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Treat the morning and evening halves of the day-night terminator as independent, isothermal, hydrostatic atmospheres with the same reference radius $R_0$, reference pressure $P_0$, composition, gravity $g$, and extinction coefficient ${\kappa }_{\lambda }$. Their atmospheric scale heights areFor $H_i\ll R_0$, the slant optical depth of half $i$ at tangent altitude $z$ is approximatelyThe standard isothermal effective altitude is thereforeup to a wavelength-independent choice of reference radius. The two semicircular limbs add in projected area, so the exoplanet transmission spectrum isEquivalently, $R_{\mathrm{tr}}^2=[(R_0+z_m{)}^2+(R_0+z_e{)}^2]/2$. Differentiating with respect to $\log {\kappa }_{\lambda }$ givesThus a homogeneous retrieval measures, to leading order,provided the opacity and composition do not themselves differ between the two limbs.

The measured mass and radius illustrate the exoplanet interior-composition degeneracy. Three plausible structures are:

An exoplanet transmission spectrum can distinguish a large-scale-height hydrogen atmosphere from compact steam or carbon-dioxide atmospheres. Molecular abundances, clouds, atmospheric mean molecular mass, and atmospheric escape constrain the envelope mass and evolution. An exoplanet emission spectrum constrains temperature, albedo, and internal cooling. A detected hydrogen-rich atmosphere favors the first scenario, a water-dominated high-molecular-weight spectrum supports the second, and a thin secondary atmosphere supports the third, although clouds can preserve degeneracies.

In the exoplanet transmission spectrum, the constant $a$ is the wavelength-independent reference transit depth, set mainly by the opaque planetary radius and any grey cloud deck. The Gaussian term can represent a resolved atomic or molecular absorption band centered at ${\lambda }_0$, with amplitude $b$ and width controlled by $\alpha$. The power-law term represents a continuum such as Rayleigh scattering or haze extinction; for Rayleigh scattering the opacity index is approximately $\gamma =-4$.

For a thin hydrostatic isothermal atmosphere, $\Delta D\simeq 2R_p{N}_{H}H/R_{\star }^2$ and $H=k_{B}T/(\mu m_{u}g)$. Hence $T\simeq \mu m_{u}g\Delta D{R}_{\star }^2/(2k_B{R}_p{N}_H)$. A measured exoplanet transmission spectrum amplitude constrains $N_{H}H$, so gravity, mean molecular mass and the number $N_H$ of sampled atmospheric scale heights are additional inputs. In a clear fixed-composition model, $N_H\simeq \log ({\kappa }_{\mathrm{band}}/{\kappa }_{\mathrm{cont}})$; clouds or abundance gradients can change it.

Transit spectroscopy infers the properties of an exoplanet atmosphere from the wavelength dependence of an exoplanet transit. Its measured product is an exoplanet transmission spectrum, while an annulus model for transmission spectroscopy connects the spectrum to atmospheric optical depth. The observing technique is described by NASA.

An exoplanet cloud deck divides the projected atmospheric annulus into cloudy and clear radial zones. Their contributions to the exoplanet transmission spectrum add as projected areas multiplied by $1-e^{-{\tau }_{\lambda }}$ for each zone's slant optical depth.