Dimensional Measurement using Vision Systems - NPL Publications ...

Measurement Good Practice Guide No. 39
While temporal coherence describes the phase relation in the direction of the light beam,
spatial coherence describes the phase relation in a plane perpendicular to the direction of
propagation. Thus, in considering the resolution of two point sources by the optical
microscope in Section 2 it was assumed that there was no fixed phase relationship existing
between the light waves emanating from these two points. The resultant intensity
distribution in the image plane is then determined by the simple addition of each intensity
pattern as shown in Figure 3.
However, in microscopy, objects are usually illuminated by light from the condenser.
Thus, the two point objects should be regarded as two pinholes in an otherwise opaque
film. If some of the light passing through each pinhole has originated from the same
incident wave train, there will be a degree of spatial coherence between the waves from
the pinholes. Now each point in the field stop will be imaged by the condenser as an Airy
disc in the object plane, with the diameter of each disc increasing as the condenser
numerical aperture is reduced. Thus the coherently illuminated area and hence the degree
of spatial coherence in the illumination of two pinholes will increase with decreasing
condenser aperture.
Theoretical analysis, taking spatial coherence into account, has shown that the minimum
resolvable pinhole separation (based on the intensity criterion used in Section 2.1) is given
by equation (1) for equal objective and condenser apertures, but with decreasing
condenser NA it rises rather more slowly than expected from the Abbe rule (based on the
mean of the objective and condenser apertures).
It is therefore evident that an objective of high numerical aperture is essential to achieve
maximum resolution. Expressed in a different way, increasing the objective NA results in
a higher proportion of light diffracted by the object that is collected by the objective and
hence, the greater the similarity between object and image. Although in theory the
condenser NA should be comparable to the objective aperture to achieve highest
resolution, in practice, with a large cone of illumination residual aberrations and multiple
reflections in the image forming optics can impair image quality. A satisfactory
compromise in terms of image resolution and contrast is often achieved using a condenser
NA approximately two-thirds that of the objective.
The degree of spatial coherence of the illumination is a critical factor in the imaging of an
opaque edge (as found, for example, in a chromium on glass photomask). Due to
diffraction effects the image of a sharp edge is slightly 'blurred', i.e. the transition from
light to dark is spread over a small distance rather than being absolutely abrupt. This is
analogous to a point source being imaged not as a point but as an Airy disc of finite size.
Theoretical analysis shows, that with spatially incoherent illumination, the computed
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