Aperture (optics)

“ Every increase above this magnifies all the optical faults of the telescope and the atmospheric difficulties as well, beside decreasing the diameter of the emergent pencil which enters the eye, and thereby causing serious loss of acuity. For the eye like any other optical instrument loses resolving power with decrease of effective aperture, and, besides, a very narrow beam entering it is subject to the interference of entoptic defects, such as floating motes and the like, to a serious extent. ”

“ The little irregularities found round the edges of the holes through the tin screen, Fig. 8, are in this respect of material assistance. They show, too, the increased optical or penetrating power that is gained by increase of aperture. Minute peculiarities, not visible under very high powers with a 10 inch diaphragm, become immediately perceptible even with less magnifying when the whole aperture is used, provided the mirror is spherical. ”

“ What cannot be seen at all with a low aperture may be seen with higher ones under totally different aspects; while in each case the apparent sharpness and clarity of the image is somewhat extraordinary.
Further in Fig. 189b in using the resolving power of the objective of high numerical aperture, the image may be quite wrecked by a little carelessness in focussing, or by mismanagement of light, so that one would hardly know that the valve had markings other than those seen with the objectives of lower aperture, and under these circumstances added magnification would do more harm than good. ”

“ As the relative aperture of the instrument increases, other things being equal, one is driven to oculars of shorter and shorter focus to obtain the same magnification and soon gets into trouble. Very few oculars below 0.20 inch in focus are made, and such are rarely advisable, although occasionally in use down to 0.15 inch or thereabouts. The usual F/15 aperture is a figure quite probably as much due to the undesirability of extremely short focus oculars as to the easier corrections of the objective. ”

“ This expression for the intensity becomes rigorously applicable when ƒ is indefinitely great, so that ordinary optical aberration disappears. The incident waves are thus plane, and are limited to a plane aperture coincident with a wave-front. The integrals are then properly functions of the direction in which the light is to be estimated.
In experiment under ordinary circumstances it makes no difference whether the collecting lens is in front of or behind the diffracting aperture. ”

“ Again, if one part of a lens employed have a different refractive power from another part of it, that is, if the flint-glass particularly is not homogeneous, a star of the first and even of the second magnitude will point out the natural defect by the exhibition of an irradiation, or what is called a wing, at one side, which no perfection of figure or of adjustment will banish, and the greater the aperture the more liable is the evil to happen. ”

“ Aperture in fact is computed by mathematicians by tracing the rays from the back focus through the system of lenses to the front focus, the front focus being the point at which the whole cone of rays converge as free as may be from aberration. If the front focus be in air, no pencil greater than 82°, “double the angle of total reflection,” can emerge from the plane front of the lens; and, obviously, if no greater cone can emerge to a focus one way, neither can any greater cone enter the body of the lens from the radiant. ”

“ We may go further, and lay it down that there can be no considerable loss of brightness until the difference of phase of the waves proceeding from the nearest and farthest parts of the aperture amounts to 1/4λ.
When the difference of phase amounts to λ, we may expect the resultant illumination to be very much reduced. In the particular case of a rectangular aperture the course of things can be readily followed, especially if we conceive ƒ to be infinite. ”

“ It is a fact which has been well known for more than a decade that in faint light, when the eye has become adapted to its situation, the pupil opens up to two or three times this diameter and there is no doubt that a fifth or a fourth of an inch aperture can be well utilized, provided the eye is properly dark-adapted. ”

“ But 150 on a 3 inch is a high power for the quantity of light obtained, to say nothing of the separate consideration and advantage of long focus. Aperture is a quality or function of the telescope considered separately from light or focus. For instance, suppose a 5 inch speculum is so thinly silvered that it gives the exact degree of light as a 2-1/2 inch refractor, the defining and separating power of the 5 inch aperture would be very superior to the 2-1/2 inch. ”

“ If we suppose the focal length to be 66 ft., a single lens is practically perfect up to an aperture of 1·7 in.
Another obvious inference from the necessary imperfection of optical images is the uselessness of attempting anything like an absolute destruction of spherical aberration. An admissible error of phase of 1/4λ will correspond to an error of 1/8λ in a reflecting and 1/2λ in a (glass) refracting surface, the incidence in both cases being perpendicular. ”

“ For, first, when the correcting lens is approximately constructed on a calculation founded on its intended aperture, and on the refractive and dispersive indices of its materials, the final and complete dispersion of colour may be effected, not by altering the lenses by grinding them anew, but by shifting the combination nearer to, or farther from, the object-glass, as occasion may require, along the tube of a telescope, by a screw motion, till the condition of achromaticity is satisfied in the best manner possible. ”

“ There is no doubt that each form of instrument possesses its special advantages: aperture for aperture the refractor is acknowledged to be superior in light-grasping power, but the ratio given by different observers is not quite concordant. A silver-on-glass mirror of 8-inches aperture is certainly equal to a 7-inch objective in this respect, while as regards dividing power and the definition of planetary markings, the reflector is equal to a refractor of the same aperture. The much shorter focal length of the reflector is an advantage not to be overlooked. ”

“ It should be observed that at the surface of bodies the refractive power is exerted, and that the light proceeds in a straight line until leaving the body. The refraction is more or less, and in all cases in proportion as the rays fall more or less obliquely on the refracting surface. It is this law of optics which has given rise to the lenses in our camera tubes, by which means we are enabled to secure a well-delineated representation of any object we choose to picture. ”

“ In fact, superfine disks of over 15 in. aperture are scarcely possible in most of the newer telescope glasses. Moreover the greater depths of the curves (or “curvature powers”) in itself neutralize more or less the advantages obtained from the reduced irrationality of dispersion. When all is taken into consideration it is scarcely possible to reduce the secondary colour aberration at the focus of such a double object-glass to less than a fourth part of that prevailing at the focus of a double objective of the same aperture and focus, but made of the ordinary crown and flint glasses. ”

“ An uncorrected residuum, rapidly increasing 163 with larger apertures, is then left, and this appears in the image amplified by the total power of the objective, so that with a non-homogeneous medium there is a maximum angular aperture which cannot be surpassed without undergoing a perceptible loss of definition, provided working distance is required. If we abolish the anterior aberration for all colours, by an immersion fluid which is equal to cover-glass in refractive and dispersive power, the difficulty is at once overcome. ”

“ It is almost universally admitted that, on bad nights, the advantages of a large aperture are neutralized by unsteady definition, and that, by reducing the diameter, the character of the images is enhanced. As regards instruments of moderate calibre the necessity is less urgent. With my 10-inch reflector I rarely, if ever, employ stops, for by reducing the aperture to 8 inches the gain in definition does not sufficiently repay for the serious loss of light. ”

“ In optical systems composed of lenses, the position, magnitude and errors of the image depend upon the refractive indices of the glass employed (see Lens, and above, “Monochromatic Aberration”) . Since the index of refraction varies with the colour or wave length of the light (see Dispersion) , it follows that a system of lenses (uncorrected) projects images of different colours in somewhat different places and sizes and with different aberrations; i.e. there are “chromatic differences” of the distances of intersection, of magnifications, and of monochromatic aberrations. ”

“ Let us suppose, then, that the telescope has been acquired, and that it is such an instrument as may very commonly be found in the hands of a beginner—a refractor, say, of 2, 21⁄2, or 3 inches aperture (diameter of object-glass) . The question of reflectors will fall to be considered later. Human nature suggests that the first thing to do with it is to unscrew all the screws and take the new acquisition to pieces, so far as possible, in order to examine into its construction. Hence many glasses whose career of usefulness is cut short before it has well begun. ”

“ When light shines through a hole or a slit the light waves are bent at the margins and the several sets, eventually overlapping, interfere with each other so as to produce a pattern of bright and dark elements depending on the size and shape of the aperture, and distributed about a central bright image of that aperture. One gets the effect well in looking through an open umbrella at a distant street light. ”

“ The light in the proposed direction is that determined by the size of the small aperture in accordance with the laws already investigated, and its phase depends upon the position of the aperture. If we take a direction such that the light (of given wave-length) from a single aperture vanishes, the evanescence continues even when the whole series of apertures is brought into contemplation. Hence, whatever else may happen, there must be a system of dark rings formed, the same as from a single small aperture. ”

“ What lens aperture, and therefore what image brightness, is feasible, is determined chiefly by the angular field that must be covered with any given excellence of definition. The largest aperture ordinarily used for work requiring good definition and flat field free from distortion is F/4.5. Anastigmatic lenses of this aperture cover an angle of 16° to 18° from the axis satisfactorily, which corresponds to an 18 × 24 centimeter plate with a lens of 50 centimeters focus. ”

“ This is where the utility of a wide aperture arises—by affording a wider difference of route of the individual wavelets, so that those from one part of the aperture may be retarded relatively to and interfere with those from another part. A small object-glass can furnish light; it takes a big object-glass to furnish darkness in the picture. ”

“ Practical Elimination of Aberrations.—The existence of an optical system, which reproduces absolutely a finite plane on another with pencils of finite aperture, is doubtful; but practical systems solve this problem with an accuracy which mostly suffices for the special purpose of each species of instrument. The problem of finding a system which reproduces a given object upon a given plane with given magnification (in so far as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties are too great. ”

“ For blue and violet it is best to employ the colours of the spectrum. The condensing-lens is then removed, in order that the light may fall directly upon the aperture of the polarizing prism.
The apparatus shown in Plate II. fig. 3. serves to analyse the light by reflexion, and is screwed into the pillar instead of the analysing prism. The screw at holds a concave lens of an equal focal distance. The unbordered mirror inclined at the angle of polarization is 7/4 inch long and 5/4 inch wide. ”

“ Fig. 54 shows the double achromatic lens, and fig. 55, the triple object-glass, as they 243 are fitted up in their cells, and placed at the object end of the telescope. In consequence of their producing a focal image free of colour they will bear a much larger aperture and a much greater magnifying power than common refracting telescopes of the same length. While a common telescope whose object-glass is 31⁄2 feet focal distance will bear an aperture of scarcely 1 inch, the 31⁄2 feet Achromatic will bear an aperture of 31⁄4 inches, and consequently transmits 101⁄2 times the quantity of light. ”

“ But we cannot increase this illuminating power beyond a certain extent, which is limited by the diameter of the object-glass. When we wish illuminating power beyond this limit, we must be furnished with an object-glass or speculum of a larger size; and hence, the rapid advance in price of instruments which have large apertures, and consequently high illuminating powers. Mr. Tulley’s 31⁄2 feet achromatics of 23⁄4 inches aperture, sell at £26 5s. When the aperture is 31⁄4 inches, the price is £42. ”