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

. (page 25 of 33)
Online LibraryJohn Adolphus FlemerAn elementary treatise on phototopographic methods and instruments, including a concise review of executed phototopographic surveys and of publicatins on this subject → online text (page 25 of 33)
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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


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.


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-

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.


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


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.











1 .25













20. o












Objects beyond
8 km. appear as
at infinite distance









J 75


















Objects beyond 28
km. appear as at
infinite distance





Objects beyond 230
kin. appear as in-

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


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

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


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.


(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


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

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


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


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


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


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


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


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


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


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


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-

Online LibraryJohn Adolphus FlemerAn elementary treatise on phototopographic methods and instruments, including a concise review of executed phototopographic surveys and of publicatins on this subject → online text (page 25 of 33)