= Solution
{c}
A <Michelson interferometer> uses a <beam splitter> to divide collimated input <light> between a fixed mirror and a moving mirror. Returning beams recombine at the <beam splitter>; one output reaches a <photodetector>. A compensator plate can equalize the glass traversed in the two arms. Moving one mirror by $x$ changes the <optical path difference> by $2x$.
\Image[/past-exam-of-the-physics-of-atmospheres-and-oceans-course-of-the-university-of-oxford/2022-michelson-layout.png]
{title=Michelson interferometer and the corresponding measurement chain}
The usual nominal <Fourier transform spectroscopy> specification is $\delta\nu\simeq1/d_{\max}$, where $d_{\max}$ is the maximum <optical path difference> measured from equal arms. It gives
$$
\boxed{d_{\max}\simeq\frac1{0.5\,\mathrm{cm}^{-1}}=2\,\mathrm{cm},\qquad
x_{\max}\simeq1\,\mathrm{cm}.}
$$
This is a nominal <spectral resolution element> convention.<FTIR Moving Mirror Travel Distance Calculation by Thermo Fisher Scientific>[optical path difference equals reciprocal resolution; mirror travel is half the optical path difference]{ref} A symmetric rectangular scan from $-d_{\max}$ to $d_{\max}$ instead has a sinc instrumental line shape with first-zero offset $1/(2d_{\max})$. Quoting that first-zero criterion would give $d_{\max}=1$ cm; <interferogram apodization> and other linewidth criteria change the numerical factor. An exact mathematical minimum requires such a criterion.
In the measurement chain, the <Michelson interferometer> is the spectral analyzer or modulator, between the collection optics and the <photodetector>. It encodes the incoming <radiation spectrum> into an <interferogram>; detector electronics digitize that signal and a <Fourier transform> reconstructs the <radiation spectrum>. It does not itself turn <radiant power> into an electrical signal.
Back to article page
