Telescopes and Rangefinders
Die Fernrohre und Entfernungsmesser. Berlin: Springer, 1923.
A. Koenig, PhD, Zeiss Works
Berlin, Springer Publishing, 1923
Translated by Ilse Roberts and Peter Abrahams
Text of this translation only, copyright 1996
[Translator’s note: Koenig uses a most obutse grammar, even for technical
German of 70 years ago. For example, many times an object will be referred
to as ‘Teil’ (part), with no grammatical logic to tie it to a particular
object, to the point where it is unclear if it is a part of a binocular or
of an earlier paragraph. For this reason, specific points of interest in
this paper should be checked with the original. Almost all of the
translation is accurate, and the parts that made least sense were those most
carefully checked.]
4. The Prism Telescope (Porro Telescope, 1850), [p52]
The image reversal of an astronomical telescope can be accepted during
astronomical and geodetic work, considering its simple construction.
However, the advantages of an erect image are obvious, especially for
orientation. In recent times, this is achieved by inserting a system of
flat mirrors or prisms. The effect of the reflections is often illustrated
by the image of a vertical line that rotates around the optical axis as it
is reflected. The optical axis is defined by a ray through the objective,
and the reflections off the prism faces must return the imaginary line to
vertical. With two mirrors, like a pentaprism, the image of the vertical
line in the reflected ray is rotated twice. In a pentaprism, two
reflections of 45 degrees each cause the exiting ray to travel at 90 degrees
to the original direction. The erect image has up and down correctly
oriented and a horizontal line in the landscape appears horizontal in the
field of view. Clockwise rotation of the image is described as positive.
An image rotated by 180 degrees is reversed; an erect but backwards image is
side reversed, and an upside down image is called height-reversed. An image
in a perpendicular mirror appears side-reversed. By rotating the mirror
around an axis perpendicular to the approaching ray, all orientations are
seen; except near zero degrees, where the usable ray bundle becomes too
narrow from foreshortening, and the mirror must be replaced by an isosceles
prism. Fig. 47 shows the effects of such a right angle prism at different
angles. For common crown glass, if the entrance angle is larger than 41
degrees, total reflection takes place and the mirror does not have to be
silvered. [p53]
[Fig. 46. The pentaprism of Goulier.]
[Fig. 47. The right angled prism, with different deflections.]
[Fig. 48. The ‘double turning’ prism.]
[Fig. 49. The reversing prism of Delaborne.]
In common glass, the width of the penetrating ray bundles is 1 : 3 for 0
degrees and 180 degrees reflections, and largest at 90 degrees and 270
degrees. The effects of refraction upon entering and exiting, are
especially seen in colored edges on distant objects. If the entry and exit
surfaces form the same angle to the reflecting surface, the refractions act
like a parallel surfaced sheet of glass inclined to the ray axis. Fig. 48
shows two prisms, bases together, where the bundle width is doubled, with
reflections from both sides; to avoid double images, the reflecting surfaces
have to be exactly parallel. If this prism is rotated around the axis of
the line of sight, the image is turned by twice the angle that the prism is
moved. In this usage, the simple prism is called the Amici reflection prism
or reversion prism. As the prism is rotated 90 degrees, the image is turned
upside down. If two of these prisms are set, one behind the other, with one
base perpendicular to the other, the image is reversed vertically and
horizontally, (fig. 49). (In this and the following diagrams, the center
ray is a solid line, the paraxial rays are dotted lines, and the arrows
showing image position are shown in the entrance and exit surface.) With
this pair of prisms, no image rotation occurs when the system is rotated
around the axis of the line of sight. This independence of image from prism
is valid for all ‘straight sighted’ [in line] reflecting systems with an
even number of reflections; and valid for all ‘back sighted’ [view objects
behind observer] reflecting systems with an odd number of reflections.
Prism systems reverse the image when they are in line with an odd number of
reflections, or ‘back sighted’ with an even number. [p54] The double prism
of Delaborne has a 90 degree mirror angle that rotates the image 180 degrees
around the mirror axis (identical to the axis of the line of sight). It can
be used to erect the image in an astronomical telescope, and in the 17th
century, mirror systems were used for this purpose. This 90 degree
reflection can also be realized in a roof prism, see fig. 50. Here, the
reflecting surfaces are used twice, first by one half of the rays and then
by the other half. The roof planes must meet at exactly 90 degrees to avoid
a double image. A cross section of the ray bundle through a prism of common
glass, is a square, whose side is about one sixth of the length of the roof
ridge. The roof prism can be modelled as a simple prism of proper
orientation, with additional image rotation. These prism erecting systems
have the disadvantage of being limited to use in nearly parallel ray
bundles, in front of or behind the telescope, because of the distortions
from their inclined entrance and exit planes. There is usually no room
between the eye and the ocular. To put the prism between the lenses, which
saves space and material, the entrance and exit planes should be
perpendicular to the light. This is also true for a prism that deflects the
light, such as the 90 degree Amici prism in fig. 51. For ‘straight through’
prisms, silvering is used, see fig. 52, the Abbe prism. It is easier to
understand when one imagines mirrors instead of roof ridges, giving a
similar light path but different rotation to the image. [or...when one
imagines perpendicular mirrors that do not rotate the image]. [p55] In
these two figures, a larger second form is shown by thin lines, which allows
cemented parts. The smaller first form has less requirements for material,
but the larger allows a greater parallel diversion of the light rays.
[Fig. 50. The ‘straight-sighted’ roof prism.]
[Fig. 51. The deflecting roof prism of Amici.]
[Fig. 52. The reversing prism of Abbe.]
[Fig. 53. A telescope with the reversing prism of Daubresse.]
[Fig. 54. A telescope with the reversing prism of Leman.]
[Fig. 55. An ‘around prism’ with a ‘back-sighted’ roof prism.]
The Abbe system uses a reflecting surface in front of and behind the
roof. The two mirrors can both be placed in front of or behind the roof
prism, see fig. 53 and 54. In fig. 53, the Daubresse prism, two surfaces
need to be silvered. The Leman prism in fig. 54 can be made in one piece,
and any surface can be made into the roof and produce image reversal. The
Daubresse was soon improved so that one of the surfaces of the pentaprism
was replaced by a roof, see fig. 66. A roof prism with a different
orientation, fig. 55, can have its roof removed to allow much easier
manufacture without its high tolerances. This results in the Porro I
system, fig. 56, consisting of two ‘back-sighted’ right angle prisms, which
simulate two pairs of mirrors, each pair of two at a 90 degree angle to each
other. The Porro I system can also be broken down into 3 or 4 prisms.
[p56] The image reversal in this system (fig. 55) comes from two 180 degree
turns around the axes of the surfaces which are perpendicular to each other.
The Porro II system (fig. 57) can be derived from the form in fig. 52 (as
can fig. 55), if the designer gives an increased deflection to the outer or
end mirrors. The Porro II can be built of two symmetric prisms or of three
or four right angle isosceles prisms. Both Porro forms can be cemented.
Fig. 156 shows a deflecting prism system with four silvered surfaces. Fig.
58 shows a ‘straight sighted’ system (Daubresse) with six silvered surfaces,
built of two identical ‘back sighted’ prisms; each prism deflects the beam
by 90 degrees three times, and each reflection is perpendicular to the other
two. It can be imagined as built of three adjacent simple prisms, in fig.
58, the first and third are drawn in faint lines. The prisms rotate the
image by 90 degrees independently of the turn from entrance to exit, but
turns it to the left or right depending on which way the light travels
through the prism. The image can be erect or reversed, depending on the
construction of the whole system. When stretched out, it shares with the
roof prism a flat, compact construction form.
[p57] Concerning the position of the prisms between the objective and the
ocular, the prism system can be made smaller when it is placed at the point
in the light path of the smallest cross-section of the ray. This is usually
immediately in front of the ocular (fig. 54). In that regard, the systems
in fig. 52 and 57 are best, because of their smaller deflection of the ray.
For some prism systems, light loss can be diminished by cementing the
prisms, and some light is lost when silvering of prism faces is needed. A
smaller tube length is often desirable for binoculars and sighting
telescopes. This can be achieved by cutting the tube into three parts,
placed adjacent to each other and thus increasing the instrument cross
section. This scheme found wide distribution in handheld Porro I prism
telescopes, see fig. 59.
[Fig. 56. The Porro I reversing prism.]
[Fig. 57. The Porro II reversing prism.]
[Fig. 58. One half of the system, for the reversing prism of Daubresse,
which has 6 reflecting surfaces.]
[Fig. 59. A prism double telescope designed by Abbe.]
[Fig. 60. A prism pair from the Brewster telescope.]
The effect of the prism system on the quality of the image is equal to a
reticle, perpendicular to the ray axis, that is as thick as the path of the
chief ray through the prisms. Prisms can have an effect on spherical and
chromatic aberrations, and astigmatism and image curvature. The objective
can be corrected for ‘axis deviation’. An imaginary thick reticle that
fills the entire space between a thin objective and the focal point of the
objective, would diminish image curvature by one third and astigmatism by
about one half.
The Brewster telescope is a scientific curiosity, it has no spherical
surfaces and uses only reflecting prisms. Fig. 60 shows a parallel ray
bundle through each of the two prisms, uniformly diminished in the plane of
deflection. Color is dispersed in a different direction than ray deflection
and so is neutralized. Magnification occurs in the plane of deflection, as
a function of the diminishing of the ray bundle, and the image is contorted
as it would be if on a flexible surface that is turned in one direction. A
number of these prism pairs, in crossed position and behind one another,
produce a telescopic effect, with a usable image at weak magnification.
5. The Terrestrial Telescope [p58]
Lenses can be used instead of prisms in a telescope, and they were used
exclusively for many years, and are still advantageous in some cases. This
design was described in 1611 by Kepler, in 1645 by Schyrl zu Rheita, and so
is also known as the Rheita telescope. If a telescope is placed behind
another, so that the entrance pupil of one almost lies in the exit pupil of
the other, the combination instrument gives an erect image and a total
magnification equal to the product of the powers of the two telescopes. If
the desired magnification is near 1, the front telescope is a diminishing
one, with an objective built like an astronomical ocular, and the ocular
like an objective. In effect, one telescope is directed against the other,
and the pair of objectives directed against each other is called a reversal
lens. For a given diameter of lenses, a longer tube is often needed for
this type of telescope. The best performance is given by utilizing the
following design. The field of view determines the longest possible focal
length of objective and ocular. The focal length f(u) of the erecting
lenses are equal to, or almost equal to, the tube length if this is large
compared to the objective and ocular focal length. From this is determined
the magnification of the second telescope, and the diameter of the exit
pupil with a given diameter of erecting lenses. The exit pupil can be made
larger by (n squared) times, when at an equal objective f.o.v. of 2w’ the
tube diameter D is enlarged n times, or the length L is diminished by (n
squared) times. Since D:fu = d:f, then D = (square root of (Ld(tg)w’)) -
approximately. If a degree of shadowing of the f.o.v. is permitted, the
length can be increased by separating the reversal lenses; which can also be
cemented together for other purposes.
[Fig. 61. Ray passage in a terrestrial telescope.]
A terrestrial telescope with greater magnification usually has a doublet
objective like an astronomical telescope. The terrestrial ocular in its
simplest common form consists of 4 separate thin planoconvex lenses. The
ray passage in fig. 61 shows that the objective and the field lens of this
ocular can together be considered as an objective similar to the Huygenian
ocular design. [p59] The second lens of this ocular is the reversal lens,
the third and fourth lens together are a common Huygenian ocular. A
terrestrial ocular with a f.o.v. of about 40 degrees is corrected similarly
to a Huygenian ocular; distortion is less, but curvature or astigmatism is
stronger, because the deviation from the Petzval condition is larger. On
axis spherical and chromatic aberration are stronger, and the objective is
often compensated to correct for this, but correction is possible for a
single ocular focal length only.
[Fig. 62. Draw tube telescope, magnification 17 power, field of view 1.9
degrees, exit pupil 2.5mm]
The on-axis defects can easily be corrected by increasing the number of
lenses, but significantly corrected image quality at the edge of the f.o.v.
has not been achieved. Off axis errors increase with a decrease in ocular
length, given an identical telescope focal length. An increase in ocular
length causes on axis errors to appear, as zones of spherical aberration and
secondary spectrum. These also get worse with an increase in f-ratio. The
most practical focal length for the astronomical ocular, contained within an
erecting ocular of length L and focal length F, is given as follows.
Astigmatism must be kept to a minimum. The erecting system has two parts,
of focal lengths f1 and f2, with a parallel ray passage between them. The
terrestrial telescope can be thought of as three partial astronomical
oculars, with the first two directed towards each other. The Petzval sums
must be kept to a minimum. If the Petzval sum has the same ratio to the
power for each part ocular, then the sum of their power is minimized. We
therefore limit ourselves to the simpler case, by supposing that the
distance between the image-side pupil and the object side focal point is 1:m
times the focal length, for all ‘partial oculars’. Thus, for the complete
ocular, the object-side focal point is the one in which the image appears.
It follows that f1 + f2 + f3 = mL. Also, (f3)(f1):(f2) = F. Calculating
this shows that for the equation f1 = f3 = –F + (square root(F2 + mLF)) for
F = 1 at mL = 10 : f1 = f3 = 2.32, f2 = 5.37; and at mL = 5 : f1 = f3 =
1.45, f2 = 2.1. This analysis explains especially well the following
curious ocular. After the rays pass through an astronomical ocular, they
are reflected back into the ocular by a mirror perpendicular to the axis,
which intercepts only half of the exit pupil. After the second passage, the
rays are reflected again, by a mirror placed in half the field stop, back
through the ocular. If one now looks through the other half of the exit
pupil, one sees in the mirror at the field stop, the erected reversed image
of the object, in half of the field of view.
An observation telescope is a terrestrial telescope with a straight axis,
used especially by the Navy, and usually retractable with one or more tubes
to shorten it for storage, and an extension for focusing (fig. 62). [p60]
A stronger magnification of 10 to 30 power is preferred, and light intensity
is low because a low f ratio leads to a greatly diminished image sharpness
towards the edge of the field of a terrestrial ocular.
6. Telescopes with Adjustable Magnification
Magnification can be changed either in a smooth transition within certain
limits, or with several available, predetermined powers. Focus on the
object must be maintained in either case. For a smooth adjustment, the
distance between lenses or spherical mirrors is changed, by moving the
lenses or by moving inner prisms, especially the ‘back sighted’ 90 degree
Porro I prisms. These telescopes are described as changeable magnification,
as pancratic, and were formerly known as ‘polyaldische’. The image should
stay in focus at the various magnifications, requiring the movement of at
least two lenses for larger changes. This pair of lenses must be corrected
to give a good image at all positions. They must each be chromatically
corrected. Near the middle position of the pair, spherical aberration must
be improved on and off axis, and simultaneously achieve the largest or
smallest value. This last requirement can be fulfilled for two moving
lenses by placing the pair at mid-telescope and symmetric at magnification
of plus or minus 1. A corrected image at various powers can also be
achieved by assigning most of the movement to one lens, which moves a
distance equal to the square of the movement of the other lens. This also
avoids larger movements of the exit pupil. The first part (magnification
lens) causes the change in magnification, and the second part (focusing
lens) maintains the position of the image plane. The second part is usually
either the ocular or an inner lens, perhaps the field lens of the
terrestrial ocular. The first part (a) the erecting lens of the ocular is
shifted, (b) the back lens of the objective is combined with a front
diverging lens and a rear collecting lens, together shifted for effect. At
middle position, magnification is –1, when a collecting lens is placed in
line (c), magnification is +1, (a diverging lens is less suitable). [p61]
Omitting the focusing lens and splitting the magnifying lens into two parts
is one approach. Depicted in fig. 63 is an approximation of this, shifting
the middle changes the magnification, and changing its distance functions to
focus the image. A weak magnification uses a ray passage shown by unbroken
lines, and higher power is shown in broken lines. If the shifted lens also
acts as an aperture stop, the diameter of the exit pupil is proportionally
reduced less than the magnification. If a change between only two
magnifications is desired, the shifting of the focusing lens can be omitted.
If the two positions of the magnifying lens are symmetrical to its position
for a power of + or - 1, it will magnify in one position as much as it
reduces in the other.
[Fig. 63. Ray passage in an erecting system for a pancratic telescope.]
[Fig. 64. A small observation double telescope with changing oculars.]
The most common method for changing magnification is to change oculars.
It is preferable for this purpose to mount the oculars on a revolving disc
(fig. 64), or for periscopes on a ring (fig. 121). The diameter of the exit
pupil is inversely proportional to the magnification. Changing objectives
allows the advantage that the exit pupil for the various magnifications can
be evened out. To retain the same length of the telescope, an objective of
longer focal length can be devised as a teleobjective, which has a
collecting lens in front and separate diverging lens behind it. The
distance between the front lens and its focal point is less for a
teleobjective than for a thin lens of equal focal length. The ratio is
reversed in an objective of short focal length, with an objective with a
diverging lens in front and collecting lens in the rear (fig. 72 on page
66). The disadvantage of this arrangement is that the position of the
sighting lens cannot be exactly maintained for measuring or aligning when
changing the magnification. [p62] If the position of the sighting lens is
important only for high power use, a special lens can be inserted into the
ray path of a common telescope (usually in front of a reversed dutch
telescope), to reduce magnification and increase f.o.v.. The boundaries of
the rays in this reversed telescope (fig. 65) can be very different than the
usual galilean telescope (p43). The objective can also be changed by
reversal or by insertion of prisms. The apparent f.o.v. is usually
determined by the astronomical ocular used, for all these types of
magnification changing devices.
[Fig. 65. Magnification changes with reversed telescope b-c, of about 2
times magnification.]
7. Periscopes
[Fig. 66. Periscope for hand use.]
[Fig. 67. Field periscope.]
These are used to provide the observer a view from an inaccessible or
dangerous position, for example to observe from a hidden position behind a
tree, an embankment, or over higher obstacles, and especially from a command
post. Entrance and exit pupils are offset by a distance, and are usually
parallel. When viewing to the front, the periscope can be used from a lying
or a standing position without modification, therefore it will be discussed
as standing only. Both magnifying elements and transfer elements are used,
depending on the need for weak (less than two power) magnification. Ten
times magnification is popular for military use with a fixed standing
periscope. These days, the tendency is to use stronger power, especially in
alternation with 10 power. For observing from behind cover, the objective
can be raised about 30 cm, but more recently it is raised to 50 cm. [p63]
The prism telescope is well suited for this. It is possible to move part of
the prism erecting system, most often placing it in front of the objective,
with the other prism in front of the focal plane (fig.66). A common
telescope can be used for occasional observation from behind cover by
placing in front of it a vertical tube with two parallel deflecting mirrors
that reflect the light by 90 degrees each. The field periscope (fig. 67) is
used for observation from dugouts, behind trees, or over larger obstacles.
This is a terrestrial telescope with a simple objective prism and ocular
prism for deflecting the optical axis. The light rays are parallel between
the reversal lenses, and a ‘between telescope’ [Zwischenrohren] can be
inserted at this point to provide a viewing height of 4 to 6 meters from the
foot of the observer. A higher view, from 9 to 26 meters high, is provided
by the mast telescope [Mastfernrohr] (fig. 68), which replaces the insecure
observation ladder. This is built onto a specially outfitted wagon, the
mast is placed in it for transport, and it is used as a platform for
observation with the extended mast, which is anchored by ropes in higher
winds. The lenses are of a large diameter, and are stowed next to the mast
in an upper compartment that is extended with the mast, and in a fixed lower
area. The top of the mast houses the objective and field lens only, and
consequently the magnification is reduced with the viewing height, and focus
changes as well. The mast is turned for viewing to the side, and for
vertical adjustment of view, the objective mirror is tilted via extendable
rods in the mast. [p64] A wider field can be viewed by lowering the
magnification to one or two power, by adding a scaled down Galilean
telescope (p62).
[Fig. 68a. The mast telescope at high observation height.]
If the objective prism is rotated to scan the horizon, the exiting rays
describe a cone around the tube axis, and the view in the ocular rotates to
upside down and back, as in other periscopes. The rotation of the image can
be cancelled by inserting a reversal prism and turning it at half speed
(fig. 69). The rotation of both prisms is coupled by a common conical wheel
differential gear (fig. 70). [p65] An indicator connected to a ring dial
in the field of view displays the direction of view. The panoramic sight is
most important as a cannon sighting device (p121).
[Fig. 68b. The mast telescope at lower observation height.]
[Fig. 69. The path of the rays in a panoramic sight.]
The [wiederholende = repeating, refers to transfer lens] type of
periscope is especially important for diving vessels, for it serves as their
eyesight. Typical magnification is one and a half power, since when viewing
through a tube, the objects seem to become somewhat smaller, and so at 1.5
power, a natural impression is maintained. The objective is usually 6 to 7
meters above the ocular. Fig. 71 shows the ray passage, explained on p58.
The upper part of the tube is often tapered in recent periscopes to reduce
water resistance. To change magnification from 1.5 to 6 power, the double
prism and both reverse [inserted] telescopes (p62) contained in the
objective head, are turned by 180 degrees around the bending point (fig.
72). A multiperiscope typically has 8 periscopes together in one tube with
a common erecting system, so that the horizon is distributed into 8 partly
overlapping fields.
[Fig. 70. Panoramic aiming sight by Goerz (p121)
[Fig. 71. Submarine periscope. P1 objective prism. O1 objective. K1 field
lens. O2-O3 erecting lens. K2-O4 ocular. P2 ocular prism. B1 & B2 first &
second image]
[Fig. 72. Changing magnification with a [Vorschalt = reversed, switched,
inserted] telescope. V1’-V2’ magnification. V1-V2 reducing reverse
telescope. P1-P2 double prism. O1 objective. K1 field lens. If O1 is
‘affiliated’ with V2’ and V2, then the objective has been changed.]
[Fig. 73. Ring image periscope. R1 ring mirror lens. O1 objective. P1
objective prism with right angle reflecting plane. K1 first field lens. O2
first erecting lens. 03 second field lens. B1 first image. B2 second image.
[p67] To view the entire horizon at once, there is a Ringbildsehrohr
[ring image periscope], which uses a ring mirror lens (fig. 73). The Aldis
form of this uses point by point imaging, and the ‘entrance plane’ is a
sphere around the axis point, half as high as this plane. The ‘exit plane’
is a sphere around the axis point, where the exiting main rays cross. The
mirror surface is a hyperboloid with these two axis points as focal points.
The image produced by the ring is virtual and about one half power. In the
middle of the ring is an image produced by a separate objective, so that the
combined view is similar to fig. 74. The central image from the objective
must be reversed from the usual periscopic image, so that the upper part of
the ring image appears upright. Fig. 73 shows the objective prism used,
which projects an image that is reversed from the image from a simple prism.
A diverging lens can be used as an objective with a simple prism for the
same result (fig. 75). The Mattscheibensehrohr [frosted glass focusing
screen periscope] uses a ground glass disc M in the focal plane, and an
ocular O2 can be used interchangeably (fig. 76). The image in the ground
glass disc is much dimmer and therefore can only be used with good light
conditions, but it allows the use of both eyes. A binocular periscope gives
a better image to both eyes, but has a much larger diameter. The periscope
can be turned and pushed in and out in a ‘stuffing box’, to observe from
different heights over the water and to completely retract, for under water
dives. [p68] For comfortable observation at all angles, an observing chair
is coordinated with the periscope.
[Fig. 74. The field of view of a ring image periscope.]
[Fig. 75. Ring image periscope with negative lens (3) as objective, and roof
penta prism (9) as ocular prism.]
[Fig. 76. Ocular head for frosted glass focusing screen periscope.]
[Fig. 77 Standing periscope of Humbrecht.]
[Fig. 78. Standing periscope of Blum.]
A captain must observe other instruments as well, and the separation of a
standing periscope with fixed viewing point from them has driven further
improvements. The standing periscope in fig. 77 reflects the light rays
with an additional prism P2. The focal length of the instrument grows by
double the distance v that P2 moves down. [p70] Between the erecting
lenses O2 and O3, the rays are parallel, and to maintain focus, the distance
between the two lenses is increased by v. Fig. 78 shows another design,
where the elimination of P2 changes the ray path & effectively lowers the
observer. When retracting this periscope, only the upper optical part to O2
is moved. The effective elevation is increased while O3 keeps its position,
with the device next to it with toothed wheel R1 and pulley. When the
objective head is completely retracted, O3 is drawn down as well; and the
ocular prism P2 is then automatically folded out of the way. The drawing
also shows a mechanism to read off the semi-circle for the side device in
the ocular.
8. The Mirror Telescopes (Reflectors) [p70]
Reflectors are telescopes where the refracting surface of a spherical
lens is replaced by a mirrored surface. One such instrument, proposed in
1639 by Mersenne, corresponds to the dutch refractor design, with a concave
spherical mirror replacing the objective and a convex mirror for the ocular.
In reality, this substitution works only for the objective and the erecting
system. Reflectors can be separated into pure (catoptric) and mixed
(catadioptric), and only the catoptric have been successful. All reflectors
are difficult to design so that the light is accessible to the eyes in such
a way that only a small amount - or none - of the rays are blocked (the use
of half-silvered mirrors is not a practical option). One solution is to
tilt the mirrors from perpendicular to the optical axis. The Herschelian
design is the simplest of these, and can be traced back to Lemaire (1732).
It uses a concave mirror tilted against the axis for an objective (fig. 79),
and is ‘backwards sighting’ and gives an upside down image. The mirror was
usually an f10, the largest made by Herschel had a diameter of 1.22 meters.
If the entering rays were at an angle to the optical axis of the mirror of
1.5 degrees, the difference between the sagittal and tangential widths
[diameter as intercepted by incoming rays] is (f(sin tg i)), in this case
4.2mm. At 400 power, this would deliver 4 diopters of astigmatism to the
eye. [p71] This large an aberration must have been balanced in the
grinding procedure. A distortion of 1:100mm at the edge of the mirror would
correct it. The Newtonian design (1672) avoids a tilted mirror by using a
second mirror (Fangspiegel = catching mirror) or prism to divert the rays by
90 degrees, so that a sharp image is provided at the rim of the tube (fig.
80). This telescope has an exit pupil at the side and gives an image
reversed right to left. The secondary has to be large enough to capture a
bundle of diameter D2:2F (D and F are the diameter and focal length of the
objective). If it is required that there be no shadowing at the edge of the
field, the diameter of the secondary has to provide a light cone larger than
the aperture stop of the ocular. Among larger Newtonians, the Lassell has
the same ratio as the Hershel, while the Parisian has a focal point of 7.15
meters with the same aperture. To reduce the size of the secondary,
Foucault let the image be produced closer to the secondary and observed with
a terrestrial ocular; the idea of tilting the secondary so that the observer
is next to the objective has no practical value since the disadvantages of
the terrestrial ocular are greater here than for Foucault’s design.
However, if the secondary is spherical, [p72]
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10 Binocular Vision [p85]
Two resources can be distinguished in the use of the eyes to judge
distance. One is the experiences stored in the memory of visual
impressions, which can only give an idea of distance. This includes the
knowledge of size and form, deductions of overlaying objects, placement of
shadows, and haze in the air in front of an object. [p86] The second
resource gives a real sensation, and includes the feeling of accomodation,
impressions when moving the eye and body, and the simultaneous use of both
eyes. The sensation of accomodation is not precise, but allows recognition
of approaching or receding objects. The other two are both based on
comparison between images in perspective, seen from different viewpoints.
Motion gives consecutive views with the overlay of one object in regards to
another of a greater or lesser importance. The simultaneous use of both
eyes allows immediate recognition of depth structure, which can be judged
with great exactitude. The two eyes see different fields, and the
difference is immediately felt as depth differences, even though most people
are unaware that the images on the two retinas are different. If two
photographs are taken from the locations of the two eyes, and then presented
to the eyes so that they appear in the same angle and position as the
object, a spatial impression is given that is identical to the view of
reality. The different perspective of the two cameras or the two eyes cause
this depth perception. The viewing line for binocular viewing is the
bisector of the angle of the viewing line of the single eyes. One sees as
with one eye in the middle, between the two eyes.
[Fig. 98. Depth distinction with binocular vision]
The distance between the eye pupils A and B that receive the perspective
(fig. 98), is called the basis (b). The eyes are perpendicular to the
basis. Point P in the f.o.v. is between viewing lines AS and BS from the
eye pupils. The distance PC = Ep of the point P from the plane through AB
perpendicular to the viewing line = b : tg (eta), where eta = APB is called
binocular parallax. The difference (delta eta) between the parallax of two
points at distances E’p and Ep with the difference (delta)Ep is: (delta eta)
= b(1/E’p - 1/Ep) = (b delta Ep)/(E’p Ep). Experience shows that delta eta
is relevant to the recognition of depth, even when viewing a near point from
the small basis AB. The measurable threshold value of delta eta is about
the same size as for ‘Nonius’ focusing (p15). At a threshold value of delta
eta = 10 seconds, objects at a distance of 1300m are just distinguishable from
infinity at a medium interocular distance of 65mm, and the object itself has
no depth cues at that distance. If delta Ep is less than Ep, the smallest
difference in distance that can be recognized, increases with the square of
the distance. The formula for delta eta is related to the formula for depth
of image (p12). If the eyes are rotated to view an object to the side, the
basis is shortened. If point P is farther than AS and BS, its position is
given by the mean Em of the distances Ea = AP and Eb = BP and the median
line of vision alpha(m) = (alpha + beta):2. Then
Em = (b(cos alpha + cos beta))/(2 sin eta) = (b (cos alpha(m)))/(tg eta).
And
(dE)/E = –(2d eta)/(sin 2 eta).
Thus, the geometrical point of equal exactness for the recognition of
differences in distance is: A circle through the points A and B with the
diameter bdE:Ed eta, when eta is small. The difference in distance between
P and P’, when the eyes rotate to the side, changes eta to eta’. Here, the
memory of sensations which depend on eta are compared to the sensations of
eta’. With the greater angle distance of P and P’, the exactness of depth
perception is considerably reduced, although the exact degree of this is
unknown. When viewing with the eyes at rest, the exactness is reduced much
more. If P and P’ are are on a line midway between the eyes, then P and P’
are not seen as a single image but as double images. Binocular depth
perception is not possible when P and P’ lie on top of each other. When
focusing on P, eta is the convergence angle of the viewing lines. The
sensation of convergence could be thought to determine the recognition of
different distances, but sensitivity to this is low. Overall, judgement of
distance by binocular perception is relatively inexact. [p88]
If binocular viewing is assisted by optical devices, the basis for three
dimensional impressions from the images in the eyes is augmented. The
center of the exit pupil is the entrance point for a line from a point on
the object, and if it is connected on each side to one point on the object
as seen on that side, the two lines will intersect in a point that is part
of the 3d image of the object (if the instrument is constructed to produce
these images). The totality of these 3d image points forms the 3d image
[Raumbild] of the object. This image makes the same three dimensional
impression on the viewer as a real object.
[Fig. 99. The reversal of depth sequence for crossed position of the virtual
eye postions.]
The relation of the image to the object must be examined, by studying the
impression received when the structure of a 3d image deviates from the usual
experience. If the position of the object and the entrance pupils is given,
the 3d image is totally determined by the distance between the entrance
pupils, the degree of convergence, the distance between the exit pupils (the
median interocular distance of 65mm), and by the position of the convergence
point of the two eyes and the corresponding point in the object space. The
convergence ratio depends on the size and also the [Vorzeichen = pattern,
sign + or -] for the image diameter parallel to the connection of the eyes,
the corresponding diameter in the object space must be parallel to the
connecting line between the entrance pupils. The convergence ratio must be
equal to the telescope magnification. The previously mentioned ‘sign’ also
determines how the vertical projection to the viewing line is pictured, for
erected ray passage in the object space. Equipped with a special optical
device, the projection in the object space can appear inverted or erect, and
as one image or two, although a properly functioning instrument will give a
single image. [The purpose of the simple diagrams with dots inside
parentheses is not fully explained.] The structure of the 3d image points
as compared to the object, independent of their distances and distortions,
results from the usual reversed position of the objects. [p89] In other
cases, it is different because the position of the entrance pupils is
reversed in relation to the image. Fig. 99 shows how the structure of depth
of the object points O1-02 appears in the image as reversed 02’-01’.
Accurate depth perception (orthoscopic) is replaced by reversed depth
(pseudoscopic). Protrusions appear as indentations and vice versa, and
knowledge of the usual forms and shadows is inapplicable. This appearance
of reversed depth can also occur during one-eyed viewing, such as when
viewing lunar craters, and especially with some perspective drawings. It is
then called an optical illusion (inversion). Depth reversal during
binocular viewing occurs by switching eye positions, as in the pseudoscope
of Ewald (fig. 100); or by left-right reversal of each image, in
Wheatstone’s pseudoscope (fig. 101). If the virtual eye positions coincide,
binocular depth perception is impossible, and the object appears flat.
Viewing through the Pinakoskop of M. von Rohr (fig. 102) makes a painting
appear as if seen with one eye. [p90] This type of viewing is often used
when both eyes are to be used with an instrument made for monocular use.
The impression of depth is still greater than when only one eye is used, but
the main advantage is less ocular fatigue.
[Fig. 103. 3d from increased distance between entrance pupils.]
The influence of the distance between entrance pupils on three
dimensional perception, when the convergence ratio is equal to 1, is shown
in fig. 103. For a distance equal to K times the interocular distance, the
3d image presents an object reduced in all directions by K times. This 3d
image should give a model of the object either diminished or enlarged by the
value of K. The impression of the view is also influenced by factors such
as an imprecise idea about the actual distance. Recognition of differences
in depth can also be termed ‘corporeality’, and is augmented to the K times
when the depth line is reduced K times; but in K times smaller distances,
recognition of depth differences is reduced K squared times. [Confusion is
probably from unclear references to distance from observer to object, or
distance from object to more distant object.] That is why the simple
arrangement of mirrors for this purpose by Helmholtz is called a
telestereoscope (fig. 104). When K = 1, telescope magnification (gamma)
affects the image as shown in fig. 105. Here, a cross section of the 3d
image shows the distance of an object point to the connecting line of the
entrance pupils appears as gamma times smaller than the distance of the
corresponding 3d image to a line between the eyes. The dimensions of width
and height are unchanged in the 3d image. The image is distorted in space
(heteromorphic), instead of correct in space (orthomorphic). [p91] The
differences in depth are increased by gamma times, as in the
telestereoscope. Compared to the naked eye, the 3d images through a
magnifying binocular telescope appear as if crowded into a stage setting, as
a result of the telescopic magnification. A double telescope with entrance
pupils at a widened distance from each other gives a 3d image that is
diminished K times in the diagonal and K(gamma) times in depth. Depth
differentiation is increased K(gamma) times. Total plasticity is K(gamma),
distinguished from specific plasticity K.
[Fig. 105. 3d image with telescopic magnification.]
[Fig. 106. Pulfrich’s mechanism to examine the effect of magnification and
the objectives’ distance from each other.]
[Fig. 107. Prong or tine prism]
In a common prism field glass, the effect of increased distance between
the objectives was demonstrated by Pulfrich as follows. Two 3d images were
simultaneously presented, one with increased interobjective distance and one
at standard distance. He attached a rhombic tined prism (fig. 107) in front
of each objective of the field glass (fig. 106). The prism allows one half
of the rays to pass between the tines and into the objective, and the other
half is first reflected through the prism.
II. The Double Telescope [p92]
A double telescope must fulfill certain conditions to produce a three
dimensional impression, including providing a good quality optical image.
First, the optical axes of the individual telescopes must be parallel,so
that objects in the distance are viewed along parallel axes. If the optical
axes are tilted towards each other by delta degrees, then two rays that are
parallel when they enter the telescopes, will be tilted towards each other
by (gamma – 1)delta when they exit the telescope. The limit of usability is
usually considered to be when the rays exit vertically askew by 1/2 degree,
horizontally diverging to the outside by 1 degree; and converging by 3
degrees, which corresponds to convergence of the eyes on a point about 1.2
meters distant. If the rays diverge vertically, no 3d image point is
produced, the rays pass each other at a small distance; but as long as the
distance is small, the eye can take the midpoint of their distance where
they cross as the 3d image point.
Second, the magnifications (gamma) must be equal. This means that for
close objects, the entrance pupils must have the same distances from the
objects. If not, only the rays that enter the telescope parallel to the
optical axes will exit parallel, and the rest will have varying angles of
exit, proportional to the difference in magnification and their angle to the
axis.
Third, there must not be rotation of the images around the exit axes, or
there will be vertical deviation at the sides and horizontal deviation at
the upper and lower edge of the field. To unite the two optical axes, it is
preferable to have double eccentric rings for the objectives, and simulate
the shifting of the object this way instead of by moving the prisms.
To adjust for interocular distance, the two exit pupils must be moved by
shifting or turning the whole single telescope, maintaining parallelness and
also retaining focus. Shifting of the whole telescope has not been
extensively used. If the on-axis rays are parallel at one point, the optics
of one telescope can be shifted behind this point. For ‘Querfernrohren’
[cross telescopes = battery commanders rangefinders] (fig. 120), one
telescope is shifted without the entrance prism in [the cross tube = the
other tube or that same tube?]. If a prism diverts the optical axis by 90
degrees in front of the ocular, the shifting of the ocular can be connected
with the prism shift, which would be half as large, using a prism like that
in fig. 51, with the roof perpendicular to the shift. [Amici roof prism, 90
degree deflection.] Focusing is changed if the shift [the scissors are
opened] is in the plane through the ocular axes and the prisms. To maintain
focus, additional devices (p60) have to be coupled with the ocular shift.
Sometimes a symmetrical shift of both sides of the telescope is necessary.
[p93]
The preferred method of adjustment is by turning. The most common method
is the joint with axis parallel to the optical axis. This dates to the
invention of the [double] telescope by Cherubin d’Orleans in 1671 (fig.
108). The use of the double or triple joint is today only suitable for
special cases, as in fig. 114. Various parts of the telescopes can be
rotated to shift the optical axes in the plane of the eye axes by equal but
opposite shifts. Both ‘Straight sighted’ and reversed prism systems must
retain unreversed images relative to each other after rotating. Prism
systems with two parallel reflecting surfaces are most simply represented by
rhombic prisms, and also the central mirror on p109, other examples are in
fig. 64 and 219. All systems described to this point have the advantage
that the telescope axes stay parallel, and adjustments are made by tilting
the exit axes of the light against each other. The distance between exit
pupils should be achieved with a minimum of tilting, and it is best to only
use the shift of the oculars against each other in the plane of their axes.
The effect on the image is the same as shifting the images or changing the
tilt of the central ray in the plane that is shifted. If the oculars are
symmetrically shifted, the reciprocal of the distance from the 3d image
point to the frontal plane through the eyes, is changed by the same amount.
This applies to all 3d image points in planes perpendicular to the axes
(fig. 8), when MPh and NPh are axes that are not shifted and Mpv and Npv are
shifted axes. The plane perpendicular to the axes is moved forward to
closer proximity. The 3d image is projected according to the same laws that
govern relief sculpture.
[Fig. 108. Double telescope of Cherubin d’Orleans.]
The double telescope as a commercial product is only about 100 years old.
The Dutch double telescope of low magnification and high light intensity has
a low production cost and is still widely used today in theater glasses.
Their design with fixed interocular distance and center focus with coupled
oculars, is essentially unchanged to this day (fig. 36). [p94] The
terrestrial telescope is somewhat unhandy as a double telescope and is not
popular in that form, especially since about 30 years ago the prism double
telescope with improved technology was created by Abbe, and has since
progressed in a victorious march.
[Fig. 110. 6 power binocular with 2.5mm exit pupil and 8.3 degree f.o.v.]
[Fig. 111. 6 power binocular with 5mm exit pupil and 8.3 degree f.o.v.]
[Fig. 112. 8 power binocular with 5mm exit pupil and 8.75 degree f.o.v.]
[Fig. 113. A large lookout telescope. 130mm objective diameter.]
Fig. 59 shows a prism construction as a hand held telescope, using the
Porro I erecting system. The increased distance between the objectives,
relative to the interocular distance, gives the glass its pleasant and handy
form, but almost doubles the specific plasticity Designs with these
distances nearly equal have been less successful. Models with diminished
distance between objectives are favored for use in the theater, because of
their compactness (fig. 109). They often have center focus that moves the
objectives in and out. Center focus is in widespread use in prism glasses,
allowing simultaneous focusing of both oculars, with one ocular retaining
individual focus to provide for differences between the eyes. [p95] Center
focus facilitates focusing over short viewing distances, as in the theater
or for races. If this is not needed, individual focus is preferable, since
this simpler construction can function for a longer time and provide a
better dust free and water tight enclosure for the optics. The overall size
of the binocular is mostly determined by the diameter of the objective.
Three hand held binoculars are shown as examples. Fig. 110, 6 power, and
only 15mm objective, thus a 2.5mm exit pupil, and light gathering ability
sufficient for daytime use only. Fig. 111, the same 6 power, but 30mm
objective, resulting in 4 times the light gathering. This superiority is
only apparent in the weak light of dusk or night. Fig. 112, 8 power, 40mm
objective, thus the same brightness as the 6x. The first two binoculars
have a 50 degree apparent f.o.v., but the third has 70 degrees, so despite
its greater magnification it has a larger true f.o.v. than the others. The
weights of each are 215, 630, and 1030 grams; the reduced weight and size of
the first are partly due to the smaller distance between the objectives.
[Fig. 114. Double telescope of Gullstrand.]
Binoculars with larger objectives can use the [Abbe roof] prism system
shown in fig. 52. The Porro II prism is in the binocular in fig. 64, where
interocular adjustment is made by turning one prism housing, with a band to
move the opposite housing an equal amount in the opposite direction. A
large ‘lookout double telescope’ with 130mm objectives is shown in fig. 113.
The simple joint is more common in smaller telescopes. A hand held
telescope by Gullstrand with triple joints and Leman prisms is shown in fig.
114, where the distance between the objectives is nearly doubled. It is
increased even more in the scissor (relief) telescope (fig. 115). The
specific plasticity is multiplied at the stretched position of the arms; and
together with the ability to view with upright arms, this gives these
instruments great value as military observation devices. Fig. 116 shows one
of these hand held telescopes, and fig. 117 a fixed [tripod] telescope.
[p96] The hand held telescope of fig. 118 and tripod telescope of fig. 119
do not have the ability to open into the stretched position, for the joint
is placed on top [between objectives]. Fig. 119 shows a telescope with
large 60mm objectives displaced by 500mm, yet this observation device is
light weight and rugged. The distance between oculars can be increased to
allow two persons to observe simultaneously. [p97]
[Fig. 115. Design of a scissors telescope by Abbe.]
[Fig. 116. Hand scissors telescope.]
[Fig. 117. Fixed scissors telescope.]
[Fig. 118. Trench hand scissors telescope (joint open).]
[Fig. 119. Trench tripod scissors telescope (joint open).]
The fixed scissors telescope in fig. 120 has a camera behind the ocular. An
image taken with this is larger in ratio to the magnification of the
telescope, than when taken with the camera alone. The depicted instrument
has an objective focal length that is increased from 20cm to 2m, with an f-
ratio of 1:40, and greater sharpness is achieved with a yellow glass filter
and 1:70 f-ratio. If increased image plasticity is most important, the
[Querfernrohr = cross telescope] is used, fig. 121, also called
[Stangenfernrohr = pole telescope]. Fig. 122 shows one with 2 meters
between objectives, and a ring ocular holder to choose between 10 and 20
power magnification.
The Gullstrand telescope allows the objective distance to be equal to the
ocular distance, which permits the observation of changes in specific
plasticity. [p98] Larger changes are shown by the older Hyposkop (fig.
123a and 123b), the fixed telescope for military observation. In the
Hyposkop, axes of single periscopes are twice deviated by 90 degrees at mid-
instrument, and both ocular and objective parts can be rotated around this
middle part of the axis. Rotating of the oculars serves to adjust
interocular distance and makes it possible for two observers to view
simultaneously. The objective arms are cranked to the outstretched position
from the turned down transport position. The objective prisms are then 3.3
meters distant, and at 15 power, depth discrimination is increased 750
times. [p99] The observation point is elevated 1.6 meters, and by cranking
the arms further up, it is elevated a total of 3 meters. However, depth
discrimination is reduced with increasing distance to the objective prisms.
By installing the instrument on an observation truck, the observation point
is brought to 6 meters. A telescopic system can be temporarily placed
behind the objective prism at the ocular in one tube, to provide a panoramic
view at 3 power. Other double telescopes with common optical parts are
described in the following chapter.
[Fig. 120. A scissors telescope with photographic camera.]
[Fig. 121. The design of a pole telescope.]
[Fig. 122. A pole telescope with 2 meter objective distance and a ring
ocular changer.]
[Fig. 123a. The Hyposkop in observing position. 123b. The design of the
Hyposkop.]
12. Double View Telescopes [p100]
Two telescopes can be joined into a double telescope with identical
halves, or in other ways for other purposes. Since the joining of more than
two telescopes offers no essential advantages, it will be mentioned only
occasionally. The distinction between common entrance and exit images must
be clear. With a common exit view, the optical axes of the ‘two telescopes’
cross at the location of the eye. Both fields of view are seen at the same
time, and if they ajoin each other, the field can be doubled in height or
width (fig. 124). The ‘second telescope’ can give less magnification, and
the same object can appear in the middle of both fields, or an image serving
to indicate or ‘read off’ can be introduced. With a common entrance pupil,
two viewers can observe the same image, shown in fig. 125. Also, entrance
view and exit view can be double, as in the crossed telescopes on p153.
[Fig. 124. Telescope with two oculars for the same eye position.]
[Fig. 125. Telescope with double viewing.]
[Fig. 126. Binocular eyepiece by Abbe. Adjusting screw D moves ocular B’ to
adjust interocular distance.]
[p101] If the optical parts are to serve both eyes, the optical axes must
be united or separated at specified places. A distinction is made between
the geometrical division of the rays, where an aperture stop is divided so
that the rays from one half of the objective go to one ocular or the other;
and the physical separation, where each ray is split by a semi-silvered
mirror or beamsplitting [birefringent?] prism. This splitting can occur
anywhere in the ray path, when one half passes and the other is reflected.
The double image micrometer (fig. 172) is an example of this common
entrance, double exit telescope. The binocular eyepiece of Abbe (fig. 126)
has prisms a & b that are separated by a thin air gap. The binocular
eyepiece in fig. 127 has erecting prisms and interocular adjustment like
fig. 64, with the first reflecting surface of the front prism made half-
silvered and cemented to a supplementary prism. The telescope of fig. 125
is for two observers, where the silvered surface of pentaprism p is half
transparent and splits the objective axis in two. A divided aperture stop
for geometric division can lie within the objective or in the prism system.
Examples of this include the heliometer (fig. 166), the terrestrial ocular
for binocular use shown in fig. 128, and the horizon distance finder in fig.
251. An example of divided f.o.v. is a telescope with one objective and two
oculars whose axes cross in the ‘eye turning point’ (fig. 124), also found
in a monocular rangefinder. In a terrestrial telescope, the divided f.o.v.
can lie in the first or second image plane. Instead of this division of the
rays, an alternation of rays can be used, as in the binocular sighting
telescope of fig. 155, which has alternating entrance as well as exit
passages. If this alternation is sufficiently fast, simultaneous
observation with both telescopes becomes possible. A telescope with
different entrance and exit views but only one reversal system is the
‘Multiperiskop’ on p65. Periscopes use a shared lens reversal system; and
double telescopes with shared lens reversal systems have optical axes that
cross each other, providing correct depth perception only with backwards
viewing, double crossing of axes, or with side reversed images. The common
erecting system is especially advantageous if a panoramic sight is to be
used as a double telescope. The reversing prism must then be positioned
close to the erecting prism.
16