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My Life and Times with the Fourier Transform Spectroscope

My Life and Times with the Fourier Transform Spectroscope. Rebecca Dell CARA Summer REU 2001 University of Chicago Advisor: Prof. Stephan Meyer. The Item:. Detector. M2 Mirrors. M1 Mirrors. Dihedral Mirrors on Carriage. Black Body Radiator. Polarizers. The Magical Thing:.

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My Life and Times with the Fourier Transform Spectroscope

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  1. My Life and Times with the Fourier Transform Spectroscope Rebecca Dell CARA Summer REU 2001 University of Chicago Advisor: Prof. Stephan Meyer

  2. The Item:

  3. Detector M2 Mirrors M1 Mirrors Dihedral Mirrors on Carriage Black Body Radiator Polarizers

  4. 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.

  5. 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.

  6. For wavenumber s, position z, the power: y (z, s) = a(s)cos(2psz) For all s: y (z) = (1/s) ∫0∞ a(s)cos(2psz)ds where s is the average wavenumber.

  7. Fourier Integral: ∫-∞∞ b(s)ei2pszds= ∫-∞0 b(s)ei2pszds + ∫0∞ b(s)ei2pszds = ∫0∞ b*(s)(ei2psz)*ds + ∫0∞ b(s)ei2pszds =2 ∫0∞Re[b(s)ei2psz]ds Now, use the handy Euler’s Fromula: eix=cos(x) + isin(x) ∫-∞∞ b(s)ei2pszds =2∫0∞ b(s)cos(2psz)ds (½) ∫-∞∞ b(s)ei2pszds =∫0∞ b(s)cos(2psz)ds If b(s) = 2 a(s)/s: y(z) = ∫-∞∞ b(s)ei2pszds

  8. A more intuitive approach: Monochromatic a(s1)cos(2ps1z) Dichromatic a(s1)cos(2ps1z) + a(s2)cos(2ps2z) Broad Band (1/s) ∫0∞ a(s)cos(2psz)ds

  9. 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

  10. 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

  11. Sample Interferogram

  12. A little closer in:

  13. Power Spectrum of the Black Body

  14. Power Spectrum of Light Transmitted through the Filter

  15. Divide the two to get the Filter Characterization

  16. Black Body What I did: FTS Detector SPECTRA Computer Hard Drive FFT

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