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What happens when you double the width of the entrance slit of a spectrograph, in turn letting in twice as much light, would there be an improvement in the Fourier transform of the measured spectral profile d(f) following to higher frequency f?

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    $\begingroup$ The slit is a cut in the transverse spatial domain, the spectrometer (assuming a dispersive-type (e.g. grating or prism)) spreads wavelength into the transverse spatial domain. Bigger slit smears out the spectrum, so no, there would be the opposite of an improvement. $\endgroup$
    – uhoh
    Mar 31 at 1:02
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    $\begingroup$ Well I think it is best if you first add more information. Are you talking about a conventional spectrometer that uses a diffraction grating, or a Fourier Transform spectrometer? Is the noise you are talking about just statistical (e.g. number of photons) or is there additional noise in the light source of some kind, or is it detector noise? Presumably data will be less noisy if you have a bigger aperture and more light and the resolution will be poorer, but it's hard to make more general statements without additional details. $\endgroup$
    – uhoh
    Mar 31 at 4:46
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    $\begingroup$ A conventional one using a diffraction grating; the noise would come from the background like heat, noise, stray light, electronic noise etc. $\endgroup$
    – Jay D
    Mar 31 at 6:23
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    $\begingroup$ @RogerWood almost all spectrographs have slits defining the illumination of the dispersive element (and as a result, do not use all the available light from a star). $\endgroup$
    – ProfRob
    May 7 at 6:47
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    $\begingroup$ @RogerWood you're dubious? Here are two links for 8-m telescopes, though why you couldn't find this I don't know. gemini.edu/instrumentation/gmos eso.org/sci/facilities/paranal/instruments/uves/inst.html $\endgroup$
    – ProfRob
    May 9 at 7:18

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