PHYS 408 HOMEWORK 5 SOLUTIONS

# Gaussian apodizing lters can be purchased too see for

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Unformatted text preview: ng Gaussian apodized pinholes,” Appl. Opt. 27, 3074-3077 (1988). Gaussian apodizing ﬁlters can be purchased, too. See, for example, the “Bullseye Apodizing Filters” sold by Reynard Corporation. An overall phase shift of π will occur for a ﬁlm of ﬁnite thickness obeying kz ∆z = π . Thus append to the gaussian aperture a thin ﬁlm of thickness ∆z = π /kz where kz . Alternatively, a π phase shift from a reﬂection could be incorporated. 3 3 lens of ﬁnite thickness 3.1 lens of negligible thickness Lengths in centimeters. Matrix for propagation through free space by 30 centimeters: Matrix for propagation through thin lens: 1 0 1 −f 1 = −(n − 1) 1 ￿ 1 R1 1 R2 − ￿ 1 0 1 0 = 1 30 (17) 1 0 −(1/2) (1/5 + 1/15) 1 Matrix for propagation over 30 cm and passage through thin lens: Thus 1 0 −2/15 1 qf 1 0 30 1 = 1 30 −2/15 −3 = 1 0 −2/15 1 (18) (19) 1 · (−iz0 ) + 30 (−2/15) · (−iz0 ) − 3 = (−7.50 cm) − i(0.0476 cm) = (20) (21) 2 where z0 = π w0...
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## This document was uploaded on 03/11/2014 for the course PHYS 408 at University of British Columbia.

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