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Incoming links: Fourier transform spectroscopy
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 338 2 b Solution Created 2026-10-03 Updated 2026-10-05
An integral field spectrograph obtains spectra throughout a two-dimensional field instead of along one slit alone. Its reduced spectral data cube is : two coordinates locate a spatial sampling element and the third labels wavelength. One slice at fixed wavelength is an image; one column at fixed spatial position is an optical spectrum. The third axis is spectral, not a third spatial direction.
- A lenslet array divides the image into spatial elements. The spectrograph disperses each lenslet’s output into a microspectrum, with spacing and orientation chosen to avoid overlap.
- A lenslet array feeding optical fibers provides contiguous sampling; the fiber outputs are rearranged into a pseudo-slit for a conventional spectrograph.
- A bare optical fiber bundle samples the image and also reformats it into a pseudo-slit. Its packing fraction and coupling can leave spatial gaps or transmission losses.
- An image slicer divides the image into strips, then rearranges them end to end. Dispersion preserves position along each strip, and the reconstruction restores the second spatial coordinate.
- A scanning Fabry–Pérot interferometer or tunable narrow-band filter records a sequence of nearly monochromatic images, stepping the transmitted band to assemble the cube.
- Imaging Fourier transform spectroscopy records an interferogram at every spatial pixel while scanning optical path length difference. Transforming each interferogram supplies the spectral coordinate.
The first four are simultaneous spatially multiplexed grating arrangements. The last two deliver equivalent cube coordinates by scanning; they are imaging spectrometers rather than simultaneous grating integral-field units, and variability during the scan can corrupt the cube. Detector packing, sampling, calibration and throughput determine the practical tradeoffs.