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Material Type: Assignment; Class: 1051 - Physical Optics; Subject: Imaging Science; University: Rochester Institute of Technology; Term: Spring 2008;
Typology: Assignments
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Read P^3 §9 Coherence and P^3 §11 Fraunhofer Diffraction
Due 16 May 2008 (Th) —: Write up ONE lab of your choice in the “long format” (including abstract, data, analysis, etc., as listed in the handout)
Due 8 May 2008 (Th) — Do the following problems; SHOW YOUR WORK
(a) Determine the frequency bandwidth for this wavelength range (b) Compute the associated coherence time and coherence length of white light.
(a) Find the expression for ∆ν (b) Derive the expression for the corresponding linewidth ∆λ (c) Derive the expression for the coherence length ∆c of the source. (d) Find the coherence length of a sodium arc that emits two narrow spectral lines:
ω 1 = 3. 195 × 1015
radians sec ω 2 = 3. 198 × 1015
radians sec
(e) Find the coherence length of a He:Ne “greenie” laser with
ω 1 = 3. 171 × 1015
radians sec ω 2 = 3. 469 × 1015 radians sec
(a) fa [x, y] is a single very small transparent aperture (“hole”) (b) fb [x, y] consists of two apertures that are very narrow along the x−axis and infinitely long along the y−axis and that are separated by d units. (c) fc [x, y] consists of an infinite number of apertures from part b that are uniformly spaced at increments of d units. MORE→→→
g [x, y] ∝ |F [ξ, η]|^2
ξ→ (^) λ 0 xz 1 ,η→ (^) λ 0 yz 1
where the 2-D Fourier transform is defined:
F [ξ, η] ≡ F 2 {f [x, y]} ≡
−∞
f [x, y] exp [− 2 πi (ξx + ηy)] dx dy
The object f [x, y] satisfies the following conditions:
f [x, y] = 1 if |x| ≤ 1 AND |y| ≤ 1 f [x, y] = 0 f [x, y] = 1 otherwise
(a) Sketch f [x, y]; (b) Calculate the diffraction pattern in the Fraunhofer diffraction region if f [x, y] is illuminated by light with wavelength λ 0 ; (c) Sketch the x-axis profile of the diffraction pattern including labels of the values on both axes.