 

planning. 

6 See Chapter 3 C 7-d, Multiplex stereotriangulation. 

n 
16 (Ch. 3C 7-c) TOPOGRAPHIC INSTRUCTIONS 

may have encircled these general areas on the 

prints; or if the principal points are included 

among the pass points--and they should be--these 

usually serve to position the model well enough 

that identification of the other pass points can 

readily be made. The points selected for horizontal pass points will not necessarily be the 

same ones used for vertical control, although 

both should be located approximately at each corner of the neat model. 

b. Identification of vertical control. --Supplemental control points are usually circled on 

the faces of the contact prints, each point being 

designated by a letter. Brief descriptions and 

the elevations of the points are shown on the back 

of the prints7 . 

c. Conversion of elevations. --Prior to leveling a model, all control elevations must be converted to millimeter values unless the multiplex 

tracing table is one of the newer types capable of 

direct readings in feet. Millimeter conversions 

are most conveniently obtained if a table is prepared beforehand to suit the plotting scale and the 

range of elevations anticipated. 

14. Establishing scale and horizontal position 

The scale of the model now in relative 

orientation is governed solely by the length of the 

air base between projectors. To scale a model, 

therefore, one of the two projectors must be 

moved in a direction parallel to the air base. 

(If the air base is not parallel to the direction of 

x-motion, appropriate amounts of y-motion and/or 

z-motion must be included in order that relative 

orientation of the model will not be disturbed. ) 

The model can then be shifted bodily until it rests 

in its correct position over the control. This can 

be done either by positioning the model with respect to the base sheet or by positioning the base 

sheet with respect to the model. Although establishing scale and establishing horizontal position 

can thus be conceived as separate operations, with 

scaling being prerequisite to positioning, the two 

operations are combined in one procedure inasmuch 

as the control plotted on the base sheet must be 

the basis for determining both scale and position. 

7 See Chapter 2 F 1, Supplemental control 

planning. 

a. Base sheet not moved.--If it is desired 

that the base sheet not be moved, the procedure 

is as follows: 

(1) Select two horizontal control positions that 

are widely separated within the model. 

For convenience- in describing this procedure, call them point a and point b. 

Place the floating mark at the observed 

height of point a. 

(2) Without changing this height, move the tracing table until its pencil is resting upon 

the plotted position of point a. 

(3) Move both projectors equally in x and equally 

in y until the image of point a is brought 

into coincidence with the floating mark. 

(The x-motions can be equalized by 

keeping the height of the point constant; 

the y-motions can be equalized by keeping y-parallax from being introduced 

into the model.) 

(4) Move the tracing table to point b, note the 

discrepancy between the model position 

and the plotted position of point b. 

(5) Estimate the component of this discrepancy 

parallel to a line between a and b as a 

proportion of the total distance between 

the points. Shrink or expand the model 

as required by altering the length of the 

air base in similar proportion. (An xmotion will have to be accompanied by 

small components of y-motion and/or 

z-motion if the air base is not parallel 

to the multiplex bar. ) 

(6) Repeat steps (1), (2), (3), and (4). 

(7) This time, estimate the component of discrepancy that is perpendicular to a line 

between a and b. This is a measure of 

the horizontal angle through which the 

model must be rotated. Swing one projector through this angle. 

(8) Using motions of the other projector to clear 

the y-parallax thus introduced, regain 

relative orientation. (Ordinarily only 

a y-motion and a swing motion will be 

necessary.) 
MULTIPLEX ORIENTATION (Ch. 3C 7-c) 17 

(9) Repeat the entire procedure if necessary until the model fits both control points at 

once. The model will satisfy all horizontal control points when it is scaled 

and positioned to any two, provided that 

the model is approximately level and 

that there are no other errors. Read 

the elevation of a vertical control point 

in each corner of the model. If the model 

is level within a millimeter, the orientation is sufficiently close for planimetry; 

if not, level the model approximately, 

as described in article 16, and repeat 

the entire scaling and positioning procedure. If the model is being oriented 

for contouring, level accurately, rather 

than approximately, before bringing the 

model to its final scale and position. 

The model can be positioned very conveniently, if only tentatively, by using the two principal points, which were plotted when the strip 

was stereotriangulated, as points a and b in the 

above procedure. The model should, of course, 

be finally positioned upon a mean of the pass 

points and other control regardless of whether 

this position satisfies the principal points or not. 

b. Base sheet moved. --Positioning is somewhat easier when the base sheet can be moved. 

The above procedure is followed with two exceptions: 

(1) In step (3), instead of moving the projectors, 

slide the base sheet, and with it the tracing table which is set over point a, until 

the floating mark is returned to coincidence with the image of point a. 

(2) In place of steps (7) and (8), set the floating 

mark first at the observed height of 

point b, then moving the tracing table 

without changing this height, set the 

tracing pencil upon the plotted position 

of point b. Pinning the base sheet to the 

table with one finger over point a, rotate 

the base sheet, moving the tracing table 

with it, until the floating mark is brought 

as closely as possible into coincidence 

with the image of point b. 

c. When to use each method. --It is occasionally necessary, for various reasons, to set 

up two nonconsecutive models on the same frame 

at the same time. When this must be done, at 

least one model must be positioned and leveled 

entirely by movements of the projectors alone. 

Ordinarily, however, it is permissible both to 

move the base sheet and to tilt the frame by 

reasonable amounts, and it is not only somewhat 

simpler, but actually preferable to move the projectors as little as possible after they have been 

approximately placed in a convenient working 

position. If the parallelism between the air base 

and the multiplex bar, which was purposely established at the outset of relative orientation, is 

to be retained through the process of absolute 

orientation, any rotating of the model about a 

vertical axis with respect to horizontal control 

must be done by moving the base sheet. 

15. Difficulty in positioning a model 

Occasionally a model will be encountered 

which, because of one error or another, cannot 

be made to fit satisfactorily upon all the pass 

points and control positions. Unless the error 

is so large as to suggest a need for re-stereotriangulation, it may be advisable to divide the 

model into segments, and to compile detail from 

one segment at a time, shifting the position of 

the model slightly for each segment. This highly 

practical procedure of "breaking" the model, as 

it is commonly called, can also be applied with 

respect to the level of the model during the contour compilation. It disposes most easily of 

small errors which accrue despite the best efforts of everyone to build and to operate equipment without errors; however, it should never 

be used as a justification for relaxing these 

efforts. 

The position or positions that are finally 

decided upon should be marked well by additional 

or supplementary pass points for use in checking the position of the model during the compilation process. 

16. Leveling the model 

Leveling is accomplished in two steps, one 

being leveling in the x-direction and the other 
18 (Ch. 3C 7-c) TOPOGRAPHIC INSTRUCTIONS 

leveling in the y-direction. The model may be 

leveled in either direction first. Two methods 

of leveling also are available to the stereo-compiler, who may choose either or combine the two. 

Method one utilizes only the motions of the projectors, the multiplex frame remaining stationary. Method two utilizes only the motions of the 

frame, the projectors moving in space inasmuch 

as they are attached to the frame and must move 

with it. 

a. Leveling in the y-direction, using the 

projectors. --A vertical control point will ordinarily be located in each of the four corners of 

the model (positions 3, 4, 5, and 6 in figure 2). 

Index on any one of the four points. Assume 

point 5 is used. 

Read the elevation of point 3 and note the error. 

This may be confirmed by reading the 

elevations at 6 and 4. 

Then x-tilt both projectors equally until further readings of the elevations indicate 

no slope of the model datum in the ydirection. 

A suggested method of estimating the proper 

amount to tilt the projectors in the above procedure 

is: 

Set the floating mark either on point 3 or 4 or 

on any point on a line between the two. 

Raise or lower the floating mark (according to 

whether the readings indicate the front 

of the model needs to be raised or lowered) an amount equal to one-half the 

error (at point 3 with respect to point 5). 

Then, when x-tilting the projectors in 

the third step above, tilt them until 

point 3 is seen to arrive at the height of 

the floating mark. As point 5 changes 

equally but in the opposite direction, the 

whole error should thus be tilted out. 

The two x-tilt motions can be temporarily 

equalized by clearing with one the y-parallax introduced by the other. The ultimate settings of each 

projector in x-tilt, however, will probably be dependent on flattening and leveling the model datum, 

rather than on y-parallax observations (see discussions of warped models in articles 11 and 19). 

If the x-tilt rotations of the two projectors 

are not about a common axis, they will disturb 

some of the other elements of relative orientation slightly, causing y-parallaxes of these elements to appear. These must be removed by 

reverting temporarily to the procedures of relative orientation. 

b. Leveling in the x-direction using the 

projectors. --Referring again to figure 2: 

Index on any one of the four elevations. Assume point 3 is used. 

Read point 4 and note the error. Assume 

this indicates the right side of the model 

is too high with respect to the left side. 

Lower projector II (or raise projector I) with 

z-motion an amount equal to the error, 

measuring its movement on the projector z-scale. (The z-motion of a projector can also be gauged by measuring 

with the tracing table the accompanying 

rise or fall of a point in the model under 

the opposite projector. ) 

Regain relative orientation by clearing the 

y-parallax thus introduced, following 

the "swing-swing" method. Ordinarily 

use of only the two y-tilt motions will 

be necessary. 

Repeat the procedure if necessary until the 

model is satisfactorily leveled. 

c. Alternative procedure of leveling in the 

x-direction, using the projectors. --The equalization of the two y-tilt motions and their proper 

coordination with the z-motion are often difficult when they are dependent solely on the recovery of the original y-parallax solution. There 

are alternative procedures that make use of elevation readings to achieve this coordination. For 

example, assume the right side of the model is 

again too high: 

Select some well defined image point near 

position 1 and observe its elevation with 

the tracing table. 
MULTIPLEX ORIENTATION (Ch. 3C 7-c) 19 

Next y-tilt projector II until the point is 

raised 13/4 the amount by which the 

right side of the model was in error. 

Then y-tilt projector I until the point is brought 

down 9/4 the amount of the original error. 

Lower the point the remaining 4/4 to its original height with the z-motion of projector II. 

The values in this procedure are based on a 

B/H ratio of 2/3. 

Except for the introduction of a small 

amount of y-parallax, a small z-motion of one 

projector alone has the effect of simply tilting 

the model datum slightly in the x-direction as 

shown in figure 4. Because the amount of y-parallax introduced by a z-motion of 0.1 or 0.2 millimeter is not objectionable, a simple z-motion 

of one projector often affords a practical means 

of removing a residual slope of this magnitude 

in the x-direction when the projectors must be 

used and when difficulty is encountered in coordinating the three usual projector adjustments 

because of their small magnitude. 

d. Leveling with the frame. --Because leveling a model by means of the frame in no way 

disturbs the relative orientation of the projectors, 

it is generally considered the simpler of the two 

methods. 

Loosen the lock screw or lock nut (if the frame 

is of a type having a pivoted junction) to 

obviate the possibility of a twisting stress 

being put on the bar. 

Read elevations as before to determine the 

slope of the model datum in the x- and 

y-direc-tions. 

Tilt the frame in the y-direction as required, 

using equal turns of the two front foot 

screws or equal turns of the two back 

foot screws. 

Tilt the frame in the x-direction as required, 

using either handwheel. Instead of the 

handwheels, the two foot screws at either 

end of the frame, preferably the pivoted 

end, however, could just as well be 

used, turning both equally. Where 

"A"-frame end uprights are used, the 

foot screws are the only means of tilting the frame, in either the x- or the 

y-direction. 

With a little experience, it is easy to estimate the number of turns of the foot screws or 

handwheels required to raise or lower one edge 

of the model 0.1 millimeter with respect to the 

opposite edge. The required number of turns 

is dependent upon the dimensions of the frame 

and upon the pitch of the screw threads, as well 

as upon the dimensions of the model. It is in no 

way dependent upon the distance of the model 

from either end of the frame. The inexperienced 

stereocompiler will find it helpful to calibrate 

and mark the handwheels and foot screws in 

terms of this 0.1 millimeter differential across 

an average model. 

e. Leveling with the projectors vs. leveling with the frame. --When two non-consecutive 

models must be set up on the same frame at the 

same time, one model, at least, must be leveled 

using the projector motions exclusively. Otherwise, the choice between using the projectors 

or using the frame for leveling is a matter of the 

stereocompiler's preference. In any case, it 

will generally be found expedient to use the projectors for the larger initial adjustments in order 

to avoid tilting the frame excessively. 

17. Effect of leveling on the position of the model 

Aside from the angular rotation of the 

model, which is the purpose of the leveling operation, the total movement of the model in space 

in the x-, y-, and z-directions depends upon the 

position of the axis of rotation with respect to 

the model. If this axis is considerably to one 

side, as it is when the frame is used for leveling 

in the x-direction, then the angular change will 

be accompanied by a considerable vertical movement of the whole model. This is compensated 

by the re-indexing of the tracing table scale, 

which must be done in any case after each leveling operation and before each rereading of the 

control elevations. 
20 (Ch. 30 7-c) TOPOGRAPHIC INSTRUCTIONS 

If the axis of rotation is much above the 

plane of the model, as it is when the projectors 

are used, leveling will be accompanied by a considerable horizontal shift of the model, making 

it mandatory that the leveling operations, when 

the projectors are used, precede the final positioning of the model. 

18. Warped models 

A model datum that is not flat obviously 

cannot be leveled. It was shown in article 11 that 

only two errors of relative orientation affect the 

flatness of the model datum, y-tilt error and xtilt error. Of these, x-tilt error is the more difficult to avoid; a model that can be leveled upon 

all four corner control elevations without further 

adjustment of the relative x-tilt being the exception rather than the rule. As an x-tilt motion of 

one projector has its maximum effect upon the 

elevations along the opposite side of the model 

and has a minimum effect on the elevations along 

the side directly under the projector (see fig. 4), 

projector I in the procedure of article 16 (a) 

should be x-tilted primarily according to the indications of elevations 4 and 6, while projector II 

should be x-tilted primarily according to the indications of elevations 3 and 5. 

19. Difficulty in leveling a model 

Sometimes a model cannot be made to agree 

exactly with all of the vertical control. The procedure in such a case depends on the cause of the 

difficulty, of which there are these possibilities: 

(1) Misidentification of a control point. 

(2) An error in copying elevation figures. 

(3) An imperfect clearing of y-parallax. 

(4) An image distortion of some sort. 

(5) An error in the control itself. 

Possibilities (1) and (2) should be eliminated 

first by checking the identification of all points and 

by checking all figures, especially the conversions 

of feet into millimeters. 

If the errors of the multiplex readings on 

the vertical control suggest a warp of the model 

datum of a kind that might be due to an error of 

relative orientation, the stereocompiler should 

eliminate this possibility by further adjusting 

the relative tilt settings of the projectors in an 

attempt to flatten the datum. It is seldom possible, however, to curve a model datum more 

than 0.1 or 0.2 millimeter by y-tilt, or to warp 

it more than 0.4 or 0.5 millimeter by x-tilt without introducing objectionable y-parallax. If 

greater errors than these exist, or if their pattern is irregular, the control elevations themselves should be suspected of error. 

Although the control elevations may be 

suspected of error, it is also possible that image 

distortion may be the source of the difficulty. 

The stereocompiler cannot, therefore, use the 

model implicitly to prove the existence of an 

error in the control. If he has access to the 

field survey notes he should check them. If no 

error is discovered there, it is suggested that 

he try setting up other models using different 

exposures of the same flight. Similar difficulty 

in leveling these models would definitely point 

to image distortion as the source of error; a reflight should be obtained if possible. When the 

difficulty is an isolated instance, however, one 

of the following courses of action must be decided upon: 

(1) Suspend compilation until the suspected 

elevations can be field checked. 

(2) Determine and use a multiplex elevation. 

(3) Accept the control elevations and force 

the model to fit them. 

If a multiplex elevation of the disputed 

point is to be established and if the point lies 

along an edge or at one corner of the model, the 

multiplex elevation should be established by setting up adjoining models and determining the 

elevation of the point from all the models in which 

the point is visible. 

If forcing the model to the given elevations 

is decided upon, there are two possible methods. 
MULTIPLEX ORIENTATION (Ch. 3C 7-c) 21 

One is to divide or "break" the model into two 

or more triangular segments bounded by control, 

and to level and contour each as one would separate models. The other method is to "establish 

a local index. " This is an especially convenient 

method for compensating small random errors 

in closely grouped points. The procedure is 

simply to index the scale or counter of the tracing table upon one control elevation, and then 

adjust it gradually to the index of adjacent control elevations as the contouring progresses toward them. As a rule, the stereocompiler will 

not continually reset the index, but will simply 

add or subtract small increments from each contour setting. 

PROGRESSIVE ACHIEVEMENT OF EXTERIOR 

ORIENTATION 

20. Effect of repetition of orientation procedures 

on degree of refinement 

In general, the operations of exterior orientation are performed in the sequence in which 

they have been described. It is seldom possible, 

however, to make any setting of y-parallax, model 

position, or model level with positive assurance 

that it will not be affected by some succeeding 

adjustment. If at any point in the procedure of 

relative or absolute orientation, any of the preceding settings appear to have been disturbed 

too greatly it is advisable to stop immediately 

and revert to the earliest setting affected and 

repeat the procedure from that point on. It is 

better still, many stereocompilers feel, to go 

through the entire procedure of exterior orientation two or three times, quickly at first, then 

more carefully, bringing a higher degree of perfection to the orientation with each repetition. 

As an example, it is suggested that a rough 

orientation be made first, which will clear yparallax (without the use of filter spectacles) 

within 1 or 2 millimeters, level the model within 3 or 4 millimeters and position it within 5 or 

6 millimeters. A second, improved orientation 

will clear y-parallax within 0.5 millimeter, level the model within 1 millimeter and position it 

within 2 millimeters. These are very general 

values, given only to suggest an approximate 

degree of refinement for each repetition. The 

stereocompiler will take but a few minutes to 

perform these rough orientations. The adjustments of the final, precise repetition should 

then be small enough not to interaffect each other 

'noticeably, and all settings will be made as accurately as possible. 

GEOLOGICAL SURVEY 

TOPOGRAPHIC INSTRUCTIONS 

Chapter 3C 7-d 

MULTIPLEX STEREOTRIANGULATION 

Contents 

Page 

Abstract 5 

Horizontal bridging 5 

1. Purpose of horizontal bridging. . 5 

2. Planning the procedure 5 

3. Orientation of the initial model . 6 

a. Short strips 6 

b. Long strips 6 

4. Accuracy of leveling required . . 6 

5. Bridging successive models . . . ▪ 7 

6. Adjusting the scale of a strip . . • 7 

7. Deformations of the strip datum 

caused by relative orientation 

errors 8 

a. Vertical deformations 9 

b. Horizontal deformations 10 

8. Procedure when horizontal 

deformations are evident 11 

9. Selecting and marking pass points 11 

10. Adjustments between adjoining 

strips 11 

Vertical bridging 12 

11. Orientation of models 12 

12. Reading the elevations 12 

13. Adjusting for cross tilt and 

bridging error 12 

Page 

Vertical bridging, continued 

14. Measuring the x- and ycoordinates of the points. . . . 13 

15. Plotting the BZ curve to 

correct for vertical bow . . . 13 

16. Procedure when the strip 

datum twists or slopes in 

the y-direction 13 

17. Effect of earth curvature . • 14 

18. Adjustments between adjoining 

strips 14 

Extension 14 

19. Stereotriangulation with 

control at only one end of 

a strip 14 

Special procedures of stereotriangulation 14 

20. Stereotriangulation with two 

projectors 14 

21. Stereotriangulation aids 15 

a. Cross flights 15 

b. Altimetric data 15 

c. Tilt data 15 

d. Shoran 15 

Illustrations 

Figure 1. Scale correction by adjustment of datum elevation 8 

2. Cumulative effects of relative orientation errors 

3. Horizontal-bow and differential-scale effects 10 

4. Example of use of BZ curves 13 

3 

Chapter 3C 7-d1 

MULTIPLEX STEREOTRIANGULATION 

ABSTRACT 

Multiplex stereotriangulation affords a means of establishing supplementary horizontal and vertical control points when relatively few 

ground survey control points are available. Horizontal bridging (stereotriangulation between control points at both ends of a strip) is accomplished by (1) orienting an initial model accurately to given control, 

(2) bridging successive models, each to the preceding model, and (3) adjusting the scale of the entire strip so that the scale is uniform and the 

set-up fits all the horizontal control. When the bridge is complete, pass 

points are selected and marked; when two adjoining parallel strips are 

bridged, the pass points common to the two strips are adjusted to give a 

single solution., Vertical bridging is accomplished by (1) establishing a 

horizontal bridge, (2) reading the elevations on pass points and ground 

survey control points, (3) plotting the BZ curves, and (4) adjusting the 

multiplex elevations according to the BZ curves. Because of the more 

rigid requirements for vertical control, vertical stereotriangulation is 

not used as extensively as horizontal stereotriangulation. Extension of 

control by stereotriangulation beyond ground survey control is readily 

performed, but there is no way of checking the accuracy of the extended 

portion and the method is therefore used only when there is no other alternative. Other procedures for multiplex stereotriangulation include a 

leap-frog method using only two projectors, and the use of auxiliary information or devices such as cross flights, altimetric data, tilt data, and 

shoran control. 

HORIZONTAL BRIDGING 

1. Purpose of horizontal bridging 

Photographic coverage of large areas is 

supplied in the form of parallel flights or strips. 

Each strip must be bridged between the lines of 

horizontal control that are usually placed crosswise to the flight direction at certain intervals. 

The exact number of models necessary to span 

the control interval depends on the ground distance 

between control and on the flight height of the 

photography. 

1T he number 3 C 7-d signifies Book 3, Part C, 

Chapter 7-d of the Geological Survey loose-leaf 

manual of Topographic Instructions. For a table 

of contents, see Chapter 1 A 2 (Circular 92). 

When each strip is bridged, pass points 

are plotted in the common side-lap area between 

adjoining strips. Finally, the pass points are 

adjusted; that is, a unique position for each pass 

point is determined wherever slight discrepancies between adjoining strips are indicated. The 

adjusted pass points are to be used for the subsequent repositioning of each model for the compilation of detail. 

2. Planning the procedure 

One of the first decisions the stereotriangulator must make is the order in which the several 

strips will be set up. The factors that enter into 

his decision are the amount and distribution of 

control and the spacing and arrangement of the 

5 
6 (Ch. 30 7-d) TOPOGRAPHIC INSTRUCTIONS 

flights. Preferably those strips having the most 

control, or the most positively identifiable control, should be oriented first. A study of the control plan and the flight index usually suggests a 

logical procedure. 

The next decision to be made is which model 

of the strip to orient first. Preferably, it should 

be a model near the center of the strip so that the 

bridging of successive models can proceed in both 

directions from it. In this way, any progressive 

accumulation of error in the absolute orientation 

of successive models will be kept at a minimum. 

It is also highly desirable that the initial model 

be one with sufficient control so that it can be 

completely and independently leveled, scaled, and 

positioned at the outset. As the horizontal control 

is usually confined to the end models, it is often 

more practical to commence orientation at either 

end and to proceed through the strip entirely in 

one direction. A compromise procedure that is 

sometimes advisable is to assume a scale for the 

initial central model, correcting this scale later 

when the bridge has progressed to the nearest 

controlled model. Once one strip has been scaled, 

its pass points can be used to furnish the initial 

scale and position of any model of the adjoining 

strips. 

3. Orientation of the initial model 

a. Short strips. --For strips of moderate 

length (7 or 8 models), both projectors of the initial 

model should be set at the mid-points of their 

y-slides and also at the mid-points of their z-slides. 

This is done to allow for a maximum deviation of 

the flight line from a straight line in any direction. 

Relative orientation of the model is completed by 

the "swing-swing" method. 

b. Long strips. --Setting the azimuth of the 

initial model of long strips (14 or 16 models) so 

that the flight line will not "rim off the bar" often 

requires careful attention. The range of the 

z-motion is not as likely to be exceeded as the 

range of the y-motion, for the altitude of an airplane can be maintained constant more easily than 

can its course. Before setting up the initial model 

of a long strip it is suggested that the base sheet 

be oriented in azimuth as follows: 

Estimate the position of the principal point 

of one of the end photographs with respect to the horizontal control and spot 

this position approximately on the base 

sheet. 

In the same manner spot the approximate 

position on the base sheet of a principal point at the opposite end of the strip. 

Position each end of the sheet in the y-direction so that each of these positions 

would fall directly below a projector 

that has its y-slide set at the mid-point. 

The initial model should now be oriented and positioned without moving the base sheet. This 

model must, of course, be one with sufficient 

control or pass points to enable its absolute 

orientation. 

4. Accuracy of leveling required 

It is not essential that the initial model be 

precisely leveled. Even if it were to be carefully leveled, it is unlikely that the succeeding 

models would maintain level datums. The probability is that the datum of each model would 

show a rather consistent downward "break" from 

the preceding one, so that the datum of the whole 

strip would be arched upward in the center. This 

vertical bow is chiefly the result of a small residual lens distortion and is the most persistent deformation of a multiplex strip. 

The only requirement of leveling is that no 

model of the strip be out of level more than the 

limit required for good planimetric accuracy 

which, depending on the amount of relief in a 

model, may be as much as 10 millimeters across 

the width of a model. Because of the severity 

of vertical bow in some instances, it is recommended, especially if the initial model is not a 

central model, that the multiplex frame be used 

to level the strip as a whole between vertical 

control at either end of the strip. This should 

be done after all the models have been brought 

to a uniform and approximately correct scale. 
MULTIPLEX STEREOTRIANGULATION (Ch. 3C 7-d) 7 

5. Bridging successive models 

When the initial model has been oriented 

as well as possible with whatever control is available, the adjoining models are successively 

brought into relative orientation by the "one projector" method. In each case, motions are applied only to the added projector, which forms a 

model with one of the projectors of the preceding 

model. The orientation of preceding models is 

not disturbed. After each model is cleared of 

y-parallax, and before the relative orientation 

of the next one is begun, the newly oriented model 

should be brought to the same scale as the preceding one by the following procedure, commonly 

called "bridging." (In its larger and more appropriate sense, the term "bridging" designates the 

entire procedure of stereotriangulation between 

control. ) 

Viewing first the initial model (whose scale 

is not to be changed), select some welldefined image point common to both 

models, the elevation of which can be 

accurately read. This point should be 

as near as possible to the center of 

that area which is overlapped by both 

models; it will normally be close to the 

principal point of the center photograph. 

Place the floating mark at the elevation 

of this point. 

View the second model and adjust the length 

of its air base by an x-motion (and components of y-motion and/or z-motion if 

needed) of the third projector until the 

elevation of the point is made equal with 

its elevation in the first model, as indicated by the floating mark, which is not 

moved. 

In this manner all the models in the strip are 

bridged, each in turn, to the preceding one. 

6. Adjusting the scale of the strip 

Because a very small error in the scale of 

the first model will accumulate as a much greater 

error in the long extension of several models, it 

is likely that, even though the initial model was 

most carefully scaled, the length of a strip will 

need further adjusting in order to fit between the 

control at the ends. This adjustment of the overall scale of a multiplex strip is similar to the 

method of scaling an individual model, with the 

exception that the adjustment must be apportioned among the several models, as described 

in the following procedure: 

(1) Select one well defined control point in 

each end model. For convenience in 

describing this procedure, call them 

point a and point b. 

(2) Set the floating mark at the observed 

height of point a, then move the tracing 

table and place its pencil over the 

plotted position of point a. 

(3) Slide the base sheet and the tracing table 

with it until the floating mark is returned to coincidence with the image 

of point a. Point a is now directly over 

its plotted position. 

(4) Set the floating mark at the observed 

height of point b, then move the tracing 

table and place its pencil over the 

plotted position of point b. 

(5) Pinning the base sheet to the table with 

one finger over point a, rotate the 

sheet and the tracing table with it until 

the floating mark is in line with points 

a and b. Note the discrepancy then remaining between the model position and 

the plotted position of point b. 

(6) Divide this discrepancy by the number of 

model widths between a and b. Lengthen (or shorten, as required) the air 

base of one model by this amount. Presumably the model containing point a 

will be used, although any model could 

be used. 

(7) Rebridge all the models, bringing them 

to the scale of the model adjusted in 

the previous step. 

(8) Repeat the procedure if necessary until 

the strip is scaled between point a and 

point b. 
DATUM ELEVATION ADJUSTMENT 

TO CORRECT 

LINE OF FLIGHT ERROR OF SCALE 

H. 360 M M 

8 (Ch. 30 7-d) TOPOGRAPHIC INSTRUCTIONS 

The adjustment in step (6) above is extremely 

critical and any method of increasing its accuracy 

is worthwhile. A change in the length of an air 

base probably can be most accurately gaged by 

measuring the resultant vertical movement of the 

model. An alternative procedure to step (6) is: 

Viewing any well-defined image point in the model, 

change the air base by an amount such that the 

point is raised or lowered, as required, an 

amount equal to Az, which is given by the expression 

H Az =xE L 

where E is the error in length at point b; H is the 

average projection distance; and L is the distance 

between point a and point b. 

By reference to figure 1, Az can also be determined graphically as follows: From the intersection of the arc representing the number of 

model widths between a and b with the arc representing the average air base length, follow a 

radial line toward the origin of the graph until 

it intercepts the known value of the total error, 

E, on the abscissa scale. Read the datum adjustment, Az, at this point on the ordinate scale. 

7. Deformations of the strip datum caused by 

relative orientation errors 

The cumulative effect upon the datum of 

the strip of a recurring error in each of the elements of relative orientation, including x-motion, 

is shown in figure 2. (Although x-motion is not 

strictly an element of relative orientation, it is 

included because an error of its setting results 

in a bridging error, the effect of which is similar to that of z-motion error.) It should be 

clearly understood that these deformations of 

the strip datum refer to the way in which the 

control points of the strip fit upon their plotted 

positions; they do not refer to the actual configuration of the terrain surface, nor do they have 

any connection with the shape of the strip as it 

is governed by the path of the airplane in flight. 

(1) 

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0 2 4 6 8 10 12 14 

TOTAL ERROR OF SCALE (M M) 

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a 

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W2 

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0 

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9 

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Figure 1. --Scale correction by adjustment of datum elevation. 
MULTIPLEX STEREOTRIANGULATION (Ch. 3C 7-d) 9 

The magnitudes of the deformations, as indicated 

by the differences between the solid and the dashed 

outlines, are greatly exaggerated in figure 2. The 

actual magnitude of a particular deformation depends upon three factors: The magnitude of the 

causative error; the rate of recurrence of the 

error in the strip; and the number of models in 

the strip. 

a. Vertical deformations. --The principal 

errors affecting the vertical datum of the strip 

are x-tilt error and y-tilt error. 

Error in x-tilt causes the datum of the 

strip to "corkscrew" or "twist" --that is, to 

slope progressively more and more in the y-direction. This slope reverses its trend across 

Y-MOTION X-TILT 

X-MOTION(BRIDGING) Y-T I LT 

Z-MOT I ON SW ING 

Figure 2. --Cumulative effects of relative orientation errors. 
HORIZONTAL BOW 

10 (Ch. 3C 7-d) TOPOGRAPHIC INSTRUCTIONS 

the width of each model, but the twisting shear 

(called cross-tilt) between successive models 

overbalances this reversal. Assuming every 

model were warped the maximum possible with 

a limit of 0.1 millimeter of y-parallax in the 

neat area, the change in the y-slope of the strip 

would average approximately 0.8 millimeter per 

model2 . 

Error in y-tilt causes "vertical bow". 

The datum of the strip as a whole bows up or 

down in the center giving the effect, in profile, 

of a number of short chords forming an approximately circular arc. The negligible curvature 

of the datum of each individual model is opposite 

to that of the strip datum. Assuming every model 

to be warped the maximum possible with a limit 

of 0.1 millimeter of y-parallax in the neat area 

the middle ordinate of the vertical bow is approximately 0.05 N2millimeter, where N is the number 

of models in the bridge. (See footnote 2. ) 

If reasonable care is taken to obtain an 

average level for the strip, twist and vertical 

bow effects are not a concern of the stereotriangulator doing horizontal stereotriangulation. The 

influence of these deformations on the procedures 

of vertical stereotriangulation will be discussed 

in articles 15 and 16. 

b. Horizontal deformations. --The principal errors affecting the horizontal datum of the 

strip are: z-motion error, bridging error, and 

swing error. 

Error in z-motion will cause a slight but 

progressive difference in the scale of each successive model (differential scale). This effect 

is shown in figure 3. Differential scale is indicated by the individual scale of one end model 

appearing too small with respect to its control 

while the scale of the other end model appears 

too large. If there is a control point in the center 

2

These values are based on a base-width 

height ratio of 2:3:3. They are approximate, 

being intended only to give a basis for estimating the magnitude of the deformations. The 

possibility that a residual y-parallax of 0.1 

millimeter (or an equivalent image distortion) 

might recur in the most unfavorable pattern in 

every model of a strip must be taken into consideration. 

of the strip, differential scale will cause a discrepancy there in the x-direction. Assuming a 

limit of 0.1 millimeter of y-parallax in every 

neat model, the maximum amount a point in the 

center of the strip could be in error is 0.033 N2 

millimeter, where N is the number of models 

in the strip. (See footnote 2.) 

DIFFERENTIAL SCALE 

Figure 3.--Horizontal-bow and differential-scale 

effects. 

Bridging error, strictly speaking, is not 

one of relative orientation. However, a repeated 

"break" in the bridge, such as shown, will have 

essentially the same effect as a repeated z-motion error. The effect of a 0.1-millimeter break 

in each bridge is approximately one-fourth the 

magnitude of the effect of z-motion error specified above. 

Swing error causes the datum of the strip 

to be deformed in a "horizontal bow", which, 

like vertical bow, is roughly circular. This 

effect is also shown in figure 3. Horizontal bow 

is indicated by the end models appearing to be 

slightly swung, in opposite directions, with 

respect to their control. If there is a control 

point in the center of the strip, bow will cause 

a discrepancy in the y-direction there. With a 

limit of 0. 1-millimeter of y-parallax in the neat 

area of every model, the maximum possible 

middle ordinate of the horizontal bow is approximately 0.025 N2millimeter, where N is the 

number of models in the strip. (See footnote 2.) 
MULTIPLEX STEREOTRIANGULATION (Ch. 3 C 7-d) 11 

An error in y-motion has no cumulative 

effect. There are, therefore, but four different 

deformations of the multiplex strip: two vertical--twist and vertical bow; and two horizontal--

differential scale and horizontal bow. 

8. Procedure when horizontal deformations are 

evident 

There is no reason to suppose that errors 

on the part of the stereotriangulator in orienting 

and bridging the models will consistently be of a 

kind that would accumulate to produce an appreciable horizontal deformation, although such is 

not impossible. One known cause of both bow and 

differential scale is tangential distortion in either 

the camera lens or the printer lens. Every precaution is taken in the assembly of these lenses 

to prevent this distortion; nevertheless it is occasionally encountered. Therefore, when the 

strip has been scaled between two points, all the 

other horizontal control points that can be seen 

in the strip should be examined, looking particularly for indications of a consistent trend in any 

discrepancies. If the strip does not agree with 

all the control, but appears to be deformed in 

either or both of the patterns of figure 3, it is 

suggested that the stereotriangulator eliminate 

his orientation as a possible cause by testing 

each model for the presence of those residual 

y-parallaxes and/or errors of bridging that might 

be capable of causing the particular horizontal 

deformation that is evident. Assuming that the 

relative orientation and bridging operations were 

done to the best of his ability in the first place, 

the stereotriangulator must do more than simply 

take another look at the models. He must test 

them by actually moving each projector very 

slightly, being desirous of accumulating a small 

amount of swing, z-motion, or bridging error in 

a direction calculated to oppose the observed deformation of the strip. By rocking each motion 

through the range within which he can see no 

change in the y-parallax (because of the limitation of visual acuity), he can adjust each motion 

just short of the point where y-parallax commences 

to be discernible. What he achieves is an orientation of the strip that is very slightly prejudiced in 

a manner tending to offset the effect of the error. 

This procedure should not be allowed to introduce 

any noticeable y-parallax, nor to overcompensate 

the deformation, although undercompensation may 

have to be accepted. If some deformation still 

remains, it can safely be attributed to a distortion beyond the stereotriangulator's control. If 

there had been any intermediate control points, 

bow and differential scale errors might have 

been minimized by "breaking" the strip, that is, 

by scaling it in two or more segments using each 

intermediate point as the end of a separate bridge 

rather than simply as a pier in a longer bridge. 

Finally, the procedure of adjusting the pass 

points to correct for differences between adjacent strips must be relied upon to eliminate any 

remaining error. 

9. Selecting and marking pass points 

When the strip is scaled and the optimumcontrol solution has been obtained, pass points 

are selected and plotted on the base sheet. These 

points should be located in the corners of each 

model and at such other positions as are necessary to provide points in the corners of the models of the adjoining strips. It is best, therefore, 

to select these points after an examination of the 

photographs of all these strips. Pass points may 

be actual points such as lone trees or intersections 

of lines, or they may be carefully drawn outlines 

of well-defined features such as sharp bends in 

roads or streams. The principal point of each 

photograph should also be plotted at this time. 

These are useful if the models are not to be preserved intact and so have to be reoriented later 

for compilation of detail. 

Pass points should be plotted and drawn 

with utmost care. Although the absolute elevations of the points may be far from correct, the 

floating mark must be placed exactly on the model 

surface when plotting or checking the position of 

any point. If this is not done, the perspective 

nature of the image projection will result in an 

erroneous position being marked. 

10. Adjustments between adjoining strips 

All the pass points except those around the 

perimeter of a project will have their positions 

determined from two adjoining strips, and small 

discrepancies in these duplicate positions are 

likely to be noted= These discrepancies should 

not be large--their magnitude depending more or 

less on the length of the strip--but nevertheless 
12 (Ch. 30 7-d) TOPOGRAPHIC INSTRUCTIONS 

a unique position for each pass point must be decided upon. A median or simple average position 

should be marked unless one strip is felt to be 

stronger than another owing to the distribution of 

control, or unless an analysis of the discrepancies between several adjoining strips suggests a 

more plausible adjustment. In such cases, the 

position finally marked for each pass point must 

be a weighted average. 

VERTICAL BRIDGING 

11. Orientation of the models 

Whether the purpose of multiplex stereotriangulation is to establish supplemental elevations or supplemental horizontal positions, the 

initial steps of orienting the models, leveling the 

strip, and bringing it to scale are much the same. 

In relative orientation, the ultimate accuracy of vertical stereotriangulation is dependent 

chiefly on the precision and uniformity with which 

this operation is performed; therefore, no attempt 

should be made to bias the y-parallax solution because of horizontal bow or differential scale. Nor 

should the y-parallax solution be biased in any 

attempt to flatten a vertical deformation of the 

strip datum. Slight vertical deformations are 

virtually unavoidable and any attempt to regulate 

them would undoubtedly require the introduction 

of visible amounts of y-parallax into each model, 

a procedure that cannot be controlled with as much 

precision as the complete removal of y-parallax. 

The correction of these errors must be done by 

analytical means. 

In leveling a strip, the very presence of 

vertical bow makes anything but an approximate 

leveling impossible. The analytical method of 

eliminating errors due to vertical bow and other 

deformations compensates at the same time for 

the manner in which the strip was leveled. However, for best results,the average slope of the 

strip datum, both from end to end and from front 

to back, should be made as nearly level as possible. 

In scaling the strip, it is not necessary 

that a perfect fit be obtained between the two end 

positions, point a and point b. The range of relief will be relatively small compared to the 

overall length of a strip, so that an error in 

length of 2 or 3 millimeters would seldom be 

responsible for as much as 0.1 millimeter of 

error in any elevation reading. 

12. Reading the elevations 

The elevations to be read (vertical pass 

points) are selected in the same general locations 

as the horizontal pass points; thus they will include one in the corner of each model plus any 

other points needed to control the corners of the 

models of adjacent strips. Points to be read 

also include all of the vertical control. The 

readings on these points indicate the probable 

nature of the vertical deformation of the strip 

datum and hence the required corrections to the 

readings on other points. All readings are made 

without changing the index of the tracing table 

scale. The index may be set on any point. 

13. Adjusting for cross tilt and bridging error 

Each corner point will be read in each of 

two adjoining models of the strip. These readings will reveal any relative tilt between the 

two model datums, also any slight error in the 

bridging of the two models. Differences between 

models of plus or minus 0.2 millimeter are very 

common. It is not practical to attempt to reduce 

these differences beyond this amount by further 

adjustments of the projectors. Rather, the readings are corrected by either of two methods, the 

first and simpler method being to adopt an average 

value wherever the readings on a point differ between the two models. The second method is to 

compute mathematically the unique value for each 

point that would be obtained if the differences 

were to be removed by carefully bridging all the 

models in succession, starting at one end and, 

with x-motion only, bridging each model exactly 

to the preceding one at both the front corner and 

the back corner of the model, assuming that such 

a procedure is possible. This method is illustrated in figure 4, wherein all the original readings are shown adjusted to the datum of the model 

at the left end of the strip. 

In practice, there is little to recommend 

one method over the other. After adjusted values 

have been obtained, they are used throughout the 

remainder of the process, and the original multiplex readings are discarded. 
MULTIPLEX STEREOTRIANGULATION (Ch. 3C 7-d) 13 

K EY 

27.2 - CONTROL VALUE 

38.0 •38.2 - MULTIPLEX READINGS -LEFT MODEL • RIGHT MODEL 

38.1 - READINGS ADJUSTED FOR CROSS TILT AND BRIDGING ERROR 

27.2 - FINAL ELEVATION TO SEA LEVEL DATUM FROM 8 Z CURVES 

32.0 

6,42.0 

42.0 

20.1 

A30.8 

33.7.33.6 31'

0 

33.8 

23.0 

*63.1 

63.1 

52.5 

4 

40.1 

50.66,50.5 

50.6 

5 

35.0.34.9 

35.0 

24.5 

2 

o

3 

45.7.45.9 

45.9 

350 

PLAN 

33.4 

43.30 

43.4 

6 

30.6 

6,40.9 

35.2835.1 41.0 

35.2 

24.9 

38.9.39.1 

39.0 

28.4 

43.78 43.8 

43.6 

33.1 

57.8 

68.16,68.3 

 67.9 

52.0 

62.06, 

61.6 

20.8 

6,30.8 

30.8 

2 

2 

cc 

O 

cr 

cc 

+11 

+10 

B C U RVES 

I 

+9 

0 4 8 12 16 20 24 28 32 

INCHES 

36 

Figure 4. --Example of use of BZ curves. 

40 44 

14. Measuring the x- and y-coordinates of the 

points 

A straight line is now lightly drawn on the 

base sheet along the center of the strip. This is 

a reference axis along which the x-coordinate of 

each vertical control and pass point should be 

measured. (Units of inches to the nearest halfinch are convenient.) The y-coordinate of each 

point should also be approximately measured. 

The latter is needed only when the slope of the 

strip in the y-direction (due to twist) in combination with excessive variation in the y-coordinates 

of the points makes it inadmissible to assume that 

all points lie at a uniform y-distance from the 

reference axis. (See article 16. ) 

15. Plotting the BZ curve to correct for vertical 

bow 

Selecting suitable scales, plot on graph 

paper the x-coordinates of the vertical control 

points as abscissae. As ordinates, plot the errors 

evident at each control point between the adjusted 

multiplex readings and the true values. Through 

these points draw a smooth curve. A spline will 

be found helpful in drawing this curve, which is 

known as the BZ curve. The ordinates under the 

BZ curve then give the corrections that must be 

subtracted from all the adjusted multiplex readings to correct for vertical bow and to reduce 

the readings to a sea level datum. 

16. Procedure when the strip datum twists or 

slopes in the y-direction 

When the elevation readings indicate that 

the strip datum either twists or slopes in the 

y-direction, two correction curves must be used. 

These may be either two BZ curves representing 

separately the error along the front edge and the 

error along the back edge of the strip, or they 

may be one BZ curve representing the error along 

the center line of the strip plus an auxiliary curve 

showing the additional error along the front and 

back edges of the strip due to the slope or twist. 

Both curves in the former instance and the auxiliary curve in the latter instance will represent 
14 (Ch. 3C 7-d) TOPOGRAPHIC INSTRUCTIONS 

the error of the strip at a uniform y-distance 

from the reference axis. In the event that the 

y-coordinate of any point differs too greatly from 

this distance, the correction obtained from the 

curves must be suitably interpolated. Interpolated values should be used in plotting the BZ or 

the twist curves as well as in obtaining corrections from them. Figure 4 provides an example 

of the use of BZ curves in correcting the errors 

of vertical bow and twist. 

17. Effect of earth curvature 

When strips covering long ground distances 

are stereotriangulated, the effect of earth curvature may be considerable. Its effect is to cause 

the datum of any strip to arch upward in a vertical bow. The height of this arch, V, is given by 

the expression 

V = 0.167 L2 (2) 

where V is in feet, and L is the length of the strip 

in miles. However, no separate calculation of 

this error is necessary, since the above-described 

method of correcting vertical bow and twist errors 

automatically corrects all vertical deformations 

of the datum, regardless of their source. 

18. Adjustments between adjoining strips 

Some discrepancies are to be expected in 

the values obtained by vertical stereotriangulation of adjoining strips. Just as a single position 

for each horizontal pass point was obtained by 

adopting a weighted average, a single value for 

the elevation of each vertical point is also decided 

upon by compromising its two values. This adjusted value is determined by weighting each of 

the two discrepant figures after giving due consideration to the distribution of control and the 

probable "strength" of each strip as revealed by 

an examination of the discrepancies between the 

several strips. 

EXTENSION 

19. Stereotriangulation with control at only one 

end of a strip 

Stereotriangulation beyond control—called 

"cantilever extension" or simply "extension" --is 

more simple to perform than bridging-type 

stereotriangulation. The results obtained, however, cannot be expected to be as accurate. 

The initial model or models will be at one end 

of the strip. They must be carefully and completely cleared of y-parallax, positioned, and 

leveled. The remaining models are then successively brought into relative orientation and 

bridged to the preceding ones. Pass points are 

then marked without further delay, because 

without control at the far end of the strip there 

is no possibility of refining the overall scale or 

of determining if any bow or differential scale 

effects are present. Vertical pass points can 

also be read if they are desired. BZ curves 

must be based on what indications are provided 

by the models at the "anchored" end of the strip. 

If no indications can be obtained, a center line 

BZ curve may be assumed on the basis of the 

orientation of another strip by the same stereotriangulator, using controlled photography 

taken by the same camera. Finally, the adjustment of pass point discrepancies between adjacent strips is made in the same manner as in 

the case of bridged strips. 

SPECIAL PROCEDURES OF 

STEREOTRIANGULATION 

20. Stereotriangulation with two projectors 

Although the length of a strip that can be 

set up is definitely limited by the length of the 

multiplex frame, it is not necessarily limited 

by the number of projectors available. If necessary, stereotriangulation can be performed by 

using only two projectors by "leap-frogging" one 

projector past the other as the successive models 

are oriented. The scale of the initial model is 

passed along by bridging successive models as 

usual, except that the elevation of the tie point 

used in each bridging operation must be read 

and recorded in one model before the trailing 

projector is removed to be used in orientingthe 

succeeding model. "Leap-frog" procedure also 

necessitates the marking of pass points from 

each model as it is set up. Errors of closure 

upon the control at the terminal end of the strip 

must be distributed among the intermediate positions and/or elevations by analytical methods. 

Graphical methods employing correction curves 

for each coordinate component of error are 
MULTIPLEX STEREOTRIANGULATION (Ch. 3C 7-d) 15 

preferred, but least-square computations similar to those used in adjUsting closure errors in 

traverse lines can be used. 

21. Stereotriangulation aids 

When stereotriangulation of sparsely controlled areas must be performed, there are a 

number of means that can be employed to supplement ground control. These include flights crossing the regular pattern at intervals; altimetric 

data; tilt data; and shoran. At present, none of 

these methods or devices are capable of the accuracy of ground surveys; therefore, they should 

be employed only when accuracy requirements 

permit. The methods of applying the information 

furnished by these aids are not as firmly established as are the more routine methods of multiplex operation. When and if the stereotriangulator has occasion to use any of them he will 

probably desire to develop his own methods to a 

large extent. A few comments can be made regarding the functions of these aids. 

a. Cross flights. --Flight strips crossing 

the main flight pattern serve to knit the regular 

or compilation strips more closely together. 

They supplant the usual lines of control, making 

only an occasional control point necessary within 

a large area. 

b. Altimetric data. --Data concerning the 

altitude of each exposure station can be recorded 

from an altimeter or a statoscope carried in the 

airplane. Fairly accurate indications of the relative heights of the exposure stations are sometimes obtained. A comparison of these data with 

the measured heights of the oriented multiplex 

projectors is used to adjust the overall level of 

a strip (in the x-direction) and to furnish the 

necessary information for plotting a BZ curve. 

One ground control elevation is desirable for an 

index point, as the absolute altitudes of the aircraft may be indicated with a relatively low degree of accuracy, 

c. Tilt data. --Tilt data, such as are furnished by a horizon camera or by gyroscopic 

means are most readily applicable in the operation of instruments such as the stereoplanigraph, 

which have calibrated scales indicating the tilts 

of the projectors. Multiplex-projector tilts can 

be measured, however, either by optical means 

that record the tilt of the principal ray, or by a 

level bubble placed upon the projector. The tilt 

values of all the projectors in a stereotriangulated strip should be employed to determine the 

level and the curvature of the strip. Tilt data 

furnish a vertical datum both in the x- and in 

the y-directions. 

d. Shoran3. --Shoran can be used to determine the position of the aircraft at each exposure station. These positions, plotted on the 

base sheet, are nadir points directly above 

which each corresponding projector should be 

oriented. There are a number of devices that 

indicate the plumb ray from each projector lens, 

such as vertical collimators, level bubbles, and 

plumb bobs. Because of random errors in the 

determination of individual positions by shoran, 

it is best to scale the strip as a unit, selecting 

the best average scale and position. This procedure of using the plumb rays of the projectors 

requires that the models be carefully leveled; 

therefore, allowances must be made for the 

slopes of some models due to the vertical bow 

of the strip. 

A full description of the shoran method 

is given in Chapter 3 C 20, Stereotriangulation 

with shoran-controlled photography. 

GEOLOGICAL SURVEY 

TOPOGRAPHIC INSTRUCTIONS 

Chapter 3C 7-e 

MAP COMPILATION BY MULTIPLEX 

Contents 

Abstract 

Multiplex compilation routine 

1. Order of compilation 

Compilation of planimetry 

2. Orientation requirements for 

planimetric compilation 

Page 

5 

5 

5 

5 

5 

3. Order of compilation of features 6 

4. The tracing operation 6 

5. Reference to contact prints . 6 

6. Inking 6 

Compilation of contours 8 

7. Visual skill required 8 

8. Orientation requirements for 

contouring 8 

Page 

Compilation of contours, continued 

9. Contour tracing 8 

10. Contouring difficult areas 8 

a. Flat terrain 9 

b. Wooded areas 9 

c. Shadows 9 

d. Images with insufficient 

contrast 9 

e. Images with excessive 

contrast 9 

11. Drawing the drainage 9 

12. Spot elevations 9 

13. Inking or repenciling 10 

Illustration 

Figure 1. --Multiplex compilation 7 

3 

Chapter 3 C 7-e 

MAP COMPILATION BY MULTIPLEX 

ABSTRACT 

Multiplex maps are compiled in two phases, planimetry and contours; planimetry is always compiled first in each model. For planimetry, 

the model must be accurately positioned but only approximately leveled, 

while for contouring it must be both positioned and leveled accurately. 

Planimetric features are compiled in a definite order, according to importance. In tracing planimetry, the height of the platen must be continuously regulated so as to keep the floating mark in contact with the model 

surface. Repeated reference to contact prints is necessary to distinguish 

obscure features. Inking is done piecemeal as the compilation progresses. 

Compilation of contours requires special visual ability. In tracing contours, the platen is clamped at the height of the chosen contour and the 

tracing table is guided so as to keep the floating mark always on the ground. 

Special measures are taken in contouring certain types of difficult areas. 

Minor drainage is drawn in pencil to serve as a guide in alining contours. 

MULTIPLEX COMPILATION ROUTINE 

1. Order of compilation 

The compilation of a topographic map by 

multiplex is divided into two principal phases: 

compilation of planimetry, and compilation of 

contours. For a given model, both phases are 

completed before the next model is begun. Within each model, the planimetry is always compiled 

first so that the contours can subsequently be 

shaped to conform with planimetric features. 

The woodland outline is a part of the planimetry, 

although it is sometimes compiled on a separate 

transparent overlay. 

COMPILATION OF PLANIMETRY 

2. Orientation requirements for planimetric 

compilation 

Reorienting individual models for planimetric compilation is required unless it has been 

1The number 3 C 7-e signifies Book 3, Part C, 

Chapter 7-e of the Geological Survey loose-leaf 

manual of Topographic Instructions. For a table 

of contents, see Chapter 1 A 2 (Circular 92). 

possible to retain the orientation of each stereotriangulated strip while adjoining strips were 

being scaled. If adjusted pass points cannot be 

obtained, or are not desired, then planimetry 

of a strip can be compiled as soon as stereotriangulation is completed, without the need of 

resetting the models. When a model is reset, 

the orientation procedures (interior, relative, 

and absolute) are performed in the usual way, 

with one permissible exception: it is not necessary that the model be absolutely leveled. Although greater tolerances might be permissible, 

a level solution within 1.0 millimeter across 

the model in both directions is quickly obtainable and affords sufficient accuracy in all cases. 

If contour compilation is to follow the compilation of planimetry, the stereocompiler may 

choose to complete the leveling of the model before starting any compilation. 

The position of the model should be checked 

at frequent intervals throughout the compilation 

process. Changes in humidity cause some basesheet materials to expand or shrink appreciably, 

thus affecting the scale and position of the model 

5 
6 (Ch. 3C 7-e) TOPOGRAPHIC INSTRUCTIONS 

with respect to the control base. If the model 

should be found out of position, either it or the 

base sheet must be repositioned and the features 

already traced checked for errors. Under extreme conditions, it may be necessary to rescale 

the model. 

3. Order of compilation of features 

It is preferable to compile all the features 

of each kind at one time; in this way the chances 

of overlooking and omitting any detail are minimized. A suggested procedure is to compile all 

main roads first, following these in order by 

secondary roads, buildings, obvious drainage, 

fence lines, and woodland outlines. Railroads, 

shore lines, and wide streams, if they occur, 

should take precedence over all of these. The 

particular details to be compiled depend upon the 

type of map being prepared. A general rule to 

follow is to compile first those features whose 

exact positioning or alinement is most important. 

4. The tracing operation 

The tracing operation is simply stated: 

Place the floating mark upon the image of the 

feature to be traced; lower the pencil to the paper; 

slide the tracing table so as to follow the outline 

of the image with the floating mark (see fig. 1). 

The floating mark may be guided through the 

more intricate detail by resting the edge of each 

hand upon the map sheet and using the fingers to 

move the tracing table. The height of the platen 

must be continuously regulated with one index 

finger, so as to keep the floating mark always in 

contact with the model surface. 

Some suggestions with respect to the tracing 

operation follow: 

Each feature should be completely traced or 

outlined with a continuous line. Retracing a line in the opposite direction provides a good check on the accuracy of 

the tracing. 

No attempt should be made to symbolize the 

features as they are traced with the 

tracing table; symbols can be added when 

the lines are repenciled or inked. 

Care should be taken when plotting objects 

having height, such as buildings and 

trees, to avoid tracing their shadows 

instead of their true positions. High 

buildings in cities may have to be plotted by their roof lines, as the photograph perspective may cause their 

bases to be partially obscured. It is 

most important to have the floating 

mark in contact with the feature being 

traced, at the correct elevation. 

Planimetry should not be compiled beyond the 

limits of the neat model, which in most 

cases is approximately the area bounded 

by the pass points. In exceptional circumstances, planimetric detail falling 

completely outside the stereoscopic 

area may be desired, but the difficulty 

of determining the proper heights at 

which to intercept the perspective 

image rays may make detail thus plotted extremely unreliable. 

5. Reference to contact prints 

It will be necessary when compiling the 

smaller and more obscure details of planimetry 

such as dense collections of buildings, railroad 

yards, trails, and streams in heavily wooded 

areas, to refer repeatedly to the contact prints. 

The brilliance and clarity of the model seen 

through a simple lens stereoscope far surpass 

that of a multiplex model and many details can 

be seen that might be overlooked if the multiplex 

models were used alone. When details have been 

identified by the use of the prints, they usually 

can be seen well enough in the multiplex model 

to be plotted accurately. 

6. Inking 

From time to time as the compilation progresses, the completed planimetry should be 

either repenciled or inked. This is necessary 

because the constant sliding of the tracing table 

over the manuscript will gradually smear and 

rub out the original lines. Inked lines are generally preferred; they are more permanent and 

provide clearer photographic copy. 
MAP COMPILATION BY MULTIPLEX (Ch. 3C 7-e) 7 

Figure 1. --Multiplex compilation. 
8 (Ch. 3C 7-e) TOPOGRAPHIC INSTRUCTIONS 

Because inking must be done piecemeal as 

the compilation progresses, it is not convenient 

to assign the operation to a special draftsman. 

The multiplex stereocompiler therefore, being 

burdened with the task, takes it as an opportunity 

to smooth out some lines, reshape others as required, and add the proper symbols2 . 

COMPILATION OF CONTOURS 

7. Visual skill required 

Skill in contouring comes only after weeks 

of practice and even then not to everyone. A 

special kind of visual ability is required, which, 

if lacking in the beginning, may prove impossible 

to develop. Multiplex trainees, therefore, should 

be selected only after a test of their innate stereoscopic ability. This test should not only measure 

their ability to perceive a depth difference between 

two points in space but also their ability to perceive the shapes of larger masses, as demonstrated by their ability to trace a reasonably approximate contour line. 

When making any stereoscopic measurement with a floating mark, but most especially 

when contouring, the observer must strive for an 

awareness of the model around, above, and below 

the mark itself. Staring at the floating mark is 

a tendency which beginners often have to overcome. 

8. Orientation requirements for contouring 

Contouring requires that the model be both 

positioned and leveled as accurately as possible. 

Even though all the models of a strip remain in 

orientation, the impracticability of accurately 

leveling more than one model at a time makes it 

compulsory to compile contours model by model, 

leveling each model in turn. 

During the compilation of contours, the 

stereocompiler should frequently check both the 

position and the level of the model. He should 

even more frequently check the consistency of 

his elevation reading on a given point (index 

reading), as his personal "index" may be subject 

to a variation of 0.1 to 0. 3 millimeter. Nearly 

2

All symbols should be drafted in accordance with Chapter 3 C 19, Photogrammetric compilation symbols. 

all observers experience this "change in index" 

at one time or another. When it does occur, it 

usually takes place during the first minutes of 

stereoscopic observation. As a person's stereoscopic experience increases, this tendency of 

his "index" to change diminishes. 

9. Contour tracing 

When he is satisfied with the orientation 

of the model and has checked his index reading, 

the stereocompiler may begin drawing the contours. The platen is set and clamped at the 

height of any suitable contour and the contour 

traced as a continuous line by guiding the floating mark wherever it must go to keep it always 

"on the ground." When enough of one contour 

line has been drawn, the platen is raised or 

lowered an amount equal to the contour interval 

and another line is traced. In this manner, 

contours are compiled over the whole model. 

The compilation can begin at any place in the 

model, but it is best to begin either at the top 

or at the bottom of a slope rather than at random 

in between. Depending on the character of the 

topography, it is usually preferable to compile 

by features, or by small groups of features, 

rather than to thread one contour across a whole 

model before starting to trace the next contour. 

In steep terrain, it is often unnecessary to trace 

every contour from the model. Every other contour, or in some cases every fourth or fifth contour will be sufficient. The intermediate contours 

can be sketched in afterward when the whole compilation is shaped or retouched to give the proper 

"expression" to the lines. 

10. Contouring, difficult.areas 

Difficulty in contouring is often experienced in areas of relatively flat terrain, in 

densely wooded areas, in shadows, and in areas 

that offer either too much or too little image 

contrast. Ordinarily, it will not be necessary 

for the stereocompiler to leave these areas uncompleted if he makes good use of the contact 

prints and if he applies a knowledge of topography. 

There are occasional situations, however, in 

which it is impossible to draw the contours with 

a sufficient degree of reliability. In such cases, 

the area in question should be left blank except 

for the notation, "Complete in field." 
MAP COMPILATION BY MULTIPLEX (Ch. 30 7-e) 9 

a. Flat terrain. --If flat terrain has any 

effect on the accuracy with which a multiplex 

elevation can be read, it is to better the accuracy. 

In contouring, however, when the average slope 

of the ground becomes too small--say, less than 

one foot in a hundred--the horizontal position of 

a contour line and hence its shape become difficult to determine. Rather than trace a contour 

as a continuous line, the stereocompiler mayfind it necessary to move the floating mark at 

right angles to the general direction of the contour in an attempt to determine a band within 

which no separation between the mark and the 

ground can be noticed. After a number of bands 

have been located, each contour line can be 

sketched in the most logical position within its 

own band. 

b. Wooded areas. --When the ground is 

completely obscured by trees, accurate contours 

cannot be traced. Whenever possible, therefore, 

aerial photography is taken when leaves are not 

on the trees, so that no difficulty is ordinarily 

experienced in seeing the ground except in areas 

of evergreen growth. When evergreens or leafedout trees must be reckoned with, contouring is 

not altogether impractical provided scattered 

glimpses of ground can be had through openings 

in the trees; if these openings are numerous 

enough, reasonably accurate contours can be 

drawn from one opening to the next by carrying 

the floating mark at a uniform distance below 

the tops of the trees. In places where the tree 

heights would logically be expected to be greater 

or less than average, an estimated allowance 

must be made for the difference in height. 

c. Shadows. --Large areas in shadow cannot be contoured unless detail can be seen in the 

shadow. Contours can be run through small shadows, however, with little difficulty if the stereocompiler does not let himself be deceived into 

mistaking the impression of relief naturally associated with shadows for a true stereoscopic 

impression. An example of this deception may 

be seen in the spotty shadows of partly leafedout trees, which often give one the impression 

that the ground is a very uneven surface although 

in reality it may be quite smooth. 

d. Images with insufficient contrast. --Unbroken fields of grass or grain or stretches of 

sand or snow often present such a monotone 

that it is impossible to make a stereoscopic 

reading upon them. If such areas are not too 

large, however, it is practical to sketch the 

contours across them with the aid of the contact 

prints, which usually resolve the texture of the 

terrain. 

e. Images with excessive contrast. --It 

is a natural tendency for white or very bright 

images to appear slightly higher or nearer to 

the eye than dark-toned images. This can be 

demonstrated if one single photograph is printed 

on two diapositives, being offset on one so that 

a stereoscopic model of the pair may be set up. 

Although this model has no relief, being formed 

by two identical images, there is a strong tendency to see alternate light and dark areas as 

an uneven surface. The stereocompiler should 

bear this phenomenon in mind when reading control elevations as well as when contouring. 

11. Drawing the drainage 

Regardless of the skill with which the 

floating mark is used in tracing the contour lines, 

some smoothing, respacing or reshaping of the 

lines will be necessary if they are to express 

the characteristic features of the terrain with 

utmost clarity and proper emphasis. As most 

land forms have arisen to some extent through 

the effects of erosion, the representation of 

drainage is of great importance in obtaining the 

proper expression of these forms. Drafting the 

proper expression into a multiplex compilation 

will always be aided if all the drainage, large 

and small, is lightly drawn in prior to the final 

inking or repenciling of the contours. Only the 

flatter drains will have to be traced from the 

model; other drains can be sketched through the 

contour re-entrants. Then, when the stereocompiler is repenciling or inking the contours, 

the drainage lines help him to aline the contours 

precisely and to shape them with the proper expression. 

12. Spot elevations3 

Spot elevations are approximately correct 

elevations of certain topographic and cultural 

features that are published in order to furnish 

3

Revised February 1953. 
10 (Ch. 3C 7-e) TOPOGRAPHIC INSTRUCTIONS 

map users with more specific elevations of these 

features than may be interpolated from the contours. Spot elevations are published for such 

objects as road forks; summits of mountains and 

prominent hills; water surfaces of lakes, ponds, 

and wide rivers; stream forks; prominent high 

points in roads; bottom elevations in depressions; 

large flat areas; and section corners, boundary 

markers, and other well-defined points. 

Spot elevations should be recorded by the 

stereocompiler wherever needed to supplement 

the contour information or to supplement spot 

elevations that may have been obtained in the 

course of field surveys. They should not be 

shown on steep slopes. On maps to be published 

as 15-minute quadrangles, the minimum density 

should be about one per square mile, and for 1--

minute quadrangles, three per square mile. 

Maximum density will depend on the nature of 

the terrain. The objective should be to show 

elevations of as many prominent features as 

practicable but not to an extent that would clutter 

the map. 

The recording of such spot elevations is 

an integral part of multiplex compilation. Each 

elevation is determined by averaging repeated 

readings in the multiplex model. All elevations 

determined by reading in the stereo -models must 

be followed by the letter T when shown on the 

manuscript, thus: 678T. When the map location 

of a spot elevation is in doubt, the point is indicated on the map sheet by a small right-angle 

cross. 

13. Inking or repenciling 

Inking or repenciling the completed contours and desired drainage lines are the remaining steps in multiplex compilation. Inking or repenciling is preferably done piecemeal as the 

compilation of the model progresses, the size of 

an area that should be compiled at one time depending on the density of the contours, the clarity 

of the original penciled lines, and the stereocompiler's working convenience. 

Inking is more practical than repenciling, 

since the lines must withstand considerable rubbing by the tracing table. The stereocompiler 

may wish to repencil first and then ink the lines. 

This affords him an opportunity to smooth and 

shape the contours to his satisfactionbefore 

committing them to the permanence of ink. Direct inking without prior repenciling saves considerable time, but requires more skill in 

achieving the proper topographic expression. 

If adjoining models are to be compiled 

subsequently on the same manuscript, the stereocompiler will want to leave a narrow band of 

contours around the joining edges uninked, so 

that he can compromise minor discrepancies in 

compilation along these edges without tedious 

erasures of inked work. 

INT.-DUP. SEC . , WASH . , D . C . 44 5 5 5