Incoherent illumination

It should be noted that the MTF expresses the modulation in the image plane of a sinusoidal object and is useful only for incoherent illumination. Under practical conditions for large features (> 3.0 m), the sinusoidal object (mask) is not a good choice when what is really relevant is a binary object. However, as the mask features approach 1.0 pm, the light intensity through the mask becomes sinusoidal and the mathematical formulation for MTF becomes relevant. 

For incoherent illumination, incident at an angle 0, the direction of the intensity maxima is given by a more general equation... 

The MTF curve can be described mathematically in terms of the above variables. As an example, the MTF [(7/( /)l of a lens employing incoherent illumination and a circular exit pupil is given by... 

R /f is the numerical aperture (N.A.) and is marked on all objective lenses, together with the magnification. For example, a x25 objective with N.A. = 0.5 is expected to resolve detail of the order of 2X 1 m, ideally. Equation (2.1) has been derived by considering diffraction by a coherently illuminated periodic object. Rayleigh s well-known criterion of resolution, derived for a nonperiodic object incoherently illuminated, gives nearly the same limit of resolution as that determined from the Abbe approach and need not be considered here (see, e.g., Giancoli 1984). 

An alternative readout system is a scanning differential phase-contrast microscope with a split detector as shown in Figure 16.5. The optical configuration is compact and easy to align. The memory medium, in which the data bits have been recorded, is located at the focus of an objective lens. The band limit of the optical transfer function (OTF) is the same as that of a conventional microscope with incoherent illumination. The resolution, especially the axial resolution of the phase-contrast microscope, is similar to that obtained by Zemike s phase-contrast microscope. The contrast of the image is much improved compared to that of Zernike s phase-contrast microscope, however, because the nondiffracted components are completely eliminated by the subtraction of signals between two detectors. The readout system is therefore sensitive to small phase changes. 

When an optical fiber with an axillary symmetric index distribution is illuminated in its transverse direction by an incoherent light source, the fiber acts as a lens so that the incident light is focused on a plane placed behind the fiber as seen from Table III. If the light intensity distribution is uniform with respect to the incident plane, the index profile can be calculated from the focused light intensity distribution. This method can be applied to preform rods as well as to fibers, and is one of the promising methods. 

FIGURE 12 Optical transfer functions related to incoherent illumination of square (left) and round (right) pupils. T is proportional to the convolution of the pupil function [see top diagram and Eq. (45).]... 

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