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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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Black Body Radiator Detector M1 Mirrors Dihedral Mirrors on Carriage M2 Mirrors 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 , position z, the power: y (z, ) = a( )cos(2 z) For all : y (z) = (1/ ) ∫ 0 ∞ a( )cos(2 z)d where is the average wavenumber.

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Fourier Integral: ∫ -∞ ∞ b( )e i2 z d = ∫ -∞ 0 b( )e i2 z d ∫ 0 ∞ b( )e i2 z d ∫ 0 ∞ b*( )(e i2 z)* d ∫ 0 ∞ b( )e i2 z d ∫ 0 ∞ Re[b( )e i2 z ]d Now, use the handy Euler’s Fromula: e ix =cos(x) + isin(x) ∫ -∞ ∞ b( )e i2 z d ∫ 0 ∞ b( )cos(2 z)d (½) ∫ -∞ ∞ b( )e i2 z d ∫ 0 ∞ b( )cos(2 z)d If b( ) = 2 a( )/ : y(z) ∫ -∞ ∞ b( )e i2 z d

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A more intuitive approach: Monochromatic a( 1 )cos(2 1 z) Dichromatic a( 1 )cos(2 1 z) + a( 2 )cos(2 2 z) Broad Band (1/ ) ∫ 0 ∞ a( )cos(2 z)d

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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 Computer Hard Drive FFT SPECTRA

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