= Solution
Three complementary methods available in the setting of this 2017 paper are:
* <Exoplanet transmission spectra> during primary transit. The planet's atmosphere filters stellar light at the <day-night terminator>. Its advantages are a bright background source and sensitivity to atomic, molecular and aerosol <opacity>; its limitations are the need for a transit, a small annular signal, <exoplanet cloud> masking, and degeneracies among abundance, reference <pressure>, <temperature> and <mean molecular weight>. The useful physical range is ultraviolet through near- and mid-infrared, subject to instrumentation. The <Hubble Space Telescope> is an appropriate example, with ultraviolet/optical instruments and near-infrared transit spectroscopy, particularly around $1.1$--$1.7\,\mu\mathrm m$ with WFC3.
* <Exoplanet secondary eclipse> spectroscopy or photometry. Subtracting the stellar-only light in eclipse from the combined light outside eclipse isolates the dayside thermal and reflected spectrum. It measures dayside <brightness temperature> and composition and can reveal an <atmospheric thermal inversion>. Limitations include eclipse geometry, a weak planet-star contrast, and the joint dependence of features on <opacity> and the <atmospheric pressure-temperature profile>. Reflection is most useful in the optical, and thermal emission in the near- to mid-infrared. The <Spitzer Space Telescope> is a major example: earlier cryogenic observations included infrared spectroscopy, while in 2017 the warm mission provided 3.6- and 4.5-micrometre photometry.
* <Exoplanet direct imaging>. Spatial separation isolates the planet's own spectrum without requiring a transit, and favours young hot giants on wide orbits. Limitations are small angular separation, overwhelming stellar leakage, restricted inner working angle and instrument contrast. Near-infrared spectra of young giants are especially useful, with optical reflected light and thermal infrared also possible for suitable targets. The <Very Large Telescope>, for example with its SPHERE imager, provides optical/near-infrared high-contrast observations using <adaptive optics> and stellar-light suppression.
\b[Transmission probes the limb, eclipses probe the dayside, and direct imaging isolates spatially resolved planetary light.] Radial velocities alone measure orbital motion rather than atmospheric composition; high-resolution planetary Doppler spectroscopy can instead detect atmospheric spectral lines if planetary light is isolated statistically.
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