GEOLOGICAL SURVEY CIRCULAR 82

July 1950

THE TWINPLEX 

A NEW STEREOPLOTTING INSTRUMENT

By Morris M. Thompson
UNITED STATES DEPARTMENT OF THE INTERIOR 

Oscar L. Chapman, Secretary

GEOLOGICAL SURVEY 

W. E. Wrather, Director

WASHINGTON, D. C.

Free on application to the Geological Survey, Washington 26, D. C.
THE TWINPLEX 

A NEW STEREOPLOTTING INSTRUMENT

By Morris M. Thompson

CONTENTS

Page Page

Introduction .................................... 1 Theory of Twinplex photography ............ 1

Objectives ...................................... 1 Operation of the Twinplex ..................... 2

ILLUSTRATIONS

	Page 

Figure 1. Camera couple for Twinplex ....................................................................... 3

2. Twinplex convergent stereoscopic pair ......................................................... 4

3. Comparison of areas covered per stereoscopic neat model ................................. 5

4. Twinplex transverse coverage at a single station ............................................ 6

5. Twinplex and operator. Orientation along flight line ....................................... 7

6. Twinplex and operator. Transverse orientation .............................................. 8
INTRODUCTION THEORY OF TWINPLEX PHOTOGRAPHY

During recent years, the technical procedures of topographic mapping have been 

profoundly altered by the use of aerial photographs as the basic source material for map 

compilation. An aerial photograph, however, 

does not in itself constitute a map. Because 

of variations in ground elevations, tilting of 

the camera, and other phenomena, the aerial 

photograph gives a distorted picture of the 

terrain; furthermore, a single aerial photograph 

affords no means of measuring variations in 

ground elevation. For converting the information contained in the photographs into accurate topographic maps, various plotting instruments have been developed. These instruments 

range from relatively simple devices, used for 

the production of maps of relatively low accuracy, to elaborate plotting machines designed 

for mapping to a high standard of precision. 

The plotting instruments that have been devised 

are, in general, increasingly complex as a 

higher degree of precision is attained. The 

Geological Survey has recently completed the 

prototype model of a new instrument of moderate 

complexity, called the "Twinplex," which 

embodies an unusual approach to the problems 

of precision and reconnaissance mapping.

The following exposition of the manner 

in which the Twinplex functions necessarily 

includes technical terminology that may be 

unfamiliar to persons who are not grounded in 

the science of photogrammetry. However, anyone 

who understands the functioning of the widely 

known Multiplex instrument should have no 

difficulty, in grasping the principles of the 

Twinplex.

OBJECTIVES

The Twinplex is a stereoplotting instrument that was conceived by Russell K. Bean of 

the Geological Survey and developed under his 

direction, during the years following World War II, 

with three principal objectives:

1. Decreasing the over-all cost of precision mapping.

2. Increasing the accuracy of mapping 

operations.

3. Producing a versatile instrument suitable for precision mapping, reconnaissance 

mapping, and aerial triangulation.

As a prerequisite to the utilization of the 

Twinplex, it is necessary to have photographs 

obtained with a special twin-camera arrangement 

consisting of a pair of wide-angle precision 

aerial cameras coupled rigidly together so that, 

assuming no tilt, their respective optical axes 

lie in a common vertical plane and form an 

angle of 20° with a plumb line and 40° with 

each other. (See fig. 1.) This gives a total 

angle of net coverage of 114 in the plane 

containing the optical axes for a 6-inch focal 

length and 9-inch square format. The shutters 

are synchronized so that simultaneous exposures are made with both cameras of the coupled 

pair. The camera system may be oriented in 

two ways:

1. Along the flight line (that is, the 

vertical plane containing the optical axes also 

contains the flight line).

2. Transverse to the flight line (that is, 

the vertical plane containing the optical axes 

is normal to the flight line).

Orientation along the flight line gives the 

convergent low-oblique photography that is the 

basis of precision mapping with the Twinplex. 

For a series of exposure stations, one of the 

two exposures at station 1 will be convergent 

with one of the two exposures at station 2. 

Likewise, the second exposure at station 2 

will be convergent with one of the two exposures 

at station 3. It is these convergent pairs of 

exposures from successive stations that overlap 

to form the stereoscopic models (fig. 2). The 

shape of the ground area covered by each 

photograph is trapezoidal, and the stereoscopic 

overlap forms a hexagon with the photographs 

overlapping each other 100 percent in the 

direction of the flight line. From the geometry 

of the oblique system, the base-height ratio 

is 1.23 and the width-height ratio is 1.27. The 

comparable values for vertical photography are 

0.65 for base-height ratio and 1.15 for widthheight ratio. Because of the increased baseheight ratio, a favorable C factor (ratio of 

flight height to the least contour interval that 

may be plotted accurately) is obtained in the 

Twinplex. This figure has tentatively been 

set at 1,000. Assuming that a 20-foot contour 

interval is desired, the flight height will be 

20,000 feet, and an area comparable to a 7.5- 

minute quadrangle can be compiled with three
Twinplex models as against twenty models in 

present wide-angle Multiplex systems. The 

economies resulting from the reduction in the 

number of photographs required, in the number 

of model set-ups required, and above all in the 

number of control points required are readily 

apparent. (See fig. 3.)

Orientation transverse to the flight line 

(fig. 4 ) is suitable for reconnaissance mapping 

at larger contour intervals. For this arrangement, the base-height ratio is 0.63 and the widthheight ratio is 2.31, making possible the 

coverage of an area with a greatly reduced 

number of flight lines. The C factor assumes a 

value of about 600. However, by flying at 

30,000 feet, only one flight and five models 

are required to compile a full 15-minute quadrangle, assuming a contour interval of 50 feet 

or larger. Each model, in transverse orientation, 

consists of all four exposures taken at two 

successive exposure stations (two at each 

station). A half model is formed by the overlap 

of the right-hand exposure of station 1 with the 

right-hand exposure of station 2. Another half 

model is formed by the overlap of the left-hand 

exposure of station 1 with the left-hand exposure 

of station 2.

OPERATION OF THE TWINPLEX

The Twinplex is essentially a doubleprojection type of stereo plotting instrument 

utilizing diapositives printed without rectification from the oblique photography described 

above. It is arranged so that it can utilize 

either orientation of the photography along the 

flight line (fig. 5) or transverse (fig. 6). However, instead of the series of single projectors 

found in conventional double-projection instruments, the Twinplex has a series of sets of 

twin projectors. In each set, the two projectors are locked together so that they move 

as a unit. The two diapositives used in a 

set of twin projectors correspond respectively 

to the two exposures made at one camera station. 

(These exposures do not make a stereoscopic 

model; each must be paired with an exposure 

from an adjacent camera station in order to 

obtain stereoscopic overlap). Physical limitations prevent the simultaneous orientation of 

both projectors of a set, as obviously the lenses 

of both projectors cannot occupy the same point

in space at the same time. Provision is made 

to allow each of the two projectors to be brought, 

in turn, into position for forming a model with 

the appropriate projector of an adjacent set. 

Whether the orientation is transverse or along 

the flight line, only one projector of each set 

of twin projectors is in use at any one time, but 

the set of projectors is so mounted that once 

either of the projectors has been oriented, the 

other can be brought into orientation by swinging 

it into, a previously calibrated second position. 

Thus, for photography along the flight line, when 

compilation of the model formed by the convergent pair from stations 1 and 2 has been completed, the twin set of projectors at station 2 

is swung into its second position. In this 

position, the projector that was not one of 

the convergent pair forming the first model 

is now oriented so that a correctly oriented 

second model can be formed by bringing the 

convergent projector at station 3 into relative 

orientation. For transverse photography, when 

compilation of the half model formed by the 

right-hand exposures of stations 1 and 2 is 

complete, both projector sets are swung into the 

second position. In this position, the half 

model formed by the left-hand exposures of 

stations 1 and 2 is automatically oriented.

Aerial triangulation can be accomplished 

when the camera system is oriented either along 

the flight line or transverse to it. More accurate 

triangulation can be achieved with orientation 

along the flight line because of the increased 

C factor. On the other hand, triangulation, with 

transverse orientation has the advantage that 

the control points at each end of the bridge can 

be spaced twice as far apart in a direction 

normal to the flight lines.

The prototype model of the Twinplex, the 

only one in existence at this time, was completed in December 1949 and exhibited at the 

January 1950 meeting of the American Society 

of Photogrammetry. The Geological Survey is 

currently engaged in an experimental mapping 

project to determine the performance characteristics of the instrument. A full appraisal 

of its qualities must necessarily await completion of this test project; however, preliminary tests indicate that the apparatus will,, 

in practice, substantiate its theoretical capabilities.
Fig. 1 Camera couple for Twinplex.
For H=12,000', area of neat model = 8.1 sq.mi.

Fig. 2 Twinplex convergent stereoscopic pair. (Photographs rectified to demonstrate coverage of the overlapping exposures from two successive stations. The 

divergent exposures are not shown.)
COMPARISON OF WORKING NEAT MODEL AREAS

FOR 

20 FT. CONTOURING

WITH 

WIDE ANGLE PHOTOGRAPHY

CH.OOO; CONVERGENT LOW OBLIQUES 

22.4 SO. Ml.

TWINPLEX (EXPECTED)

C-1.000; VERTICALS 

IQ3 SO. Ml.

C-850; VERTICALS 

74SQ.MI.

C-750; VERTICALS 

5.8SQ.MI.

C-600; VERTICALS 

37SQ.MI.

(MULTIPLEX)

IF EQUAL C-FACTORS ARE CONSIDERED, THE 

RATIO OF THE AREA COVERED BY TWINPLEX 

PHOTOGRAPHY TO VERTICAL PHOTOGRAPHY 

IS 2.2 T01.

r r rtn-nn FLIGHT HEIGHT G-UIAUUK CONTOUR INTERVAL

Fig. 3 Comparison of areas covered per stereos opic neat model.
For H=12,000', area of neat model5 7.6 sq. mi.

Fig. 4 Twinplex transverse coverage at a single station. (This is not a stereoscopic pair; the adjacent exposures that overlap this coverage are not shown.)
Fig. 5 Twinplex and operator. Orientation along flight line.
Fig. 6 Twinplex and operator. Transverse orientation.

Interior Duplicating Section, Washington, D. C.

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