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A New Method for Determining the Shape and Size of Ultramicroscopic Objects1
S. Vavilov.
The limit of the resolving power of the microscope, as is well known, is determined by diffraction phenomena. The dimensions of the limiting object still accessible to microscopic observation with respect to magnitude and shape are given by the relation:
\[ d = \frac{\lambda}{2A}, \tag{1} \]
Fig. 1.
where \(\lambda\) is the wavelength of light, and \(A\) is the numerical aperture of the microscope. Formula (1) apparently imposes an entirely insurmountable limit with respect to the possible increase of resolving power. The numerical aperture can be increased only within very limited bounds; hopes for the use of very short waves are still
A NEW METHOD FOR DETERMINING THE SHAPE AND DIMENSIONS
did not lead to anything of practically very great significance. On the other hand, the ultramicroscope makes it possible only to establish the presence of discrete small particles, and only by indirect means; from ultramicroscopic observations one can form an approximate idea of the sizes and shapes of the particles.
Fig. 2.
Fig. 3.
In the brief preliminary communication being reviewed, Siedentopf indicates a way of going around the boundary (1). Siedentopf’s method is an application to the microscope of the interference technique by means of which Michelson succeeded in measuring the angular diameter of certain fixed stars1.
Close the aperture of the microscope objective, leaving only two small slits at the ends of a diameter. The diffraction circle that was obtained from the microscopic object with the objective open will now be stretched out along the straight line joining the two slits. This elongated strip will also be crossed by interference bands (see Fig. 1). If the size of the particle in the direction joining the two slits is exactly equal to the limiting value \(d\) in formula (1), then the interference bands disappear. On particles of other sizes the bands remain. If the distance between the slits is decreased, then the bands will be coarser and the disappearance of the bands will occur for particles of correspondingly larger sizes. In photograph 1 a large number of such elongated spots with interference bands can be seen. Almost in the center one can notice a spot in which the band is almost imperceptible. The width of the bands is connected with the dimensions of the particles in the given direction.
If the screen with the slits is rotated relative to the object, one can measure the dimensions of the particles in other directions and thus establish deviations from circular form.
The distance between the slits in this method is no greater than the diameter of the objective; therefore all the measurements indicated are possible only for objects that are within the resolving power of the microscope. In order to—
Fig. 4.
To overcome these limits, Siedentopf resorts to the method schematically shown in Figs. 2 and 3. By means of prisms or mirrors one can, as it were, enlarge the dimensions of the objective. If, for example, the objective has an aperture of 1.3, then, by taking the distance between the prisms to be 10 times greater than the opening of the objective, one can measure the sizes and forms of particles 10 times smaller than the limiting value (1). This procedure thus breaks down the insurmountability of limit (1); “one of the fundamental prohibitive limits in the cognition of nature can be removed,” as the author says, and a new method of interferential ultramicroscopic measurements is opened to the investigator and inventor.
In the practical realization of the method (Fig. 3), an additional achromatic lens \(AB\) must be placed behind the objective, its focus falling precisely at the place where the real image from the objective is formed. The parallel beams, by means of a series of prisms shown in the figure, are then brought to the second lens.
Figure 4 shows a microscope with Siedentopf’s interference apparatus. The entire interferometric part can be removed from the microscope by means of the groove \(A\). By means of the projection \(B\), the whole interferometer can be rotated about the axis of the microscope. The interferometer is centered with the screws \(C\) and \(D\). The distance between the slits is read from the divisions on the drum \(E\).
By means of the groove \(F\), the first prisms can be withdrawn, freeing the field of view for ordinary observation. The limit of measurable dimensions is determined not only by the distance between the slits, but also by the choice of the objective.
The more widely the slits are spaced, the narrower and more crowded the interference fringes. With a tenfold increase in the distance, the fringes are compressed tenfold. To examine them, a second auxiliary microscope is used, inserted into the tube of the eyepiece. In this way one can attain “magnifications” of 20,000 times and more, although, of course, here one must speak of magnification in a completely special sense.
The communication is very brief; many details are still unclear, and the method is still in the development stage.