My Life and Times with the Fourier Transform Spectroscope

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My Life and Times with the Fourier Transform
Spectroscope

• Rebecca Dell
• CARA Summer REU 2001
• University of Chicago
• Advisor Prof. Stephan Meyer

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The Item
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Detector
M2 Mirrors
M1 Mirrors
Dihedral Mirrors on Carriage
Black Body Radiator
Polarizers
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The Magical Thing
The Fourier transform of the interferogram is the
spectrum of the light that you sent through the
FTS in the first place.
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Some Mathy Stuff
The fundamental concept of this coming
mathematics is that the sum of an infinite number
of cosine waves is exactly the Fourier Transform
integral. It is demonstrating the magical
principle so recently stated.
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For wavenumber s, position z, the power y (z, s)
a(s)cos(2psz) For all s y (z) (1/s) ?08
a(s)cos(2psz)ds where s is the average wavenumber.
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• Fourier Integral
• ?-88 b(s)ei2pszds ?-80 b(s)ei2pszds ?08
  b(s)ei2pszds
• ?08 b(s)(ei2psz)ds ?08 b(s)ei2pszds
• 2 ?08Reb(s)ei2pszds
• Now, use the handy Eulers Fromula
• eixcos(x) isin(x)
• ?-88 b(s)ei2pszds 2?08 b(s)cos(2psz)ds
• (½) ?-88 b(s)ei2pszds ?08 b(s)cos(2psz)ds
• If b(s) 2 a(s)/s
• y(z) ?-88 b(s)ei2pszds

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A more intuitive approach
Monochromatic a(s1)cos(2ps1z)
Dichromatic a(s1)cos(2ps1z) a(s2)cos(2ps2z)
Broad Band (1/s) ?08 a(s)cos(2psz)ds
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Advantages of the FTS

• THROUGHPUT all the light makes it through the
  instrument and is measured
• MULTIPLEX all frequencies are measured all the
  time
• Works for any area of the E-M spectrum equally
  well (almost)
• Inexpensive, small
• Fast scanning time

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What is the FTS good for?

• Measuring the luminous ether, like Michelson and
  Morley
• Measuring the CMBR, like COBE
• Characterizing filters, like me
• Any time one wants to characterize the nature of
  E-M radiation

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Sample Interferogram
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A little closer in
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Power Spectrum of the Black Body
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Power Spectrum of Light Transmitted through the
Filter
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Divide the two to get the Filter Characterization
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What I did
Black Body
FTS
Detector
SPECTRA
Computer
Hard Drive
FFT