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The limit up to which two small objects are still seen separately is used as a measure of the resolving power of a microscope. A certain distance d0 exists where this limit is reached. It can also be calculated theoretically.
First of all, it is important to know that the objective and tube lens do not image a point in the object – for example a minute hole in a metal foil – as a bright disk with sharply defined edges, but as a slightly blurred spot surrounded by diffraction rings, called “Airy disks” after their discoverer. The diffraction rings are caused by the limiting function of the objective aperture: the objective acts as a hole, behind which diffraction rings are found. The higher the aperture of the objective (N.A. Obj.) and of the condenser (N.A. cond.), the smaller d0 will be.
A short wavelength is also beneficial for the resolving power.
d0 = | 1.22 λ |
 |
N.A.obj + N.A.Cond |
or more simply:
d0 = | λ |
|
2 N.A. |
λ = wavelength of light, e.g. 550 nm (green)
The factor “1.22” has been taken from the calculation for the case shown in accompanying Figure. The intensity profiles of two diffraction disks have been superimposed. If the two image points are far away from each other, they are easy to recognize as separate objects. If the distance is increasingly reduced, the limit point is reached when the principal maximum of object 2 (---) coincides with the first minimum of object 1 (–). The superimposed profiles display two brightness maxima which are separated by a “valley”. The intensity in the “valley” is reduced by approx. 20 % compared with the two maxima. This is just sufficient for the human eye to see two separate points (Rayleigh criterion).
A comparison may help to make this easier to understand:
It is most unlikely that a telephone cable would be used for the electronic transfer of the delicate sound of a violin, since the bandwidth of this medium is very restricted (“small aperture”). Much better results are obtained if high-quality microphones and amplifiers are used, the frequency range of which is identical to the human range of hearing (“high aperture”). In music, information is contained in the medium sound frequencies; however, the fine nuances of sound are contained in the high overtones. In the microscope, the subtleties of a structure are “coded” into the diffracted light. If we want to see them again behind the objective, we must make sure that they are first gathered by the objective. This becomes easier, the higher the aperture angle and thus the numerical aperture.
continue with numerical aperture of objectives
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