The following article was written to bring before the officers of the naval service a few of the more interesting optical principles and their relation to the development of modern naval gun-sighting telescopes.
There has been no attempt to make this article a complete treatise on optics and any discussion of a technical or mathematical nature has been avoided.
As this article is intended for general circulation, it was necessary to omit all reference to any special features of construction of the instruments used in the U. S. Navy.
Attention is called to an article on "Optical Glass Manufacture and Optical Faults and Tests," appearing in a recent number of the Journal of the American Society of Naval Engineers.
This article is subdivided into sections as follows:
Section I. Introductory,
Section II. Elementary terrestrial telescope. Parallax.
Section III. Focusing caps.
Section IV. Total reflection in prisms. Penta prisms.
Section V. Chromatic aberration. Achromatic lenses. Secondary spectrum.
Section VI. Spherical aberration.
As far as possible each section is complete in itself, so that the sections may be read independently.
Especial attention is called to Sections II and III.
In the preparation of this article the following have been consulted: Lieut. Comdr. Mustin's personal notes. "Optical Tables and Data," Silvanus Thompson; "Light for Students," Edwin Edser; "Practical Light," Reginald Clay.
The present high standard of efficiency of the ships of the U. S. Navy at long range target practice, and at night torpedo-defence practice, is due to many correlated factors; but there is no single factor that has played a more important part than the development and extensive use of the modern gun-sight telescope.
It can be stated without hesitation that the ranges at which target practice is habitually held would be impossible with the old type of telescope.
The application of the telescope for gun-sighting purposes and its development to its present perfected state are due largely to three men: Rear Admiral Bradley A. Fiske, U. S. Navy; Mr. George N. Saegmuller, for many years a well-known instrument maker of Washington, D. C., and now vice-president of the Bausch & Lomb Optical Company, Rochester, N. Y.; and Lieut. Comdr. Henry C. Mustin, U. S. Navy.
Rear Admiral Fiske, if not the originator of telescopic sights, was at least the first officer to suggest their use in the U. S. Navy, and to carry out his suggestion in actual practice.
Mr. Saegmuller has been identified with the development of gun-sighting telescopes since their inception, the first telescopes being constructed by him before the Spanish War at the request of Commander W. T. Sampson, U. S. N., at that time Chief of the Bureau of Ordnance.
Mr. Saegmuller has constructed practically every telescope used in the U. S. Navy since that time, and the continual advance in the design and quality of the ordnance optical instruments would have been impossible without the co-operation and initiative of Mr. Saegmuller and the Bausch & Lomb Optical Company, whose entire resources were at all times available to the Bureau of Ordnance and its officers without restriction and without charge. Too great credit cannot be given Mr. Saegmuller for the part he has had in this development.
To Lieutenant Commander Mustin alone is due the original designs of our present turret telescopes and earlier broadside telescopes. While the general feature of design of these telescopes were not unknown to optical instrument makers, Mustin was the first to apply these features to gun-sighting telescopes and make their use possible in our service. These telescopes were the result of Mustin's independent work and experiments in optical design, a field up to that time practically unknown to officers. When it is considered that the great advances in telescope construction from the old Mark VII and Mark X telescopes to the new telescopes, and from the old parallel-motion turret sight to the new turret trunnion sight are due to the thorough and conscientious work of this officer, the value of his services, resulting as they have in the increased efficiency of the fleet, cannot well be estimated.
It should be remembered that while many advances have been made since Mustin's original designs were introduced, the fundamental principles of design introduced by Mustin are embodied in all our telescopes and will always be a feature of any future design.
(“Fig. 1” – not replicated here.)
ERECT ELEMENTARY TERRESTRIAL TELESCOPE
Expressed in the simplest terms, a terrestrial or erecting telescope (which is the type used for gunsighting) consists of an objective lens, which forms, at some point in rear of the lens, a real inverted image of the object viewed; an erecting system, which transforms the real inverted image into a real erect image; and a magnifying eyepiece, by means of which an enlarged virtual image is seen.
In Fig. 1 is shown a terrestrial telescope represented by the Gauss system of principal planes. (A full presentation of this very, interesting method can be found in the Bureau of Ordnance pamphlet on elementary optics.)
Fig. i shows clearly the position of the inverted image at II’ and the erect image at SS’. If the erect image is at the first focal plane of the eyepiece as shown, we have an elementary terrestrial telescope by means of which the eye sees an enlarged image in its proper position.
As previously stated, the erect image formed in rear of the erecting system is real and can be seen on a screen placed at the proper point. This image is, however, very small and it is necessary to magnify it by means of the eyepiece. The image actually seen by the observer is a virtual image of the erect real image. This virtual image is projected out in front of the eyepiece at a distance approximately equal to the distance of the object itself.
(“Fig. 2” – not replicated here.)
When an object is viewed through a telescope the final virtual image appears much nearer than the object; but, as stated above, this is not the case, the final virtual image and the object occupying practically the same point. The apparent nearness of the image is an optical illusion, caused by the increase in detail due to the magnification.
All that is necessary to convert this telescope into a gun-sighting telescope is to place cross wires, or a cross line glass, either in the second focal plane of the objective lens, where the inverted image II' is formed, or in the first focal plane of the eyepiece lens, where the erect image SS' is formed. The eye will then see image and cross lines in the same plane. If, however, the cross lines are not in the same plane as the image, there will be parallax of the cross lines, the cross lines apparently moving on the image as the eye is moved, as shown by Fig. 2.
An examination of Fig. 2 shows that if the cross lines appear to move down on the image when the eye is moved up from the axis at E to the point E', and vice versa, the cross lines are in rear of the image.
If, on the other hand, the cross lines appear to move up on the image when the eye is moved up from the axis, and vice versa, the cross lines are in front of the image. The remedy to be applied is obvious.
The reduction of parallax by placing inside the eye guard a disc with a central pin hole is simply due to the fact that the eye is mechanically kept close to the optical axis of the telescope.
The use of focusing caps is directly connected with the question of parallax.
One of the simplest optical principles lies in the fact that parallel pencils of light from a distant object passing through a positive, or convergent, lens will be refracted and will form a real image at the focal plane of that lens.
Conversely, if we place an object in the focal plane of a positive lens, the rays of light coming from that object and passing through the lens will emerge in parallel lines as if the object was at an optically infinite distance.
All ordnance optical instruments are constructed on the telescopic principle, i. e., that the pencils of light entering the objective lens will be parallel, and the cross lines are placed in the focal plane, either of the objective lens or of the eyepiece combination.
If the pencils of light proceed, not from a distant object, but from an object only a short distance away, such as a dotter target, the pencils will be divergent when they strike the objective lens and the resultant image will be formed in rear of the cross lines, resulting in parallax.
Many of the telescopes have no adjustment for parallax. In other telescopes, while the cross lines may be moved with reference to the objective lens so as to place the cross lines in the new image plane, the telescope itself cannot be sharply focused on such an image and the pencils emerging from the eyepiece are not parallel and the eye is strained. A compromise has to be made between indistinct focus with no parallax and sharp focus with parallax.
A single lens could be used to project the dotter target to an infinite distance, but, as pointed out above, the dotter target would have to be placed in the focal plane of the lens, or a lens of different focal length would have to be used for each different dotter; either procedure would be impracticable.
(“Fig. 3” & “Fig.4”– not replicated here.)
The use of the focusing cap overcomes all these difficulties.
The focusing cap consists of a positive and a negative lens so mounted that the distance between them may be varied at will. Increasing the distance between the lenses decreases the equivalent focal length of the combination, and vice versa ( Figs. 3 and 4), so that simply by moving the draw tube of the focusing cap in and out a dotter target at any distance may be brought into sharp focus, the telescope cross lines being free from parallax at the same time.
It would appear at first thought that the use of the focusing cap would reduce the field of the telescope, but this is not the case. An examination of Fig. 5 will show that while the use of the focusing cap materially reduces the amount of light entering the objective lens; we still have parallel pencils from the center and from each extremity of the field falling upon that portion of the objective lens which is not stopped down by the focusing cap.
In using, the telescope should be focused and free from parallax on a distant object. The focusing cap is then shipped in place on the objective end of the telescope, the telescope directed toward the dotter target and the draw tube moved in and out until the target appears clear and distinct and the telescope cross lines are sharp and. without parallax.
The adjustment of the focusing cap covers a wide range as it can be used with dotter targets whose distance from the telescope objective varies from a few inches to many feet.
It is not essential that the focusing cap be placed close to the objective lens of the telescope. Good results have been obtained with the focusing cap two feet distant from the objective lens, with a mirror between the focusing cap and the objective lens, but two requirements must be fulfilled in using focusing caps.
(“Fig. 5” – not replicated here.)
First. The focusing cap must be so rigidly attached to the telescope as to partake of every movement of the telescope.
Second. The space between the telescope objective lens and the focusing cap should be preferably completely enclosed so that no light strikes the telescope objective lens unless it passes through the lenses of the focusing cap. Owing to the fact that the interposition of the two lenses of the focusing cap between the object observed and the telescope objective lens cause a certain change in the line of sight, it is not advisable to use focusing caps while boresighting on battens for target practice, as the telescopes would point incorrectly after the focusing caps were removed.
Focusing caps can, however, be put to very effective use when battens are used for installing sights or for checking them. The use of focusing caps makes possible a very sharp focus and a complete elimination of parallax at any distance desired. While, as pointed out above, the focusing cap causes a displacement in the line of sight, this displacement for any one focusing cap is always the same as long as the focusing cap is not moved.
At present parallax and indistinct focus on the sight adjusting battens are undoubtedly the cause of considerable trouble and uncertainty and very probably lead to serious error. By using focusing caps on all telescopes in connection with the new boresight telescope, accurate determination can be made of the parallelism of the lines of sight of pointers' and trainers' telescopes and of the axis of the bore of the guns themselves in turrets through the entire range from 0 to 20,000 yards.
In addition, accurate determination can be made of the true vertical and horizontal movement of any telescope through the entire range and azimuth adjustment.
(“Fig. 6” – not replicated here.)
TOTAL REFLECTION IN PRISMS
The optical property of refraction, insofar as it relates to light passing from air into a denser medium, is so well known that it will not be discussed.
The case of light passing out of one medium into a medium less dense is of such extensive application in all prism instruments that its presentation here is considered essential.
Here the refracted ray is bent away from the normal and the ratio between a and ß is less than unity. As a increases, value is reached such that ß=90° and the ray is refracted along the surface separating the two media, in the direction of CB. This value of a is called the "critical angle" for that medium as any greater value of a will cause the ray to be totally reflected internally.1
This total reflection is the most perfect reflection that can be obtained, less than one per cent of the light being lost at the reflecting surface, and is extensively used in constructing optical instruments.
In Fig. 7 is shown a 90° prism.
(“Fig. 7” – not replicated here.)
A ray of light PC falling normally upon the face AB of the prism will be totally reflected from the inclined face AL and, if the prism angles are accurate, will emerge in a direction making an angle of 90° with the entering ray.
Fig. 7 shows that such a prism will invert (turn upside down) or will reverse (turn right for left), according to the position of the prism, an object reflected by it.
It also shows that the field of such a prism must be small; for a ray such as P'G will be refracted at G in such a way as to strike the reflecting face at an angle less than the critical angle, with the result that part of the light will be refracted through to D "and only part of the light will be reflected to D', causing a loss of light from the edges of the field. Calculation shows that for perfect reflection the angle that P'G makes with the normal to the entering face cannot exceed 6° 7' 6", which gives an angle of field of the prism=2° 14' 12".
1In Fig. 6 we have the equation
sin a =FL'. When ß = 90°, sin ß=I and sin a = µ’.
If we assume u=1.525 for prism crown glass then µ’=I/u=sin a=1/1.525 a=40°—58'—32" which is the critical angle for that kind of glass.
Fig. 8 shows another disadvantage of the 90° prism. If the prism is displaced through any angle a, the entering ray of light makes that angle with the normal to the entering face. The emergent ray of light makes the same angle with the normal to the emergent face, but lies on the opposite side of the normal, and the angle between the entering and the emergent rays is 90° ± 2 a, which doubles the error.
(“Fig. 8” – not replicated here.)
The disadvantages of the single-reflecting 90° prism are overcome by the use of double-reflecting prisms; the penta prism and the Porro prism are the best known types of the double reflecting prisms. The principle of double reflection is expressed by the statement that if a ray of light is reflected by each of two plane surfaces, its deviation is equal to double the angle between the two reflecting surfaces.
If the angle between the two reflecting faces is 45°, as in the penta prism, the deviation of the ray is 90°. If the angle between the two reflecting faces is 90°, as in the Porro prism, the deviation of the ray is 180°. Figs. 9 and 10 show the penta prism.
(“Fig. 9” & “Fig. 10” – not replicated here.)
These figures show that the reflected image is not reversed. As the ray of light strikes both reflecting faces at an angle less than the critical angle it is necessary to silver the reflecting faces. The disadvantage of the penta prism compared to the 90° prism is that more light is lost in transmission. The one disadvantage in the use of penta prisms is overcome by the far-reaching advantage of this type of prism for range finders, where there are two optical systems.
The great advantage of the penta prism lies in the principle of the optical square that the entering and emergent rays will always make a 90° angle with each other regardless of the angular displacement of the prism in a plane at right angles to the entering and the emergent faces.
This is clearly shown in Fig. 10.
CHROMATIC AND SPHERICAL ABERRATION
Owing to the nature of refraction, there are two errors in refracting optical instruments that have to be corrected or minimized: one (chromatic aberration), due to the unequal refraction of light of different colors; the other (spherical aberration), due to the inexact focus of refracted rays.
A lens that will bring light from a point on one side to an exact point focus on the other side is known as accurately "stigmatic." Any failure of a lens to produce a perfectly definite and undistorted image is known as aberration.
Any glass has a greater refracting effect on blue light than it has on red light. This is shown by the production of spectrum colors by prisms. The refractive index has a different value for each different color and any lens made of a single kind of glass will have a different focal length for each color of light. The focal length is shorter for blue than for red light.
Fig. 11 shows an equi-convex lens of dense flint glass (Jena glass 041). The radii of curvature r1 and r2are 200 millimeters, or .2 meter. The curvature of each surface in dioptres is the reciprocal of the radius=— I/r 1/.2=5 dioptres. The total surface curvature is I/r1— + I/r2=10 dioptres. The total surface curvature multiplied by the refractivity gives the power in dioptres, which is the reciprocal of the focal length in meters.
Reference to Table I of refractive indices on page 1447 will show that this dense flint glass has these values of µ:
Red light (A ray) 1.7030.
Yellow light (D ray) 1.7174.
Blue light (G ray) 1.7501.
The corresponding refractivities (µ—I) are:
Red light .7030.
Yellow light .7174.
Blue light .7501.
(“Fig. 11” – not replicated here.)
The corresponding power [(µ—I) (I/r1+ I/r2)] are:
Red light 7.03 dioptres.
Yellow light, 7.17 dioptres.
Blue light 7.50 dioptres.
The corresponding focal lengths are (ƒ=I/p) are:
Red light I/7.03 M = 142.2 mm.
Yellow light I/7.7 M = 139.4 mm.
Blue light I/7.50 M = 133.3 mm.
The focal point for blue light is 8.9 millimeters nearer the lens than for red light.
The difference between the refractions of different colors is known as the dispersion.
In the table, the refractive index for mean light (yellow light of the sodium D line) is given in the column D or µD. There is also tabulated the medium dispersion (the difference between the refractive index for red light of the "C" line and the refractive index µF for blue green light of the "F" line). This is written
µF—µC or ?µ
If the medium dispersion were always proportional to the mean refraction the fraction
would be the same for all optical glass and chromatic aberration could not be corrected.
An inspection of the last column of Table I shows that the value of this ratio varies greatly. This ratio is all important in lens calculation. It gives the amount of refraction for a given amount of dispersion and is usually denoted by the Greek letter v. In the table for the lightest crown v=70, while for the heaviest flint v=19.7.
If we wish to combine, two lenses so that each will neutralize the dispersion of the other, two conditions must be complied with.
First. The lenses must be of opposite kinds; one positive, the other negative.
Second. Their refracting powers must be so chosen that the lens of greater refracting power will cause exactly as much dispersion as the lens of less refracting power.
The second condition is met by making the respective power of each lens proportional to its value Of v.
For example, in the case of the hard silicate crown glass (O374 Table I) with a value of v=60.5 and the dense silicate flint (O41 Table I) with a value of v=29.5, the crown glass produces very nearly double the amount of refraction for the same dispersion as the flint.
(“Table 1. REFRACTIVE INDICES” – full page chart not replicated here.)
If we select a convexo-plane (positive) crown lens of +6.05 dioptres and a plano-concave (negative) lens of —2.95 dioptres (which are respectively proportional to their values of v) they will have equal and opposite dispersions and the refractive power or ability of the lens will be the algebraic sum of the two powers selected, +6.05 — 2.95 = +3.10 dioptres.
(“Fig. 12” – not replicated here.)
The two lenses cemented together, as in Fig. 12, will give an achromatic lens of a power of +3.10 dioptries.
For a negative achromatic lense the powers would have to be —6.05 and+ 2.95 dioptres.
While this combination is achromatic, it is not a satisfactory lens, as it produces spherical aberration and distortion of field.
(“Fig. 13” – not replicated here.)
Two of these lenses placed as in Fig. 13 will give an excellent lens free from chromatic and spherical aberration and with very little distortion of field.
Satisfactory objectives and other lenses vary widely in form and curvature, depending upon their use. Figs. 14 and 15 show two very satisfactory objectives.
(“Fig. 14” & “Fig. 15” – not replicated here.)
In the above calculation for an achromatic lens we have taken the medium dispersion between the red (C) line and the blue-green (F) line of the spectrum. The lens is corrected for these two colors, which are exactly focused at the same point; but there are other parts of the spectrum which are not brought accurately to the same focus as the two colors for which correction has been made. The uncorrected rays are those of intermediate wave length (yellow and green) and those of shorter wave length (blue, violet and ultra violet).
The residual chromatic aberration is called the secondary spectrum.
Lack of space prevents discussing the means of correcting the secondary spectrum. This subject is fully dealt with in the Bureau of Ordnance pamphlet on elementary optics.
There have been developed lately several glasses that, when corrected for primary color abberration, are also practically free from the secondary spectrum, but, like all exceptional optical glasses, this freedom from secondary color seems to have been attained by a sacrifice of other desirable qualities, as some of these special glasses are relatively unstable and easily affected by atmospheric moisture.
For this reason, while these glasses are undoubtedly of value for certain purposes, it would be a fatal error to use them for ordnance optical instruments.
It has been reported that the optics of the telescopes for certain foreign battleships became badly spotted after a short time in service and had to be returned to the makers for correction in this respect. While no report has been received as to the cause of this spotting, it is believed to be due to the use of unstable glass, probably in an endeavor by the makers to prevent secondary color. The only way that such a fault could be remedied would be by supplying new optics made of a more stable glass.
Up to the present time, the telescopes used in the U. S. Navy have been remarkably free from such faults. In an experience of some years, covering the personal examination of several thousand telescopes, many of which had been in service for months and years, the writer has found but one case, that of an objective lens, where the optics of a telescope were noticeably spotted by the action of atmospheric agents. The condition of the other parts of the telescope in question, including the objective lens retaining ring, showed that the telescope had been exposed to the weather for a considerable period of time.
If we were dealing with monochromatic light and had thus overcome the difficulty of light of different colors being brought to a focus at different points, we would find that even a lens ground to perfect sphericity of figure would not give a perfectly focused image. All the rays would not come to a point. The rays passing through the margin of the lens would come to a focus nearer the lens than those passing through the center. Fig. 16 shows, exaggerated, parallel light passing through a plano-convex lens. The marginal rays focus at J, the central rays at F.
At some point between J and F, the rays form the narrowest bundle. The resulting small round spot is called the circle of least confusion and is the nearest approach to a point focus.
(“Fig. 16” & “Fig. 17” – not replicated here.)
The spherical aberration might be reduced by the use of a diaphragm cutting off the marginal rays, but this method would result in loss of light. The marginal zone refracts the light too much. If the curvature of the marginal zone is flattened by grinding, a correction can be made for the aberration inseparable from .sphericity of figure. This method is followed in the case of objective lenses for large telescopes. When passing through a surface, the greater angle that the ray makes with the normal to that surface, the greater will be the refraction and the spherical aberration of that ray. The more the ray passes through normally to the surface, the less will be the aberration. To insure the minimum aberration it becomes necessary to divide the refraction about evenly at the two surfaces of the lens. In other words, the angles of incidence and emergence must be equal or nearly so. As shown in Fig. 17, turning the plano-convex lens around so that the curved face will be presented to the light will lessen the aberration considerably.
Of all lenses of equal "power" that could be used to carry parallel light to or from a focus, the best form is a bi-convex lens having the curvature of the faces in the ratio of 1 to 6, the flatter face being toward the focus. A lens having such a form is known as a crossed lens (Fig. 18).
The amount of longitudinal spherical aberration of a crossed lens is only 3/14 as great as that of an equi-convex lens of the same focal length and aperture.
The spherical aberration of a crossed lens is, however, very little less than that of a convexo-plane lens; as a consequence, crossed lenses are seldom used.
(“Fig. 18” – not replicated here.)
Though it is necessary to correct lenses for both spherical and chromatic aberration, the latter is much more important. In an equi-convex lens of crown glass, the chromatic aberration is sixteen times as large as the spherical aberration. In an equi-convex lens of flint glass, the chromatic aberration is twenty-seven times as large as the spherical aberration.
THE DESIGN OF TELESCOPES FOR NIGHT USE
Until recently, the generally accepted idea was that any increase of magnifying power lessened the amount of light passing through the telescope, making the object observed darker and less distinct, and therefore, for efficient night use, a telescope must have a low magnification (not more than 3 or 4 diameters). This belief was on account of the poor results obtained at night with the earlier telescopes and binoculars of high magnification. The poor results were due, not to the high magnification, but to the fact that the designers had neglected the simplest optical principles essential to an efficient night telescope.
If we disregard all other considerations, and our telescope is correctly designed, so that the aperture of the objective lens is sufficiently large, it is an axiom that night efficiency increases with magnification; for the reason that a distant target, which, when viewed through a low magnification telescope, appears either as a shapeless luminous spot in a dark field, or as a shapeless dark spot in a luminous field; will, when viewed through a high magnification telescope, appear larger and will take on form and detail, permitting more accurate pointing. Small objects, invisible with a low magnification, are distinctly seen with a high magnification.
When we observe an object having a fixed intensity of illumination, its apparent brightness depends upon the angular dimensions of the pencils of light that, proceeding from every point of the object, enter the eye and are brought to a focus on the retina.
Unless the object is very close, its distance will not affect the angular dimensions of the pencils of light inside the eye. The angular dimensions of these pencils depend solely on the diameter of the pupil or aperture of the eye if this aperture is unobstructed.
Consequently, when viewed by the unaided eye, the apparent brightness of an object having a fixed intensity of illumination is dependent only on the size of the pupil of the eye. It is well known that the pupil of the eye is dilated at night to a diameter considerably larger than it is in the day time. This is the involuntary effort of the eye to increase the apparent brightness of dimly illuminated objects.
It is clear that a night glass of any form should not fail to utilize the whole area of the dilated eye pupil. It is evident that no optical instrument can increase the brightness of the object, for no arrangement can increase the dilation of the eye pupil, but if the pencils in passing through the instrument are, at the point of entrance to the eye, cut down to a diameter less than the diameter of the eye pupil, a portion of the eye pupil is not utilized. In such a case, the object appears less bright than if viewed by the unaided eye.
When a telescope is well focused for other than near-sighted eyes, the emergent pencils are practically parallel and have a diameter which is dependent on a certain relation between the magnifying power and the aperture of the objective lens. At the eye point, where the eye must be placed in order to take in the full field, there is formed an image of the aperture. This image is called the exit pupil and it has a diameter about equal to the diameter of the emergent pencils. This is illustrated by the following figure, where E the eye point and e is the diameter of the exit pupil.
As there seemed to be no agreement of optical authorities on the size of the dilated eye pupil in a very dim light, a series of independent tests were made by different observers to determine this vital point.
A number of thin opaque discs large enough to completely screen the eye were each pierced with a round hole of a known diameter. The diameter of .the smallest hole was .1", the next .12", the next .14", up to .26"; the largest. A small dimly illuminated target was set up at one end of a dark building. The discs were mixed up, the observers stood at a distance from the target and viewed it alternately with the unobstructed eye and through the holes in the discs. The discs that caused the target to appear dimmer than when viewed with the unaided eye were separated from those that had no dimming effect. It was found that each observer, in laying aside all discs having a dimming effect, had selected all the discs having holes smaller than .2", and in laying aside all discs having no dimming effect, had selected all discs having holes .2", or greater.
(“Fig. 19” – not replicated here.)
Consequently, the dilated eye pupil in a very dim light was taken as .2".
It was thus determined that,
The first essential point for the design of an efficient night telescope is that the pencils of light, after passing through the telescope, must have a diameter of not less than .2" at the point where they enter the eye.
This is called the "exit pupil."
The exit pupil may be seen by holding the telescope at some distance from the eye and directing it toward the light. A bright spot will be seen in the center of the eye lens. This is the exit pupil and shows the size of the pencils of rays which the system of lenses and stops passes through to the eye. The exit pupil may be measured by placing a scale in rear of the eye lens at the point where a sharply defined round spot is formed. It may also be obtained by the equation
where e is the diameter of the exit pupil.
A the clear aperture of the objective lens.
M the magnification.
This equation shows that, with a fixed aperture of the objective lens, an increase of magnification decreases the exit pupil. In a variable power telescope we must use, at night, a magnifying power that will give an exit pupil of at least .2" diameter.
When a variable power telescope is set to the magnification that gives an exit pupil of the same size as the pupillary opening of the eye it is said to have normal magnification (this term must not be confused with "unit magnification"). If the telescope is adjusted above the normal magnification, the apparent brightness of the target is decreased in the radio m2/M2 where m is the normal magnification and M is the new magnification. An adjustment below the normal magnification gives an exit pupil larger than the pupillary opening of the eye without decreasing the apparent brightness of the target.
There is a certain percentage of light lost at each entering and emergent face of a lens, or a prism and a small amount lost in passing through the lens or prism; but in a well designed telescope with good optics, this loss cannot be reduced beyond a certain minimum. If the exit pupil is sufficiently large, the apparent brightness of a target is not decreased by increase of magnification; but, as pointed out above, its apparent linear magnitude is increased and the night efficiency increases with increase of magnification. Unfortunately, the field of a telescope decreases with increase of magnification, so that our limit of magnification is soon reached because of the resulting small field.
The magnification of an object seen through a telescope is evidently the ratio between the angle subtended at the eye by the final virtual image and by the object itself when seen by the unaided eye.
The ratio of magnification and field is expressed by the simple formula
where ? is the field of the telescope.
? is the field of the eyepiece.
M is the magnification.
Referring to Fig. 19 it would seem that all that would be required to enlarge the field of the telescope would be to enlarge the eyepiece; but in practice, the eyepiece is limited by spherical aberration to such a diameter that the angle is not greater than 40°. In practice, the angle ?) is generally about 35° or 36°. A stop or diaphragm is usually fitted in the plane of the erect image of such an opening that it cuts off all rays outside these angular limits.
As a telescope field of at least 4° is demanded by service conditions, the magnification, consequently, cannot exceed 8 or 9 diameters.
The objective lens is usually made larger than necessary because it is more or less imperfect near the edge. The lens is partially covered or stopped down until the clear aperture is of the proper diameter to admit the light desired and to limit the field to prevent spherical aberration.
The following table gives the optical characteristics of the old Mark X telescope:
M. A. e ? ?
8 .84” .1” 36° 4° 30’
4.25 .85” .2” 36° 8° 28’
It will be noted, that with this telescope, the highest magnification that could be used efficiently at night is 4¼ diameters. With the magnification of 8, the diameter of the pencils of light passing through the telescope and entering the eye is one-half the diameter of the pupillary opening and this telescope at a magnification of 8 would cut off 75% of the light that the eye could use at night.
This is shown by Fig. 20, where the outer circle is the pupillary opening, the inner circle the exit pupil; and the shaded area the amount of light cut off from the eye.
Where the exit pupil is of the same size as the pupillary opening, care is required in positioning the eye; for if the eye pupil overlaps the exit pupil, a loss of light results. For this reason, whenever possible, the exit pupil of all telescopes should be made slightly larger than the pupillary opening.
The best sight for night use is the one that can be used in the dimmest light. The efficiency of a night sight is thus inversely proportional to the intensity of illumination per unit of area required on the target or (when the target appears in silhouette) in the field. A very exact comparison of the value of any two telescopes for night use may be made by obtaining the relative intensities of illumination required for picking up the target.
(“Fig. 20” – not replicated here.)
A comparative test was made to obtain the relative night efficiencies of three telescopes submitted for test. A target was selected of a size to represent a destroyer bows on at 4000 yards and the intensity of illumination varied by moving a shaded light away from or toward the target. (The intensity of illumination varies inversely as the square of the distance of the source of light.) In each case, the illumination was just sufficient to pick up the target. The results were as follows:
Intensity of Night
Telescope Magnifying power illumination efficiency
A 8 1 1
B 4 3 1/3
C 3½ 4 ¼
The exit pupils of all these telescopes were sufficiently large, the night efficiency being apparently proportional to the magnification.
With the illumination so that the target appeared only as a dim, indistinct blur to the naked eye, it was clearly defined when viewed through telescope A, and would have made an excellent target. Through telescope C with 3½ magnification, the target appeared small and indistinct. When the magnification of the telescope C was increased to 8, the target could not be seen, showing the effect of the decrease of the exit pupil.
If a telescope is designed for night use in accordance with the principles above, the target can be :picked up when there is so little illumination that the cross lines are not visible. Some form of cross line illumination is therefore necessary.
When a target is .not illuminated, but is visible because of light in the field, it appears as a silhouette and the cross lines require only a faint illumination. When the field is dark and the target is illuminated, the cross lines require stronger illumination. That is, the intensity of illumination per unit of area of the cross lines must considerably exceed the unit intensity y of illumination of the target, otherwise that part of the cross lines lying across the target will be invisible.
Any light between the target and the eye affects the apparent brightness of the target; this is clearly shown by pointing any telescope provided with cross-line illumination at a dimly illuminated target and gradually increasing the intensity of the cross-line illumination; as the cross lines grow brighter the target apparently grows dimmer and finally is lost.
It is apparent that cross-line illumination is of vital importance in connection with night use.
To obtain the best results at night, it is necessary to have the telescope clean and well .focused. The eyes of the pointer and trainer should be completely shielded from all light except that from the target and the cross lines. The rubber eye guard protects the eye in use; the other eye should be protected as well. Closing the unused eye is not a sufficient protection, as the eye lid is not opaque, and, in addition, the strain of keeping one eye closed is tiring and injurious.