Where was modern optical imaging technology born

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Diffraction and Image Formation
Where was modern optical imaging technology born?
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Geometrical Optics
point images
f
f
implies perfect resolution.
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Physical Optics
diffracting source
Imperfect image
Every lens is a diffracting aperture.
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Multiple Slits
Each j gets two slits (left term is top, right
term is bottom)
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Central maximum
Principle maxima
secondary maxima
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Diffraction Grating
A special corner of multi-slit-space N 104, a
l, b l
b l central maximum is very large!
a l principle maxima are highly
separated! (most dont exist)
N 104 Principle maxima are very narrow!
Secondary maxima are very low!
typical grating specs 900 g/mm, 1 cm grating.
N 9,000
a 1.11 microns
l 0.633 microns!
b 1.11 microns
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m 1
first order
grating
m 0
Maxima at
monochromatic light
You dont need diffraction to understand a
diffraction grating!!!!
Sometimes they are called interference
gratings, but thats based on how they are made,
not how they work.
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Abbe Theory of Image Formation
grating
m 1
m 0
m -1
focal plane
diffraction plane
transform plane
The spatial Fourier Transform of the object!
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Abbe Theory of Image Formation
grating
m 1
Resulting interference pattern is the image
m 0
m -1
diffraction plane
transform plane
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Image formation requires a lens large enough to
capture the first order diffraction.
m 1
Grating Equation
a
D
m 0
f
To resolve a
Resolution (diffraction limited)
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Rectangular Apertures
P(X,Y,Z)
a
b
Rather than an aperture, consider an object
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Remember, the integral is over the aperture area
Lets rearrange that a little it (this is where
the magic happens)
THATS A FOURIER TRANSFORM!!
EP(X,Y,Z) FEFeynman
Where does diffraction put the spatial
frequencies in EFeynman?