Image formation by a thin lens in terms of Fourier optics

3 Image formation by a thin lens in terms of Fourier optics  

We can use Huygens principle to explain qualitatively the essential features of diffraction, but a quantitative treatment involves casting Huygens principle into a precise mathematical form, the Fresnel-Kirchhoff formula  

Equation (1.15) can be interpreted in the following way. A spherical wave of complex amplitude U from S, incident upon the aperture, gives rise to a secondary spherical wave, 

If we assume, for simplicity, that the angular spread of the diffracted light is small enough for the obliquity factor to be taken as constant over the aperture, and that the variation of Up with r and r in the denominator of Eq. (1.13) is small compared with the exponential term, then Eq. (1.13) becomes 

Note that, for simplicity, we have omitted the constant multiplying factor Cof Eq. (1.16). 

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