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 31 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 31 of 33)
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this same degree of accuracy in the angular values of the lines of
direction may be obtained iconometrically from the panorama

The plotting from photographic perspectives being dependent
on the measurements of coordinates made directly on the pho-
tographic perspectives, the attainable degree of accuracy will
greatly depend both upon a good definition and upon the mathe-
matically correct representation in perspective of the landscape
upon the flat field of the perspective (negative).

The precision in the mechanical determination of the coor-
dinates of any point pictured in the photographic perspective
depends not only upon the more or less good definition of the pic-
tured point, but also upon the means used for measuring these
coordinates. According to Dr. Meydenbaur, the definition of a
photograph obtained with a suitable lens will be sufficiently
good for phototopographic purposes if a point, or rather its
" phase," or the circle of diffused light that represents the point on
the picture, does not exceed o.i mm. in diameter; hence all pic-
tured lengths should be obtainable within a limit of dxdy^o.i
mm. Unless special measuring devices are employed, this
value will also represent the attainable degree of accuracy in
making direct measurements on clear and well-defined nega-
tives with ordinary drawing instruments (dividers and trans-
verse scale). It is evident from the foregoing that a computa-
tion carried out to several places of decimals (analytic method)
cannot increase the accuracy of the resulting map as long as the
elements of the perspectives upon which such computations
are based have been obtained with a degree of accuracy not
closer than o.i mm. All iconometric plotting being dependent
on direct measurements executed on the photographic plates,


the transcription of the pictured data into the horizontal pro-
jection plane is best done graphically.

Numerous experiments have shown that 0.14 mm. is the
smallest discernible difference in length that the average eye
may distinguish without optical aids. With a beveled' scale
graduated to 0.5 mm. a fairly well-trained eye can determine
lengths correctly within o.i mm., while a well-trained eye reaches
the limit at 0.06 mm. By the use of special scales fitted with
verniers and microscopes the attainable degree of accuracy in
the measured lengths may be increased to reach 0.03 mm.

The attainable degree of precision in the angles may be found
from the equations


tan a= (for horizontal angles),


tan/?= (for vertical angles),

where x = abscissa of the pictured point;
}' = ordinate of the pictured point;
D= distance line of the perspective.

By differentiation we find
d tan a =

If we express x by an aliquot part of D, x = , and disregard


f x\ i
rj) = ~a an d introduce the arcs in place of the tangents of the


angles, we will find


da (in seconds of arc) = 206265-^-;

d^ (in seconds of arc) = 206265-^-.

These equations show that the angular errors are directly
proportional to the degree of accuracy attainable in the measured
lengths (on the photographs) and indirectly proportional to the
focal lengths of the lenses that are used. Assuming the attaina-
ble degree of accuracy in the measured lengths to be dx = dy=o.i
mm., we will find the attainable degree of accuracy for the
angles for the following five focal lengths to be:

For a focal length = 20 cm. the angular accuracy is i' 43"

it t( ii _ ~ ^ < < (( it << << T / -//

ti tc 11 =20 '' ll tl tl l( T f on"

(( _.,- ' ' C/ Co"
" " " =40 " " " " lt o' 52"

The longer the focal length of the lens the smaller the angu-
lar error will be, and although it is desirable to have the photo-
graphic details as large as possible for a better identification
of the terrene points on different photographs and to increase
the attainable degree of accuracy, still, to reduce the weight of
the instrument as much as possible the focal length will natu-
rally be circumscribed for instruments to be used in mountainous
regions, where portability and compactness are among the prime
factors to be considered in their construction.

The attainable degree of accuracy for any particular camera
may be ascertained experimentally, after the methods of Dr. W.
Jordan and Capt. E. Deville, by observing a series of horizontal
and vertical angles, included between lines of directions, to a
senes of well-defined points of known positions and elevations,


taking also a photograph of the same points (in vertical plane)
from the same station and from the same elevation. The hori-
zontal optical axis of the camera should have the same height
as the horizontal optical axis of the transit telescope when the
angles were measured, or the difference in the elevation between
both should be taken into account.

The focal length of the photographic perspective and the
correct positions of its horizon line and principal point may now
be determined from the requisite number of observed directions
to the known and plotted points. The remaining angles, meas-
ured in excess of the required number just referred to, may
well be used for comparison with the corresponding values,
obtained iconometrically from the oriented picture trace, to
arrive at a knowledge of the attainable degree of accuracy of
the camera in question.

If the camera-lens was of good quality (for surveying pur-
poses), if the selected points were well denned (both in nature
and on the negative), if the sensitized surface of the plate con-
tained no gross inequalities or irregularities, and finally, if the
measurements of the coordinates were carefully made on the
negative, the lengths obtained iconometrically on the plotting-
sheet, compared with those obtained trigonometrically, should
differ by no more than o.i mm. in actual length, and the icono-
metric angles should differ from those that were observed by
no more than from i to 2 minutes in arc for objectives with
focal lengths from 350 to 150 mm. and commanding a hori-
zontal field of view from 50 to 60 degrees.

This degree of precision may be increased by a reduction
in the field of view of the lens by using plate glass for the nega-
tives and by making microscopical measurements of the coor-
dinates of the pictured points. Still, when photography is applied
in this way, including precise computations (analytic method),
for surveying purposes, one of its main advantages is lost sight
of and sacrificed, since one of the chief advantages in photo-
topography rests in the numerous and varied constructions (based


on the laws of perspective) that are available in transferring
the photographically recorded data to the plotting-sheet.

The attainable degree of accuracy in the elevations obtained
iconometrically may also be ascertained in the manner indicated,
but the results will only hold good for points having the same
distances as those observed upon with the transit from the camera

To find the limit in the distances that are to be included
for a certain lens when a given degree of accuracy in the ele-
vations is to be maintained, we may proceed in the following
manner :

We have the known relation


where a = distance between object and second nodal point of

the lens;
b= distance between image and second nodal plane of

the lens;

/ = constant focal length of the camera-lens.
We had seen that the elevation (B) of any pictured point
above the horizon line stands in the same relation to the ele-
tion (A) of the point itself, above the horizontal plane that passes
through the horizon line, as the horizontal distance (b) between
lens and image is to the horizontal distance (a) between the
lens and the horizontal projection of the point itself.


*L = J_

A a-f


In topographic surveys the distance a will be so great compared
with / that the latter may be neglected in comparison with a,
and we will have, with close approximation,

- L A 't

Ad B

Hence, whenever the considered distances a are large com-
pared with the focal length, we may place & = /, which means
that the photo topographic cameras may be constructed with
constant focal lengths, which in point of fact is the general

If differences in the elevations of points of the terrene are
to be deduced photogrammetrically within a limit of error not
exceeding one meter, the pictured length (B) of a meter in nature
(A) should not appear shorter than o.i mm., and we find for
the following four typical values of focal lengths the correspond-
ing values for a, representing the extreme distance limit between
the camera station and an object one meter high that is to have
a pictured height of at least o.i mm. as follows:

a=75om. 1000 m. 2000 m. 2500 m.
for /= 75 mm. 100 mm. 200 mm. 250 mm.

It would require the exercise of special care and the measure-
ments of the coordinates would have to be made directly on
the negatives if this limit of error is to be maintained. Care-
fully made contact prints permit measurements to be taken
(with the ordinary instruments of the draughtsman) correctly,
with an average error of not less than 0.25 mm., and taking
this limit as commensurate with good work, we will now have:

<z=3oom. 400 m. 800 m. 1000 m.
for /= 75 mm. 100 mm. 200 mm. 250 mm.

These \alues clearly demonstrate the necessity for a close
disDOsition of the camera stations over the area to be surveyed


(from 600 to 2000 m. apart) for detailed work, thus materially
circumscribing the 'advantages of phototopography, practically
excluding its application to the topographic surveys of rugged
mountains, a terrene for which the phototopographic methods
are best suited and to which, as a matter of fact, they have pri-
marily been applied with the greatest success as long as larger
errors (exceeding one meter) in the elevations were permissible.
Thus, if the error in the iconometrically determined elevations
may attain twenty meters, and if the coordinate measures may
be correctly obtained on the prints within an error of 0.25 mm.,
we will find the following values for the effective range for the
same four focal lengths to be:

a 6000 m. 8000 m. 16000 m. 20000 m.
for /= 75 mm. 100 mm. 200 mm. 250 mm.

For a permissible error in the elevations of twenty meters
the camera stations may be located at intervals of from 10,000
to 40,000 meters, for cameras with focal lengths from 75 to 250
mm., provided the character of the terrene does not require a
closer disposition of the stations to obtain a better development
of the intervening terrene forms.

Attempts have been made to increase the effective range of
the surveying-cameras by constructing them with variable or
adjustable focal lengths; this, however, produces complications
and opens additional sources of error. Better success in this
direction has been obtained indirectly by using photographic
enlargements (" optical projections ") of the original negatives
in the iconometric plotting. This method is successfully pursued
in Canada under Capt. E. Deville, Surveyor-general of Dominion
Lands, who advises the use of enlarged positives on glass for work
requiring a high degree of accuracy.

If the reconnaissance of a given terrene has established the
greatest limit between the camera stations to be 2#, we can,


for a required degree of accuracy, find the proper focal length
of the camera from the equation

The accuracy attainable in iconometric plotting depends
greatly upon the distances between the several camera stations.
We had seen that the precision of a plotted line of direction
depends upon the accuracy with which the abscissa x may
be transferred from the photographic perspective to the plotted
picture trace. The camera station being fixed, the accuracy
in the direction of the ray will depend solely upon the value
or the amount of the error dx with which the measured abscissa
x may be affected. With a given limit dx for a constant
focal length /, the error in position of a plotted point will increase
with the distance of the latter from the camera station. All
plotted points falling between the picture trace and the plotted
camera station are affected by no errors larger than dx, and if
the permissible limit of error in the map is not to exceed dx,
we will have to select the camera stations sufficiently close together
that no points are determined iconometrically which fall beyond
the traces of the pictures from stations whence the latter were
obtained. The base-line lengths are plotted to scale, while the
constant focal length of the camera enters into the iconometric
construction in its original length; hence the reduced lengths
separating successive camera stations on the plan should not
surpass the true focal length /. For a scale of map of i/n
the largest base line should be ^j-n, measured in millimeters.
For a focal length of / = 2oo mm. and a scale of map of 1/20000
the base line should not exceed 200 X 20000 mm. or 4000 meters,
measured in the plotting-scale.

All elevations determined from the photographs should be
corrected for curvature and refraction. Refraction apparently
affects directions more in the vertical than in the horizontal


sense. Prof. S. Finsterwalder found in his phototopographic
surveys made in 1888 and 1889 that the accuracy in the ele-
vations increases directly with the distance of the observed point.
The elevation of a point 500 m. or less distant from the camera
station was three times less accurately obtainable, iconometric-
ally, than the elevations of points between 2500 to 5000 m. dis-

Generally speaking, terrene points determined iconometrically
will not be provided with signals, and the identification of a well-
defined point on several photographs may be affected by an
error of from one to two minutes in arc. Even points that may
have been supplied with signal poles of the ordinary size and
length, when five hundred meters and more distant from the
camera stations, will appear on the photographs as having no
signals, yet when viewed through the telescope of the ordinary
field transit, the same poles may appear very clearly and well
defined, even at distances up to several kilometers. Artificial
signals will, therefore, be of little use in general iconometric
plotting; still, as well-defined points are a necessity to insure
good results, the camera stations should be located not too far
apart, and thp selected reference points of the pictures should
not only be sharply defined, but the instrumental measurements
to the same objects (to provide the needed data for the orienta-
tion of the picture traces and for the control) should be made
as nearly as possible at the time of the exposure of the plates,
that such points may be seen under the same conditions of illu-
mination that prevailed when they were photographed.

Regarding the expeditiousness of the phototopograghic
methods considered in the preceding chapters, it may be stated,
from the experience of Dr. S. Finsterwalder, that so-called
topographic surveys of mountain regions, for which an artistic
representation of the terrene, 'in conformity to its natural appear-
ance, may be claimed rather than accuracy, may be made by
an expert plane-tabler, combining liberal sketching with the
instrumental survey, on 1/25000 scale in less time than it would


take the phototopographer to select, locate, and occupy the
camera stations required for an " accurate " phototopographic
survey to be plotted on i/ioooo scale. This holds good for
surveys in mountains of an Alpine character and sparse vegetation.

Besides the errors considered in the preceding paragraphs,
there still remains another source of error to be considered in
the photographic developing and fixing process of both the nega-
tives and their positives. Distortion in the sensitized gelatine
coating of the modern dry-plate during the process of develop-
ment is rarely perceptible if the work is carefully done to avoid
so-called " frilling " of the film. The mean value of such dis-
tortion, according to Dr. H. C. Vogel, amounts to o.oi per centum
of the length, and as the plates used in phototopography are'
never large, the errors due to this cause may be disregarded

The distortion in the positives (particularly if made on paper
that requires subsequent development), however, is mostly so
large that it must be considered when using such prints
iconometrically. This distortion, moreover, is irregular, being
smaller in the direction with the grain or fibers of the paper,
where it may amount to 0.5 per centum of the length, and larger
in the direction across the fibers, where it will amount to about
i per centum. The constants of the camera, therefore, and
the coordinates of the principal points of control should pref-
erably be obtained from the negatives. For the iconometric
plotting of the topographic details enlarged projections on bromide
paper may be used. Capt. Deville has recently substituted a
heavily coated " platino-bromide " paper for the ordinary silver
bromide paper heretofore in use. The length of exposure for
the enlargement is made directly dependent upon the density
of the original negative.

To give ready means for controlling or correcting the dis-
tortion affecting the paper prints nearly all modern surveying-
cameras are provided with a metal frame permanently fixed in
the image plane of the lens with constant focal length, the inner


margins of the frame having a graduation that is photographically
reproduced on the outer margins of the negative; thus the amount
of distortion that may affect the positive can readily be ascer-
tained in the directions of both the horizon and the principal
line of the photographic perspective. " Backing " the paper
prints would open another source of error even greater than
those just referred to. Dr. Stolze observed a permanent expan-
sion of five per centum for prints that had been mounted while
in a damp condition.

III. General Remarks on Telephotography or Long-distance


The range in the field of application of photography to sur-
veying and military reconnaissance has been considerably enlarged
during the past few years by the invention of the telephoto-
lens combination, used for obtaining well-defined photographic
views of objects at long distances, sacrificing or reducing the
angular value that the plain lens commands for the sake of
enlargement of the view, producing thereby the same effect as
if the view had been taken from a point of view much nearer
to the distant object.

Long-distance photography (" telephotography ") was proba-
bly first studied in France, principally by Matthieu and Lacombe,
and more recently by Guillemont and Jarret. This subject
continues to receive much attention in France, particularly among
the army officers stationed at Grenoble, as has been mentioned
in Chapter I. Quite recently telephoto instruments have been
devised and placed upon the general market by Hondaide
and Derogy in Paris. The lunette d'Etat-Major, one of the
smaller types of telephoto instruments, manufactured by Arizard
in Paris, controls distances up to 5 km. and weighs only about
8 kg.

The Intelligence Office of the British War Department is
also doing a great deal towards promoting the efficiency of the


telephoto instruments and towards familiarizing British officers
with the telephotographic reconnaissance methods. The inven-
tion of the telephotographic lens combination is ascribed by
Th. R. Dallmeyer to Peter Barlow, who combined a negative
lens with the astronomical telescope as early as 1834.

Researches in long-distance photography have notably been
made by T. R. Dallmeyer, London; Dr. A. Miethe, Potsdam;
Dr. Steinheil, Munich; Prof. R. Spitaler, Vienna, and others.

One of the main defects in phototopography rests in the small
scale to which the distant landscape features are reduced on
the negative, requiring precise and minute measurements to be
made on the negative in connection with the iconometric con-
structions. This defect is primarily conditioned by reducing
the weight of the survey ing- cameras to a minimum. Cameras
with constant focal lengths are principally in use for topographic
surveys in mountainous regions, where the reduction in weight,
as previously stated, means a great deal toward ultimate success.
For this class of work the use of objectives of long focal
lengths is precluded ano\ we find topographic- surveying cameras
supplied with lenses having constant focal lengths from 75 to
350 mm.

In the preceding chapter the effective ranges of four-lens
types have been discussed, fully demonstrating the desirability
of providing means for obtaining special perspective views of
terrene sections lying beyond the reach of the ordinary camera-
lens, for certain inaccessible localities and particularly for mili-
tary reconnoitering purposes.

By adding the so-called telephoto attachment to the original
camera-lens an enlarged image of the view is photographed
directly on the plate (in the field). The use of the telephoto
attachment (it may easily be removed) has the advantage that
the selection of the distant views rests entirely with the topog-
rapher in the field, as he can best decide whether by taking
such a telephotographic view from one of the ordinary camera
stations a lengthy trip of the party in that direction may be saved,


or whether a special advantage may be derived from a series
of such views taken during the occupation of some prominent
or isolated peak. In short, the phototopographer can best tell
whether time may be saved by supplementing the ordinary pano-
rama views with some special long-distance views.'

In high altitudes mists and clouds frequently hide the higher
peaks from view for weeks at a time, and it may often save many
days of waiting if the phototopographer be provided with a
telephoto attachment for his camera-lens, to enable him to photo-
graph distant terrene features that may casually be visible on
a clear day while taking the panorama views for the develop-
ment of the topography in the immediate neighborhood of the

The topographer may not see the same peaks free from " cloud -
hoods " again during the rest of the season, at least not from
that particular direction. It will seldom require more than one
such telephoto view in several panorama sets, the critical points
pictured on the other plates being near enough to the station
not to need special enlarging.

Little regarding the telephotographic results, obtained prin-
cipally under military auspices, reached the general public
until Dr. A. Miethe, in Germany, and T. R. Dallmeyer, in Eng-
land, each apparently independent of the other, published de-
scriptions of their telephoto-lens combinations. The . principal
difference between their combinations seems to be that Dall-
meyer uses a " portrait-lens " in connection with the " nega-
tive-lens combination," while Dr. Miethe combines a photo-
graphic lens of the " rapid landscape type " (Steinheil's) with
the negative combination. The construction of both these
telephoto objectives rests upon the same principles, and their
combination is composed of two biconvex lenses interposed
between the camera-lens and the sensitive plate. By changing
the distance between the biconvex lenses more or less enlarged
images will be photographed on the plate. These enlarge-
ments are made at a sacrifice of the field of view commanded


by the camera-lens alone, and it would require a large number
of plates to cover the entire horizon with telephoto views; still,
in phototopography the general panorama views will be taken
with the simple camera-lens, adding the telephoto attachment
only for special views of distant " heads," or saddles of valleys,
inacessible mountain peaks, etc.

Since the " negative element " of the telephoto combination
lens produces a picture of the distant view hi the image plane
of the camera with a sharp definition and a richness in detail

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 31 of 33)