## 2 Astronomical Parameters
### Transit-Spectroscopy Parameters  
In order to obtain the infrared transmission spectrum from a planetary terminator atmosphere during primary transit and the blocked atmospheric spectrum in secondary eclipse, relevant spectral-signal parameters need to be calculated. Transit spectroscopy relies on the measurements of a multiwavelength high-precision light curve when the exoplanet passes by the host star. Each light curve has different characteristic transit depths during transit, measured by the contrast ratio (CR) between the transit depth during the primary transit and the extrasolar system flux while out of transit (OOT) [11]. The CR is defined as  
\[CR(\lambda)=\frac{S_{OOT}(\lambda)-S_{IT}(\lambda)}{S_{OOT}(\lambda)}=\frac{S_ {p}(\lambda)+S_{A}(\lambda)}{S_{OOT}(\lambda)}, \tag{1}\]  
where \(S_{IT}(\lambda)\) and \(S_{OOT}(\lambda)\) are spectral signals measured in and out of transit, respectively. \(S_{OOT}(\lambda)-S_{IT}(\lambda)\) is the reduced part of a star signal during transit that has two components, namely, the star signal blocked by the planet alone, \(S_{p}(\lambda)\), and the star signal absorbed by the planetary atmosphere, \(S_{A}(\lambda)\). When a simplified system model with absence of limb darkening is adopted, the ratio between the signal blocked by the planet and the OOT star signal is a constant at any wavelength, corresponding to the projected area ratio of the planet and star, i.e., \(S_{p}(\lambda)/S_{OOT}(\lambda)=\left(r_{p}/r_{s}\right)^{2}\), where \(r_{p}\) and \(r_{s}\) are the radii of the planet and star, respectively. \(S_{A}(\lambda)/S_{OOT}(\lambda)\) can be regarded as additional wavelength-dependent contribution [12] coming from the atmosphere, \(A_{pt}(\lambda)\), as shown in Figure 1b. The CR spectrum with atmospheric absorption [13] can be expressed as  
\[CR(\lambda)=\left(r_{p}/r_{s}\right)^{2}+A_{pt}(\lambda). \tag{2}\]  
Atmospheric contribution at any wavelength \(A_{pt}(\lambda)\) in Equation (2) can be established as follows. \[A_{pt}(\lambda)\approx n_{H}(\lambda)\frac{2r_{s}}{r_{s}^{2}}\frac{kT_{p}}{ \xi\mu}, \tag{3}\]  
Figure 1: (**a**) Primary transit spectroscopy with light curves at different wavelengths. \(T_{2}\) and \(T_{3}\) indicate the time when the planetary projection completely enters and just exits the star. (**b**) Chart of contrast-ratio composition. Contrast ratio is composed of constant planetary component \((r_{p}/r_{s})^{2}\), as indicated by the horizontal line, and wavelength-dependent atmospheric contribution \(A_{pt}(\lambda)\). Red, blue, and green lines represent observation results at different wavelengths. where \(k\) is the Boltzman constant, \(T_{p}\) is the mean planetary atmospheric temperature, \(\mu\) is the mean molecular mass, \(g\) is surface gravity, and \(n_{H}(\lambda)\) is the scale factor, which depends on feature intensity, varying with opacity [14]. The calculation results of Equation (3) in a variety of planetary systems show that a transit signal is more obvious around smaller stars, and the frequency of transits also increases, which allows for utilizing more revisits to improve the SNR. Therefore, the signal of a planet is higher around an M dwarf, which is called \"M-dwarf advantage\" [15]. This should be taken into account when selecting planetary candidates as observation targets. The SNR of atmospheric contribution is given by the ratio of \(A_{pt}\) to noise.