A scanning Michelson interferometer is used as a Fourier-transform 'lambda-meter' to…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Optics & Photonics · Coherence and statistical optics

What an Instrument Can See, Ch Temporal coherence: correlation, spectrum and the interferometer

Problem

A scanning Michelson interferometer is used as a Fourier-transform 'lambda-meter' to characterise a tunable diode laser. The required spectral resolution is

\delta\sigma = 0.010\ \mathrm{cm^{-1}}

. ((a)) Find the maximum path difference

L_{\max}

the scanning mirror must reach to deliver this resolution, using an unapodised (rectangular-window) interferogram. ((b)) The laser under test has a Lorentzian linewidth

\Delta\nu = 50\ \mathrm{MHz}

. Compute its coherence length

\ell_c

. ((c)) Compute the fringe visibility

|\gamma_{11}|

at the path difference

L_{\max}

found in part (a), and state, with a numerical reason, whether this laser is a workable source for a scan reaching

L_{\max}

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