Ways to observe
There are a few approaches to polarimetry in visible, infrared, and ultraviolet wavelengths. Typically polarimeters require moving parts to measure the direction of the electric field oscillations which means more time is needed to collect the same number of photons, although there are designs of polarimeters that do not have moving parts and which measure the Stokes vectors simultaneously.
Spectropolarimetry
Taking a spectrum is taking light and spreading it in wavelength space. Having wavelength information as well as intensity, particularly at moderate or high resolution, allows us to detect species (gases) absorbing the light. In spectropolarimetry, you are doing the same thing but also getting the polarization (E field orientation) in addition to the wavelength and intensity of the light. In polarized light a spectrum is especially useful for retrieving accurate molecular abundances and doing radial velocity cross correlation (template matching). The polarized spectra can look vaguely like a regular spectrum in shape but if one is measuring fractional polarization it’s important to consider that the ultimate fate of the photons can change that because multiple scattering will depolarize light. In astrobiology, the spectrum of light in Stokes V (circularly polarized light) can show distinct features like the Cotton effect where the sign flips at the same wavelength as the maximum spectral absorption. Such signatures could be used as a biosignature of alien life.
Aperture
Some of the highest precision polarimeters in the world basically just act like light buckets, performing aperture polarimetry or photometry. Here no image nor a spectrum is created. A filter may be used to control the band pass (useful if you want to determine if the source of polarization is mostly Rayleigh scattering, for example, but don’t need a detailed spectrum), or the pathway may be left clear to maximize the light collection.
Imaging
In studies of circumstellar disks, imaging polarimetry has already been used to constrain their orientation and to some degree the grain size. This could in theory also be used to study hot young planets in polarized light, or brown dwarfs (or possibly other worlds in reflected light in the far future). The benefit is that the data is easily interpreted by we visual humans. A coronagraph can be used to block the star’s light. While many stars do not produce much polarization, some, especially more active stars, do. So some other method to “erase” the stellar signal like a coronagraph might be useful in some cases, however it is important to note that this can also block signals from planets very near the star.
Noise and “Noise”
In recent observations of exoplanet systems we’ve learned a lot about sources of physical “noise” (polarization from real things we’re just not trying to measure such as contributions from the ISM or the star an exoplanet orbits.) and how to characterize true noise (statistical, poisson, telescope, etc.). Good resources for examining the treatment of these noise sources are Bailey et al 2020, Bott et al 2018, and Bailey, Kedziora-Chudczer & Bott 2018 . Specifics noise/contributions from on telescope and instrument polarization, stellar and ISM polarization, and on debris disks are also available from the HIPPI group as well as other aperture and imagine polarimeters.
A list of the (optical/NUV/NIR) polarimeters of the world:
You can view and comment on the list here. This is a living document being updated continuously by the optical astronomical polarimetry community.