243s2008-m1-soln

# 243s2008-m1-soln - EE243 Sp 2008 Midterm Exam Solutions...

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1 EE243 Sp 2008 Midterm Exam Solutions Solutions Problem 1 (a) (i) For z=0 Note that E(x) crosses zero at some value of x with Imin = 0 at that position x. Therefore, Image Contrast = 1. (ii) By altering the E o and E 1 values at the lens pupil Several ways to make Imin =0 ( or Emin=0) : (A) Block out or completely attenuate the Eo beam in the lens aperture center (B) Attenuate the E+1 and E-1 beams so that amplitude of E+1 =Eo/2 = 0.25 using spatial attenuator across aperture (iii) When cos (2 π x/P) = 0 or x= P/4 (mask edge) I = EE * will be independent of z. (b) Approach 1 : We can use two separate material layers for the PSM material. With two controllable thickness, one can tailor the proper combination of attenuation and phase shift. Approach 2 : The PSM material will control the attenuation. Etching of the uncovered substrate will be used to comtrol the phase ahift difference. (C ) A*m ~0 implies bleachable fraction m will have negligible effect on total absorption coefiicient (Am+B) (i) I(z,t) z ~ [ - B I(z,t) ] or I(z) proportional το exp[-Bz] , an exponential decay with depth (ii ) I(z,t) ~ I(z) is insensitive to exposure time t

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## This note was uploaded on 11/02/2010 for the course EECS 243 taught by Professor Ee243 during the Spring '03 term at University of California, Berkeley.

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243s2008-m1-soln - EE243 Sp 2008 Midterm Exam Solutions...

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