On the field of view of a Galilean telescope

Transcription

1 Transactions of the Optical Society On the field of view of a Galilean telescope To cite this article: H A Hughes and P F Everitt 1920 Trans. Opt. Soc View the article online for updates and enhanceents. Related content - Note on the Galilean binocular T Sith - The relations between field illuination and the optiu visual field for observational instruents L C Martin and T C Richards - Vignetting in visual instruents R C Lane and R S Longhurst This content was downloaded fro IP address on 23/08/2018 at 00:48

2 ON THE FIELD OF VIEW OF A GALILEAN TELESCOPE BY H. A. HUGHES, F.O.S., AND P. F. EVERITT, BSc., F.R.A.S., F.INsT.P., F.O.S. Read and discussed, 14th October, OF recent years there b s been a re-awakening of interest in the Galilean telescope with the natural consequence that the proble of enlarging its field of view has again received attention. Unfortunately the theory of the subject as developed in various text-books has not been treated in the siplest anner and the purpose of this short paper is to present a ethod of considering the subject in such a way as ay, we hope, clear away a good deal of the fog at this oent surrounding it. In every telescopic syste we have an entrance pupil and an exit pupil which are so related to each other that the exit pupil is the iage of the entrance pupil, and, if the agnification of the telescope be, the exit pupil will be -- ties the size of the entrance pupil. In the first place we will suppose the telescope to consist of two thin lenses, a positive of focnl length fi foring the objective, and a negative of focal lengthf, (nuerical) which will for the ocular. They will of course be separated by the difference of their focal lengths, to give a telescopic syste of agnification. The observer s eye will be placed behind the ocular and the distance of the centre of rotation of the eye fro the ocular will be denoted by d. The entrance pupil will be the aperture of the objective and its sei-diaeter will be called P. The exit pupil is then of sei-diaeter - and is situated a distance?n= - I -.- fi in front of the ocular. It is clear that the pupil of the observer s eye cannot be brought into this position, consequently the exit pupil will operate as a porthole bounding the field of view ; further, since the observer s eye is accoodated for telescopic vision and the porthole is only a short distance in front of the eye, the porthole will not be sharply defined. When it is desired to search the field of view of a telescope, the eye is rotated to bring the iage of each part of the field in turn on the fovea centralis, and therefore the centre of projection to deterine the field of view of the Galilean telescope will be, not the pupil of the observer s eye, but its centre of rotation, which lies at a distance d behind the ocular. Returning to the exit pupil of sei- P - I diaeter its distance fro the centre of rotation of the eye is - f2 + d and it will consequently subtend a sei-angle whose tangent is P - I -- divided by -fa + d. P I

3 16 H. A. Hughes and P. F. Everitt Hitherto it has been tacitly assued that the diaeter of the pencil of parallel rays entering the eye through the telescope fro any object has been infinitely narrow. If the pupil of the eye has a sei-diaeter p, and the eye be directed at the edge of the porthole, it is obvious that only about half the pupil of the eye will be receiving light fro the object; to fill copletely the pupil of the eye, the eye ust be directed at a point at a distance p inside the porthole edge. Siilarly, when directed at a point distant p outside the porthole edge, the eye will just fail to receive any light at all. We have thus found three fields of view: the field of axiu illuination for which the whole of the eye pupil is filled with light, the extree field lying inside the boundary at which the eye pupil just fails to receive any light, and the field whose boundary lies betwe$n these and for which the eye pupil is half filled with light. We ay write these in atheatical for. The field of view of axiu illuination D!-- - P P - p = 2 tan-l = 2 tan-1 - ~ -I -f2 + (- 1)f2 + d d Siilarlv the total field of view and the so-called ean field of view P = 2 tan-1 (- 1)f2 + d These forulae are necessarily the sae as those arrived at in the usual text-books; the ter (- I ) f2, which is the distance between the objective and ocular, ight have been called I the length of the telescope, but it will be seen presently that its present for is the ore useful one when considering by what eans the field of view ay be enlarged. In practice, the field of view outside the so-called ean field ay be disregarded, as the illuination is less than half of that at the centre. It will be found convenient to call the field of axiu intensity the central field and the outer region up to the liit of the ean field the outer field. In the central field, since the pupil of the observer s eye is copletely filled with light, the brightness of the iage is the sae as that of the object viewed directly (less the sall percentage due to reflections and absorption), and this is true irrespective of the agnification or diaeter of the objective. Thus the fir belief of so any users of Galilean binoculars, that larger objectives will give a brighter iage, is seen to be contrary to fact. The effect of increasing the diaeter of the objective (i.e. increasing P) is to increase the size of the central field, not its brightness; the diaeter of the ean field is also increased by the sae aount. Unfortunately there are liits to the advantage so to be gained in binoculars, owing to the inter-pupillary distance restricting the diaeter of the objective to a little over 2 inches. The next factor availahle isf,, the focal length of the ocular; it is at once obvious that by decreasing the value of f, both the central and ean fields will be enlarged

4 On the Field of View of a Galilean Telescope 7 in the sae proportion. This is rather interesting as it shows that it is possible to construct two different Galilean binoculars having the sae agnification and central field, but one having a larger ean field than the other, according to whether the size of the central field is obtained by decreasingf, or increasing P. The gain in field that ay be obtained in this anner is liited by the difficulty of correcting the aberrations sufficiently well when fi is reduced uch below I inch. There are still two ore factors d and ; d, the distance of the centre of rotation of the observer s eye fro the ocular, is not under the control of the optical designer, although it is an iportant factor. It serves to reind us how iportant it is to get the eyes as close to the oculars as possible; further, an observer wearing spectacles or having very deeply sunk eyes will not get such a large field of view as another not wearing spectacles or having proinent eyes. The agnification reains to be considered ; this is generally specified beforehand, so that it is not usually possible to vary it in any way. The effect of any alteration in is of a twofold nature, as it affects the central field and the ean field rather differently. The effect of increasing is to decrease the ean field, but the effect on the central field is ore serious, as it is decreased still ore than the ean field, owing to the increasing value of the subtractive ter p in the nuerator. The proportion of the central field to the ean field is thus reduced by increasing the agnification. The sei-diaeter of the eye pupil, p, is also not under control, although it varies considerably fro id-day to dusk. The effect produced is to restrict the area of the central field as the pupil enlarges, but there is no effect on the ean field. Obviously the effect is ore serious the larger the agnification. Hitherto only thin lenses have been considered. It is now necessary to exaine the effect of utilising lenses (as ust be done in all actual constructions) of finite thickness. In the first place the ocular will not have a central thickness uch exceeding I to I:., the effect of which ay be disregarded unless the lens be of a eniscus for. In that case the principal points will lie on the side with the deeper curve, lvhich \vi11 be towards the eye, but the gain so obtained except for very low agnifications will be about neutralised by the observer s inability to get his eye quite as close as before to the ocular, provided the lens is reasonably thin. If the ocular \Yere ade in the for of a very thick eniscus, it is conceivable that soe advantage could be obtained which would be ore pronounced as the agnifying power is increased. Considering the objective, with suitable thickness for actual constructions, the entrance pupil still reains the front edge of the objective cell and the position of the iage of this fored now by the objective and ocular is practically the sae as in the case of the thin lens; the effect is sall and cannot well be used as a factor in designing, although in nearly every case of a doublet objective it will help the field a little. There reains the possibility of using for either objective or ocular copound systes containing considerable separations. Taking the ocular first, it is possible to have either two negative lenses with a separation or a front negative lens with a positive next the eye; in the first case the principal points will lie inside and the effect is to increase artificially the Optical XXII 2

5 18 H. A. Hughes and P. F. Everitt distance fro the second principal point to the centre of rotation of the eye, so that field is lost; in the second case, although the effective distance to the centre of rotation of the eye is decreased, the front negative lens, if ade of existing optical aterials, will of necessity have such a sall diaeter that it will act as a field stop and there will be no gain but a probable loss. There reains the case of the objective consisting of two coponents with a separation. If both coponents are positive, the edge of the front lens cell will be the entrance pupil and will lie in front of the first principal point so that its iage through the coplete objective will lie in front of the second principal point and there will be a loss, not gain, of field. This is the construction given by Mr H. S. Ryland*. It is not suggested that he did not get an increase of field, but the cause ust be looked for in the short focus of the ocular (18.) and not in the additional positive lens which should be regarded as foring the second eber of a copound objective syste. An alternative construction of a front positive lens with a negative at a suitable distance behind it really aounts to using an ocular consisting of two separated negatives, and as already shown, this is inferior, as regards the field of view obtainable, to a single ocular of the sae focal length as the cobination. Description of Exhibits. By the courtesy of Messrs Henry Hughes & Son, Ltd., the following exaples of Galilean constructions were exhibited to illustrate the application of the general theory. The I Liverpool. A day and night binocular of power 4x and field 4p, having object glasses of 29 inches aperture. This glass has fixed interocular distance and ay be regarded as the older standard type of arine binocular. The Pilot. A low power night glass of power 24x and field varying fro 8+ to IO according to how close the observer s eye is placed with respect to the ocular. The object glasses have 2 inches diaeter and fixed interocular distance. The field has been obtained by reducing the value of fi, thus producing a short glass which is very convenient for the pocket. The Bridge. A day and night glass siilar to the Liverpool in type and having power 4x with a field of 4)o to 5. The objectives are, however, only 12 inches in diaeter to enable a good range of interocular distance to be given by the usual bending bar construction. Although this glass, is uch saller than the Liverpool, it has the sae agnification, together with a rather larger field. The diensions are so reduced that this glass will conveniently go into the pocket. Galilean Monocular. This glass has been designed for use in sextants and g ives a power of 2x with over 12 of field. The object glass aperture is 1.6 inches, so that the length becoes very short indeed, as will be seen when the above data are inserted in the forulae given and the focal lengths ascertained. * H. S. Ryland, Tra. Opt. Soc. 19 (1918), 101.

6 On the FieU of View of a Galilean Telescope I9 DISCUSSION Mr H. S. Ryland said that in the design of the Galilean binocular which he (the speaker) had described to the Society, the chief ai was to increase the aperture ratio of the objective. In the saple instruents constructed the extree liit had been reached. Instructor-Coander T. Y. Baker suggested that it would have been ore useful to put the forula for the ain field in ters of the aperture ratio of the objective. He pointed out that extra field could be obtained by oving the eyes slightly off the optical axes of the binocular. The author, in reply, said that he had obtained the sae result as Mr Ryland, but with less loss of light. He agreed that the field of view could be artificially increased by oving the eyes or by aking the interocular distance soewhat saller than the correct value, but he thought that such a procedure was a isuse of the instruent and one not to be recoended. 2-2