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To derive the Fresnel-Huygens diffraction integral using scalar diffraction theory, we start from basic wave optics principles, particularly the Kirchhoff’s diffraction formula, derived from the Huygens-Fresnel principle. We aim to derive the expression: $$ U(P) = \frac{iE_0}{\lambda} \iint_A \left( \frac{e^{ikr}}{r} \right) d\xi d\eta $$ --- ### Step-by-step Derivation: #### Step 1: Huygens-Fresnel Principle (Qualitative Foundation) Each point on a wavefront acts as a secondary source of spherical wavelets. The amplitude at a point $P$ in space due to these secondary sources is the superposition (i.e., integral) ______ _______ _________ ____ _____ ________ _____ ______ ___ ___.
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