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Lecture 19

# Lecture 19 - Lecture 19 Lecture 19 SCALAR DIFFRACTION...

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Lecture 19 1 © Jeffrey Bokor, 2000, all rights reserved Lecture 19 SCALAR DIFFRACTION THEORY [Reading assignment: Hect 10.2.4-10.2.6,10.2.8, 11.3.3] Scalar Electromagnetic theory: monochromatic wave P : position t : time : optical frequency u(P, t) represents the E or H field strength for a particular transverse polarization component U(P) : represents the complex field amplitude : real Diffraction: Approximations: 1. We impose the boundary condition on U , that U = 0 on the screen. 2. The field in the aperture is not affected by the presence of the screen. uPt  Re U P e j t  = 2  = UP uP e j P = aperture P o screen P 1 o 1 j ---- 1 = jkr 01 exp r 01 -------------------------- ds expanding spherical r 01 »

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Lecture 19 2 © Jeffrey Bokor, 2000, all rights reserved This equation expresses the Huygens-Fresnel principle: The observed field is expressed as a superpo- sition of point sources in the aperture, with a weighting factor . Fresnel approximation Huygens-Fresnel integral in rectangular coordinates: The Fresnel approximation involves setting: in the denominator, and in exponent This is equivalent to the paraxial approximation in ray optics. (A) Let’s examine the validity of the Fresnel approximation in the Fresnel integral. The next higher order term in exponent must be small compared to 1.
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Lecture 19 - Lecture 19 Lecture 19 SCALAR DIFFRACTION...

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