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Unformatted text preview: ng Gaussian apodized pinholes,” Appl. Opt. 27, 30743077 (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.
 Fall '11
 KirkW.Madison
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