GEOLOGICAL SURVEY CIRCULAR 222 

TWIN LOW-OBLIQUE PHOTOGRAPHY 

AND THE TWINPLEX PLOTTER 

Prepared by Topographic Division 

Research and Technical Control Branch 

Section of Photogrammetry 

UNITED STATES DEPARTMENT OF THE INTERIOR 

Oscar L. Chapman, Secretary 

GEOLOGICAL SURVEY 

W. E. Wrather, Director 

GEOLOGICAL SURVEY CIRCULAR 222 

TWIN LOW-OBLIQUE PHOTOGRAPHY .AND THE TWINPLEX PLOTTER 

Prepared by 

Topographic Division 

Research and Technical Control Branch 

Section of Photogrammetry 

The text of this circular is an adaptation 

and combination of the following papers: 

1. Hopkins, B. T., 1951, The Twinplex 

plotter for low-oblique photography. [Unpublished.] 

2. Radlinski, W. A., 1952, Convergent lowoblique photography and its application to 

the Twinplex; Photogrammetric Engineering, 

vol. 18, no. 3, pp. 591-597. 

3. Thompson, M. M., 1950, The Twinplex, a 

new stereoplotting instrument; U. S. Geological Survey Circ. 82. 

Washington, D. C., 195~ 

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

Page 

Introduction. . . . . . . . . . . . . . . . . 1 

Objectives . . . . . . . . . . . . . . . . . 1 

Geometry of twin low-oblique photography. 2 

Camera arrangement . . . . . . . . . . 2 

Convergent low-oblique photography . . 2 

Transverse low-oblique photography . . 8 

The Twinplex plotter . . . . . . . 8 

Principles of construction and 

operation . . . . . . . . . . . 8 

Stereotriangulation . . . . . . 9 

Ellipsoidal reflector projectors 9 

The Twinplex plotter--Continued 

Ellipsoidal reflector projectors 

Compilation with pairs of single projectors. ......•......• 

Experimental compilation project •. 

Geometry of the test models . 

Scaling procedure. . . 

Model quality . . . . • . 

Compilation and tests 

Conclusion .......•• 

ILLUSTRATIONS 

Twin-camera arrangement . 

Convergent low-oblique coverage 

Convergent stereoscopic pair . . . . ..... 

Comparison of areas covered per stereoscopic neat model ....•... 

Transverse low-oblique coverage ...... . 

Page 

9 

12 

12 

12 

14 

14 

16 

18 

3 

4 

5 

7 

10 

11 

Figure 1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

Transverse coverage at a single station . . . . 

Prototype Twinplex - convergent orientation. . . . • . . 12 

10. 

11. 

12. 

Prototype Twinplex - transverse orientation ...... . 

Improved Twinplex with ellipsoidal-reflector projectors . 

General assembly--ellipsoidal-reflector projector .... 

Ellipsoidal-reflector projector arranged for vertical photography . 

Ellipsoidal-reflector projectors mounted on standard multiplex bar 

for single-model compilation of convergent photography ..... . 

iii 

13 

14 

15 

16 

17 
TWIN LOW-OBLIQUE PHOTOGRAPHY· AND THE TWINPLEX PLO'ITER 

INTRODUCTION 

During recent years, the technical procedures of topographic mapping have been profoundly altered by the use of aerial photographs 

as one of the basic source materials 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 ms.chines designed for mapping 

to a high standard of precision. The plotting instruments that have been devised are, in qeneral, 

increasingly complex as a higher degree of precision is attained. 

In 1950, the Geological Survey completed 

the prototype model of a new plotting instrument 

of moderate complexity, called the "Twinplex, " 

that embodies an unusual approach to the diverse 

problems of precision and reconnaissance mapping. The Twinplex instrument is designed to 

accommodate low-oblique photography taken by 

twin cameras, whereas most of the existing 

techniques for precision aerial mapping utilize 

vertical photography (taken with the optical axis 

of the single camera in a vertical or near-vertical position). A low-oblique photograph is defined as a photograph taken with the optical axis 

intentionally deviated from the vertical, but not 

sufficiently to include the horizon in the exposure. 

1 

This report discusses the objectives of twin 

low-oblique photogrammetry, the geometry of 

twin low-oblique photography, and techniques for 

utilizing low-oblique photography in the Twinplex 

and other plotting instruments. 

OB.TECTIVES 

The objectives of photogrammetric techniques utilizing twin low-oblique photography are 

as follows: 

1. Decreasing the over-all cost of mapping. 

2. Increasing the accuracy of mapping 

operations. 

3. Making possible the use of higher flying 

with no departure from standard accuracy. 

4. Allowance of greater latitude in the positioning of flights. 

5. Decreasing the flying time required for 

photography over a given area. 

The Twinplex plotting instrument was developed by the Geological Survey under the direction of Russell K. Bean, with the following objectives: 

1. Providing an instrument that accomodates twin low-oblique photography readily and 

is capable of exploiting the advantages of such 

photography. 

2. Providing a versatile instrument suitable for aerial triangulation, precision mapping, 

and reconnaissance mapping. 
GEOMETRY OF 

TWIN LOVl-OBLIQUE PHOTOGRAPHY 

Camera arrangement 

Twin low-oblique photography is obtained 

with a special twin-camera ar:--<r:2ment consisting of a pair of wide-angle precision aerial 

cameras coupled rigidly together. The respective optical axes of the cameras lie in a common 

vertical plane and form an angle of 20 o with a 

plumb line (assuming no tilt) and 40° with each 

other (fig. 1). The 20 o angle was chosen because 

it gives the greatest amount of stereoscopic coverage 1100 percent in the line of flight) with the 

least amount of obliquity and the most favorable 

air base. This arrangement gives a total angle 

of net coverage of 114 o 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). This orientation gives convergent low-oblique photography that is suitable 

for precision mapping. 

2. Transverse to the flight line (that is, 

the vertical plane containing the optical axes is 

normal to the flight line). This orientation is 

suitable for reconnaissance mapping. 

Convergent low-oblique photography 

When exposures are taken with the twin 

cameras oriented along the flight line, the exposure in the forward-looking camera at one exposure station is convergent with the exposure in 

the backward-looking camera at the next exposure station {figs. 2 and 3, see pages 4 and 5). 

If the exposure stations are so spaced that the 

convergent photographs overlap each other by 

100 percent, the effective ratio of the base between exposures to the flying height (base-height 

ratio) is 1. 23. For an efficient spacing of such 

flights, the effective ratio of the width of the 

strip to the flying height (width-height ratio) is 

1. 27. The comparable values for vertical photography are: base-height ratio = 0. 63 and 

2 

width-height ratio = 1. 15. The doubling of the 

base-height ratio is one of the important advantages of convergent low-oblique photography. 

Von Gruber has shown mathematically that when 

the base-height ratio is doubled, the errors in 

relative orientation and deformations in the 

stereoscopic model are only half as great. 1 

Furthermore, the increase in the base gives a 

more exaggerated stereoscopic impression of 

relief, making vertical measurements easier to 

determine. Because of the stronger intersection 

of conjugate image rays, the operator of a stereoscopic plotting instrument using this photography 

is more positive that his ''floating mark is on the 

ground.'' These advantages, attributable to the 

increase in the base-height ratio, are strong contributors to the C -factor (ratio of flying height to 

the least contour interval that may be plotted accurately)--the contribution being such that it can 

be safely said that the C -factor of a precise instrument using convergent low-oblique photography is substantially increased (probably doubled) 

over its C -factor when using vertical photography. 

It is also interesting to note that the complete working model of convergent low-oblique 

photography is contained within a 75 o angle of 

camera coverage. By eliminating the necessity 

to work beyond this limit, the present problems 

of model "fall off, .. which frequently occur in the 

outer areas for the wide-angle metrogon lens, 

are also eliminated. 

Another very important advantage of convergent low-oblique photography is the extent of 

the ground area covered. The orientation of the 

cameras along the flight line provides workingmodel coverage that is 2. 2 times the area of a 

corresponding model from vertical photography 

assuming equal flying heights; however, inasmuch 

as the C -factor of convergent low-oblique photography is greater, the comparison of ground covered should take into account the higher flying 

height possible with convergent photography. On 

the basis of a 1, 000 C -factor for the convergent 

system as compared to a 600 C -factor for a vertical system, the ground area covered by convergent photography is 6 times greater (fig. 4, see 

page 7). By way of illustration, an area of 66 

1 von Gruber, Otto, 1942, Photogrammetry, 

collected lectures and essays; translated by 

G. T. McCaw and F. A. Cazalet; Boston, American 

Photographic Publishing Co., pp. 47-48. 
Figure 1. --Twin camera arrangement. Lower view shows two 5-inch precision aerial cameras 

installed in an aircraft modified for twin low-oblique photography. (Photograph by 

courtesy of Mark Hurd Mapping Co.) Upper view is a schematic representation of the coupled cameras. 

3 
Flight 

Line 

--

Flight 

Line 

-- -- --

Sta.I 

Plumb 

Line 

Sta.II 

Plumb 

Line 

Figure 2. --Convergent low- oblique coverage. 

4 

------ -
For H =12,000, area of neatmodel =8.1sq.mi., 

area of gross model= t4.1 sq.mi., 

Total forward overlap = I. 84 H. 

8 H =t.23, 

~ = 1.23, 

w H = I. 2:7 

~ = 1.41 

Neat model area A= 5.6 x 10-8 H2 Gross model area A= 9.82 x 10-8 H2 

E!.ia.ht 

Line 

Figure 3. --Convergent stereoscopic pair. (Photographs rectified to demonstrate 

coverage of the overlapping exposures from two successive stations. The 

divergent exposures a re not shown. ) 

5 
square miles, which is slightly greater than the 

area of an average 7!-minute quadrangle, can be 

compiled with 20-foot contours using only 3 convergent low-oblique models compared with about 

18 models for comparable 600 C -factor vertical 

photography. The advantages c;>f having to compile only one-sixth as many models are obvious; 

more important still is the considerable saving 

in time and money resulting from the requirement of only one-sixth as many control points. 

It is noteworthy that 43 percent of the gross 

stereoscopic model falls outside the working model limits; that is, the gross stereo model is 1. 7 

times as great as the working model. This feature permits greater leeway in supplemental control planning and simplifies the task of the aerial 

photographer by allowing him more tolerance in 

the positioning of his exposures. 

It would be imprudent to discuss the merits 

of convergent low-oblique photography without 

also considering the arguments against it. In 

the main, these are: the variation in scale;! due 

to obliquity, reduction in horizontal accuracy, 

and hidden ground due to relief. The first of 

these, variation in scale, would be a serious 

drawback if compilation were to be accomplished 

from the prints, but such is not the case. To be 

successful, convergent photography must be compiled in stereoplotting instruments wherein the 

exact conditions of exposure can be recaptured 

at model scale without any rectification of diapositives being necessary. After orientation in 

the stereoplotting instrument, there is no scale 

variation in the model. It has also been said 

that convergent photography gives a ''poor" perspective. Actually the perspective of the model 

is no different than that presented by vertical 

photography as the method of projection in both 

cases is identical. Because the low-oblique exposure embraces a larger ground area than the 

vertical exposure, it necessarily includes lower 

angles of view in the added area--but this can be 

an advantage because the bases of objects are 

more readily identifiable for the selection and 

plotting of control points. Prints required by 

the fieldman and stereo-operator for stereoscopic examination purposes can be made on a 

fixed rectifier. This process need not be precise inasmuch as the rectification is necessary 

only to facilitate the verification of imagery and 

the identification of control by stereoscopic means. 

6 

The second argument against convergent 

low-oblique photography, the reduction in horizontal accuracy, is outweighed by the more important result of greater vertical accuracy. The 

ideal condition for equal horizontal and vertical 

accuracies occurs when the base..-height ratio is 

1. 0. Convergent photography, which is flown at 

a base-height ratio of 1. 23, is closer to the ideal 

value of 1. 0 than the present vertical photography 

that is flown at a base-height ratio of 0. 63. When 

the base-height ratio is greater than unity, the 

vertical positioning is favored; conversely when 

it is less than unity, the horizontal positioning 

is favored; however, horizontal positioning is not 

nearly as critical as vertical positioning. Consider a 5-foot horizontal error on a 1:7,200 compilation--it is less than a pencil-line width. Yet 

a vertical error of 5 feet at this scale could represent a half contour interval and would therefore be serious. The aim is to increase vertical 

accuracy (C -factor is based on vertical accuracy), 

and low-oblique convergent photography provides 

us with the desirable increase. 

The third argument against convergent lowoblique photography is the hidden ground caused 

by relief. It should be pointed out, however, that 

hidden ground also occurs in vertical photography 

as theoretically the only point at which high relief 

would not obscure detail is the nadir point. At 

the extreme corner of the full working model of 

convergent photography, the horizontal component of the hidden ground is 1. 4 times the change 

in relief. This value compares with 0. 85 times 

the change in relief for the corresponding point 

in the model from wide-angle vertical photography. While the possibility of having additional 

hidden ground in the convergent model is increased, 

there is also an increase in the ground area covered. On the basis of equal C -factors, the convergent model covers the same area as the vertical model without any increase in the hidden 

ground--plus an added coverage of 1. 2 times. 

Taking advantage of the increased C -factor (hence 

higher flying) the convergent model covers 3. 7 

times the area of a 600 C -factor vertical model 

without any increase in the amount of hidden 

ground--plus an added coverage of 2. 3 times 

wherein the amount of hidden ground may be 

slightly increased. It is therefore true that if 

full advantage is taken of the 6 times greater area 

coverage offered by convergent photography, consideration must be given during the planning stage 
COMPARISON OF WORKING NEAT MODEL AREAS 

FOR 

20 FT. CONTOURING 

WITH 

WIDE ANGLE PHOTOGRAPHY 

C=1.000; CONVERGENT LOW OBLIQUES 

22.4 SQ.MI. 

C=I.OOO; VERTICALS 

10.3 SQ. MI. 

C•850; VERTICALS 

7.4 SQ.MI. 

C•750; VERTICALS 

5.8 SQ.MI. 

C•600: VERTICALS 

3.7 SQ. MI. 

(MULTIPLEX) 

TWINPLEX (EXPECTED) 

IF EQUAL C-FACTORS ARE CONSIDERED, THE 

RATIO OF THE AREA COVERED BY TWINPLEX 

PHOTOGRAPHY TO VERTICAL PHOTOGRAPHY 

IS 2.2 TO I. 

FLIGHT HEIGHT 

C=C·FACTOR" CONTOUR INTERVAL 

Figure 4. --Comparison of areas covered per stereoscopic neat model. 

7 
to the type of terrain. For precipitous country, 

the base-height and width-height ratios may have 

to be reduced. In most cases it would be desirable to take the risk of obtaining some blind 

areas in favor of other advantages. When choosing the maximum permissible base length in this 

type of country, consideration must also be given 

to this conditl.on: objects cannot be plotted stereoscopically if they are in a surface that, if extended, 

will intersect the air base. 2 

·Transverse low-oblique photography 

Orientation of the camera couple normal 

to the flight line results in transverse low-oblique 

photography (figs. 5 and 6, see pages 10 and 11) 

in which each model is composed- of the 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 I with the right-hand exposure of station II. 

Similarly, another half-model is formed by the 

left-hand exposures at the same exposure stations. In the transverse neat model, the baseheight ratio is 0. 63 and the width-height ratio is 

2. 31. The extreme width-height ratio would 

permit coverage of an area having a reduced 

number of flight lines; however, the base-height 

ratio would probably not permit a C -factor 

greater than 600 for standard map accuracy. A 

stereoplotting instrument accommodating transverse low-oblique photography would permit reconnaissance mapping of large areas at relatively 

low cost. For instance, by flying at 30,000 feet 

and assuming a contour interval of 50 feet or 

greater, a full15-minute quadrangle could be 

compiled from one flight of five models. For a 

single flight, the net stereoscopic gain per model 

is approximately a rectangular area whose length 

is equal to the air base and whose width extends 

to the limits of the photographic coverage normal to the flight line. The reduction in the number of flight lines permits a decrease in the number of ground-control points required and a decrease in flying time and distance, factors which 

are especially important in military operations. 

To date, the Geological Survey has not had an 

2 Zeller, Dr. M., 1952, Textbook of photogrammetry; translated by E. A. Miskin and R. Powell; London, H. K. Lewis & Co., Ltd., p. 116. 

8 

opportunity to test this system of photography, 

but an extensive test project is in the planning 

stage. 

THE TWINPLEX PLOTTER 

Principles of construction and operation 

The Twinplex stereoplotting instrument is 

based on the principle of double projection and 

recreates the spatial model by anaglyphic means 

in a manner similar to the multiplex and the 

Kelsh plotter. Diapositives, at a reduced scale, 

are printed without rectification from the oblique 

photography obtained from either the convergent 

orientation of the camera couple or the transverse orientation. The instrument makes use of 

sets of twin projectors enclosed in a cage. Each 

set of projectors is analogous to the camera couple. 

in the airplane and may be swung into proper position to accept either the convergent photography 

(fig. 7, see page 12) or the transverse photography (fig. 8, see page 13). 

The two diapositives in a set of twin projectors correspond respectively to the two exposures made at one camera station. In the convergent low-oblique system one projector projects 

the exposure of the forward-looking camera and 

its twin projects the exposure of the backwardlooking camera at a given exposure station. In 

operation, one projector of a set forms a model 

with the convergent projector of the adjacent set 

along the flight line. 

The two cameras used for the twin photography are so mounted that their respective lenses 

are separated in space by a certain fixed distance. 

This separation is a matter of inches and is negligible if considered in relation to the flying 

heights in normal use. Therefore, at mapping 

scales, the positions of the two lenses can be considered as occupying the same point. The pair 

of exposures at a given exposure station do not 

make a stereoscopic model; each exposure must 

be paired with an exposure from an adjacent exposure station to obtain stereoscopic coverage. For 

single model compilation there is no mechanical 

problem connected with the spatial positioning of 

the projectors. An instrument designed for stereotriangulation, however, must provide a series 

of sets of projectors so mounted that their respective optical axes can assume an angle with each 
other that corresponds to the angle in the camera. 

installation. It must also be possible to swing 

each projector cage into proper position to accommodate either convergent or transverse lowoblique photography. It is obviously impossible 

for two projectors of a set to occupy the same 

position in space at the same time. Therefore, 

it becomes a basic requirement of an instrument 

designed for bridging that means be provided to 

bring each projector of a set, in turn, into the 

proper position for forming a model with the appropriate projector of the adjacent set. It is a 

further requirement that such movement of the 

projectors should be accomplished without disturbing the orientation, either relative or absolute, of the models. Therein lies a critical mechanical problem in the design and construction 

of the Twinplex plotting instrument. In either 

orientation, only one projector of each set is 

used at any one time. For convergent photography the convergent pair from camera stations 

I and II are oriented to form Model I-II. For the 

orientation of the adjacent Model II-III, the projector at station II, which was convergent with 

a projector at station I, is swung out of projecting position and its twin swung into its previously 

calibrated projecting position so that it will be 

convergent with a projector at station III. Model 

II-III can now be formed by the relative orientation of the projector set at station III, and can 

be brought to the same scale as Model I-II by 

adjustment of the air base of the second model. 

Any projector can be swung into or out of its 

projecting position at will. 

In the camera couple for the twin low-oblique photography, the camera mounts would, 

under ideal conditions, be so calibrated that a 

vertical plane containing the optical axes also 

contains a pair of fiducial marks for each camera. 

It would therefore be necessary, in the interior 

orientation procedure for each projector set, not 

only to center each diapositive with respect to 

the optical axis of each projector, but to orient 

each diapositive so that a vertical plane through 

the optical axes of the two projectors will contain 

the corresponding pairs of fiducial marks. 

Under c~:mditions likely to be encountered 

in military use, it is doubtful that such precise 

calibration of the cameras in their mount can be 

attained. \Vith this in mind the camera obliquity 

9 

was designed to provide an overlap between the 

twin exposures at each station amounting to sixtenths of the flight height (figs. 2 and 5). The 

correct azimuthal relation of the two diapositive 

plates of a set can be determined by observing 

common image points, within this overlap area, 

as projected alternately by the two projectors of 

a set. Simple observation of these common 

points projected alternately on the tracing table 

will show any lack of agreement between them. 

Appropriate adjustments to the plates will bring 

the common image points into coincidence and 

thus recover the correct azimuthal relation. A 

strong check of the interior orientation is obtained 

by observing the coincidence of the common image 

points at upper and lower positions of the tracingtable platen. 

Stereo triangulation 

The two cameras used in twin low-oblique 

photography are coupled rigidly together, and 

are simultaneously subject to tilt, crab, and 

other deviations that may be expected in normal 

aerial photography. As the Twinplex is designed 

to permit stereotriangulation through bridging 

techniques, it is so constructed that the various 

relative orientation adjustments are made to each 

twin-projector set as a unit. If a pair of single 

projectors is used for compilation, this requirement is unnecessary. 

Horizontal and vertical stereotriangulation 

can be accomplished with either orientation of the 

projector sets; however, accuracy is greater with 

the use of convergent low-oblique photography. 

Considering equal contour intervals, it is theoretically possible to span one 7!-minute quadrangle with one bridge of three models as compared with four bridges of five or six models 

each, required with the multiplex. The use of 

transverse low -oblique photography, while not 

as accurate, permits considerable reduction in 

the number of basic horizontal-control points 

inasmuch as the number of flights and models for 

a given area is decreased. 

Ellipsoidal reflector projectors 

In the prototype Twinplex instrument, using 

multiplex-type projectors, the illumination of the 

models is rather weak. An improved Twinplex 
I 

I 

I 

Right Hand 

Exposure Sta. I 

Right Hand 

Exposure 

Sta.IT -- -- ---

+"' Q) 

.I:. c 

tlO ·-

t_ ti:...J .-1 

-- -- -- -- --- ---- --

Hand 

Exposure Sta.I 

Left Hand 

Exposure 

Sta.li 

I ------ -- Legend -- ---- ~.,....---

Gross Model ~ Neat Model (Area Flying) 

Net Gain in Stereoscopic Coverage (Single Flight) 

Area Common to Twin Exposures at Sta. I 

Figure 5. --Transve:.r:-se low-oblique coverage. 

10 

--... 
instrument, completed in 1952, (fig. 9, see 

page 14), utilizes a new type of projector designed to give greatly improved model illumination. This projector, designated as ER-55, 

makes use of an ellipsoidal reflector to direct the 

rays from the light source, at one focus of the 

ellipsoid, to the projecting lens at the other focus (fig. 10, see page 15). It can be used with 

either vertical or low-oblique photography. The 

proper color filter and the diapositive are appropriately placed in the lighting system for projection of the image. The principal distance in the 

new projector is 55 millimeters, the projection 

distance is 500 millimeters and the diapositive 

format is approximately 110 by 110 millimeters 

as compared with 64 by 64 millimeters for the 

multiplex. Consequently, less reduction is required from the aerial negative to the diapositive; 

also, the magnification is less from the diapositive to the projected model. The first ellipsoidal 

reflector projector was delivered in August 1952 

and initial tests disclosed that it gives very brilliant and evenly distributed illumination (fig. 11, 

see page 16). 

For H = 12,000, area of neat model= 7.6 sq.mi., 

area of gross model= 23.4sq.mi., 

Total forward overlap = 0. 7 7 H 

B H = .63, 

B H = .63, 

w H = 2.31 

~ = 3.07 

Neat model area A= 5.22 xI o·s H2 

Flight I Line 

I 

I 

Gross model · area A= 16.3 x I o·e W 

Figure 6. --Transverse coverage at a single station. (This is not a stereoscopic 

pair; the adjacent exposures that overlap this coverage are not shown. ) 

11 
Figure 7. --Prototype Twinplex - convergent orientation. 

COMPILATION WITH PAIRS OF SINGLE 

PROJECTORS 

If extensive operations are planned using 

twin low-oblique photography, it is contemplated 

that the Twinplex stereoplotting instrument will 

be used primarily for stereotriangulation. Compilation can be accomplished by means of pairs 

of single projectors, either multiplex, Kelsh, or 

ER-55 (fig. 12, see page 17). The multiplex and 

Kelsh require a minor adaptation. Multiplex projectors are adapted for a 20° obliquity, in either 

orientation, by means of simple wedge-shaped 

pieces fitted between the bracket and the gimbal 

mount. The Kelsh projectors are adapted for 

convergent photography by providing a 20° -step 

tilt in addition to the present slow Y -tilt motion. 

12 

EXPERIMENTAL COMPILATION PROJECT 

Geometry of the test models 

The prototype Twinplex stereoplotting instrument, (see fig. 7), using two pairs of multiplextype projectors, was completed early in 1950. In 

order to evaluate the performance characteristics 

of this instrument, a test project was set up consisting of the compilation of a 7~ -minute qu~ 

rangle, Miamisburg SE, Ohio, at a scale of 

1:10,000 with 20-foot contours on the slopes and 

10-foot contours in the flats. 

The available convergent photography for 

this a rea did not meet the theoretically most efficient values for base-height and width-height 
Figure 8. --Prototype Twinplex - transverse orientation. 

r atios. The values actually obtained were 1.16 

for base-height ratio and 0. 92 for width-height 

r atio, resulting in an excess of side lap. Four 

flights of three models each covered the entire 

quadr angle . The flight height was approximately 

12, 000 feet above mean-ground elevation. 

In the prototype model of the Twinplex instrument, the principal distance of the convergent projectors of the two pairs was changed 

from 30 millimeters to 29.64 millimeters. This 

change increased the optimum projection distance from 360 millimeters to approximately 

400 millimeters, thus providing for the increased 

length of the rays due to the 20° inclination. 

There was no noticeable improvement in· the 

models as a result of this change, although theo -

retically such a change was desirable . 

13 

As a projected image ray from the horizon 

side of any diapositive of a convergent model is 

extremely long (approximately 500 millimeters 

at a scale of 1:10, 000), there is a definite advantage in compiling at smaller scales when using 

multiplex-type projectors. The quality of a test 

model was noticeably better at a scale of 1:12,000 

than a t 1:10,000 . The smaller s cale probably 

could not be accommodated in the prototype Twinplex because of interference of the projector 

cages. However, in using a pair of multiplextype projectors for single - model compilation, with 

appropriate wedges to allow the 20° convergent 

tilt, there would be no interference and the smaller scale could be accommodated. 
Figure 9. --Improved Twinplex with ellipsoidal-reflector projectors. 

Scaling procedure 

As the prototype model of the Twinplex 

consisted of only two sets of projectors, it was 

necessary to adopt a system of scaling suitable 

to a single-model instrument. It was decided to 

use the stereo-templet system developed by M. 

B. Scher of the Geological Survey for control 

bridging with the Kelsh plotter. This is a variation of the conventional slotted-templet system, 

in which pass points are picked and templets prepared from horizontalized models. Since the 

models are leveled before the picking of pass 

points, there are no tilt or relief displacements 

in the templets and the only function of the templets is to bring all models to a common scale. 

The stereo-templets were prepared by 

pricking onto the templet material the location 

of the pass points selected from the horizontalized model. This was accomplished by using a 

needle point in place of the pencil on the tracing 

table. Duplicates were prepared from each 

templet by pricking the location of each pass 

point through the original onto the duplicate. 

14 

Inasmuch as the pass points a re located on 

the templet from horizontalized models, it is not 

necessary tha t the slots radiate from the isocenter. Therefore, any pass pass point on the ternplet may be used as a pivot point. In order to 

obtain a strong azimuth line for each templet, a 

pass point in one corner of the original templet 

was selected as a pivot point, and a second pivot 

point was selected in the diagonally opposite corner of the duplicate templet. Slots were cut radially from each pivot point and the templet laydown assembled in the usual way. 

Model quality 

In the prototype model of the Twinplex, 

using multiplex-type projectors, the plane of best 

focus of any projector, being normal to the principal axis of the projector, is inclined approximately 20° to the horizontal plane of the slate 

table and the Scheimpflug condition3 is not satisfied. As the model is viewed on planes parallel 

3

Scheim.:p:flug condit.i.an: IJDages are in sharp 

focus if the planes of the object, the image, and 

the lens intersect on a common line. 
-TO,.VI[W--

WIT•u.l'~cTOtl..~t:O 

-IQ'T'T'OMVIfW-

- P\CTORJA.L. VI[WFigure 10. --General assembly--ellipsoidal-reflector projector. 

to the slate table, it is obvious that very little 

of the model area is observed at the optimum 

focus. In the design of the new projectors for 

the Twinplex instruments, the Scheimpflug condition is s a tisfied by canting the projector lens 

15 

slightly, about 1t o, with respect to the principal 

axis of the projector. 

The illumination of the model in the prototype Twinplex, as projected by the multiplex-type 
Figure 11. --Ellipsoidal-reflector projector arranged for vertical photography. 

projectors, was very uneven . This was offset 

by printing dia.p ositives each of which varied in 

density from fairly dark on the side conta ining 

the nadir point to light on the opposite side. It 

is expected tha t this procedure will not be necessary with the new projectors using the ellipsoidal 

r eflectors. ' 

16 

Compilation and tests 

During the compila tion, each oriented model was leveled on the four elevations in the corners of the model , a nd the points controlling the 

center of the model wer e then read. Two models 

read 0 . 2 millimeter high on thes e points; the 
Figure 12. --Ellipsoidal-reflector projectors mounted on standard multiplex bar 

for single-model compilation of convergent photogr aphy . 

remaining ten models read flat. This indicate s 

a very strong Y -tilt parallax solution. The compilation procedure for the quadr:angle followed 

the standard practice adopted for the multiplex. 

Contouring was relatively easy due to the strong 

intersection of the conjugate image rays. 

17 

The cont act prints from the convergent 

oblique photography were not suitable for stereoscopic examination because of the difference in 

scale between the nadir side and the horizon side. 

Accordingly, a set of rectified prints was required. 

This rectification, which need not be precise , was 
readily accomplished by tilting the easel of the 

rectifier 20° in the plane containing the flight 

line. The prints were larger than the conventional 9-inch contact prints, and somewhat inconvenient to use with a pocket stereoscope. A 

mirror~type stereoscope with a binocular eyepiece proved satisfactory for observing the rectified prints. 

As part of the compilation procedure, spot 

elevations were read on easily recoverable planimetric features within the quadrangle, andrecorded on the manuscript. These elevations 

were checked by stadia lines during the fieldcompletion survey with the following results: 

Of 73 points read and checked, the mean error 

was 2 feet. Two points were 5 feet in error, 

one was 6 feet in ·error, and one was 7 feet in 

error. These points were read from the oriented 

model using a Williamson direct-reading tracing 

table with a least graduation of 5 feet; and were 

selected to provide an over-all test for each 

model. Wherever possible, points most favorable for reading were used. The average spotheight reading error for this test project, expressed as a fraction of the flight height, was 

H/6,000. 

The specifications for compilation of the 

quadrangle called for 20-foot contours, with the 

addition of 10-foot intermediate contours in the 

flats. During the compilation, it was considered 

that the 10-foot contours.might be below standard as the area in the valley bottoms was generally very flat and not suitable for contouring by 

the usual stereoscopic methods. The bulk of the 

corrections to contours made during the fieldcompletion survey was in these flat areas; however, the differences in elevation as expressed 

18 

by the contour changes were generally less than 

one-half the 10-foot contour interval. 

Accuracy-test lines were laid out on the 

north and south halves of the quadrangle and were 

run by the field-completion engineers, using the 

method of plane-table traverse. Of 106 points 

tested, the mean error was 2 feet and the standard deviation was 3 feet; one point was found to 

be in error more than one-half the 20-foot contour interval (16 feet). The field elevation for 

each point was checked against the elevation of 

the same point as interpolated from the contours. 

CONCLUSION 

While no general conclusions can be drawn 

from only one test, the check of the initial Twinplex compilation appears to substantiate the theory 

of low-oblique convergent photography and the 

Twinplex instrument. Further and more extensive tests are contemplated using the new ER -55 

projectors and modified Kelsh and multiplex projectors. 

It is not claimed that convergent low-oblique photography and the Twinplex instrument 

will solve all photogrammetric problems. No 

one system or instrument can do that, because 

of the varying conditions and objectives confronting the mapmaker. On the other hand, photogrammetrists should not be indifferent toward 

the investigation of convergent low-oblique 

photography as a more efficient means of meeting the growing demands for topographic maps 

by military and Civilian users. In theory, it is 

desirable; in practice, it has worked successfully; and now instruments have been developed 

that take advantage of its possibilities. 

INT .-DuP. SEC., lASH., D.C. 12 2115