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COMPOUND

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Originally appearing in Volume V18, Page 397 of the 1911 Encyclopedia Britannica.
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COMPOUND MICROSCOPE The view held by early opticians, that a compound microscope could never produce such good images as an instrument of the simple type, has proved erroneous; and the principal attention of modern opticians has been directed to the compound instrument. Although we now know how the errors of lenses may be corrected, and how the simple microscope may be improved, this instrument remains with relatively feeble magnification, and to obtain stronger magnifications the compound form is necessary. By compounding two lenses or Iens systems separated by a definite interval, a system is obtained having a focal length considerably less than the focal lengths of the separate systems. If f and f' be the focal lengths of the combination, f1' and f2, f2' the focal lengths of the two components, and 0 the distance between the inner foci of the components, then f = —fJ fz/A, f' =fi' f2'/ A (see LENS). A is also equal to the distance F1'F2. The accented f's are always on the image side, whilst the unaccented are on the object side. From this formula it follows, for example, that one obtains a system of s in. focal length by compounding two positive systems of I in. each, whose focal planes, turned towards one another, are separated by 8 in. A microscope objective being made in essentially the same way as a simple microscope, and the front focus of the compound system being situated before the front focus of the objective, the magnification due to the simple system makes the free object distance greater than that obtained with a simple microscope of equal magnification. Moreover, this distance between the object and eye is substantially increased in the compound microscope by the stand; the inconveniences, and in certain circumstances also the dangers, to the eye which may arise, for example by warming the object, are also avoided. The convenient and rapid change in the magnification obtained by changing the eyepiece or the objective is also a special advantage of the compound form. In the commonest compound microscopes, which consist of two positive systems a real magnified image is produced by the objective. This permits researches which are impossible with the simple micro-scope. For example, the real image may be recorded on a photo-graphic plate; it may be measured; it can be physically altered by polarization, by spectrum analysis of the light employed by absorbing layers, &c. The greatest advantage of the compound microscope is that it represents a larger area, and this much more completely than is possible in the simple form. According to the laws of optics it is only possible either to portray a small object near one of the foci of the system with wide pencils, or to produce an image from a relatively large object by correspondingly narrow pencils. The simple microscope is subject to either limitation. As we shall see later, one of the principal functions of the microscope objective is the representation with wide pencils. In that case, however, in the compound microscope a small object may always be represented by means of wider pencils, one of the foci of the objective (not of the collective system) being near it. For the eyepiece the other rule holds; the object is represented by narrow pencils, and it is hence possible to subject the relatively great object, viz. the magnified real image, to a further representation. History of the Compound Microscope.—The arrangement of two lenses so that small objects can be seen magnified followed soon after the discovery of the telescope. The first compound miscroscope (discovered probably by the Middelburg lens-grinders, Johann and Zacharias Janssen about 1590) was a combination of a strong biconvex with a still stronger biconcave lens; it had thus, as well as the first telescope, a negative eyepiece. In 1646 Fontana described a microscope which had a positive eyepiece. The development of the compound microscope essentially depends on the improvement of the objective; but no distinct improvement was made in its construction in the two centuries following the discovery. In 1668 the Italian Divini employed several doublets, i.e. pairs of piano-convex lenses, and his example was followed by Griendl von Ach. But even with such moderate magnification as these instruments permitted many faults were apparent. A microscope, using concave mirrors, was proposed in 1672 by Sir Isaac Newton; and he was succeededby Barker, R. Smith, B. Martin, D. Brewster, and, above all, Amici. More recently these catadioptric microscopes were disregarded because they yielded unfavourable results. From 183o onwards many improvements were made in the miscroscope objective; these may be best followed from a discussion of the faults of the image. Position and Size of Image.—In most microscopic observations the object is mounted on a plane glass plate or slide about o•o6 in. thick, embedded in a liquid such as water, glycerine or Canada balsam, and covered with a plane glass plate of about o•oo8 to 0.006 in. thick, called the cover-slip. If we consider the production of the image of an object of this kind by the two positive systems of a compound microscope shown in fig. 13, the objective Li forms a real magnified image O'01'; the object 001 must therefore lie some-what in front of the front focus F1 of the objective. Let 001=y, 0'01' =y', the focal distance of the image F1'O'=0, and the image-side focal length fl', then the magnification M=Y'/Y=A/L'. (3) The distance 0 is called the " optical tube length." Weak and strong microscope objectives act differently. Weak systems act like photographic objectives. In this case the optical tube length may be altered within fixed limits without spoiling the image; at the same time the objective magnification M is also altered. This change is usually effected by mounting the objective and eye-piece on two telescoping tubes, so that by drawing apart or pushing in the tube length is increased or diminished at will. For strong objectives there is, however, only one optical tube length in which it is possible to obtain a good image by means of wide pencils, any alteration of the tube length involving a considerable spoiling of the image. This limitation is examined below. When forming an image by a micro-scope objective it often happens that the transparent media bounding the system have different optical proper-ties. A series of objectives with short focal lengths are available, which permit the placing of a liquid between the cover-slip and the front lens of the objective; such lenses are known as "immersion systems "; objectives bounded on both sides by air are called " dry systems." The immersion liquids in common use are water, glycerine, cedar-wood oil, monobromnaphthalene, &c. Immersion systems in which the embedding liquid, cover-slip, immersion-liquid and front lens have equal refractive indices are called " homogeneous immersion systems." In immersion systems the object-side focal length is greater than the image-side focal length. Nothing is altered as to objective magnification, however, as the first surface is plane, and the employment of the immersion means that the value of fj' is unaltered. If we assume that a normal eye observes the image through the eye-piece, the eyepiece must project a distant image from the real image produced by the objective. This is the case if the image 0'01' lies in the front focal plane of the eyepiece. In this case the optical tube length equals the distance of the adjacent focal planes of the two systems, which equals the distance of the image-side focus of the objective F1' from the object-side focus of the eyepiece F2. The image viewed through the eyepiece appears then to the observer under the angle w", and as with the single microscope tan w"/Y'=I/fz (4) where f'z is the image-side focal length of the eyepiece. F L1=objective, L2 L3 =eye-piece of the Ramsden type. F1, , F1'=object- and im- age-side foci of objective. Fz=front focus of eye-piece. P'Pl'=exit pupil of objective. P"P1"=exit pupil of complete microscope. D D = diaphragm of field of view. 396 To obtain the magnification of the complete microscope we must combine the objective magnification M with the action of the eye-piece. If we replace y' in equation (4) by the value given by (3), we obtain tan w"/y=A/fi . i/f2"=V, (5) the magnification of the complete microscope. The magnification therefore equals the power of the joint system. The magnification is also expressed as the ratio of the apparent size of the object observed through the microscope to the apparent size of the object seen with the naked eye. As the conventional distance for clear vision with naked eye is To in., it results from fig. i that the apparent size is tan w=y/l. If this value of y be inserted in equation (5), we obtain the magnification number of the compound microscope: — N =tan w"/ tan w=Ol/fi'fa =Vl. (6) The magnification number increases then with the optical tube-length and with the diminution of the focal lengths of objective and eyepiece. As with the simple microscope, different observers see differently in the same compound microscope; and hence the magnification varies with the power of accommodation. The image produced by a microscope formed of two positive systems (fig. 13) is inverted, the objective Li tracing from the object 001 a, real inverted image 0'O'i, and the eyepiece L2L3 maintaining this arrangement. " For many purposes it is immaterial whether the image is inverted or upright; but in some cases an upright image lightens the work, or may be indispensable. The simplest microscope which produces an upright image has a negative lens as eyepiece. As shown in fig. 14, the real image formed by the objective must fall on the object-side focal plane of the eye-piece F2, where a normal eye without accommodation can observe it. But as the object-side focus F2 lies behind the eyepiece, the real image is not produced, but the converging pencils from the objective are changed by the eyepiece in-to parallels; and the point 01 in the top of the object y appears at the top to the eye, i.e. the image is upright. The erection of inverted images by prisms, which was applied to the simple telescope by Porro, and to the binocular (q.v.) by A. A. Boulanger was employed by K. Bratuscheck in the Greenough double microscope; these inverting prisms permit a convenient adaptation of the instrument to the interpupillary distance of the observer. Double microscopes, which produce a correct impression of the solidity of the object, must project upright images. The terrestrial eyepiece (see TELESCOPE), which likewise ensures an upright image, but which involves an inconvenient lengthening, has also been employed in the binocular microscope. Regulation of the Rays.—Weak and medium microscope objectives work like photographic objectives in episcopic or diascopic projection; in the microscope, however, the projected image is not intercepted on a screen, but a real image in air is formed. This must lie in the front focal plane of the eyepiece if we retain the supposition that it is to be viewed by a normal eye with passive accommodation. The plane in the object conjugate to the focal plane of the eye-piece is the plane mission in compound sharply portrayed (a perfect objective microscope with a nega- being assumed). Object points lying out tive eyepiece. of the focal plane, on the other hand, are L1=weak achromatic ob- projected as circles of confusion on the jective. plane focused for, the centre of the L2= negative eyepiece. entrance pupil being the centre of pro- Fi, =object- and im- jection and the circles of confusion con- age-side foci of objec- stituting, with the points of the focal tive. plane, the object-side imago. As the F2, F2' =object- and im- pencils used in the representations are of age-side foci of eye- wide aperture on the object-side, only piece. such points as are proportionately very P'Pi'=exit pupil of ob- near the focal plane can produce such . small dispersion circles on the plane P'jectiPi'=vevirtual image of focused for, that they, so far as the PiPi'=exit pupil of objective- and eyepiece-magnification complete microscope. permit, appear as points to the eye. It follows that the depth of definition of the microscope is in general very trifling. As it is entirely afunction of the aperture and the magnification, it can be increased by diminishing the entrance pupil, the magnification remaining unchanged. A diminution of the aperture, however, would injure a very much more important property, viz. the resolving power (see below). With powerful systems, object-points lying quite near the plane focused for would be represented by such large dispersion circles that practically only the points lying in one plane appear simultaneously sharp; and it is only by varying the focus that the object-points lying in other planes can be observed. The position of the diaphragm limiting the pencils proceeding from the object-points is not constant in the compound microscope. In all microscopes the rays are limited, not in the eyepiece, but in the objective, or before the objective when using a condenser. If the pencils are limited in the objective, the restriction of the pencil proceeding from the object-point is effected by either the front lens itself, by the boundary of a lens lying behind, by a real diaphragm placed between or behind the objective, or by a diaphragm-image. The centre of the entrance pupil is the point of intersection of the principal rays; and it is therefore determinative for the perspective representation on the plane focused for. In fig. 15 the centre of the (After M. v. Rohr.) objective. E=plane focused for; O1*, O2*=projections of 0102 on E; Z= centre of projection; P PI =a virtual image of real diaphragm P'P1' with regard to the preceding part of the objective is the entrance pupil. entrance pupil lies behind the focal plane, and consequently nearer objects appear larger, and farther objects smaller (" entocentric transmission," see below). If a diaphragm lying in the back focal plane of the objective forms the exit pupil for the objective, as in figs. 13 and 14, so that its image, the entrance pupil, lies at infinity, all the principal rays in the object-space are parallel to the axis, and we have on the object-side " telecentric " transmission. The size of the imago on the focal plane is always equal to its actual size, and is independent of the distance of the object from the plane focused for. This representation acquires a special importance if the object be micrometrically measured, for an inaccuracy in focusing does not involve an alteration of the size of the image. To ensure the telecentric transmission, the diaphragm in the back focus of the objective may be replaced by a diaphragm in the front focal plane of the condenser, supposing that uniformly illuminated objects are being dealt with; for in this case all the principal rays in the object-space are transmitted parallel to the axis. With uniformly illuminated objects it may happen that the pencil in the object-space may be limited before passing the object, either through the size of the source of light employed or through a diaphragm connected with the illuminating system. In fig. 16 (After M. v. Rohr.) E, 01*, 0* and Z as in fig. 15. PP1 is the entrance pupil. the intersection of the principal rays lies in front of the object, and consequently objects in front of the plane focused for will be projected on E magnified and the objects lying behind it diminished (" hypercentric' transmission). It produces a perspective representation entirely opposed to ordinary vision. As objects lying near us appear smaller in the case of hypercentric trans-mission than those lying farther from us, we receive a false impression of the spatial arrangement of the object. Whether the entrance pupil be before or behind the object, in general its position is such that it lies not too near the object, so that the principal rays will have in the object space only trifling inclinations towards one another or are strictly parallel. This is specially important, for otherwise pencils from points placed somewhat later-ally to the, axis arrive with diminished aperture at the image. We see from fig. 13 that the objective's exit pupil P'Pi' is portrayed by the positive eyepiece, the image P"Pi" limits the pencil proceeding from the eyepiece. This image P"Pl" is then the exit pupil of the combined system, and consequently the image of the entrance pupil of the combined system. As the exit pupil P'Pi' for the objective lies before the front focus of the eyepiece, generally at some distance and near the objective, the eyepiece projects a real image from it behind its image-side focus, so that if this point is accessible it is the exit pupil P"PI". If, e.g. in the object-space the objective has telecentric transmission, the exit pupil must coincide with the back focal plane of the combined system, and it always lies behind the image-side focus of the eyepiece. The exit pupil, often called Ramsden's circle, is thus accessible to the observer, who by head- and eye-movements may survey the whole field. We can now understand the ray transmission in the compound microscope, shown in fig. 13. Points of a small object (compared with the focus of the objective) send to the objective wide pencils. The diaphragm limiting them, i.e. the entrance pupil, is placed so that the principal rays are either parallel or slightly inclined. The pencils producing the real image are very much more acute, and their inclination is the smaller the stronger the magnification. The eyepiece, which by means of narrow pencils represents the relatively large real image at infinity, transmits from all points of this real image parallel pencils, whereby the inclination of the principal rays becomes further increased. The point of intersection, i.e. the centre of the exit pupil, is accessible to the eye of the observer. In the case of the negative eyepiece, on the other hand, the divergence of the principal rays through the eyepiece is also further augmented, but their point of intersection is not accessible to the eye. This property shows the superiority of the collective eyepiece over the dispersive. The increase of the inclination of the principal rays, which arises with the microscope, influences the perception of the relief of the object. In entocentric transmission this phenomenon appears in general as in the case of the contemplation of perspective representations at a too short distance, the objects appearing flattened. Although in the case of the spatial comprehension of a perspective representation experience plays a large part, in observing through a microscope it does not count, or only a little, for the object is presumably quite unknown. In telecentric and hypercentric transmission we obtain a false conception of the spatial arrangement of the objects or their details; in these cases one focusses by turns on the different details, and so obtains an approximate idea of their spatial arrangement. While the limiting of the pencil is almost always effected by the objective, the limiting of the field of view is effected by the eyepiece, and indeed it is carried out by a real diaphragm DD arranged in the plane of the real image O'OI' (fig. 13) projected from the objective. The entrance window is then the real image of this diaphragm projected by the objective in the surface conjugate to the plane focused for, and the exit window is the image projected by the eyepiece; this happens with the image of the object lying at infinity. The result must be that the field of view exhibits a sharp border. In the case of the dispersive eyepiece, on the contrary, no sharply limited field can arise, but vignetting must occur. Illumination.—The dependence of the clearness of the image on the aperture of the system, i.e. on the angular aperture of the image-producing pencil, holds for all instruments. The brightnesses of image points in a median section of the pencil are proportional to the aperture of the lens, supposing that the rays are completely reunited. This is valid so long as the pencil is in air; but if, on the other hand, the pencil passes from air through a plane surface into an optically denser medium, e.g. water or glass, the pencil becomes more acute and the aperture smaller. But since no rays are lost in this transmission (apart from the slight loss due to reflection) the brightness of the image point in the water is as large as that in air, although the apertures have become less. Fig. 17 shows a pencil in air, A, dispersing in water, W, from the semi-aperture u,, or a pencil in water dispersing in air from the semi-aperture u2. If the value of the clearness in air be taken as sin uI, then by the law of refraction N =sin ul/sin u2, the value for the clearness in water is N sin u2. This rule is general. The value of the clearness of an image-point in a median section is the sine of the semi-aperture of the pencil multiplied with the refractive index of the medium. An illustration of this principle is the immersion experiment. A view taken under water from the point 0 (fig. 18) sees not only the whole horizon, but also a part of the bed of the sea. The whole field of view in air of 18o° is compressed to one of 97.5° in water. The rays from 0 which have a greater inclination to the verticalthan 48.75° cannot come out into the air, but are totally reflected. If pencils proceed from media of high optical density to media of low density, and have a semi-aperture greater than the critical angle, total reflection occurs; in such cases no plane surface can be employed, hence front lenses have small radii of curvature in order to permit the wide pencils to reach the air (see fig. 19, in which P is the preparation, 0 the object-point in it, D the cover slip, I the immersing fluid, and L the front lens). The function n sin u = A, for the microscope, has been called by Abbe the numerical aperture. In dry-systems only the sine of the semi-aperture is concerned; in immersion-systems it is the product of the refractive index of the immersion-liquid and the sine of the object-side semi-aperture. In the case of the brightness of large objects obviously the whole pencil is involved, and hence the clearness is the squares of these values, i.e. sin' u or n'sin2 u. As the semi-aperture of a pencil proceeding from an object point cannot exceed 90°, the numerical aperture of a dry-system cannot be greater than r. On the other hand, in immersion-systems the numerical aperture can almost amount to the refractive index, for A=n sin u End of Article: COMPOUND
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