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Unformatted text preview: Notes on Fourier Transforms I will state as fact, that the most general Fourier series expansion for a function f(x) is a sum of complex exponentials! f ( x ) = lim m →∞ m X n =- m γ n e inπx c The only restriction is that f(x) must be a periodic function, of period 2c. The coefficients γ n are defined as: γ n = 1 2 c Z c- c f ( x ) e- inπx c d x Remember the trig. identity, e iy ≡ cos y + i sin y From the above theory we can work out the solution to the problem for the Fourier optics lab.-- screen diffraction pattern lens f = 20 cm 50 ln/cm grating O I In the figure we see the experimental setup in the lab. The screen has an image of the grating on it formed by the 20 cm lens and in the focal plane of the lens we see the diffraction pattern for the grating. The distance from the grating to the lens is the image distance I. The distance from the lens to the screen is the object distance O. The image of the grating on the screen is caleed the ”true image”. The lens formula gives the position of the true image. e.g....
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- Fall '08
- Fourier Series, a+b, γn, a+b a+b