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] =========================================================== 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