EE383P NAME: ____________________________
MFB
Spring 1999 Fourier Optics EE383P
EXAM #2
April 12, 1999
This is a closed book, open note sheet exam (two pages 8.5x11"; sheet from
Exam #1 and a new page). The time limit is 1.5 hours. Do your work on these pages
attach extra sheets only if needed.
1. (25 points) A coherent plane wave is incident on a positive focal length lens as
shown below. Plane Wave
Focal Plane
Lens
a.) What is the nature of the wave just to
the right of the lens? Give an equation.
b.) How does the wave in a.) relate to a
spherical wave of radius of curvature R?
(R can be positive for waves concave to
the left - i.e. converging, and negative for waves concave to the right - i.e. diverging.)
2. (40 points) A positive focal length lens, of diameter d, can give both an image and
an approximate Fourier transform of an object as shown below. f
f
Obj.
Image
z
F.T.
zo zi
z=0
a.) Although the Fourier
transform is not exact in the
plane z = f, an exact
transform can be obtained if
the Fourier transform is
projected onto a curved
surface that intersects the z-axis at z = f. What is the surface and how much is it
curved?
b.) Sketch on the diagram above the direction of curvature of the exact Fourier
transform surface.
c.) What are the disadvantages of obtaining an exact Fourier transform in this way?
