Announcements 3/28/12
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Prayer
Exam review problems for sign-up
Calvin & Hobbes
Reading Quiz
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A lens placed after a diffraction aperture causes
the Fraunhofer pattern to be produced:
a. before the focal length
b. at the focal length
c. after the focal length (but at a finite
distance)
d. at infinity
Lenses
Lenses
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What it object is not at infinity?
a. What appears at q?
b. What appears at f?
Object at f:
f
f
f
f
“Fourier transform plane”
Lens Fourier Transforms
at focus of lens
From Hecht
“Fourier Transform smoothing”
Before
From Hecht
After
Reading Quiz
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What does the “Rayleigh criterion” tell us?
a. The angle at which both light polarizations
have equal reflection coefficients
b. The angle at which p-polarized light has
minimum reflection
c. The angular separation resolvable by an
imaging system
d. The number of orders produced by a
diffraction grating
Reading Quiz
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The Rayleigh criterion for resolving two point
light sources comes from:
a. Fourier transforms of delta functions.
b. Jinc functions’ maxima and minima.
c. Lagrange multipliers.
d. Parallax of stars.
Simple Telescope
Circular Aperture, again
What do you get in this situation?
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What if there’s a lens in the hole?
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What if there isn’t a board?
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What if you have two light sources?
pattern at infinity
f
superimposed
pattern at focus
patterns at focus
board with hole
Rayleigh: 2nd peak at
position of first minimum
Rayleigh Criterion
Curve is
(J1(x)/x)2
plotted vs (krb/f), = qD/l (using sinq  q)
Mathematica “FindRoot” command: q/l = 1.21967…
qmin.resolve  1.22
l
(= first zero of J1(x))
D Rayleigh Criterion