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Unformatted text preview: Solution: The first system is the usual singlelens imaging system, so it satisfies: 1 1 1 imaging condition: + = S 1 S 2 f S 2 lateral magnification: m = S 1 where, from the way the lens is described, 1 1 1 2 = ( n f g 1) R = ( n R g 1) R The second system is best modeled anew using the matrix formulation for ray propa gation: 1 2.71/2.710 Optics Practice Exam 3 Solutions Spring 09 1. A thin biconvex lens with the same absolute curvature on both faces is used in the two imaging systems shown below. In the first, both object and image are in air, whereas in the second the object is immersed in a material of index n < n g , where n g is the index of the glass used to make the lens. Compare the two imaging systems in terms of imaging condition and magnification. 1 1 n g img 1 1 = R n g n 1 n obj R x img S 2 1 1 1 S 1 1 n x obj 1 1 1 1 f n obj = S S 1 2 1 1 1 n x obj S 1 1 1 = n f f n obj S 1 S 1 S 2 S 2 S + 1 x 2 n n f f obj 1 n + 1 2 where = n (note f > f ) f g 2 R x img S 1 S 1 S n Imaging condition: = 0 1 1 S + 2 2 = 0 + = obj n n f S 1 S 2 f Assuming the imaging condition is satisfied, the system equation becomes: S 1 1 = img 1 n f f n obj x img 1 S 2 f x obj x img S 2 n S 2 m = = 1 = (from the imaging condition) x obj f S 1 2. In the configuration below, lenses L1 and L2 are identical with focal length f , and we consider them to be infinite aperture. The system is illuminated coherently by an onaxis plane wave. 2 (a) Write an expression for the field at x in terms of the thin complex transparencies g 1 ,g 2 . Solution: The first part (to the left of g 2 ( x )) is a Fouriertransforming system: The second part (to the right of g 2 ) is a singlelens imaging system with unit magnification: x The field at 2 2 x = exp i ( x + y ) G 1 g 2 ( x ) 2 f f (Note that the first exponential term could have been omitted...) (b) Consider the specific case with f = 10 cm and g 1 , g 2 defined as: 3 If = 1 m, derive and sketch the intensity at the output plane x . Solution: The binary grating has fundamental period = 20 m and duty cycle 50%, i.e. it is of the form: 1 2 x 1 n = x g 1 ( x ) = 1 + sgn cos sinc e i 2 2 2 2 n = x 1 G 1 = sinc f 2 n = n x 1 2 f Mind the coordinates! f 1 m 20cm Since = = 1 cm, the g 2 transparency only lets orders 1 , , +1 20 m to pass through, therefore the field (or intensity) at the output plane is three bright spots. 4 Example: OTF of the Zernicke phase mask The thin phase transparency whose schematic is given below is placed at the Fourier plane of a unit magnification telescope with focal length f = 10cm. What is the optical transfer function for quasimonochromatic illumination at wavelength = 1 m?...
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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.
 Spring '09
 SeBaekOh

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