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 14 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 14 of 33)
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The relation which exists between the position of a luminous
point (S) and that of its image (P) may be briefly expressed in
the following equation:

where, with reference to Fig. 87, Plate XLIV,

/= principal focal length of lens;

a = distance (SH=SiN) between the lens (its first nodal plane)

and the luminous point (5);
b= distance (NiPi) between the lens (its second nodal plane)

and the image plane


From the above equation we deduce


With these simple formulae any question concerning the
distance between the image and the lens (its focal planes) may
be solved.

We may have, for example, a lens of 15 cm. focal length
and the object (the luminous point 5, Fig. 87, Plate XLIV)
may be 50 cm. away from the lens. It is desired to find the
distance between the nodal and image planes (the distance P\Ni).

For/= 15 and a= 50 we find,

from b=-j,


= 21.4 cm.

I. Conjugate Foci and Conjugate Planes.

The image P v , Fig. 87, Plate XLIV, of a luminous point U,
situated on the optical axis of a biconvex or positive lens, will
also be on the optical axis of the lens, but on the opposite side
of the latter. The incident ray UIu, emanating from the axial
point Uj will be refracted beyond //, and its course may be found
by drawing a ray FH', parallel with UIu, through the first prin-
cipal focus F, which ray, after having traversed the lens, will
emerge in a direction H'Gu, parallel to the direction of the
optical axis. This fictitious or auxiliary ray H'Gu intersects


the second focal plane F\G\ at Gj/, and if we draw a line from
KU through GU it will represent the path of the emergent ray
originally emanating from U, and the intersection P v of FF\
with KjjGu will locate the image P v of the luminous axial point U.

The point U and its image P v (when axial points) are termed
" con jugate foci."

The planes TyPy and TV, both vertical to the optical axis
and passing through the conjugate foci U and P Uy are termed
conjugate planes.

K. To Find the Image of any Luminous Point for the
Biconvex Lens.

The image TV, Fig. 87, Plate XLIV, of any luminous point T.
in the conjugate plane UT may be found by locating the point
of intersection T v of the emergent rays of:

First, an incident ray TI IV M, drawn parallel to the axis FF\ ;

Second, an incident ray TN, drawn through the first nodal
point AT, and,

Third, an incident ray TF, drawn through the first principal
focus F.

If the conjugate plane TyPy had already been located,
the drawing of the third ray TF would suffice to locate the image
TU of T, as it is in the intersection of TjjPu with the emergent
ray H'T V of the incident ray TF.

Knowing how to locate the image P of any luminous point
S or T for the biconvex or positive lens we can now locate the
images of lines (as these may be regarded as a series of an infinite
number of points), and also of surfaces (being composed of an
infinite number of lines), provided the objects are not too far
away from the optical axis of the lens.

The image P of any luminous point 5, Fig. 87, Plate XLIV,
not on the optical axis is found graphically by locating the point
of intersection (after refraction) of the three following specific
rays emanating from the point S:


First. Draw a ray from 5 through the first principal focus F
and produce it to the intersection with the first nodal
plane at K, whence it continues in a direction parallel
to the principal axis (having passed through the first
principal focus).

Second. Draw a ray from S parallel with the optical axis
of the lens to its intersection HI with the second nodal
plane, whence it converges to the second principal focus FI
(having arrived at the lens in a direction parallel to its
optical axis) and produce it to its intersection in P with PK.
Third. Draw a ray from S to the first nodal point N; it
will pass through the second nodal point NI, and it will
emerge at E' in a direction E'P parallel to the direction
of the incident ray SI'N.

The image of any point 5 situated in a plane 55 1 perpen-
dicular to the optical axis will fall within the conjugate plane P\P.
In Fig. 90, Plate XLV, where similar points are designated
by the same letters correspondingly used in Figs. 87 and 89,
it has been shown how the image P'P\P of a line 55 15' may
be found if the incident rays are refracted by a biconvex lens.
The preceding definitions and formulae are applicable only
to light-rays which make small angles with the optical axis (for
lenses with diaphragm stops), and they serve to illustrate and
explain the formation of images.

More rigid (and consequently more complicated) formulae
would have to be applied to ascertain the best shape of lenses for
special purposes.

L. The Biconcave or Negative Lens.

The biconcave or negative lens produces upright virtual
images of originals which are beyond the principal plane, whereas
the biconvex or positive lens, as has been shown in Fig. 90,
Plate XLV, produces inverted real images of objects.

If the object UT, Fig. 91, Plate XL VI, is situated between


a positive lens and its principal focal plane FG, its rays will
produce a virtual upright image PU^U-

Incident rays that are parallel to the optical axis of a posi-
tive lens will converge to the principal focus of the lens, but
with the negative lens such rays will, after refraction, diverge
in directions coming from the principal focus.

It will readily be seen, with reference to Fig. 89, Plate XLV,
that the image PPi of an object SSi is upright and virtual.
The paths of the light-rays are given in full lines and similar
points are given the corresponding designation as in the pre-
ceding figures for the biconvex lens.

M. To Find the Image of a Luminous Point for a
Biconcave Lens.

To find the image P of a luminous point S beyond the prin-
cipal focal plane FiGi, Fig. 89, Plate XLV, three incident rays
are drawn:

5/i, parallel to the optical axis;

5/2, through the principal point F;

5/3, through the first nodal point N.

The intersection of the backward prolongation of the three
corresponding emergent rays, PEi, PE 2 , and PE%, will locate
the image P of the luminous point 5. These two points, P
and 5, are termed conjugate points, the same as mentioned for
the positive lens.

N. Lens Combinations.

In Fig. 92, Plate XL VI, a combination of a single positive
and one negative lens is shown. The positive lens may have:

FN = F 1 N 1 = focal length ;
FG and -FiGi = focal planes;
NM and N\H P = nodal planes.


The negative lens may have:

JFW = Fi'Ni' = focal length ;

F'G' and F\G\ = principal focal planes;

N'K and N\L = nodal planes.

To find the principal focal planes of the lens combination we
proceed in the same way as with a single lens, bearing in mind
that the incident ray of the second lens is now the emergent ray
of the first lens.

The line 57 represents an incident ray arriving at the positive
lens in a direction parallel to the optical axis; it is produced or
continued in its course until it reaches the second nodal plane
of the positive lens, where it changes its direction to one bisecting
the second principal focus of this lens. In this direction it is again
produced until it reaches the first nodal plane, in K, of the nega-
tive lens, whence it continues to the second nodal plane Ni'L
to the point L, the line KL being parallel to the optical axis.

Now we draw through the first principal focus F f of the nega-
tive lens the auxiliary ray YF' parallel with HFi. YX, drawn
parallel to the optical axis, intersects the second focal plane FiG\
of the negative lens in X, and XL will be the direction of the final
emergent ray; its intersection FI" with the optical axis is the second
principal focus of the lens combination.

This point, FI", may be checked with a second incident ray
Si/i, and F\"Gi" will be the second principal focal plane of this
lens combination.

In a similar manner two incident rays PI' and PI/I' arriving
at the negative lens from the other side of the combination, under
a direction parallel to the optical axis, will locate the first prin-
cipal focal plane F"G" of this lens combination.

The first nodal plane of this combination ( = N"a/3) is located
by determining the intersections a and ft of the original incident
rays P/' and . PI/I' with the final emergent rays F"T and FT\

The second nodal plane of this lens combination is fixed by


the intersections of the original incident rays 57 and Si/i with
the final emergent rays Fi'X and F\"Xi respectively.

0. Diaphragms or Lens Stops.

It had already been mentioned incidentally that diaphragms
are used to reduce the aberrations of light-rays which arrive at
the marginal zones of a lens, by excluding them from action
upon the photographic plate.

By selecting a sufficiently small aperture in the diaphragm
all rays may be excluded from reaching the interior of the camera,
which make an angle with the optical axis larger than the angle
controlling the limit of the central field of the lens that may be
regarded free from distortion.

This would comprise that effective circular disc of a lens for
which the preceding optical laws and rules have been given, as
the conditions are different for the extra-axial zones of a lens,
and those rules are not applicable to the latter. The laws given
in the preceding pages become less and less true the nearer the
outer margin of the lens is. approached.

By the insertion of a diaphragm stop, a more or less great
amount of light will be excluded from action upon the sensitized
film of the photographic plate, and the smaller the aperture in
the diaphragm the longer the exposure will have to be made in
order to reduce a given amount of silver in the sensitized film.

Generally speaking, the quantity of light admitted into the
camera will be proportional to the square of the diameter of the
diaphragm aperture.

P. Rapidity of a Lens.

Lenses with comparatively short focal lengths will produce
brighter images than such with long focal lengths, the brightness
of the image being inversely proportional to the square of the
focal length. The more light is allowed to enter the camera the


quicker the reduction of the chemical compounds of the sensi-
tized film will take place; the rapidity of a lens depends in a great
measure upon the quantity of light which the lens will suffer to
reach the plate.

Small apertures necessarily will permit more light to reach
the central part of the plate than reaches its extra- axial parts,
and photographs obtained through small diaphragm apertures
often are darker and lack good definition on the edges.

If the sensitive plate could be made less sensitive to the action
of the light in its central part than it is on the edges this draw-
back would be overcome, in a great measure at least ; practically,
however, the sensitized coating is of a uniform character.

If d represents the diameter of the diaphragm aperture, and
if / represents the focal length of the lens, then the rapidity of the
lens (or the brightness of the image produced with that lens)
will be proportional to the fraction

Q. Length of Exposure.

Generally speaking, the length of exposure that should be given
a plate is inversely proportional to the rapidity of the lens, hence
proportional to the fraction

R. Distortion Produced by Diaphragms.

When a diaphragm is placed in front of a positive lens so-called
" barrel-shape " distortion (Fig. 80, Plate XLII) frequently
ensues in the border regions of the image, and a diaphragm placed
behind the lens is apt to produce so-called " pincushion " dis-
tortion (Fig. 79, Plate XLII). It has been sought to compensate


these distorting effects by using two lenses and inserting the
diaphragm between them.

S. Chromatic Aberration of Light-rays.

The researches of Dolland, made with a view to reduce or
overcome chromatic aberration of telescopic lenses, led to the
combination of different glass compounds in the same lens, or
better, to the combination of two or more lenses each of which
was made of a glass mixture of different but well-known qualities
regarding both dispersoin and refraction. He was successful in
thus eliminating from the old-style lenses the greater part of the
chromatic aberration which shows itself in the more or less
pronounced appearance of colors on the borders of an image with
a simultaneous indistinctness of outline.

The improvement in this respect of all modern photographic
lenses is principally due to the results obtained in the optical
factory of Zeiss in Jena, where extensive experimental researches
were made by Dr. Schott by direction of Prof. Abbe. By a
judicious selection and combination of the glasses obtainable
from the works at Jena, opticians can now produce lenses more
fully answering the different requirements for the various uses
to which photography may be applied than has heretofore been
deemed possible.

Still, so-called achromatic photographic lenses cannot yet be
made free from all chromatic aberration, as no two kinds of glass
have yet been compounded to precisely counteract or neutralize
the refractive errors inherent to each.

That amount of aberration with which so-called achromatic
lenses still remain affected is known as secondary chromatic
aberration. It has been reduced to such a degree that its dis-
turbing effect in achromatic telescopes where small angles of
the field are only used disappears altogether, but in lens com-
binations for photographic work, and particularly in phototopog-
raphy (where large field angles are used), this permanent defect


is still seriously felt, particularly when short focal lengths of the
camera-lenses become desirable.

Achromatic photographic double lenses are composed of
two or three lenses each, the glass of the single lenses being care-
fully selected with a view towards overcoming the chromatic
aberration of the light-rays as much as possible.

So-called white or colorless light is composed of a series of
colored light-rays intermingled in such a way that their joint
effect is that of colorless light. The main characteristic of these
color rays with reference to our subject is " each of the different
light- rays that form the. component parts of white light has a
different refractive index for the same medium;" or, light-
rays of different colors will be refracted under different angles
for the same refractive medium. Red rays, for example, are
less refracted than yellow rays, and these again are less refracted
than the blue and violet light- rays for the same refracting medium.

If a pencil of white light be intercepted by a glass prism
it will become separated into its component color rays; each
different color, representing a different wave-length, is differently
refracted by the prism, each color having its own special index
of refraction.

The prism separates and disperses the different color rays
which compose the white light, and when the refracted rays
are cast upon a white screen in a dark-room, the band of colors
appearing on the screen is termed the spectrum of the particular
light used.

If a pencil of sunlight had been used in the experiment the
solar spectrum would appear on the screen and the red rays
will be less refracted than the orange, the green, the blue, and
the violet rays.

We had seen (Fig. 77, Plate XLI) that a biconvex lens may
be regarded as a series of concentric prismatic rings, one super-
imposed upon the other, and it will be Evident that a chromatic
lens will retract red rays less strongly than 'the orange, green,
or violet rays. The lens will have a shorter focus for the violet



and blue rays than it has for the orange or red rays, and the focal
length of such a lens will vary according to the particular color
of the emergent ray (Fig. 93, Plate XL VII).

As the retina of our eye is more sensitive to the yellow and
green light rays than to those of another color, we will, whem
focusing upon a landscape view, perceive the best definition
when the focusing-plate falls together with the focal plane of the
lens focus for the yellow or light-green light- rays.

Generally speaking, however, the ordinary photographic
dry-plate emulsion is less sensitive to yellow light and more
sensitive to blue or violet light- rays, and in order to obtain a
good negative, the plate should be exposed in the focal plane
of the blue or violet light- rays instead of being exposed in the
focal plane of the yellow rays, as it would be if exposed in the
position as determined with the ground glass for the best ocular

The distance D, Fig. 93, Plate XL VII, between the focal
planes of the yellow rays (active rays optically or visually) and
the blue-violet (or chemically active) rays is termed the chro-
matic aberration or variation of the rays. Lenses affected with
chromatic aberration have a chemical focus, differing more or
less from the optical or visual focus, according to the more or
less great amount of chromatic aberration by which the lens may
be affected.

Compositions of glass of different indices of refraction will
separate white light into spectra of different lengths. Lenses
made of glass having a small refractive index will show a small
difference in the focal variation D, Fig. 93, Plate XL VII (between
the focal lengths), of the red and violet light-rays. Such glass
is generally known as crown glass and its index of refraction is
from 1.5 to 1.6.

Lenses made of a composition of glass having a strong refrac-
tive power will show a greater focal variation. Such glass is
known as flint glass and its index of refraction is from 1.6 to 1.9.

Any crown-glass positive lens of a given focal length may


be matched with a flint-glass negative lens of a larger focal length
(Fig. 92) that maybe of such a refractive power to bring the chem-
ical focus of the combined pair almost into coincidence with the
optical or visual focus without annulling the entire refractive
power of the positive lens. A lens combination of this character
which still retains the characteristics of the positive lens (posi-
tive focal length and real image of a distant object) and which
is almost free from chromatic aberration is termed an achro-
matic lens combination.



PHOTOGRAPHIC surveying instruments have already under-
gone many changes and various patterns are in use in differ-
ent localities. Until quite recently photogrammeters were not
procurable in open market. Nearly every observer who made
use of the photographic method for topographic surveys had
an apparatus constructed especially for his particular needs and
according to his personal ideas. Thus we find:

First. The ordinary photographic field camera (with bellows
extension) converted into a surveying camera by a few
simple additions and mechanical modifications.
Second. A specially constructed surveying camera with a
constant focal length and special devices for leveling (to
bring the sensitive film into vertical plane).
Third. A surveying camera combined with some geodetic sur-
veying instrument (with a surveyor's compass, a transit,
or with a plane table). Such combination may be per-
manent, or it may be effected in such a way that the camera
is detachable and both may be used independently and

The practical value of a photogrammeter depends largely
upon the quality and general uniformity of the lens or lens com-
bination upon the rigidity of the component parts of the apparatus,
its transportability, and upon the rapidity with which it may
be adjusted and placed in position for use.



The principal lenses that have been employed for photo-
topographic purposes are Dallmeyer's rapid rectilinear, Stein-
heil's aplanatic, Busch's pantoscopic, Gorz's double anastig-
matic, Voigtlander's collinear, and more recently Zeiss's anastig-
matic lens.

The nodal points, the focal length, the arc of visibility, and
the arc which is perfectly free from distortion of any kind should
be known for every lens used for phototopographic purposes,
and the manufacturers of lenses of good quality are best fitted
to determine these values with great precision.


A good surveying camera or photogrammeter for topographic
work should produce negatives that are geometrically true per-
spectives. The elements of the latter should be known and the
following desiderata should be fulfilled:

First. The photographic plates should be adjustable in ver-
tical plane.

Second. The distance between nodal and image plane
should be maintained unchanged for all exposures.

Third. This distance the constant focal length must be
known, or will have to be determined for every instru-

Fourth. Means should be provided to trace the horizon line
(line of intersection of the horizon plane with the vertical
photographic plate) upon every negative.

Fifth. Means should be provided for locating the principal
point (the point of intersection of the horizontal optical
axis of the camera with the vertical sensitive plate) upon
every negative.

Sixth. A ready orientation of the photographs for icono-
metric plotting should be possible; and we may add as


Seventh. Enough characteristic stations (outside of the tri-
angulation scheme) are to be occupied with the camera
to give a full development of the terrene, which is to be

I. Ordinary Cameras (with Extension Bellows) Converted into

These survey ing- cameras have been constructed primarily for
economical reasons and their use should not be extended beyond
preliminary work or beyond surveys made for experimental study.
For extensive use the results will not be sufficiently uniform and

Such cameras are generally supported by three leveling-screws
upon a tripod and they are provided with a circular level /, Fig. 95,
Plate XL VIII, or with two cross-levels L, Fig. 94, Plate XL VII,
for adjusting the sensitive plate into vertical plane. The dis-
tance between nodal plane and photographic plate is made invari-
able, generally by means of two metal rods R, as shown in Fig. 94,
Plate XL VII (Werner's apparatus made by R. Lechner in
Vienna, Austria).

In Fig. 95, Plate XL VIII (apparatus of Dr. Vogel and Prof,
Doergens, made by Stegeman in Berlin, Prussia), this has been
accomplished by means of the clamp M. After the bellows
have been extended sufficiently to establish the desired focal
length, which may be read off on the vernier n, the screw M is
securely clamped. The pinion K with rack movement zz serves
to give the needed slow motion (when extending the bellows)
to set the vernier n.

Dr. G. Le Bon also used a modified field camera for his
archaeological researches in India, which were carried on under
the auspices of the French Ministry of Culture.

The braces H in Fig. 95, Plate XL VIII, and R in Fig. 94,
Plate XL VII, give the plate receivers a vertical position upon
the level extension boards.


The short brass points m in Fig. 95, Plate XL VIII, locate
the principal and horizon lines by their reproduction on the
negatives. They are brought into actual contact with the plate
(before exposure) by turning the buttons h, thus producing a
sharp image of their outlines on the margins of the negatives.

Fig. 96, Plate XL VIII, shows an arrangement for setting
the four teeth (which locate the horizon line hhi and the prin-
cipal line Wi on the negative) close against the sensitive film
surface, which has been used a great deal in Germany. By
turning the arms r the teeth may be brought into direct contact
with the plate, and when the camera should be used to obtain
pictures for their pictorial value only the teeth may be removed
from the plate by turning the buttons a, b, c, and d back.

The original Coast Survey Camera was provided with a
device which would operate all four teeth together by turning
but one button.

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 14 of 33)