Name:_________________________________
EE 8390: Fourier Optics
Exam 1
March 12, 2008
Take Home
Due Monday March 24, In Class at 3:30
Exam Rules:
1. Scientific calculators and extra scratch paper may be used.
2. Exam is open book [class text], open notes. Do not discuss
this test with anyone.
3. Clearly designate results, e.g., by underlining them or
placing boxes around them.
4. Derived equations may be used, but some explanation of
their origin should be given
5. Numerical results (computer) may be used to validate and
plot results but full credit will only be earned for analytical
results unless otherwise directed.
6. State any assumptions you make.
7. Show your work.
8. Use extra paper as needed, present your solutions in an
organized fashion.
9. The Honor Code applies to this exam
Name:_________________________________
1)
Below are 4 different “aperture” patterns (unity transmission in the white regions and
zero transmission in the gray). For each of the apertures shown below, separately sketch
the Fraunhofer Diffraction Pattern and justify your sketch. By sketch I mean sketch. You
do not need to plot the results in a Mathematical package. You do need to justify the
overall shape and any features which appear. Pay special attention to the relative changes
between apertures in each column (make your sketches have salient features
accordingly). If you choose to simply plot the result in a mathematical package and do
not explain or justify the changes between the plots then relatively little credit will be
given. (20 points)
2)
You are asked to design a pinhole camera with Gaussian amplitude apodization in the
pinhole. So, rather than a perfectly clear circular “hole” for a pinhole, the “hole” is a
piece of material which has increasing attenuation (less than unity amplitude
transmission) as the distance from the center of the pinhole increases. The mathematical
form of this attenuation is a Gaussian. You may assume the transmission has a constant
phase over the entire function. The distance from the pinhole to the film will be 2.54 cm
and the wavelength of design will be 540 nm. Determine the optimum standard
deviation (sigma) for the Gaussian function (akin to the size of the pinhole). This is
similar, but not identical to the optimum pinhole homework problem. Here the amplitude
transmission is not a Circ function but rather a Gaussian. Compare and contrast the
resolution and light gathering ability of this Gaussian Pinhole camera with a clear pinhole
camera. (30 points)
Name:_________________________________
3)
You are asked to analyze a camera which has a diamond shaped iris (located at the exit
pupil of the system). The pupil is shown in the figure below. It is oriented with it’s a
width of D along the x-axis and a height of 3D along the y-axis. Analytically determine
the OTF of this system along the Fx and Fy axes. Plot the results. You may assume
an incoherent source with a single wavelength (20 points)
Name:_________________________________
4)
The optical system below is comprised of 4 lenses. The first two lenses have focal length
f1 and are separated by a distance f1. The second two lenses have focal length f2, and are
separated by a distance f2. A phase and amplitude transparency is placed at the input
plane (I1(x,y)) and another is sandwiched between the 2nd and 3rd lenses (I2(x,y)).
Analyze the optical system and determine the light wave present at the various
locations throughout the optical system assuming the input is illuminated by a
monochromatic plane wave. The locations are: 1) Immediately after the 1st
transparency, 2) Immediately after the first lens, 3) Immediately before the second
lens, 4) Immediately after the 2nd transparence, and 5) at the final system output.
You may assume all lenses elements are “thin”. If you use any other attributes of the
system, define them. Describe any possible utility of such an optical system. (30 points)
f1
1
2
f1
3
4
f1 f2
f2
5
f2