## 1 Introduction  
Solar-induced chlorophyll fluorescence (SIF), stimulated by vegetation-absorbed sunlight, is one of the three primary sun-releasing paths, along with photosynthesis and non-photochemical quenching (NPQ) [1]. As an effective proxy of vegetation photosynthetic functions, SIF has been proven to be more efficiently related to the gross primary productivity (GPP) compared with traditional reflectance vegetation indexes [2]. To illustrate this, SIF signals cover the 650-800 nm spectra and have two emission peaks: red light bands (around 685 nm) and near-infrared bands (around 740 nm). The former is mainly stimulated during photosystem II (PSII), whereas the latter is emitted by both photosystem I (PSI) and PSII [3]. SIF, as signals emitted actively by vegetation themselves, can also be detected by remote-sensing sensors, like reflectance spectra. To illustrate this, SIF signal retrieval refers to inverting atmospheric transference through known solar irradiances and surface radiances, thus reconstructing biochemical actions at the foliage level, including photosynthesis, fluorescence emission, and reflectance. Among the present sensors, there are several satellites with the potential to be utilized for SIF extraction: the Greenhouse Gases Observing Satellite (GOSAT), Global Ozone Monitoring Experiment-2 (GOME-2), SCIAMACHY, TanSat, and Orbiting Carbon Observatory 2 (OCC-2) [2, 4, 5, 6]. Furthermore, the European Space Agency's Fluorescence Explorer (FLEX) project is on schedule, and with the development of hyperspectral technology, computer technology, and their further applications in remote sensing, researchers have obtained information on the field, airborne, and satellite platforms. Thus, SIF has been successfully retrieved from remote sensing data and utilized in the real world [2; 7; 8; 9]. There exist three main application categories of SIF: exploring vegetation photosynthesis, detecting vegetation growth stress effects, and other innovative applications [3; 10]. First, numerous studies have shown that SIF can be used as one of the indicators to directly measure photosynthesis [11; 12; 13; 14], and it can also be used to investigate the presently ambiguous relationships between SIF and many other photosynthesis factors (shown in Table 1). To be specific, significant progress has been made in unearthing the relationships between factors, such as the GPP [15; 16], absorbed photosynthetic active radiation (APAR) [17; 18], light use efficiency (LUE) [14; 17; 19], seasonal dynamics [17; 20; 21], vegetation type [22; 23], and chlorophyll content [24; 25]. Secondly, using SIF to reveal the stress effects of water, nitrogen, and other factors is also an important research field [26; 27; 28]. Furthermore, there are also some novel applications, such as canopy temperature detection [29], extreme events analysis [30; 31; 32], and so on. Those prosperous prospects promise a future for SIF applications. At present, SIF retrieval methods fall into three categories: algorithms based on atmospheric radiative transmission, simplified physically based model algorithms, and data-driven algorithms [33]. Based on atmospheric radiation transmission and simulating the absorption and scattering of solar radiation, the atmospheric radiation transmission methods were established to simultaneously solve SIF signals. The Fraunhofer line discrimination (FLD) algorithms, spectral fitting method (SFM), and their derivative methods are representative examples. These algorithms have an excellent physical basis, whereas the disadvantage is that the accuracy could interfere with the exactitude of the solar radiation, input as parameters. Fortunately, the SFM algorithms have been adopted as the SIF inversion algorithm of the FLEX project [18]. There are also two families of algorithms: the simplified physically based model methods and the data-driven statistical approaches. The latter always involve some traditional statistical methods, like principal component analysis (PCA), or singular value decomposition (SVD) analysis.