the image correctly to a few thousandths of millimetres, the object itself is measured accurately to some hundred-thousandths of millimetres, if it has been magnified a hundred times by the objective. To keep up this degree of exactitude the magnification of the objective must be carefully ascertained, e.g. by using an objective micrometer. A fine scale with known intervals is put on the stage plate, and by determining the distance between the graduations of the objective micrometer formed through the same objective, by means of the screw micrometer ocular, the magnification of the objective is determined. As the errors in the graduation of the objective micrometer are also magnified, very exact scales are necessary. When determining the magnification the microscope must be used under exactly the same conditions: neither the length of the tube nor the focal length of the objective may be altered. A fixed eyepiece micrometer is simpler and more popular. This consists of a scale on a little glass plate, which, instead of a cross wire, is placed in the eyepiece. The adjustment must be such that the image produced by the objective falls exactly in the plane of the scale. The size of the image is determined by calculating the entire interval taken up by it. By using an objective micrometer in place of the object, the magnification of the objective can be ascertained and from this the actual size of the object. As fractions of intervals can only be estimated in this method, a measurement with such an eyepiece scale can of course not be as exact as with a screw micrometer ocular. However, such a determination of size is often quite accurate enough.
A third method employs a drawing prism. The object and the drawing plane are seen at the same time and the outlines can be readily drawn. If, as before, an objective micrometer is placed below the microscope in the place of the object, and the size of a special micrometer-interval is drawn on the same board, then the actual size of the object can be ascertained. Instead of first drawing the object and the objective micrometer, they can of course be projected at the same moment on a scale on the drawing board. The errors attending the determination of the size of a microscopic object depend chiefly on the accuracy of the objective micrometer; any errors in the micrometer being magnified by the objective. These may be diminished by using different parts of the objective micrometer for the correction of the eyepiece scale, and the calculation of the size is based on the found mean value. A second error can arise through the inaccuracy of the eyepiece micrometer, and also in the case of a screw micrometer through periodic faults of the screw, and through dead motion. The eyepiece micrometer allows its errors to be diminished, if one measures at different points and then fixes a mean value. The dead motion of a micrometer screw is best avoided by working the screw always from one and the same side. The thickness of the cross wire may also occasion a fault. For this reason there is sometimes employed two very narrow threads lying beside one another, and which limit the image as nearly as possible.
The Testing of the Microscope
The excellence of a microscope objective depends on its definition and its resolving power.
Fig. 55.
DD =diaphragm.
K1K2＝condenser.
L＝front lens of the objective.
The lower figure shows the plan of the transmission.
The definition is better according as the chromatic and spherical aberrations are removed; there always remains in even the best constructions some slight aberration. In consequence of these residual aberrations, every object-point is not reproduced in an ideal image-point, but as a small circle of aberration. These circles will be objectionable when the smallest details are examined.
The size of these circles depends, in the case of equal tube lengths, only on the type of the objective, and not on the focal length, exact execution being assumed. Object details will only be well seen if the aberration circles are small in comparison. The size of these details in the image depends only on the magnification of the objective, M＝Δ/f1′, and can by appropriate choice of the focal length of the objective be brought to the right value. In the case of a suitable ocular magnification, the details will be well seen, while the aberration circles remain invisible. It is therefore possible to judge the excellence of the focusing of objectives on the strength of the ocular-magnification, or the over-magnification, which they permit.
E. Abbe, through the so-called delicate ray transmission, suggested a way by which the quality of the images of objectives can be observed. The ray transmission, shown in fig. 55, is obtained by means of a stop of the form shown in the lower figure and placed under the condenser in the plane of the iris diaphragm. The entrance pupil is in this way reduced on two small separate fields, which nevertheless contain rays of all zones. It is necessary that the outside edge of the diaphragm coincides with the edge of the entrance pupil. This can be attained by drawing the iris diaphragm so far as to form the entrance pupil. The double diaphragm is then in such a position that the edge of the outer diaphragm coincides with the edge of the iris diaphragm.
The object employed must have distinct boundaries. Abbe’s test plate consists of an object carrier on which six cover glasses of exactly determined thickness (between 0·09 mm. and 0·24 mm.) are cemented. The cover glasses are silvered on their under surfaces, and in the silvering fine lines are drawn; these lines form the test object. This plate admits at the same time of a correct determination of the thickness of the cover glass, for which the best correction exists. So long as the object is not sharply focused two separate dispersion figures will be seen. 'The defects of the objective are revealed, e.g. two adjacent sharp images are formed, which become indistinct if they coincide, or one pencil produces a distinct, the other an indistinct image, or that the images are surrounded with coloured rings. Owing to the curvature of the image, all parts of the object are not seen distinctly at one and the same time.
The resolving power of an objective depends on its numerical aperture. The numerical aperture can be determined in two ways. A diaphragm with a very narrow hole is placed on the stage, and the microscope sharply focused on the edges of the hole. The illuminating mirror is turned aside and a graduated scale is laid on the foot of the microscope. Strong systems produce in the proximity of their back focal plane an image of the scale, which can be inspected with a weak auxiliary microscope, and the length of the visible part of the graduation determined. The ratio of half the length of the visible piece of the scale to its distance from the diaphragm on the stage gives the tangent of half the angular aperture. The sine of this angle is the numerical aperture for dry lenses. With weak systems no auxiliary microscope is necessary, the eyepiece being removed and the scale viewed directly in the tube.
E. Abbe constructed a simple instrument for the determination of the aperture, termed the apertometer (fig. 56). A semi-circular glass plate bears two scales, over which two black thin metal plates bent back at right angles may be moved.
Fig. 56.—Abbe’s Apertometer (Zeiss).
A little hole in the silvered plate a marks the centre of this circle. Through this hole the points of the metal plates b can be observed by total reflection on the surface c. The apertometer is laid on the stage, so that the hole lies in the axis of the microscope, and the hole is sharply focused. The eyepiece being removed the image of the metal plates b produced by the objective is seen. In order to ensure for the eye a central position, there is fixed on the upper end of the tube in place of the eyepiece a disk of pasteboard or metal with an axial hole. The metal plates b are then moved till the points just cut off the edge of the field to be surveyed. The angular or numerical aperture can then be read off. With strong systems the vanishing of the points is observed with an auxiliary microscope, formed by means of the inner tube. In immersion systems the immersion liquid is placed between the front lens and apertometer.
If the numerical aperture be known the resolving power is easily found. The resolving power can also be determined by using different fine test objects. Norbert’s test plates, which bear graduated groups of extremely fine and narrow divisions are very useful, while the tests of Amphipleura pellucida and Surirella gemma are often employed.
The magnification of a microscope is determined from the focal lengths of the two optical systems and the optical tube length, for N=250 Δ/f1′f2. To determine the optical tube length A, it is necessary to know the position of the focal planes of the objective and of the ocular. If one focuses an auxiliary microscope, carried in the inner tube, on the image situated in the back focal plane of the objective of a distant object, and then on the dust particles lying on a slide pressed against the end of the outer tube, the displacement of the auxiliary microscope gives the distance of the back focal plane of the objective from the end of the outer tube. To determine the position of the anterior focal plane of the eyepiece, the eyepiece is placed on the stage with the eye-lens downwards. An auxiliary microscope is now focused first on the image of a distant object and then on the plane of the edge of the setting. This plane can be marked by a small piece of paper. This gives the distance of the anterior focal plane of the eyepiece from the bottom edge of the setting of the eyepiece and consequently also of the edge of the eyepiece carried by the upper end of the tube. These measurements determine the optical tube length Δ.
