John Adolphus Flemer. # An elementary treatise on phototopographic methods and instruments, including a concise review of executed phototopographic surveys and of publicatins on this subject online

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As d will always be a small angle we can substitute the tangent

for the angle.

If we designate by R the range of the field that is con-

trolled by the total effect of relief, we will have

E EXG

j^rX xG = 5

e o

After substitution of this value in the above equation for dD we

finally find

D 2

Numerous experiments have shown that the angular parallax

(d), the angle under which objects situated in different but very

distant frontal planes cease to appear to be at different depths

when examined under binocular vision, amounts to 30 seconds

for normal eyes (Helmholtz gives = i").

Hence we find from

For small angles we can substitute for one second the value

1:206265; hence for an interocular distance of 65 mm.,

730 0.065

0.065 = , , or r= 206265;

206265 30

7=446.9 m., or in round numbers, 450 m.

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 313

The "hunting" or "sporting" telemeter has a base of 32 cm.,

a telescopic magnification of 4, and a scale for reading distances

from 20 to 500 meters. Objects beyond 8000 meters appear as

infinitely far off. The weight of this instrument is about 2\ kgr.

Fig. i, Plate CVIII, shows a general view of the Zeiss sporting-

telemeter.

The "infantry telemeter" has a 51 -cm. base, a telescopic

magnification of 8, and a scale for distance reading from 90

to 3000 meters. Objects beyond 28 km. appear at infinite dis-

tance. This instrument has a weight of about 3^ kg., and it

cannot well be manipulated without a support. The telemeter

with suitable (tubular) stand weighs 6J to 9^ kg.

The so-called "stand telemeters" (the central part of one is

shown in Fig. 2, Plate CVIII) have a i.44-m. base, a telescopic

magnification of 23, and a scale for reading distances ranging

from 500 to 8000 meters. Objects beyond 230 km. appear at

infinite distance. 'Jhese stereotelemeters require a rigid sup-

port, and the Zeiss firm has devised a special tripod for them.

The weight without tripod is 15 J kg. The packing-case weighs

20^ kg. The tripod with fork- rest and tilting joint weighs 18^ kg.

The attachment marked B in Fig. 2, Plate CVIII, is to be

secured to the right eyepiece for illuminating the image planes

in the binocular microscope of the stand telemeter when ad-

justing the ocular scale in the stereoscopic image plane. It is

used in connection with a pair of Gautier-Prandl prisms that

may be adjusted over the objectives, as indicated by dotted lines

in the diagram, Plate CIX. When these Gautier-Prandl and

the eyepiece prisms are in the position shown, the light-rays

entering o' through the prism B will pass from m' to O', thence

through the right Gautier-Prandl prism, through the left prism,

through O and m, emerging through o, illuminating both image

planes in their course, as indicated by the dotted line, Plate CIX.

We will not refer here to the adjustments nor to detailed

directions for using the different types of stereotelemeters, as

printed directions are sent out with every instrument.

3 H PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

The errors affecting the readings of these telemeters increase

with the square of the distance. There is a certain zone of un-

certainty for all points in a frontal plane. That is to say, that

for a certain reading made with the well-adjusted telemeter the

distance, as read off on the aerial scale, may be too long or too

short by a certain amount; each reading will be affected by a

positive or a negative error.

In the table opposite the probable errors,

Affecting different distances, read with the three types of telem-

eters, have been tabulated for comparison.

To use a stereoscopic telemeter successfully the observer

must be able to see " stereoscopically " ; this, of course, excludes

all persons with defective vision or who have developed the power

of vision in one eye at the expense of the other, or whose eyes

are abnormally spaced, less than 58 or more than 72 mm. apart.

Both eyes should be used simultaneously, and it will require quite

a little practice before the observer will become expert in dis-

tinguishing differences in the distance between objects appar-

ently close together in the stereoscopic field and yet in different

frontal planes.

To test an observer's ability to see stereoscopically, Dr.

Pulfrich has constructed a stereoscopic " test-plate " (" Prue-

fungstafel fuer stereoskopisches Sehen "), which is issued together

with his treatise, " Ueber eine Pruefungstafel fuer stereoskop-

isches Sehen," published in the Zeitschrift fuer instrumenten-

kunde, Heft 9, 1901. The figures and diagrams shown in

that test-plate not only give the means for a quantitative test

but they are also designed for making a qualitative test of the

observer's stereoscopic vision.

Plates CII and CHI show roughly made diagrams for test-

ing stereoscopic vision in the quantitative sense only. The

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 315

Distance =Z>

in Meters.

Probable Error in Meters for the

Sporting Telemeter:

Base = 32 cm.,

Magnification 4.

Infantry Telemeter:

Base = 51 cm.,

Magnification 8.

Stand Telemeter:

Base = 1.44 m..

Magnification 23.

2O

3

40

0.05

O.II

O.2O

5

0.31

75

0.70

90

0.3

IOO

1 .25

-3

125

2.8

0.5

0.8

^"^""^

175

i.i

200

5-

1.4

300

400

"3

20. o

3-2

6

500

600

3i-3

9

2-5

2.8

700

17

3.6

750

800

900

IOOO

1250

Objects beyond

8 km. appear as

at infinite distance

23

29

35

4.4

6.7

9-9

18

1500

80

22

J 75

109

27

2000

2250

140

181

33

39

2500

223

54

2750

270

70

3000

35

320

no

156

4000

5000

6000

7000

8000

Objects beyond 28

km. appear as at

infinite distance

215

278

352

440

9000

10000

Objects beyond 230

kin. appear as in-

finite

circles, Plate CII, are numbered with their increase in distance,

No. i being nearest and No. 9 farthest. In Plate CIII the pyra-

mid is nearest the eyes; then follow the cross, concentric rings,

circle near the cross, large ring or circle (inclosing the figures),

central wheel with four spokes, cube, smaller circle (below the

316 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

cube), base of large cone, and finally the base of the small cone.

The axes of the two cones are not in line and the base of the

pyramid is not in a plane parallel with the large circle, its left

corner being tilted up a little. The Maltese cross, too, has its

upper two arms tilted forward toward the observer, the end

of the left upper arm being somewhat nearer than the upper

end of the right arm. A careful examination of these plates

will show whether the observer can see stereoscopically.

In looking into the stereotelemeter the aerial distance scale

should appear free in space, in a plane slightly raised toward

the distant end of the scale. As soon as the particular part

of the scale has been determined, by inspection, which coincides

with the object, the distance of the latter is obtained within a

certain margin of limitation, as already referred to in the pre-

ceding paragraphs.

The more expert the observer, the smaller the limit of differ-

entiation will be, although there will always remain a certain

margin of uncertainty corresponding to the limit of power of

the stereoscopic definition, as noted in the table previously

cited.

To become efficient in the rapid use of the stereotelemeter,

it is essential that the observer make himself thoroughly familiar

with the divisions of the aerial scale of his instrument. It should

be noted that the subdivisions of the scale apparently grow

smaller with increasing distance, and the observer should not

only be able to read off each actual scale mark quickly and cor-

rectly, but he should also be trained to estimate fractions of the

subdivisional scale lengths accurately. (Attention may be called

to the fact that the nearest half- reading between two successive

scale marks falls a little beyond the space center, the quarter

a little beyond the geometrical quarter- space, etc.)

Plate CI represents the measuring- scale used in the Carl

Zeiss hunting stereotelemeter. The marks of this scale are

arranged in four sections, the scale appearing as a zigzag line.

The first section, from 20 to 25 m., apparently appears in front

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 317

of the diaphragm or circle which incloses the scale. The four

sections control distances as follows:

(1) 20 to 25 m., divided into i -meter spaces;

(2) 25 to 50 m., divided into i -meter spaces;

(3) 5 to 7 m -> divided into 2, and 70 to 100 m., into 5 m.

spaces;

(4) loo to 1 60 m., in 10, 160 to 300 m., in 20, and 300 to

500 m., divided into 50 m. spaces.

The reproduction of this scale on Plate CI is faulty; inasmuch

as the triangular division marks 4 and 6, representing the 40 and

60 m. divisions of the scale, are considerably out of line, some

of the other marks show similar imperfections, but less marked

than these two.

The glass plate having the aerial distance scale etched into its

surface is also provided with a transverse scale (divided into

twenty equal parts, Plate CI) for measuring widths and heights

of objects. In the stereoscopic fields of the telemeters both

scales stand out very clear and distinct, being photographic

reductions of the large-scale originals.

For the first practice work with the stereotelemeter, well-

defined objects, preferably those that are silhouetted against

the sky, should be selected. The instrument is first directed

toward the sky, the interocular distance adjusted, and the eye-

pieces focused. The instrument is now gently revolved down-

ward until the object ranged upon appears in the lower field,

when the aerial scale should appear free in space above the

object. It will now remain for the observer to find that place

of the scale which coincides with the object (which will be in

the same frontal plane with it) to estimate the fractional dis-

tance from nearest scale mark to object.

The scale divisions are indicated by small triangles, the acute

angle pointing downward, and to determine the position of an

object with reference to the scale, the highest point of the object

3l8 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

is brought as close as possible to the imaginary line, connecting

the scale marks near the object, when the mark to the near side

of the observer and close to the object is picked out, the observer

estimating the distance of the object beyond this mark to arrive

at the actual distance. Should the mark just beyond the object

be observed, instead the nearer one as just stated, the tendency

generally seems to be towards overestimating the distance.

The Carl Zeiss firm has also constructed a stereoscopic telem-

eter without an aerial scale. The stereoscopic field of this

telemeter shows an index mark which is movable by the aid of a

micrometer screw. With this instrument several independent

measurements of the distance between two objects may be made,

similar in manner to the method of repetitions.

The Carl Zeiss stand stereotelemeter may be used at night

for estimating or measuring the distances of lights (vessels, light-

houses, etc.), by illuminating the scale on the diaphragm plate,

means for doing this being provided if a suitable lantern be at

hand.

The binocular microscope of the stereocomparator, of which

a description follows, is built after the model of the stereo-

telemeter, its telescope with prisms being here replaced by a

binocular microscope with reflecting mirrors, through which the

upright stereoscopic images are examined under enlargement.

B. The Stereocomparator and the Stereo photo graphic

Surveying Method.

The angle included at a distant point between the visual

rays from the eyes of the observer is known as the parallactic

angle, or parallax. The parallax increases when the point

approaches the observer and vice versa. For a point at in-

finite distance the two visual rays will be parallel; the parallax

will be =o.

The estimation of the distance of a point, when observed

with both eyes, depends largely upon the subconscious gaug-

ing, or mental measurement of the parallax. The distance of

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 319

an object when viewed with one eye only may still be estimated,

but in monocular vision such estimates must be based mainly

upon the degree of diminution in the apparent size of the object

if a familiar one, or the reduction in size of closely neighboring

bodies of which the actual sizes are known; for instance, a per-

son or an animal that may be standing near the distant object.

The stereophotogrammetric method is based on measure-

ments made simultaneously on two stereoscopic pictures show-

ing the same terrene and exposed from all the ends of a compara-

tively short base line. These simultaneous measurements, on

corresponding plate pairs, of the coordinates to locate identical

terrene points with reference to the horizon and principal lines

are made with the "stereocomparator," ingeniously devised by

Dr. C. Pulfrich, a member of the scientific staff of the Carl Zeiss

Optical Works in Jena!

The principle underlying the construction of the stereo-

comparator may be elucidated in the following manner, sug-

gested by P. Seliger of the Prussian Topographic Bureau. Two

pointers, made of black wire of equal thickness and of equal

lengths, when suspended over the face of two stereoscopic views

secured in a stereoscope will become superimposed and appear

as a single wire in the stereoscopic image of the two views.

If we now move one wire over the face of the picture, bring-

ing it a little closer to the wire over the other picture (we reduce

the parallax), the apparent position of the wire index in the

stereoscopic image will have become more distant, and as soon

as the distance between the two wires is made to coincide with

the interocular distance the superimposed images of the wires

will appear infinitely far off in the stereoscopic field. By thus

changing the relative positions of the two wires, the observer

can transfer their stereoscopic image to any point of the stereo-

scopic field.

All points of the stereoscopic image that are hi a vertical plane

parallel to the stereoscopic base have the same vertical distance

from the base line. Since the vertical distance of such frontal

. 320 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

plane has the sam^ ratio to the base length as the focal length

of the camera has to the parallax, we can compute such distance

if we know the parallax, the base and the focal length being

constant for every stereoscopic picture pair.

The stereoscopic picture pairs are placed on the stereocom-

parator to be measured through a binocular microscope similar

in construction as the Zeiss "stereoscopic telemeter," by means

of which the two coordinates and the parallax of any pictured

point may be measured, after optical bisection, by reading the

corresponding verniers of the three scales that are connected

with the stereocomparator. The data thus obtained suffice for

the cartographic location of the point in both the horizontal and

vertical sense.

Referring to Plate CIV, which shows the general arrangement

of the stereocomparator, we designate by

Pi and P2 the left and the right pictures;

H the rack-and-pinion motion for moving both pictures together

from left to right and vice versa;

M f a screw for moving the right picture alone and in the same

sense as the motion imparted by H\

M a screw for turning the right picture;

N a screw for raising or lowering the right picture;

T the turntable for the right picture;

5 a screw for moving the left picture independently from right

to left and vice versa; ,

R and h plates running in grooves, to be raised, lowered, or

moved transversely;

A and B scales for measuring the coordinates of points pictured

on both plates;

a scale for measuring the parallax of pictured points;

C binocular microscope; it may be raised or lowered by turning

the screw F, the amount of such change in altitude to be

read off within o.i mm. on the vernier of scale B.

To be viewed stereoscopically the two pictures Pi and P2

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 32!

are placed on their plates, R and T, in a position correspond-

ing to that they had when the exposure was made, with their

principal lines made parallel and vertical. If the base-line ends

are not of the same elevation, the right plate is raised or lowered

until corresponding points appear equally high when examined

through the binocular microscope.

The binocular microscope may be moved toward or away

from the negatives by turning E and each eyepiece is inde-

pendently adjustable to the eyes of the observer. The objec-

tives also are movable in the direction of the optical axes, to

give a range of magnification of 4 to 8 diameters. Two index

marks have been provided, one in each image plane of the micro-

scopes, for bisecting identical terrene points. By turning the

micrometer screw F the index of the right microscope may

be moved, changing the apparent distance of its stereoscopic

image. For one turn of the micrometer F the index will

be moved 0.2 mm., which would correspond with a change of

the right plate of 0.3, 0.2, and 0.15 mm., using a magnification

of 4, 6, and 8, respectively.

To find the parallax of a pictured point the stereoscopic

image of the index mark is set at apparent infinite distance and

both plates are now moved and adjusted until the terrene point

to be measured coincides with this index mark. The motion

of the right plate, accomplished by turning the screw M',

to bring the mark and point into contact, is read off on the vernier

a, which reads to 0.02 mm. By estimation, however, the

value for the parallax may be obtained within o.oi mm. After

the index has been made to bisect the point the readings of

the verniers A and B will give the coordinates of the pictured

point with reference to the left picture (left base station).

The main advantage claimed for the use of the stereocom-

parator in phototopography rests in the fact that one pointing

of the index on the point at once gives the elements for the car-

tographic location of the point, whereas with the plane-table or

radial method three distinct measurements would have to be

322 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

made before the pictured point may be plotted, involving the

separate measures of two abscissae and one ordinate. With

trie stereocomparator the coordinates are measured directly on

the negatives with microscopes and verniers, and the accuracy

obtained should be greater than obtainable with the plane-table

or radial method, using paper prints, dividers, and scales.

The index mark being placed upon each terrene point that

is to be plotted from the pairs of pictures, it is evident that the

better the definition of such points the closer will be their sub-

sequent cartographic location.

The three readings made on the scales A, B, and a give the

data for locating any pictured point (bisected with the movable

index mark) in regard to direction, distance, and elevation, and

with reference to the left station.

The abscissa oc (Plate CV, Fig. i), read off on scale A, is

plotted in the usual manner by laying off the distance on the

picture trace T from the principal point O, a line SR, drawn

through the end of oc from the left station S gives the line of

direction to the bisected point P.

The distance is ascertained from the vernier reading of scale

a which gives the linear parallax of the bisected point. The

distance may be computed from the equation

A:B=f:a,

where B is the distance between the two stations,

/ the constant focal length of the camera, and

a the parallax as read off on the scale.

In Fig. i, Plate CV, TT represents the picture trace,

x the abscissa of the point P, the plotted position of which

will be on the radial SR. The value for A, as computed

above, is laid off on the principal line from S. A parallel

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 323

to TT, drawn through the end of A, will bisect SR in P,

which is the horizontal projection of the bisected point.

Dr. Pulfrich recommends a graphical solution of the equation

of which the product B-f is a constant for every pair of pictures.

Referring to Fig. 2, Plate CV,

SSi = B= base line;

TT= picture trace of left picture;

a = vernier reading for parallax, laid off on TT from O.

If we now draw the radial Sr, the intersection of the latter

with 6*16, drawn parallel with SO, will cut off the distance

A on Sib, and the point to be plotted will be on the line

MN, drawn parallel to TT at the distance A from S. ' The

plotted position may now readily be found by laying off the

abscissa x from O and drawing the radial SR', the intersection

of the latter with M N locates the plotted position of the point P.

Fig. 3, Plate CV, shows the simple device suggested by Dr.

Pulfrich for the graphical solution of the equation for A.

A drawing-board is covered with a tough paper and a line SO

is drawn parallel with its lower edge. On SO, at a distance

1.5 /. from 5, a vertical UT is erected and a scale of divisional

parts equal to 1.5 mm. is laid off on UT. The line SO

is provided with a looo-meter graduation in the plotting- scale

(say 1:25000). LL is a straight edge secured to the board

parallel with SO. G is a transparent film of celluloid

attached to a brass strip k in such a way that it may readily

be slid along LL over SO. This transparent plate G has two

graduation, tt and /', in the reduced scale of the map. The

ruler SR, also provided with the reduced scale of the map

(1:25000), may be revolved about the pin in S.

To use this device the base line for a pair of plates is laid

324 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

off on //, say in tenfold scale of the map. After the parallax

a has been read off on the scale of the stereocomparator,

the ruler SR is placed on UT to cut off the length 100, and G is

moved until the base end, marked off on //, coincides with the

fiducial edge of SR. The corresponding value for A may now

be read off on SO, using the scale t r for the subdivisional parts

of 50.

To find the distance SP of the plotted point from the

left station S, the position of G is maintained unchanged,

while the edge of SR is made to coincide with that division

mark of the scale UT which corresponds with the abscissa

x of the pictured point. The distance SP may now be read off

on SR to be transferred to the radial SR, Fig. i, Plate CV.

The difference in elevation of pictured-point and left-base

station,

i

may also be found graphically. After the distance SP has

been read off, G is held in the same position and SR is

brought to coincide with that scale division on UT which

corresponds with the ordinate (read off on scale B of the

stereocomparator), when the reading of the scale //, between

SO and SR, will give the value for h in meters. Instead

of moving SR to bisect the end of the ordinate y on UT

it is desirable to use a multiple part of y, say icy, and

divide the final reading by 10. The elevation of the plotted

point is now derived from the elevation of the left station in the

customary manner, referring h to the elevation of the horizon

line of the instrument at the station and allowing for curvature

and refraction for points over 2000 m. distant from S.

The apparent length of the index mark in the stereoscopic

image plane of course corresponds to different heights, accord-

ing to the distance of the bisected object; the relation between

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 325

both, however, may readily be ascertained when the actual or

absolute length of the index mark be known. This length is best

found by bringing the upper end of the mark into contact with

a well-defined horizontal line in the picture and noting the read-

ing of the scale of ordinates (scale B), then bringing the lower

end of the mark into contact with the same horizontal line and

again noting the vernier reading of the scale B. The differ-,

ence between the two readings will equal the absolute length

of the index mark (=m).

The comparative length value =M of the index mark for a

distance =A may be computed from the formula

;;." - ,;-,. 7 ;.. M-J.A.

If the value for m be found 0.75 mm. and the constant

focal length of the camera be 250 mm. the value for M would

be 0.003 A. Now, say the lower end of the index mark coin-

for the angle.

If we designate by R the range of the field that is con-

trolled by the total effect of relief, we will have

E EXG

j^rX xG = 5

e o

After substitution of this value in the above equation for dD we

finally find

D 2

Numerous experiments have shown that the angular parallax

(d), the angle under which objects situated in different but very

distant frontal planes cease to appear to be at different depths

when examined under binocular vision, amounts to 30 seconds

for normal eyes (Helmholtz gives = i").

Hence we find from

For small angles we can substitute for one second the value

1:206265; hence for an interocular distance of 65 mm.,

730 0.065

0.065 = , , or r= 206265;

206265 30

7=446.9 m., or in round numbers, 450 m.

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 313

The "hunting" or "sporting" telemeter has a base of 32 cm.,

a telescopic magnification of 4, and a scale for reading distances

from 20 to 500 meters. Objects beyond 8000 meters appear as

infinitely far off. The weight of this instrument is about 2\ kgr.

Fig. i, Plate CVIII, shows a general view of the Zeiss sporting-

telemeter.

The "infantry telemeter" has a 51 -cm. base, a telescopic

magnification of 8, and a scale for distance reading from 90

to 3000 meters. Objects beyond 28 km. appear at infinite dis-

tance. This instrument has a weight of about 3^ kg., and it

cannot well be manipulated without a support. The telemeter

with suitable (tubular) stand weighs 6J to 9^ kg.

The so-called "stand telemeters" (the central part of one is

shown in Fig. 2, Plate CVIII) have a i.44-m. base, a telescopic

magnification of 23, and a scale for reading distances ranging

from 500 to 8000 meters. Objects beyond 230 km. appear at

infinite distance. 'Jhese stereotelemeters require a rigid sup-

port, and the Zeiss firm has devised a special tripod for them.

The weight without tripod is 15 J kg. The packing-case weighs

20^ kg. The tripod with fork- rest and tilting joint weighs 18^ kg.

The attachment marked B in Fig. 2, Plate CVIII, is to be

secured to the right eyepiece for illuminating the image planes

in the binocular microscope of the stand telemeter when ad-

justing the ocular scale in the stereoscopic image plane. It is

used in connection with a pair of Gautier-Prandl prisms that

may be adjusted over the objectives, as indicated by dotted lines

in the diagram, Plate CIX. When these Gautier-Prandl and

the eyepiece prisms are in the position shown, the light-rays

entering o' through the prism B will pass from m' to O', thence

through the right Gautier-Prandl prism, through the left prism,

through O and m, emerging through o, illuminating both image

planes in their course, as indicated by the dotted line, Plate CIX.

We will not refer here to the adjustments nor to detailed

directions for using the different types of stereotelemeters, as

printed directions are sent out with every instrument.

3 H PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

The errors affecting the readings of these telemeters increase

with the square of the distance. There is a certain zone of un-

certainty for all points in a frontal plane. That is to say, that

for a certain reading made with the well-adjusted telemeter the

distance, as read off on the aerial scale, may be too long or too

short by a certain amount; each reading will be affected by a

positive or a negative error.

In the table opposite the probable errors,

Affecting different distances, read with the three types of telem-

eters, have been tabulated for comparison.

To use a stereoscopic telemeter successfully the observer

must be able to see " stereoscopically " ; this, of course, excludes

all persons with defective vision or who have developed the power

of vision in one eye at the expense of the other, or whose eyes

are abnormally spaced, less than 58 or more than 72 mm. apart.

Both eyes should be used simultaneously, and it will require quite

a little practice before the observer will become expert in dis-

tinguishing differences in the distance between objects appar-

ently close together in the stereoscopic field and yet in different

frontal planes.

To test an observer's ability to see stereoscopically, Dr.

Pulfrich has constructed a stereoscopic " test-plate " (" Prue-

fungstafel fuer stereoskopisches Sehen "), which is issued together

with his treatise, " Ueber eine Pruefungstafel fuer stereoskop-

isches Sehen," published in the Zeitschrift fuer instrumenten-

kunde, Heft 9, 1901. The figures and diagrams shown in

that test-plate not only give the means for a quantitative test

but they are also designed for making a qualitative test of the

observer's stereoscopic vision.

Plates CII and CHI show roughly made diagrams for test-

ing stereoscopic vision in the quantitative sense only. The

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 315

Distance =Z>

in Meters.

Probable Error in Meters for the

Sporting Telemeter:

Base = 32 cm.,

Magnification 4.

Infantry Telemeter:

Base = 51 cm.,

Magnification 8.

Stand Telemeter:

Base = 1.44 m..

Magnification 23.

2O

3

40

0.05

O.II

O.2O

5

0.31

75

0.70

90

0.3

IOO

1 .25

-3

125

2.8

0.5

0.8

^"^""^

175

i.i

200

5-

1.4

300

400

"3

20. o

3-2

6

500

600

3i-3

9

2-5

2.8

700

17

3.6

750

800

900

IOOO

1250

Objects beyond

8 km. appear as

at infinite distance

23

29

35

4.4

6.7

9-9

18

1500

80

22

J 75

109

27

2000

2250

140

181

33

39

2500

223

54

2750

270

70

3000

35

320

no

156

4000

5000

6000

7000

8000

Objects beyond 28

km. appear as at

infinite distance

215

278

352

440

9000

10000

Objects beyond 230

kin. appear as in-

finite

circles, Plate CII, are numbered with their increase in distance,

No. i being nearest and No. 9 farthest. In Plate CIII the pyra-

mid is nearest the eyes; then follow the cross, concentric rings,

circle near the cross, large ring or circle (inclosing the figures),

central wheel with four spokes, cube, smaller circle (below the

316 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

cube), base of large cone, and finally the base of the small cone.

The axes of the two cones are not in line and the base of the

pyramid is not in a plane parallel with the large circle, its left

corner being tilted up a little. The Maltese cross, too, has its

upper two arms tilted forward toward the observer, the end

of the left upper arm being somewhat nearer than the upper

end of the right arm. A careful examination of these plates

will show whether the observer can see stereoscopically.

In looking into the stereotelemeter the aerial distance scale

should appear free in space, in a plane slightly raised toward

the distant end of the scale. As soon as the particular part

of the scale has been determined, by inspection, which coincides

with the object, the distance of the latter is obtained within a

certain margin of limitation, as already referred to in the pre-

ceding paragraphs.

The more expert the observer, the smaller the limit of differ-

entiation will be, although there will always remain a certain

margin of uncertainty corresponding to the limit of power of

the stereoscopic definition, as noted in the table previously

cited.

To become efficient in the rapid use of the stereotelemeter,

it is essential that the observer make himself thoroughly familiar

with the divisions of the aerial scale of his instrument. It should

be noted that the subdivisions of the scale apparently grow

smaller with increasing distance, and the observer should not

only be able to read off each actual scale mark quickly and cor-

rectly, but he should also be trained to estimate fractions of the

subdivisional scale lengths accurately. (Attention may be called

to the fact that the nearest half- reading between two successive

scale marks falls a little beyond the space center, the quarter

a little beyond the geometrical quarter- space, etc.)

Plate CI represents the measuring- scale used in the Carl

Zeiss hunting stereotelemeter. The marks of this scale are

arranged in four sections, the scale appearing as a zigzag line.

The first section, from 20 to 25 m., apparently appears in front

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 317

of the diaphragm or circle which incloses the scale. The four

sections control distances as follows:

(1) 20 to 25 m., divided into i -meter spaces;

(2) 25 to 50 m., divided into i -meter spaces;

(3) 5 to 7 m -> divided into 2, and 70 to 100 m., into 5 m.

spaces;

(4) loo to 1 60 m., in 10, 160 to 300 m., in 20, and 300 to

500 m., divided into 50 m. spaces.

The reproduction of this scale on Plate CI is faulty; inasmuch

as the triangular division marks 4 and 6, representing the 40 and

60 m. divisions of the scale, are considerably out of line, some

of the other marks show similar imperfections, but less marked

than these two.

The glass plate having the aerial distance scale etched into its

surface is also provided with a transverse scale (divided into

twenty equal parts, Plate CI) for measuring widths and heights

of objects. In the stereoscopic fields of the telemeters both

scales stand out very clear and distinct, being photographic

reductions of the large-scale originals.

For the first practice work with the stereotelemeter, well-

defined objects, preferably those that are silhouetted against

the sky, should be selected. The instrument is first directed

toward the sky, the interocular distance adjusted, and the eye-

pieces focused. The instrument is now gently revolved down-

ward until the object ranged upon appears in the lower field,

when the aerial scale should appear free in space above the

object. It will now remain for the observer to find that place

of the scale which coincides with the object (which will be in

the same frontal plane with it) to estimate the fractional dis-

tance from nearest scale mark to object.

The scale divisions are indicated by small triangles, the acute

angle pointing downward, and to determine the position of an

object with reference to the scale, the highest point of the object

3l8 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

is brought as close as possible to the imaginary line, connecting

the scale marks near the object, when the mark to the near side

of the observer and close to the object is picked out, the observer

estimating the distance of the object beyond this mark to arrive

at the actual distance. Should the mark just beyond the object

be observed, instead the nearer one as just stated, the tendency

generally seems to be towards overestimating the distance.

The Carl Zeiss firm has also constructed a stereoscopic telem-

eter without an aerial scale. The stereoscopic field of this

telemeter shows an index mark which is movable by the aid of a

micrometer screw. With this instrument several independent

measurements of the distance between two objects may be made,

similar in manner to the method of repetitions.

The Carl Zeiss stand stereotelemeter may be used at night

for estimating or measuring the distances of lights (vessels, light-

houses, etc.), by illuminating the scale on the diaphragm plate,

means for doing this being provided if a suitable lantern be at

hand.

The binocular microscope of the stereocomparator, of which

a description follows, is built after the model of the stereo-

telemeter, its telescope with prisms being here replaced by a

binocular microscope with reflecting mirrors, through which the

upright stereoscopic images are examined under enlargement.

B. The Stereocomparator and the Stereo photo graphic

Surveying Method.

The angle included at a distant point between the visual

rays from the eyes of the observer is known as the parallactic

angle, or parallax. The parallax increases when the point

approaches the observer and vice versa. For a point at in-

finite distance the two visual rays will be parallel; the parallax

will be =o.

The estimation of the distance of a point, when observed

with both eyes, depends largely upon the subconscious gaug-

ing, or mental measurement of the parallax. The distance of

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 319

an object when viewed with one eye only may still be estimated,

but in monocular vision such estimates must be based mainly

upon the degree of diminution in the apparent size of the object

if a familiar one, or the reduction in size of closely neighboring

bodies of which the actual sizes are known; for instance, a per-

son or an animal that may be standing near the distant object.

The stereophotogrammetric method is based on measure-

ments made simultaneously on two stereoscopic pictures show-

ing the same terrene and exposed from all the ends of a compara-

tively short base line. These simultaneous measurements, on

corresponding plate pairs, of the coordinates to locate identical

terrene points with reference to the horizon and principal lines

are made with the "stereocomparator," ingeniously devised by

Dr. C. Pulfrich, a member of the scientific staff of the Carl Zeiss

Optical Works in Jena!

The principle underlying the construction of the stereo-

comparator may be elucidated in the following manner, sug-

gested by P. Seliger of the Prussian Topographic Bureau. Two

pointers, made of black wire of equal thickness and of equal

lengths, when suspended over the face of two stereoscopic views

secured in a stereoscope will become superimposed and appear

as a single wire in the stereoscopic image of the two views.

If we now move one wire over the face of the picture, bring-

ing it a little closer to the wire over the other picture (we reduce

the parallax), the apparent position of the wire index in the

stereoscopic image will have become more distant, and as soon

as the distance between the two wires is made to coincide with

the interocular distance the superimposed images of the wires

will appear infinitely far off in the stereoscopic field. By thus

changing the relative positions of the two wires, the observer

can transfer their stereoscopic image to any point of the stereo-

scopic field.

All points of the stereoscopic image that are hi a vertical plane

parallel to the stereoscopic base have the same vertical distance

from the base line. Since the vertical distance of such frontal

. 320 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

plane has the sam^ ratio to the base length as the focal length

of the camera has to the parallax, we can compute such distance

if we know the parallax, the base and the focal length being

constant for every stereoscopic picture pair.

The stereoscopic picture pairs are placed on the stereocom-

parator to be measured through a binocular microscope similar

in construction as the Zeiss "stereoscopic telemeter," by means

of which the two coordinates and the parallax of any pictured

point may be measured, after optical bisection, by reading the

corresponding verniers of the three scales that are connected

with the stereocomparator. The data thus obtained suffice for

the cartographic location of the point in both the horizontal and

vertical sense.

Referring to Plate CIV, which shows the general arrangement

of the stereocomparator, we designate by

Pi and P2 the left and the right pictures;

H the rack-and-pinion motion for moving both pictures together

from left to right and vice versa;

M f a screw for moving the right picture alone and in the same

sense as the motion imparted by H\

M a screw for turning the right picture;

N a screw for raising or lowering the right picture;

T the turntable for the right picture;

5 a screw for moving the left picture independently from right

to left and vice versa; ,

R and h plates running in grooves, to be raised, lowered, or

moved transversely;

A and B scales for measuring the coordinates of points pictured

on both plates;

a scale for measuring the parallax of pictured points;

C binocular microscope; it may be raised or lowered by turning

the screw F, the amount of such change in altitude to be

read off within o.i mm. on the vernier of scale B.

To be viewed stereoscopically the two pictures Pi and P2

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 32!

are placed on their plates, R and T, in a position correspond-

ing to that they had when the exposure was made, with their

principal lines made parallel and vertical. If the base-line ends

are not of the same elevation, the right plate is raised or lowered

until corresponding points appear equally high when examined

through the binocular microscope.

The binocular microscope may be moved toward or away

from the negatives by turning E and each eyepiece is inde-

pendently adjustable to the eyes of the observer. The objec-

tives also are movable in the direction of the optical axes, to

give a range of magnification of 4 to 8 diameters. Two index

marks have been provided, one in each image plane of the micro-

scopes, for bisecting identical terrene points. By turning the

micrometer screw F the index of the right microscope may

be moved, changing the apparent distance of its stereoscopic

image. For one turn of the micrometer F the index will

be moved 0.2 mm., which would correspond with a change of

the right plate of 0.3, 0.2, and 0.15 mm., using a magnification

of 4, 6, and 8, respectively.

To find the parallax of a pictured point the stereoscopic

image of the index mark is set at apparent infinite distance and

both plates are now moved and adjusted until the terrene point

to be measured coincides with this index mark. The motion

of the right plate, accomplished by turning the screw M',

to bring the mark and point into contact, is read off on the vernier

a, which reads to 0.02 mm. By estimation, however, the

value for the parallax may be obtained within o.oi mm. After

the index has been made to bisect the point the readings of

the verniers A and B will give the coordinates of the pictured

point with reference to the left picture (left base station).

The main advantage claimed for the use of the stereocom-

parator in phototopography rests in the fact that one pointing

of the index on the point at once gives the elements for the car-

tographic location of the point, whereas with the plane-table or

radial method three distinct measurements would have to be

322 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

made before the pictured point may be plotted, involving the

separate measures of two abscissae and one ordinate. With

trie stereocomparator the coordinates are measured directly on

the negatives with microscopes and verniers, and the accuracy

obtained should be greater than obtainable with the plane-table

or radial method, using paper prints, dividers, and scales.

The index mark being placed upon each terrene point that

is to be plotted from the pairs of pictures, it is evident that the

better the definition of such points the closer will be their sub-

sequent cartographic location.

The three readings made on the scales A, B, and a give the

data for locating any pictured point (bisected with the movable

index mark) in regard to direction, distance, and elevation, and

with reference to the left station.

The abscissa oc (Plate CV, Fig. i), read off on scale A, is

plotted in the usual manner by laying off the distance on the

picture trace T from the principal point O, a line SR, drawn

through the end of oc from the left station S gives the line of

direction to the bisected point P.

The distance is ascertained from the vernier reading of scale

a which gives the linear parallax of the bisected point. The

distance may be computed from the equation

A:B=f:a,

where B is the distance between the two stations,

/ the constant focal length of the camera, and

a the parallax as read off on the scale.

In Fig. i, Plate CV, TT represents the picture trace,

x the abscissa of the point P, the plotted position of which

will be on the radial SR. The value for A, as computed

above, is laid off on the principal line from S. A parallel

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 323

to TT, drawn through the end of A, will bisect SR in P,

which is the horizontal projection of the bisected point.

Dr. Pulfrich recommends a graphical solution of the equation

of which the product B-f is a constant for every pair of pictures.

Referring to Fig. 2, Plate CV,

SSi = B= base line;

TT= picture trace of left picture;

a = vernier reading for parallax, laid off on TT from O.

If we now draw the radial Sr, the intersection of the latter

with 6*16, drawn parallel with SO, will cut off the distance

A on Sib, and the point to be plotted will be on the line

MN, drawn parallel to TT at the distance A from S. ' The

plotted position may now readily be found by laying off the

abscissa x from O and drawing the radial SR', the intersection

of the latter with M N locates the plotted position of the point P.

Fig. 3, Plate CV, shows the simple device suggested by Dr.

Pulfrich for the graphical solution of the equation for A.

A drawing-board is covered with a tough paper and a line SO

is drawn parallel with its lower edge. On SO, at a distance

1.5 /. from 5, a vertical UT is erected and a scale of divisional

parts equal to 1.5 mm. is laid off on UT. The line SO

is provided with a looo-meter graduation in the plotting- scale

(say 1:25000). LL is a straight edge secured to the board

parallel with SO. G is a transparent film of celluloid

attached to a brass strip k in such a way that it may readily

be slid along LL over SO. This transparent plate G has two

graduation, tt and /', in the reduced scale of the map. The

ruler SR, also provided with the reduced scale of the map

(1:25000), may be revolved about the pin in S.

To use this device the base line for a pair of plates is laid

324 PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.

off on //, say in tenfold scale of the map. After the parallax

a has been read off on the scale of the stereocomparator,

the ruler SR is placed on UT to cut off the length 100, and G is

moved until the base end, marked off on //, coincides with the

fiducial edge of SR. The corresponding value for A may now

be read off on SO, using the scale t r for the subdivisional parts

of 50.

To find the distance SP of the plotted point from the

left station S, the position of G is maintained unchanged,

while the edge of SR is made to coincide with that division

mark of the scale UT which corresponds with the abscissa

x of the pictured point. The distance SP may now be read off

on SR to be transferred to the radial SR, Fig. i, Plate CV.

The difference in elevation of pictured-point and left-base

station,

i

may also be found graphically. After the distance SP has

been read off, G is held in the same position and SR is

brought to coincide with that scale division on UT which

corresponds with the ordinate (read off on scale B of the

stereocomparator), when the reading of the scale //, between

SO and SR, will give the value for h in meters. Instead

of moving SR to bisect the end of the ordinate y on UT

it is desirable to use a multiple part of y, say icy, and

divide the final reading by 10. The elevation of the plotted

point is now derived from the elevation of the left station in the

customary manner, referring h to the elevation of the horizon

line of the instrument at the station and allowing for curvature

and refraction for points over 2000 m. distant from S.

The apparent length of the index mark in the stereoscopic

image plane of course corresponds to different heights, accord-

ing to the distance of the bisected object; the relation between

STEREOSCOPIC TELEMETER AND STEREOCOMPARATOR. 325

both, however, may readily be ascertained when the actual or

absolute length of the index mark be known. This length is best

found by bringing the upper end of the mark into contact with

a well-defined horizontal line in the picture and noting the read-

ing of the scale of ordinates (scale B), then bringing the lower

end of the mark into contact with the same horizontal line and

again noting the vernier reading of the scale B. The differ-,

ence between the two readings will equal the absolute length

of the index mark (=m).

The comparative length value =M of the index mark for a

distance =A may be computed from the formula

;;." - ,;-,. 7 ;.. M-J.A.

If the value for m be found 0.75 mm. and the constant

focal length of the camera be 250 mm. the value for M would

be 0.003 A. Now, say the lower end of the index mark coin-