MIT2_71S09_uquiz2_sol

# MIT2_71S09_uquiz2_sol - 2.71 Optics 1 Solution Quiz 2...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2.71 Optics 1. Solution: Quiz 2 Solutions Spring `09 z g1 (x, z) = a1 exp i2 sin + cos , 6 6 x z g2 (x, z) = a2 exp i2 - sin + cos , 3 3 x At z = 0, a1 = 1 a2 = 1 2 x 1 x 3 2 I(x) = | 1 (x, 0) + g2 (x, 0)|2 = a1 ei2 2 + a2 e-i2 2 g 2a1 a2 x 1 3 2 2 = (a + a2 ) 1 + 2 cos 2 + 1 2 a + a2 2 2 1 21 1 1 x 1+ 3 2 = 1+ 1+ cos 2 1 4 2 1+ 4 x 5 4 2 = 1 + cos 2 where = 4 5 1+ 3 m= 4 2 period contrast = 5 1+ 3 5 4 5 9 9 1 I(0) = 1 + = = =2 4 4 5 5 4 4 After phase-shifting g1 by /2, we get x 5 4 5 1 I(0) = = 1 I(x) = 1 + cos 2 + 4 5 2 4 4 2. (a) Solution: x 1 gt (x) = 1 + cos 2 2 1 1 i2 x 1 -i2 x + e = 1 + e 2 2 2 1 1 1 1 1 Gt (u) = (u) + u - + u+ 2 2 2 x gP P - (x ) Gt f 1 1 f 1 f = (x ) + x - + x + 2 4 4 f 1m 5cm = = 5mm 10m Fourier: Scaling: 1 (b) Solution: To preserve all the input's details to the outputs, all diffracted orders must pass the pupil mask. a > 1cm. (c) Solution: Yes. If the illumination is ei2 then: gin (x) = gillum (x)gt (x) 1 i2 x 1 i2( + 1 )x 1 i2( - 1 )x = e + e + e 2 2 2 1 1 1 1 1 Gin (u) = u - + u- - + u- + 2 4 4 1 1 f 1 f gP P - (x ) (x - f ) + x - f - + x - f + 2 4 4 So all diffracted orders shift by f at the pupil plane. The original limit amin = 1cm is not enough to accommodate all orders. A pupil mask that is symmetric around the optical axis must be extended to f + f : x 2 (d) Solution: The glass plate shifts the 0th order by : 1 1 1 gP P - (x ) = (x ) + (x - 5) + (x + 5) 2 4 4 1 1 1 gP P + (x ) = - (x ) + (x - 5) + (x + 5) 4 2 4 phase shift by no change Fourier: Scaling: 1 1 1 GP P + (u) = - + ei2u5mm + e-i2u5mm 2 4 4 x x x 1 1 i2 10m 1 -i2 10m gout (x ) = GP P + =- + e + e f 2 4 4 1 1 x 1 x = - + cos 2 = - 1 - cos 2 2 2 10m 2 10m 2 2 1 x Iout (x ) = gout (x ) = 1 - cos 2 4 10m 2 1 2x 2x 2 = 2 sin 2 = sin 2 4 10m 10m 3 MIT OpenCourseWare http://ocw.mit.edu Spring 2009 2.71 / 2.710 Optics For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. ...
View Full Document

## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.710 taught by Professor Sebaekoh during the Spring '09 term at MIT.

Ask a homework question - tutors are online