About New Kinds of Telescopes, Especially for Handheld Use.
Lecture held at the session of the 
Society for Advancement of Industrial Activity on January 7, 1895
by Dr. S. Czapski, 
Scientific Colleague of the Optical Laboratory of Carl Zeiss in Jena
Continuation, Number 3; from the 'Central-Zeitung fur Optik und Mechanik'
(Journal for Optics and Mechanics), Berlin, 01 Feb., 1896
Translation by Ilse Roberts and Peter Abrahams

Allow me now to get to the actual point of my lecture: these new 
designs.  As you have seen, the attempts to construct a short telescope of 
medium magnification and sufficient light gathering, based on one of the 
known designs of erecting telescopes, were in vain.  Theoretical and 
practical improvements to the Dutch and the terrestrial telescope have been 
made under the direction of professor Abbe for some time as a peripheral 
project at Zeiss.  But these led to the same result which I already cited 
for the Dutch telescope:  Improvements are achievable, but these 
improvements require costly materials, which hardly seem to have a sensible 
ratio to the achievement.  These designs were easily abandoned, as a new, 
quite different one promised much better success, and even the complete 
attainment of the goal.

This new path consisted of achieving the erection of the inverted image 
created by the objective, neither as in the Dutch nor as in the terrestrial 
telescope or any others that use dioptric means (refractions at lenses), 
but instead by catoptric methods, with reflections at mirrors.  A typical 
Keplerian astronomical telescope, giving inverted images, can give an erect 
image and still keep all other characteristics, when a system of image 
erecting mirrors is added.  The advantages or practicality of the system 
depend only on the physical dimensions of the mirrors or of the complete 
system.

Reversing (re-erecting) an image produced by an optical instrument with 
mirrors instead of more lenses, is not a new idea, and even for the 
telescope it had been proposed and attempted.  The reflecting device 
invented by Amici in the middle of this century and first introduced by 
Nachet in Paris (and therefore often named after him) is well known.  This 
ingenious "prisme redresseur", is put on the ocular of (an image reversing) 
compound microscope, and erects the image.  It is mostly used for preparing 
slides under the microscope.  (*A description is given in Dippel, Das 
Mikroskop, Braunschweig, 1882, p590.)  But this has a characteristic, 
advantageous for the microscope and perhaps also many other uses, which is 
absolutely impractical for hand held use, at least in the form and use of 
the inventor, because it brings about, at the same time as the image 
reversal, a deviation of the viewing direction by a large angle.

It does not deviate the image when used in a different configuration, 
and it can be made "straight sighted".  This introduces another problem 
which precludes general usage.  This problem was encountered in the 
reflecting devices which Chevalier and Stephenson used in their 
microscopes, and a similar design was specified and used by Dove in a 
telescope.  With these devices, the [converging] rays are strongly 
refracted at the exterior surfaces of the prisms, onto the total reflection 
surface, and strongly refracted again on exiting the prism, to continue in 
the original direction.  A homocentric [circular cross section?] ray bundle 
is transformed into an astigmatic one by refraction at a steeply inclined 
surface, and even more by repeated refractions.  This defect is often seen 
with poor photographic lenses, at the edge of the field.  This "eccentric 
aberration" can not be compensated with any device in the telescope optics, 
and it ruins the image throughout the whole f.o.v.

The solution is to place the erecting prisms in the light path where the 
rays form parallel bundles, i.e. outside of the objective or in front of 
the ocular.  Parallel ray bundles remain parallel on refraction at plane 
surfaces.  Astigmatism only appears in bundles which converge towards a 
nearby point or diverge from it.  However, placing the prisms in front or 
behind the telescope means a longer, more costly telescope, compared to 
installation within the tube, somewhere between the lenses.  Placing the 
prism between eye and ocular diminishes the f.o.v., and one of the main 
advantages [compared to a Galilean] of an astronomical telescope would be 
eliminated.

For these reasons, this type of device has only been experimentally used 
in telescopes, to test the principle, and to my knowledge was never widely 
adopted.  These experiments resulted in a precise definition of the 
requirements which a system of erecting mirrors or prisms has to satisfy 
for use in (especially handheld) telescopes.

1. The system has to be ‘straight sighted’,  it must not cause any 
deviation of the optical axis.

2. The rays must enter or exit the prisms at a perpendicular incidence, 
at least the center ray or axis of the ray bundle.  (*Astigmatism does not 
appear with parallel rays, when the prism in dioptric terms acts as a disk 
with parallel surfaces, and it can be placed in the ray path at any 
position without compromising the image.  The small aberrations normally 
caused by adding a flat glass element are centric, and can be totally 
eliminated with additional lenses inside the telescope).

3. Total reflection within a prism results in almost no loss of light, 
and this is the main reason that prisms are used instead of mirrors.  If 
prisms are used, they should be designed as totally reflecting prisms [not 
silvered], if possible.

There are only two systems of four mirrors or mirror prisms, which meet 
these three conditions. The prisms are right angled isosceles; with the 
hypotenuse being the reflecting surface, and the adjacent sides the 
entrance or exit surfaces for the rays.  The shorter prism surfaces that 
face each other in each prism pair must be parallel to each other to 
fulfill condition 2.  Fig. 4 shows one arrangement, where prisms 1 and 2 
face each other symmetrically (so that their reflecting hypotenuse surfaces 
form a right angle with each other), as do prisms 3 and 4.  Prism 3, and 
with it also 4, is perpendicular to prism 2 [error in original].  The 
figure shows the path of a ray striking the short side of 1 and then 
through the four prisms.

Fig. 5 shows a second arrangement, derived from the first by moving 
prism 4, keeping it parallel to its position in the first arrangement, 
until it is directly in front of prism 1.  The ray enters that prism from 
the opposite direction as before and proceeds through the system, as seen 
in the figure.

These two arrangements completely fulfill the above three conditions.  
Each ray, exiting the prism system is parallel to the corresponding 
entering one, so that the direction of view is not changed.  However, the 
first arrangement results in an image that is reversed left to right from 
the image of the second.

To give an approximate explanation for the effect of these prism 
systems, the well known effect of the "angle mirrors" may be recalled.  The 
subject of multiple reflections is taught in physics for middle schools 
extensively and with pleasure, and contains as its simplest example, that 
of the angle mirror.  The images produced in the angle mirror, from a given 
object, are created or evaluated according to position, number, and 
orientation, and to their dependance on the width of the opening of the 
mirror and the position of the object in relation to it.  A simple example 
is when the angle is 90 degrees, when an image of an extended object is 
produced by double reflection.  A superficial observation can confuse this 
image with a common simple reflection.  A closer view, actual or 
theoretical, shows that it is not the familiar reflected image, where the 
object becomes an image symmetrical to the mirror plane.  Angle mirrors at 
90 degrees produce an image wherein the object is congruent to itself 
around an axis parallel to the mirror edge, and turned by 180 degrees.  
This image is a reversed one, in the image either right and left are 
reversed, or up and down are, depending upon the position of the apex 
between the mirrors. A 90 degree angle mirror can be paired with a second 
one whose apex is perpendicular to the first, so that the rays leaving the 
first, enter the second and are reversed in a direction perpendicular to 
the first reversal.  Together they bring about a complete reversal of left 
& right, and up & down.

The prism system shown in fig. 4 acts like two such right angle mirror 
pairs crossed to each other at right angle.  1,2 is the first pair, and 
2,3, the second pair.  Fig 5 represents a system, as already said, derived 
from the first one in a simple way.  This effect will occur whether the 
four mirrors are traversed by the rays in the order 1,2,3,4, or 4,1,2,3.  
The inclination of the mirrors to each other is the same, and that is what 
is required.  (The squence 2,3,4,1, and 3,4,1,2, leads to identical 
consequences.)  (These prisms, along with the Dove, and Amici prisms, were 
explained with models and demonstrated by means of Skiopticon-projection 
during the lecture.)

If one of these prism systems is combined with the lens system of a 
telescope or microscope, so that the optical axis of the lenses corresponds 
to the prism’s perpendicular entrance ray, then the instrument will give 
erect images, instead of the inverted images it gave without the prisms.  
The sequence of the four prisms within the lens system is immaterial, since 
(in the required circumstances,) each prism changes the direction of the 
rays; and otherwise acts as an optical flat with parallel surfaces and a 
thickness equal to the ‘short length’ of the prism, perpendicular to the 
optical axis, and inserted in the same place as the prism.  Consequently, 
all four prisms can be placed in front of the objective or behind the 
ocular, or between objective and ocular at arbitrary distances from each 
other; or any group of the prisms in front of the objective, another group 
between objective and ocular, and a third in or behind the ocular.  The 
sequence of the prisms must always correspond to one of the sequences in 
fig. 4 and 5.  The dimensions of the prisms are determined by the position 
of each in relation to the objective and ocular, so that neither the clear 
aperture of the objective nor the f.o.v. is stopped-down or dimmed.  These 
prism dimensions are governed by the same rules that would limit the 
aperture of a diaphragm in place of the prism.

In actual use, the four-prism system should have as few glass-air 
boundaries as possible, unless their entry and exit planes are not used to 
to replace lenses, as described later.  The fewest boundaries are given by 
a single solid glass body with only one entry and one exit plane.  This is 
shown in fig 6 in perspective projection, based on the design from fig 4; 
and in fig. 7, based on fig 5.  In fig. 6, the glass body can be built of 
two isosceles right angle prisms, both with a hypotenuse that is a 
rectangle with sides of 1:2 ratio; glued together by these surfaces, in 
crossed position.  In the second case (fig 7) the prism is built of two 
congruent sphenoids (tetrahedron) with two obtuse corners each, glued 
together in opposed position.  (Compare with fig. 15, later.)





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