On the Aperture of Object-Glasses

The principle consisted in placing a lens of short focal length over the top of the lowest eye-piece of the ordinary microscope, so that the focus of the emergent pencil, and that of the examining-lens should be coincident; as thus adjusted, the microscope is converted into a kind of telescope, and a view of objects, at an infinite distance, may be obtained. On rotating the microscope in a horizontal plane, taking the focus of the object-glass as the centre of motion, a distant object will be seen throughout the arc, that includes the aperture of the objective. When the object is bisected, or becomes very indistinct, this point will be the limits of useful aperture.

The foregoing method has been objected to, on the ground that it is as much a measurement of field of view as aperture, but this is by no means the case, as the three eye-lenses form an optical combination that takes up the rays from the objective at its posterior, or conjugate focal point ; and but a very minute portion of the field lens of the eye-piece comes into action, for by substituting a stop of only l-20th of an inch in diameter in place of the ordinary one, there is no difference in the resulting measurement,—in fact, the definition and distinctness is rather improved by it than otherwise. It is, perhaps, advisable to have a small stop at a short distance above the upper lens, as it will serve to keep the eye central.

On first considering the modus operandi of this instrument, it would appear that as it causes the focus of the object-glass to be an infinite one, that there is no similarity between focal distance and the relation of aperture, and its effect on objects seen with a microscope under ordinary circumstances ; or, in short, that the aperture of the object-glass, in the form that it is usually understood, is apparently quite destroyed ; but it is a property existing in the object-glass, thus circumstanced, that it is still capable of receiving rays from distant objects, at every incidence within its aperture, and forming them into an image in the axis of the microscope, and it is a somewhat important feature in the principle, that we can ascertain the relative distinctness of the image at the same time that the aperture is being measured. I did-not recommend this for the purpose of superseding existing methods of measurement, as Mr. Lister’s is perfectly accurate up to a certain number of degrees ; but it is more especially useful as a means of corroboration, and for detecting errors that Mr. Lister’s plan will not always show ; for example, if an object-glass be selected with a large aperture that is surrounded by coloured zones, or a false light, and measured with the examining-lens attached, on reaching the extreme, if this lens be removed, it is then simply Mr. Lister’s arrangement, and the clear light from the candle will be seen exactly to bisect the field of view ; but the coloured rings, and all other light that does not tend to form an image, will be outside, and not included within the aperture.

I have found the method very serviceable, and am the more inclined to advocate it from the circumstance of its having been employed by Professor Amici, whose practical experience in the construction of object-glasses gives his opinion much weight.

There is another plan of measuring apertures, contrived by Mr. Gillett, lately described before the Royal Society, and which has been announced, in the last Journal, as being, “a very perfect instrument for measuring the angle of aperture.” Supposing this assumes all preceding methods to be imperfect, I will venture to give some reason for believing that it does not advance to such a standard. In describing the instrument, I infer that proper arrangements have been made for ensuring accuracy of motion and centering, and which fully answer the required end.

The principle of action is as follows :—The object-glass, whose aperture is to be measured, is attached to an ordinary microscope body, fixed in an horizontal position ; a candle or lamp is placed close in front of the eye-piece, which is removed, and a cap, with a very small aperture, inserted in its stead. Under these circumstances the rays will pass through the lenses of the objective, and on finally emerging therefrom, will form a cone of light corresponding to its aperture. It is merely the simple measurement of the angle of this cone that Mr. Gillett has endeavoured to arrive at. To effect this, he has thought it necessary to employ another microscope, with eye-piece and object-glass complete ; the focal point of which is made to rotate horizontally from a centre coincident with the axis and focus of the first microscope. The traverse of what may be termed the examining microscope is indicated by an arc divided into degrees. This arrangement is not new to me, as I have used the same for some years, for examining the oblique correction of object-glasses ; but I always considered it to be too incorrect for a measurer of angular aperture, for the indication will be nearly as the sum of the two object-glasses ; or a large portion of the aperture of the examining-glass is added to the angle of the objective to be measured, and for this there is no direct ratio. I have two object-glasses, one having a clear and definite aperture of 95°, and the other 90°, which, when applied together in this way, the indicated angle is very near 180°.

Mr. Gillett appears to have discovered this source of error, as he has since attempted to remedy it by making an alteration in his instrument, which now somewhat differs from that originally described. To explain the improvement, I’ will consider the two microscopes and objectives placed with their axes in the same right line with foci coincident. A patch or stop is then placed over the front of the examining object-glass, which cuts off exactly one half of its area in a vertical position. Supposing this stop to occupy the left-hand side, the body of the examining microscope is then moved to the right ; and when the light disappears, the number of degrees are noted. The microscope is next moved back to its linear position, and the stop shifted round, so as to cut off the right hand half, and the degrees taken from this direction, added to the first indication, will give the angular aperture. This has thus to be obtained by means of a double traverse and shifting of the stop, which must be, to some extent, detrimental to accuracy. The last modification certainly reduces the aperture of the examining object-glass, but the same may also be done by using a stop with a very narrow vertical slit ; the whole angle can then be taken at one operation, without shifting the stop. I have tried both these arrangements with different assortments of object-glasses, but still find that there are some curious discrepancies.

If every precaution be taken for obtaining an accurate result according to Mr. Gillett’s method, and then the instrument be reversed, so as to rotate or traverse the object-glass with the aperture to be measured, the same indication will be obtained. This, then, merely, resolves itself into Mr. Lister’s method of measurement, and which will certainly perform better, and be more accurate, if the optical arrangement which intervenes, and only serves as an impediment to the free passage of the light, is removed ; in short, I am of opinion that Mr. Gillett’s complex contrivance will not prove serviceable to the practical optician. If it is only the measurement of the angle of the cone of light emergent from the object-glass that he desires to accomplish, it may be accurately effected by means of a very simple and portable instrument, without any optical appliances whatever, as these only tend to falsify the result; but, for many reasons, I do not approve of measuring apertures in this manner.

There is a paper in the Proceedings of the Royal Irish Academy for January 23rd, 1854, ‘On a New Method of Measuring the Angular Aperture of the Objectives of Microscopes,’ by the Rev. T. R. Robinson. This is perfectly accurate in principle, and, as the paper contains some original information that leads the way to matters of much practical utility, I shall refer to it at some length.

The mode of measurement cannot be better described than by using the author’s own words. “As a lucid point in the focus of the objective sends out from the eye-piece rays nearly parallel, so light sent in the opposite direction through the microscope will converge at that focus, and then diverge in a cone, whose angle equals the aperture of the objective. If this cone be intercepted at right angles to its axis, by a screen, and the diameter of its section, together with the distance of the screen from the surface (focus) of the objective, be carefully measured, they give the aperture.”

The luminous source may be either a camphine lamp or sunlight ; the latter gives “a beautiful map of the objective’s light territory,” and shows with remarkable distinctness the most minute errors of workmanship in any of the lenses, such as scratches, defective centering, dirt, &c. Another important application of Professor Robinson’s principle, is the measurement of the diminution of effective aperture that the object-glass sustains, when used upon an object immersed in balsam, or other medium ; I do not think that this measurement can be so well effected by any other method than that here spoken of. The author mentions the fact that objects in balsam will be less illuminated than in the other way ; this alludes to the diminished angle of the illuminating pencil, and the same reasoning also applies to the aperture of the object-glass. The annexed diagram will show to what extent various angles of aperture are reduced, when viewing a structure immersed in Canada balsam. The exterior aperture is 170°, which is assumed to be the largest effective pencil that can be got through an object-glass ; this is at once reduced to 82° or less, and the inner angle of 90° is brought down to about 55°.

I may here observe that a parallel plate of glass over ail object, mounted dry, has no effect in reducing the aperture, for the rays, after being deflected by the first surface, emerge again from the second one parallel to their original direction, and all converge to a point at the same angle as at first, consequently the object is seen through the glass with an angle of aperture the same as if it was not interposed. This is not the case when the object is immersed in a refracting medium with a plane surface, for the first, or single deflection, is not compensated for a second time, and hence the angle of aperture will be considerably reduced, according to the refractive power of the medium. Without resorting to theory to demonstrate what the reduction of aperture ought to be, I will show, practically, what it really is. In order to ascertain this, I employed a piece of polished plate-glass with parallel sides, 0·508 of an inch thick, which possessed very nearly the same refractive power as Canada balsam ; I ascertained this by filling a plano-concave lens that I had by me, made of the same glass, with that material ; when the concave side was placed on the plate of glass, on looking through them both, no optical effect could be discovered.

The method of using the glass plate was as follows :—I first covered one side of it with a thin film of bees’-wax, to serve as a screen, and laid this downwards on the stage of the microscope. I then focussed the object-glass to be measured, exactly upon the upper transparent surface of the plate. Without shifting the microscope from its horizontal position, I next placed a candle before the eye-piece ; a bright circle of light appeared on the bees’-wax screen, the diameter of which I carefully measured ; an angle was taken from the circumference of the circle to the focal point of the objective (the distance being equal to the thickness of the glass plate). The angle thus obtained will represent the effective aperture of the object-glass for an object mounted in Canada balsam. The glass plate was now removed without disturbing the other adjustments, and a paper, or card screen placed in exactly the same plane as the bees’-wax film formerly occupied. The diameter of the circle of light was again measured : an angle taken from the circumference to the same point as before represents the aperture for an object mounted dry.

This last is in strict accordance with Professor Robinson’s method. The following were the results :—A l-12th, having an aperture of 146° on a object mounted dry, was reduced to 75° on an object in balsam ; an l-8th of 125° to 71° ; a l-5th of 105° to 68° ; and a 4-10ths of 90° to 56°.

I have not had an opportunity of trying to what extent the aperture is reduced by the various other known media used in mounting objects. This may be very easily done by filling a parallel glass cell with the fluid, and it will exactly represent the conditions under which such objects are mounted.

These experiments will readily account for the difficulty of discovering the markings or structure of a severe test when mounted in balsam ; for, as thus seen, it may be inferred that no aperture exceeding 85° can be made to bear upon it, and this is even supposing that the largest aperture object-glass that has ever been constructed is used. Such being the case, I am somewhat puzzled at an announcement that appears to contradict this fact, coming from one that must be considered an authority in these matters. I refer to Professor Bailey, who, in a letter addressed to Matthew Marshall, Esq., dated January 20th, 1852, first speaks of an American object-glass of very large aperture (⁠⁠), and its performance on the most difficult tests known, and then proceeds to say : “In all these cases (and, in fact, whenever I allude to a test object), I mean the balsam-mounted specimens. The dry shells I never use as tests.” This assertion seems to me to be extraordinary, and very like saying that an aperture of 85° or 90° will do everything that is required. I have invariably found that when very difficult tests are mounted in balsam, I cannot discover the markings, and certainly, the reasons herein given will account for it. It is to be hoped that the American opticians have discovered some new and peculiar principle in object-glasses, that will render a smaller amount of aperture serviceable ; but however this may be, I think that Professor Bailey’s statement requires some further explanation.

As the nature of the markings on test objects is now exciting some degree of attention I will offer some remarks on the subject. The prevailing opinion with some theorists is, that the striæ are rendered visible by the contrast induced by an inherent refraction of the siliceous prominences, throwing a portion of the rays from the source of illumination without the limits of the aperture of the object-glass, and thus causing the markings to appear opaque. This is, in effect, comparing the object to a piece of fluted glass. Now, if this were correct, if even the most easy of this class of objects were to be mounted in Canada balsam, the refractive index of this and silex being so nearly the same, every appearance of structure would be entirely obliterated ; but it is found not to be so, for the markings have the same appearance when in balsam as out of it ; what want of distinctness there may be is partly accounted for by the effect of diminished aperture, which is, of necessity, reduced under this condition, and therefore, less of the radiations from the object are collected.

I cannot persuade myself that any vital organism can be so devoid of structure, and so perfectly homogeneous as this theory would imply. I believe that all test objects are seen in the same way as any other transparent ones, by means of the different degrees of opacity of the parts. This opacity may arise from varying thicknesses, or from an imperviousness to light arising from colour, or the aggregated structure of the markings. In any of these cases refraction is not called into operation ; and, further, I can show the markings on the most difficult tests when illuminated as opaque objects under such circumstances, that no light can be refracted from the striæ into the object-glass.

Those who advance such speculations as these appear to forget that the definition of tests depends entirely upon aperture, and that this must be increased in proportion to the closeness of the lines or dots upon the object, and if the aperture of the objective is insufficient, no method of illumination will call them into view ; there is no occasion even to employ a microscope to ascertain this fact. In my paper on illumination, contained in the last Journal, I have made comparison between the optical properties of the eye and a microscope ; this has been rather doubtfully received, for some cannot see the analogy ; but I must again refer to the same organ for a demonstration of the properties of aperture.

If we place some small print against a wall, and retire to such a distance that the words are barely legible, and then apply to the eye an optical combination similar to an opera-glass, which will give it greater aperture, without increase of magnifying power; it is most remarkable how this assists vision, and appears to illuminate the object, enabling the print to be easily read.

The eye by itself is also a natural lens, possessing some amount of linear aperture, and if further comparison were wanting, the marginal rays show evident symptoms of imperfect achromatism ;—but to return to the point in question. If we hold the blade of a penknife diametrically across the pupil, and examine the flame of a candle, it will appear double ; as the images formed at the opposite extremes of the pupil, or aperture, do not unite on the retina, this is quite analogous to the diffracting spectrum seen in the microscope.^* By using a piece of paper in the form of a cross, in place of the penknife, four images may even be obtained. The apparent mobility of distant objects, when a body is brought in a line with them at a short distance from the eye, may be attributed to the same causes.

To illustrate the effects of the aperture of the eye in separating lines, suspend in a good light a piece of textile fabric, printed either in stripes or dots. Stand at such a distance off that the lines and interspaces are just clearly defined. Now examine them through a small perforation, made with a pin in a black card. The lines or dots will become invisible ; approach nearer and they will reappear ; by substituting a smaller stop they will vanish as before, and again become distinct at a shorter distance. 1 cannot go further than merely to mention this fact, which has been thoroughly investigated by Mr. Lister, who from the three data, of size of stops, number of lines in a given space, and distance of the eye from the object, has obtained very practical results, and ascertained the degree of aperture necessary for separating lines or spaces a certain distance asunder. In making comparison between experiments with the eye and microscopic object-glass, it is assuming angular and linear apertures to be the same in effect, of which fact there can be no question.

For a demonstration of aperture I will again quote Professor Robinson’s paper :—” The effect of angular aperture is merely an increase of illuminating power analogous to that of linear aperture in a telescope. Let O be a point of an object seen by an objective whose anterior surface is A B ; this point, in case of a test object, may be considered as self-luminous, and equally so in every direction.”

This exactly confirms what I have endeavoured to explain, that aperture is just effective in proportion to the quantity of radiations collected from the object.

All these facts must tend to prove that the separation of distances and definition of tests is entirely dependant upon aperture, and not upon illumination, as the latter will be quite ineffectual without the former. In concluding these remarks I may mention, that of two object-glasses of equal performance, the best is that which does its work with the least amount of aperture. Microscopists are but too apt to judge of the value of objectives, and select them entirely by the latter element.

Some years ago I announced my opinion that 150° might be considered as the limits of useful aperture. This was asserted from practical data, and theory has led Professor Robinson to the same conclusion. There is little to be gained beyond this; and now that 160° and even 170° are not uncommon, I consider it quite absurd to suppose any wonderful effects will be produced from an extra ⁠. Besides the small assistance and little light to be obtained by means of the most oblique rays, they have another bad effect in giving a distorted image of the object. This latter circumstance alone has made me desirous of trying any method that would give the probable result of causing an object-glass to perform effectively with a less degree of aperture. Apparently this can only be accomplished through the reduction of the obliquity of the exterior rays, incident upon the first surface, by making the front of the anterior lens concave. For many years foreign glasses of this form have been sold, but their performance has not been such as to tempt an imitation of any peculiarity in their construction. Some time ago I gave this a trial, but not with that degree of care necessary to ensure a certain result.

The concave form has been investigated mathematically by Professor Robinson with such good promise, that I have been once more induced to take it in hand, though he to some extent over-estimates the advantages to be gained from it ; for he assumes the first surface to be dense flint, which would reflect a greater quantity of light, whereas this loss is lessened, as all our best object-glasses have of late years been made with triple fronts, with the first lens of crown glass.

With excessive difficulty I have succeeded in making l-8th of 1383 with two separate anterior combinations, each giving the same degree of aperture and magnifying power. The first has a plane incident surface. The second front is worked to a concave radius of 0·625 of an inch. On comparing them together I could not discover any appreciable advantage, in point of quantity of light, in favour of the one with the concave surface. I have tried the experiment with every degree of care, and consider that it sets this point finally at rest, and that it is a theory that does not tell in practice ; I also understand that Ross has long ago arrived at the same result. A front combination of this form considerably increases the difficulty of correcting the oblique pencils