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 5 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 5 of 33)
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and center of projection, with reference to phototopography
we may premise, with reference to Fig. 2, Plate I:

A The picture plane VV (photographic plate) is sup-
posed to be vertical.
B Through the center of projection O (eye-point) a

horizontal plane HH is placed (" horizon plane").
C A vertical plane is laid through the center O, inter-
secting the picture plane at right angles in the line w;
it is the so-called " principal plane."
D A plane GG (" ground plane ") is placed parallel
with the horizon plane HH, but falls below it; the
distance OO between the two planes is equal to the
elevation of the point of view O (in the horizon plane)
above the datum plane (to which all elevations of
the survey are referred). The ground or datum
plane in iconometric plotting is identical with the
plan and it is represented by the surface of the paper
upon which the topographic map is being plotted.
The line of intersection gg, Fig. i, Plate I, of the ground plane
GG with the picture plane VV is known as the " ground line "
of the perspective.


The line of intersection hh, Fig. i, Plate I, of the horizon
plane HH with the picture plane VV is termed the " horizon
line " of the perspective.

The line of intersection vv of the plane (" principal plane ")
passing through O and intersecting the vertical picture plane VV
at right angles, Fig. 2, Plate I, is called the " principal line "
of the perspective.

The intersection O r of the two lines hh and w, Fig. 2, Plate I,
is the " principal point " of the perspective. It marks the point
of penetration in the picture plane of the " principal ray " OO f .
The principal ray is drawn from the center O (point of view
or nodal point) horizontally to intersect the picture plane VV
at right angles.

The point O\ where the vertical through the station O pierces
the ground plane GG is termed the " foot of the station."

The length of the principal ray OO', equal to the vertical
distance of the point of view O from the picture plane, is termed
the "distance line."

When the point of view coincides with the second nodal point
of a camera-lens this same line, the distance line, is known as
the "focal length" of the camera.

The perspective view a of a luminous point, A, Fig. 2, PL I,
in the vertical picture plane VV is identical with the point of pene-
tration of the visual ray OA, passing from the luminous point A
to the center of projection O (point of view or nodal point).

If we have several parallel vertical picture planes VV, V'V,
V"V", . . . , Fig. 3, PL II, the impression produced on the retina
of the eye at O will remain unchanged, no matter which plane
VV of the series may be retained in its position while the others
are removed.

All planes V'V', V"V",.;., placed parallel to the picture
plane VV are termed "front planes" and any line drawn in a
front plane will be parallel to the picture plane and is called a
"front line." Front planes may be placed either before or behind
the picture plane.


The perspective view ab of a line AB is found in the vertical
picture plane VV, Fig. 4, PL II, by joining the perspectives a and b
of its end-points. The perspective ab of a line AB coincides
with the trace produced in the vertical picture plane VV by a plane
(so-called "visual plane") passing through O and AB', it is the
intersection of these two planes.

The perspective a, b, c, d, e of a curve A, B, C, D, E is found
by locating the perspectives of a series of its points, a, 6, c, d, e,
Fig. i, PL I, hi the vertical plane VV and drawing a continuous
curve through these points. The perspective of a curve may
also be obtained by locating the perspectives of a series of tangen-
tial lines enveloping the curve. The perspective of a curve
a, b, c, d, e is the intersection with the picture plane of that conical
visual plane which contains the curve A, B, C, D, E as trace
and which has its apex in O.

To draw the perspectives of the superficial planes of bodies,
the figures inclosing the same (f.L, the perspective of the pentagon
A, B, C, D, E, Fig. 4, PL II) are drawn in perspective by con-
structing the central projections of their perimeters.

The perspectives of parallel lines when produced will inter-
sect each other in one point, the so-called "vanishing point."

The perspectives of all horizontal lines (AB and A '', Fig. 5,
PL III) have their vanishing point (D) on the horizon line hh
in the picture plane VV.

Lines perpendicular to the picture plane have the principal
point of the perspective as vanishing point (in the picture plane).

Horizontal lines intersecting the picture plane under an angle
of 45 vanish in the so-called "distance points" on the horizon
line, one on either side of the principal point. Their distances
from the principal point are equal to the distance line of the per-

The so-called upper and lower distance points are the vanishing
points for lines falling within the principal plane or that are
parallel with it and which intersect the picture plane under an
angle of 45. The distances of these two points from the principal


point are likewise equal to the distance line of the perspec-

Lines parallel with the picture plane, lines in front planes,
have no vanishing points in the picture plane. Their perspectives
are lines parallel to the original lines.

Vertical lines (are parallel to the picture plane in our case)
have no vanishing points and their perspectives are parallel with
the principal line vv, Fig. 5, PI. III.

Horizontal lines when parallel with the picture plane have
perspectives that are parallel with the horizon line.

The scale of a front plane is the proportion between the per-
.spective and the original. It is expressed by the ratio between
the distances from the station (point of view) to the picture plane,
the distance line, and that to the figure's front plane (the plane
containing the original figure).

The relationship between object (prism ABCD-A f B'C'D'\
picture plane (VV), and ground plane (GG) may be shown more
clearly with reference to Fig. 5, PL III:

O is the station, eye-point, point of view, nodal point, etc.
A vertical line passing through O will intersect the ground plane
in O\. The point Oi is the orthogonal (vertical) projection in
horizontal plan of the station O and it is called the "foot of the
station" O.

The perspective a\ of a point A i', situated in the ground plane
GG, is obtained by joining the foot of the station O\ with the point
A i', erecting a perpendicular to the ground plane in the point of
intersection a\ of O\A\ with gg and joining O with A\ . The
intersection of the ray OA\ with the vertical a\a\ just mentioned
will be the perspective of the point AI' of the ground plane GG.

AAi being a vertical line in space, its perspective aa\ will be
paraUel with the line w, and, if we draw the ray OA, its inter-
section a with the line drawn parallel to vv through a\, previously
found, will be the perspective of A.

To find the perspective of a line AB, the perspectives a and b
of its terminal points A and B may be located in VV and joined


by a straight line ab. Frequently it will be more convenient,
however, to use the intersection T of the line AB with the picture
plane VV together with the vanishing point D of the line ab to
locate the perspective ab of the line AB. This vanishing point D
is the intersection with the picture plane VV of a line drawn
through the station O and parallel with the line AB. If AB is
horizontal, the line OD will fall within the horizon plane and
intersect the horizon line hh at D.

The line TT' y which is the trace in the picture plane VV of
the plane ABA 'B', is termed the "vanishing line "of the plane


THE photographic camera produces perspectives upon the
photographic plate through the chemical action of the light
rays upon the sensitized film, and to establish the conditions
that are to be fulfilled, in order to regard a photograph as a true
perspective, we will first consider the so-called " pinhole pic-
tures," which are produced by a camera of the simplest form.

The pinhole camera consists of a box made entirely light-
tight with the exception of a minute hole O, Fig. 6, Plate IV,
in the front wall of the box. The rear side of the box is remov-
able and may be replaced by either a photographic plate-holder
or a ground-glass plate. With such a " camera obscura " photo-
graphs may be obtained without a lens or optical apparatus,
simply by means of the small round aperture O in the thin front
wall of the box.

I. Diameter of the Pinhole.

When exercising some care, the pinhole may be made by
burning it into a thin blackened cardboard with a needle heated
to red heat. The following table gives the diameter in inches
that may thus be burnt into the cardboard with needles of differ-
ent sizes:

Commercial number of sewing-needle 3 6 8 9

Diameter of burnt hole in inches 1/26 1/34 1/44 1/49




The best results, however, have been obtained with a round
hole carefully drilled into a sheet of copper or brass 0.2 mm.
thick. The border of the hole should be perfectly smooth, with-
out " burr," and it should be beveled that the hole forms a
truncated cone, the larger circle or base of the cone to face the
sensitized plate in the camera-box.

II. Length of Exposure.

The following table, published by F. C. Lambert, gives the
corresponding exposures, in minutes, for pinhole-camera expos-
ures, if, with the same plate-brand, identical illumination, same
subject, and a lens working at //i6, the correct exposure would
have been one second.

Distance of
Pinhole from

Diameter of Pinhole, in Inches.

the Sensitized

Plate Surface, in























3 2






3 2












This table plainly indicates that there is little danger of over-
exposing a plate in the pinhole camera, particularly as these
exposures are not strictly limited to the time given in the table;
they depend greatly on the general character of the plate, on the
developer, and on the general conditions of illumination during
the exposure, thus giving the operator a wide range regarding the
time limit erf the exposure.


III. Focal Lengths of Pinhole Cameras.

The depth of focus is practically unlimited, as shown in the
preceding table of F. C. Lambert. Still, there will always be a
certain distance between image plane and pinhole that will give
the best result for a given aperture, and Capt. Colson recom-
mends the following focal distances for a set of apertures of
four different sizes:

Diameter of pinhole in millimeters 0.3 0.4 0.5 0.6

The best definition is at a focal length, in centimeters . . . 1 1 20 30 44

Using the focal length corresponding to the size of aperture,
as given in the above table, the time of exposure for a plate in the
pinhole camera, compared with the exposure required when using
a lens under identical conditions and with a medium stop, may
be generally accepted to be:

25 50 100 200 times longer for a diameter of hole of:

0.3 0.4 0.5 0.6 mm.

The size of a pictured object, when photographed in a pin-
hole camera, is proportional to the ratio between the distance
of the object from the camera and the distance from the pin-
hole to the sensitized film surface.

IV. Determination of the Values of the Pinhole-camera Constants.

It will be a simple matter to determine the values of the con-
stants of a pinhole camera that are required to be known for
making iconometric constructions.

If the angles of the box are exactly 90, if the aperture is in
the point of intersection of the diagonals of the camera front,
and if means are provided for setting the camera level (for exposing
the plate in vertical plane), the two lines joining the opposite


middles of the four sides which compose the rear frame of the
box will represent the horizon line (HH) and the principal
line (VV) of the photographic perspective. The intersection (P)
of these two lines will be the principal point and the distance (OP)
between the aperture and the sensitive film surface will be the
constant focal length or the distance line of the photographic
perspective a, b, c, Fig. 6, Plate IV.

By referring to Fig. 6, Plate IV, it will readily be seen that
the rays of an object A, B, C, after passing through the aper-
ture O, produce an inverted image a, b, c on the photographic
plate. The image obtained in a pinhole camera originates in
the same way as a perspective is drawn, with the exception
that the picture plane V'V is not interposed between the eye-
point O and the original A, B, C, but is here placed behind the
eye-point, at a distance PO equal to OP', producing an inverted
and reduced image a, b, c of the original A, B, C.

By introducing the " negative " with the image a, b, c between
the eye-point O and the original A, B, C at V'V, Fig. 6, Plate IV,
and at a distance from O equal OP' = OP (in- and reverted),
it would become a " positive." P' being in the prolongation
of the distance line OP and VV intersecting the line OP' at
right angles, the line hh of the " positive " will be horizontal
and w vertical. The point a will again be in the point of inter-
section of the light-ray OA, the point b in the intersection of
the light-ray OB, and the point c in the intersection of the light-
ray OC with the plane of the positive VV. A positive copy
of a negative will be as true a perspective of the original as the
negative. Negatives, however, may be used for obtaining any
measurements that may be required from the perspective for
the iconometric plotting. Measurements are often preferably
made on the negatives, as the production of the positives without
distortion requires considerable care and experience, the amount
of distortion depending greatly on the character of the material
on which the positives are made.

The data given in this chapter may prove useful when a


pinhole camera is selected for phototopographic or photogram-
metric experimental studies in case of an emergency, or when
the cost of the apparatus must be considered, the pinhole camera
being recommendable chiefly on account of its cheapness and



UNDER " iconometry " we understand the measuring of
dimensions of objects from their perspective views (" Bildmess-
kunst "). It refers to the plotting of terrene forms directly on
the plotting-sheet from the photographs of the landscape.

If a photographic perspective of an object, the focal length
(" distance line "), the second nodal point (" principal point ")
of the camera-lens, and the horizon line of the perspective are
given if the point of view and the central projection of an object
are given these data will be insufficient for the determination
of the object with reference to position and size.

If, however, two such perspectives of the same object, obtained
from two suitably located stations, be given, the dimensions of
the object and its position with reference to the two stations may
be determined iconometrically, very much in a manner analogous
to that in which a point is located (by intersection or by the so-
called radial method) on the plane-table sheet by being observed
upon from two known plane-table stations.

I. Orienting the Picture Traces on the Plotting-sheet.

The positions of two camera stations A and A', their linear
horizontal distance A A' and two photographs, exposed in ver-
tical plane, one from each station, may be given. Each picture
may, furthermore, contain the image / of the same object 7*
and the image a of the other camera station, Fig. 7, Plate IV.



After the base line A A' has been laid down in reduced scale
AiA^ y Fig. 7, Plate IV, and the pictures MN and M'N' are
brought into the same relative positions with reference to the
line AiAi', which they had with reference to the base line AA f
in the field at the time of their exposure, the position T of the
point pictured as / and t' on the respective pictures MN and
M'N' may be located (with reference to the line A\Ai f ) by
drawing the radials A\t and A^ti ', when their point of intersec-
tion will fix the relative position of T with reference to A\ and A.

The position of T on the map, plotted to scale with refer-
ence to the reduced base line or with reference to the plotted
stations A\ and A\', would be found by projecting the point
of intersection T into the plotting or ground plane.

A topographic map being the orthogonal projection of the
terrene forms into horizontal plan, the horizontal projections
into the plotting-plane of the rays A\t, A\a\ f , A\1f, and A\a are
used to locate the plotted positions of pictured points / and a
and the horizontal projections of the picture planes (which now
become " picture traces ") are utilized in this connection, instead
of actually using the pictures in the iconometric plotting as was
indicated in the diagram of Fig. 7, Plate IV.

In order, therefore, to plot the horizontal projection T\ of
a pictured point / with reference to the plotted base line A\A\' >
it will become necessary to ascertain the correct positions of
the picture traces with reference to A\ and -4i' it will become
necessary to " orient " the picture traces hh and h'h', Fig. 8,
Plate V.

This orientation of the picture traces forms a very important
part in iconometric plotting, as the subsequent fixing of loca-
tions of pictured points is accomplished mainly by bringing
the horizontal projections of their radials (lines of horizontal
directions drawn from the different stations to identical terrene
points) to intersect. Any error in the orientation of the picture
trace produces corresponding errors in the plotted positions of
pictured points.


A. Iconometric Plotting when using a Surveying Camera only.

A base line measured in the field may have been plotted to
scale, AiAi', Fig. 8, Plate V, and two pictures, MN and M'N',
Fig. 9, Plate V, may have been obtained from the camera sta-
tions A and A' respectively by means of a surveying camera.
The focal lengths of the pictures =/ and /' respectively, the
positions of the principal points P and P f and the horizon lines
HH and H'H' may be known. It is desired to locate T\ with
reference to the plotted base line A\Ai f .

Wehave4iPi=/; 4i'Pi'=/'; the length of the base =4i4i',
and the abscissa /iP = /iPi, *i'P' =/i'Pi', Pa/ =Pia/, P'a l = Pi'a lf
Figs. 8 and 9, Plate V.

The distances A\ai'j and Ai'ai, Fig. 8, may be found graph-
ically by constructing the right- angle triangles A \P\a\ and
Ai'Pi'ai, or they may be computed from

These distances are laid off upon A\A\ from A\ and from A\'
respectively a semicircle is described over each length, A\a\
and Aidi, and two circles are drawn about A\ and A\ with
/ and f respectively as radii. The intersections of these two
pairs of circles will locate the horizontal projections PI and P\
of the principal points P and P' on the two picture traces hh
and h'hf, the latter being represented by the tangents P\a\
and Pi'ai.

B. Plotting the Picture-trace when using a Camera or

In this case the angles a and a', Fig. 8, Plate V, may be
measured directly in the field and plotted on the base line AiAi',
a at A i and a' at A\ . We lay off the distances



(found by construction or computation) and describe circles
about A i and A i with / and /' respectively as radii. The
tangents drawn from a\ and a\ to these circles will locate P\
and PI respectively when PI/I should equal tiP=x, measured
on the picture MN, and PiV = PV=^ on M'N'.

When using a phototheodolite a well-defined point T may
be bisected with the principal lines VV and F'F', Fig. 9, Plate V,
from the two stations A and AI, in which case these angles of
orientation are laid off upon the base line at AI and at AI re-
spectively, and the distances / and /' are laid off on the lines
AiTi and A l r T l respectively (=A 1 P ] _ and =A l 'P l '), when the
perpendiculars to A\P\ in PI and to A\P\ in P\ will represent
the picture traces hh and h'hf in correct orientation with refer-
ence to AI, AI, and T\.

When the pictures of several triangulation points B, C, and D
and the base line are given, the orientation of the picture traces
hh and h'h' upon the plotting-sheet may be accomplished as
follows :

The radials A\B\, Aid, A\D\ . . . , as well as the radials
A\B\, Ai'Ci, Ai'Di . . . , are drawn upon the iconometric plot-
ting-sheet, the points BI, C\, DI . . . being already plotted on
the same. The points 61, ci, P, d\, and a\ are then transferred
from the horizon line OO\ of the photographic perspective MN,
Fig. n, Plate VI, upon the perfectly straight edge of a strip
of paper, which now is placed upon the radials converging to A\,
as a center, Fig. 10, Plate V, and moved about until

bi falls upon the radial line

r tt (i n ( ( tt

" " " " "
" " " base "

The line A\P\ should then be perpendicular to the straight
edge hh of the paper strip, Fig. 10, Plate V, and the line hh,
drawn along the paper strip's edge on the plotting-sheet will



represent the oriented picture trace of M,N\ A\P\ will be the
distance line and PI the horizontal projection of the principal
point P.

The same having been done regarding the point A\ r , its
picture M'N' and the paper strip OiO/ (Fig. n, Plate VI),
both picture traces hh and h'h' will have been oriented. The
plotted positions of any other pictured points that may be iden-
tified on both pictures MN and M'N' may be similarly located
by plotting their abscissae (measured on the horizon lines OOi
and O'Oi') upon the picture traces hh and h'h r (Fig. 10, Plate V)
on the proper sides of the principal points PI and PI'.

Lines drawn from the station points A\A\ through such
corresponding points, transferred to their respective picture
traces, will locate the relative positions of such points on the
plotting-sheet by their points of intersection.

II. Arithmetical Determination of the Principal and of the
Horizon Line on the Photographic Perspectives.

In the preceding paragraphs it has been assumed that the
photographic perspectives were already provided with the prin-
cipal and the horizon lines. Such, in point of fact, would be
the case with an adjusted surveying camera or phototheodolite.
If the instrument is out of adjustment or if an ordinary camera
be used (one provided with a device for maintaining the image
plane in a vertical position during the exposure of the plate),
the correct positions of the principal and horizon lines, as well
as the length of the distance line, must be ascertained. In photo-
topographic work this may be accomplished in various ways.

A. Determination of the Principal Point and Distance Line of
the Photographic Perspective.

A plumb line suspended in front of the camera in such a
way that the line iru, Fig. 12, Plate VI, may be photographed


upon the negative will serve to establish the direction of the
principal line on the trial plate. This negative may, further-
more, contain the images a, b, c ... of three or more points A y
B, C, . . . of known positions and elevations. A line hh is drawn
at right angles to the pictured plumb line w on the photographic
perspective and a strip of paper is placed with its straight edge
along this line. The images a, b, c ... of the known points

A, B, C . . . are projected upon the paper straight edge, held
in position at hh, by drawing parallels to vv through these pic-
tured points.

After the radials from the plotted station Si, Fig. 12, Plate VI r
have been drawn through the plotted points A\, BI, C\ . . .
the paper strip is adjusted upon those radials in such manner
that the image projections ai, bi, c\ . . . (previously marked

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 5 of 33)