The function of a microscope objective is to resolve fine detail in an object and to magnify it. The resolution limit of two adjacent Airy disks (the images of point objects) is given by Rayleigh's formula: Resolution=0.61Î»nsinU, where Î» is the wavelength of light, n is the refractive index of the medium in which the object is immersed, and sinU is the sine of the marginal ray angle at the object. The product nsinU is the numerical aperture (NA). In order to produce good images close to the optical axis the objective must be aplanatic, so we can assume that it obeys the sine condition. In this case sinU is equal to the paraxial marginal ray angle u, even when this approaches the upper limit of 1.0.
Equation (7.1) indicates that increasing the NA and reducing Î» can improve the resolution. This assumes that the objective design is diffraction limited when, by Rayleigh's criterion, its wavefront aberrations are less than Î»/4. In fact, most modern designs have much smaller aberrations than this.
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