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4500PF14

4500PF14 - k for ± ± 2 k 3 Δ k ± ±< 1< ± ± 2 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 ) =

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Unformatted text preview: k for ± ± 2 k 3 Δ k ± ± < 1 < ± ± 2 k Δ k ± ± 1 2Δ k for ± ± 2 k Δ k ± ± < 1 where k is the wavevector magnitude ( k = 2 π/λ = 2 π v ), and Δ k is the wavevector bandwidth. This spectrum is shown below. For this spectrum, calculate, showing all work, the interferogram, I ( δ ), produced by the FTIR for this spectrum, where δ is the optical path diﬀerence between the two arms of the Michelson interferometer. Simplify your answer for I ( δ ) as much as possible. Put your ±nal answer in the space provided. I ( δ ) = . Prepare an accurate (computer-based) plot of the resulting interferogram. The x axis of your plot should cover from Δ k δ/π =-8 to Δ k δ/π = +8. The y axis of your plot should cover from-. 02 to 0 . 16....
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4500PF14 - k for ± ± 2 k 3 Δ k ± ±< 1< ± ± 2 k...

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