A New Telescope Eyepiece with Extremely Large Field of View by Horst Kohler, Oberkochen from Optik, Journal for Light and Electron Optics Special Reprint, Optik 17 (1960), pp500-509 Translated by Ilse Roberts and Peter Abrahams Text of this translation copyright 1996 Abstract. The development of telescope eyepieces presenting to the eye a field angle (2w’) of more than 90 degrees was discontinued towards the end of the war but has been taken up again by Carl Zeiss. The first result of this development was an eyepiece with a 3 element Smyth lens, which gave an adequate field correction for a subjective field of view 2w’ = 110 degrees. Details of this eyepeice together with some observational results which seem typical for large fields of view are given. 1. Preliminary Remarks In the following we shall report about a newly developed telescope eyepiece with a subjective f.o.v. of about 120 degrees, which is used in a 15 x 75 observation telescope. In addition to this application, this paper may be of general interest, since there is little literature about eyepieces with such a large f.o.v., and a report on the status of this technique seems appropiate since experiences with this ocular seem to be typical for optics with such large fields of view. 2. History As predecessors of the described development, the author knows only the designs achieved before 1945 at Zeiss in Jena. They are documented in a patent application (1) and internal factory literature. These older developments were exclusively applied to U-boat periscopes, where the requirement for a large f.o.v.is obvious. As an example of this work, the arrangement of lenses and the correction diagram of an older ocular with the f.o.v. of 120 degrees is given in fig.1. (Fig. 1. Older ocular for 2w'=120 degrees. The given chromatic magnification difference is for the color F in regards to C) It consists of two collecting elements which are separated by a large air space. The objective side element consists of two lenses, and the ocular side element of seven lenses. The focal plane (virtual image) is behind the first collecting element. This type of ocular can be considered a Huygenian, even if it has only the two collecting elements and the virtual image plane in common with the classical Huygens ocular. The correction diagram in fig. 1 is for an ocular focal length of 100 mm. Since the collecting lenses of this type of ocular are in the majority, the Petzval sum is relatively large, it is about 0.8 times larger than the ocular’s refractive power. Thus the off-axis errors are large, as one can see from the correction diagram. Here we have to note that a 10mm length divergence in the image plane at an ocular focal length of 100mm corresponds to a divergence of 1 dioptre at the eye; at a focal length of 100 mm one has an astigmatism of about 4 dioptries, at an ocular focal lengthof 5Omm, double that: 8 dioptries. This type of ocular consequently is not suitable for focal lengths shorter than about 60 mm. A similar lower limit for focal length is given by the short distance of the exit pupil from the lens apex closest to the eye, which is about 12 mm, at an ocular focal length of lOOmm. In the U-boat periscopes, for which these oculars were originally provided, such a large focal length was not a problem, because of the long length of the instrument; but the use of the same ocular for telescopes of average size leads to intolerable dimensions, as fig. 2 shows for the 15 x 75 telescope. It is to be noted that the objective side ocular lens has a diameter of 180 mm while the objective is only 75mm.(Fig. 2. Wide angle telescope, 15 x 75, with the older ocular of fig. 1. Distance of exit pupil from eye side lens is 12 mm.)(Fig. 3. Wide angle telescope, 15 x 75, with newly developed ocular.) 3. Description of the New Development (*Brief comments on this type of ocular and the optical specifications for a similar system are found on pp.63 and 167 of A. Konig & H. Kohler, ‘Die Fernrohre und Entfernungsmesser’, Telescopes and Rangefinders, 3 volume edition, Berlin, 1959.) This report concerns a design in which the above disadvantage was avoided by the use of an ocular of the Kerber type. It consists of a complex collecting system at the eye side and has a Smyth lens in front of the image plane. This construction results in a distance of the exit pupil from the eye side lens apex of about 50% of the focal length; and because of the Smyth lens, in a favorable Petzval sum of 0.24 times the total refractive power of the ocular. These favorable ratios permit an ocular focal length of as low as 26 mm at an eye relief of 12mm, and the use in a fifteen power telescope, down to an objective focal length of 390 mm. Fig.3 shows the construction of an observation telescope 15 x 75 with this type of ocular. The short ocular focal length of this type permits an objective focal length of less than a third of that in Fig 2. The collecting lenses of the ocular have a focal length of 46.3 mm, and that of the Smyth lens is 137.6 mm. The use of strong Smyth lenses for large f.o.v. has been avoided, since such a lens diverges the main ray from the axis and consequently requires the other ocular lenses to be of large diameter. Because this ocular type permits the use of a relatively short focal length, the diameter stays below that of the older solution, in spite of the strong divergence of the axial ray. In the old design, the ocular lens diameter was decided by the larger ocular focal length, and consequently, the larger image plane diameter. In the following chart the optical specifications of the ocular are given in reference to a focal length of 100 length units. The arrangement of the chart follows the ray path. r1 is thus the first radius of the Smyth lens, on the objective side. 4. Results The 15 x 75 wide angle telescope has an an objective f.o.v. of 2w’ = 8 degrees, corresponding to a subjective f.o.v. of 2w’ = 120 degrees when adhering to the [Winkelbedingung = ‘angle condition’ or prerequisite]. In fig. 4 are some of the trigonometric calculations and in fig. 5 are some photos of dispersion of meridional rays. Corresponding data for the Zeiss 8 x 30 binocular are given in both figures. Noteworthy is the good astigmatic correction in such a large f.o.v. (fig. 4), essentially no worse than the 8 x 30. Although coma and chromatic aberration are a little worse than a typical binocular’s, they are justifiable when considering the high degree of correction in the 8 x 30. The tested dispersion essentially matches the values in the trigonometric calculation. The greatest dispersion is in green light, where it is about double that of the 8 x 30, whose f.o.v. is w’ = 24 degrees, less than half of the f.o.v. of the new ocular. The ocular is noticably worse than the binocular with its violet tails in white light (photos in the second line of fig. 5), a consequence of the greater magnification of the ocular. These tails are definitely acceptable when considering the large increase in f.o.v. Visual observation shows an exceptionally sharp image up to the edge, and despite the large field, this edge sharpness seemed to be better than that of some typical binoculars of normal f.o.v. (Fig. 4. Results of trigonometric calculations for the 15 x 75 (2w’ = 113 degrees.) Compared with a Zeiss binocular 8 x 30 (2w’ = 70 degrees.) (Fig. 5. Photo of dispersion numbers for the 15 x 75.) Fig. 6 shows the nature of the distortion, at the edge of the f.o.v., it is 32%. Also noted is the course of distortion with the ‘angle condition’ [ w’/w = gamma base o = constant ]. Also when the condition tg(w/2) is kept (tg(w’/2))/(tg(w/2)) = gamma base o = constant. The resulting distortion does not exactly correspond to the ‘angle condition’, as originally expected. (When adhering to it, for the given objective f.o.v. of 2w = 8 degrees, a subjective f.o.v. of 2w’ = 120 degrees would have reusulted.) This is not a disadvantage, as the observation trials reported later have shown. Fig. 7 shows the diagram of the telescope construction and fig. 8 a photo of the instrument. The telescope is a tripod telescope with a Porro II prism system The specifications of the telescope are quite different than the typical telescope. The ocular is larger than the objective, but since it is mounted on a tripod, it is still usable. (Fig. 6. Distortions of the 15 x 75 telescope.) (Fig. 7. Schematic of construction of the 15 x 75 telescope.) 5. Observation Trials Trials of the new telescope were executed by several trained observers. It was tested on the tripod and off. The tests were designed to give data about the distortions as felt by the users. For comparison, two 15 x 60 binoculars with subjective f.o.v. of 70 degrees were built. One had distortions corresponding to the ‘angle condition’ (similar to the telescope number 3 in reference 2). The other comparison telescope had substantially lower distortions, similar to telescope number 1 in reference 2. The results obtained in an earlier work of mine (reference 2), for 8 x 30 binoculars with a subjective f.o.v. of 70 degrees, could be confirmed in these trials of the 15 x 70, with larger f.o.v. of about 120 degrees. Both the earlier tests and these trials found that judgements of distortions had to distinguish between observations with a tripod and free hand observations. Tripod use could confirm that a large f.o.v. glass produces an observable bending of the contour of straight objects that corresponds to the theoretical distortion, thus the tangent condition (tgw’)/(tgw) = gamma base o = constant. (*These results contrast those of Sonnefeld, ref. 3 & 4, for tripod telescopes. Those studies require adherence to the ‘angle condition’ in principle, and also in regards to the observed ‘straightness’ of the contours of straight objects. The present report, as well as earlier studies by the author, have shown that this is not the case.) When swinging the telescope, another unnatural effect can occur, as reported (reference 2), which I called at the time ‘image bending’. According to these earlier trials, this effect can be corrected if the telescope is corrected according to the angle condition (w’/w) = gamma base o = constant. This was confirmed for that telescope, the image-bending effect did not occur when swinging the telescope. The distortions of the telescope did not quite correspond to the ‘angle condition’, as mentioned above, but the small deviation from the ‘angle condition’ did not cause problems. [Probably referring to to the flare or expansion of an image when crossing the f.o.v. as a telescope is swivelled and the image enters one side, is larger or clearer at the middle of the field, and exits the opposite side.] Finally we should mention a trivial consequence of the large f.o.v. of the ocular, not thought of at first, and explained in fig. 9. Above left, fig. 9, the ray path is shown during the observation of an image in the center of the field. Light rays near the edge of the f.o.v., at an angle of 60 degrees from the axis, are still seen by the periphery of the eye, which covers almost 180 degrees. The large f.o.v. of the telescope fulfills its purpose at this position of the eye, and movements and stimulus from the edge of the f.o.v. are seen by the eye, as in naked eye observation. Imagine if the observer now wants to observe an object at the edge of the f.o.v., with the sharp vision of the fovea and without swiveling the telescope. By turning the head to the side, the eye will be put into position to make this observation, as shown above right. As can be seen in the picture, the opposite edge of the large f.o.v. of the telescope cannot be seen by the eye. The telescope would need a f.o.v. of 220 degrees for both edges to be seen. This trivial sounding phenomenon is actually disturbing when one wishes to fix the edge with a quick movement. It is probably the reason that binoculars with larger f.o.v. than 70 degrees never became popular. As one can see in the lower diagram in fig. 9, this phenomenon does not occur with an ocular with a subjective f.o.v. (2w’) of 70 degrees. This phenomenon seems to limit the use of oculars with very large f.o.v. to cases where the large peripheral f.o.v. is required. For example, the civil and military air surveillance and elsewhere when there is a compelling necessity to view an expansive field through a given opening, such as from a submarine or into a nuclear reactor. For these special applications, the design described here should be a significant step forward from previous techniques. (Fig. 8. View of the 15 x 75 telescope.) (Fig. 9. The geometry of the ‘keyhole observation’ with large f.o.v.) (Bibliography) 5