Lecture 20

Lecture 20 - Lecture 20 Lecture 20 DIFFRACTION THEORY OF A...

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Lecture 20 1 © Jeffrey Bokor, 2000, all rights reserved Lecture 20 DIFFRACTION THEORY OF A LENS We have previously seen that light passing through a lens experiences a phase delay given by: (neglecting the constant phase) The focal length, f is given by: The “lens makers formula” The transmission function is now: This is the paraxial approximation to the spherical phase Note: the incident plane-wave is converted to a spherical wave converging to a point at f behind the lens ( f positive) or diverging from the point at f in front of lens ( f negative). Diffraction from the lens pupil Suppose the lens is illuminated by a plane wave, amplitude A. The lens “pupil function” is . The full effect of the lens is We now use the Fresnel formula to find the amplitude at the “back focal plane” z = f The phase terms that are quadratic in cancel each other.   jk n 1 2 2 + 2 -----------------   1 R 1 ----- 1 R 2 exp = 1 f -- n 1 1 R 1 1 R 2 j k 2 f ---- 2 2 + exp = f f P  U l '  P = U l ' P j k 2 f 2 2 + exp = U f xy j k 2 f x 2 y 2 + exp j f -------------------------------------------- e jkf  d U l ' j k 2 f 2 2 + j 2 f ------ x y + exp exp d = 2 2 +
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Lecture 20 2 © Jeffrey Bokor, 2000, all rights reserved (A) This is precisely the Fraunhofer diffraction pattern of ! Note that a large z criterion does not apply here.
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Lecture 20 - Lecture 20 Lecture 20 DIFFRACTION THEORY OF A...

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