4500PF14 - k for 2 k 3 k < 1 < 2 k k...

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Fourier Transform Infrared Spectrometer 5 A Fourier Transform InfraRed (FTIR) spectrometer is based on a Michelson in- terferometer. An FTIR spectrometer is capable of determining the spectral content of a light source. This is accomplished by scanning one of the mirrors of the Michelson in- terferometer and recording the output interferogram as a function of the optical path difference between the two interfering beams. In an FTIR, the wavelength of a wave is typically represented by its wavenumber v where v = 1 λ , and λ is the freespace wavelength. A particular optical source emits a hypothetical tri- angular spectrum. To obtain the interferogram, the spectrum may be considered to be an even function centered at k = 0. The spectrum is thus represented by B ( k )= 0 for ± ± 2 k k ± ± 1 1
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Unformatted text preview: k for 2 k 3 k < 1 < 2 k k 1 2 k for 2 k k < 1 where k is the wavevector magnitude ( k = 2 / = 2 v ), and k is the wavevector bandwidth. This spectrum is shown below. For this spectrum, calculate, showing all work, the interferogram, I ( ), produced by the FTIR for this spectrum, where is the optical path dierence between the two arms of the Michelson interferometer. Simplify your answer for I ( ) as much as possible. Put your nal answer in the space provided. I ( ) = . Prepare an accurate (computer-based) plot of the resulting interferogram. The x axis of your plot should cover from k / =-8 to k / = +8. The y axis of your plot should cover from-. 02 to 0 . 16....
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This note was uploaded on 04/29/2008 for the course ECE 4500 taught by Professor Gaylord during the Spring '08 term at Georgia Institute of Technology.

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4500PF14 - k for 2 k 3 k < 1 < 2 k k...

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