## 1 Introduction  
A characteristic spectral emission known as Solar-Induced chlorophyll Fluorescence (SIF) can be observed in the red and far-red spectral regions. Photosynthesis is driven by the energy absorbed by chlorophyll molecules. When a chlorophyll molecule absorbs a photon, it will be transferred from the ground state to an excited state and become extremely unstable. There are three pathways for the excited molecule to return to the ground state [1]. First, the chlorophyll can re-emit a photon with a longer wavelength (because part of the energy is converted into heat)--this is the process of fluorescence. Second, all the energy of the excited chlorophyll can be converted into heat with no emission of a photon. Third, the energy can be transferred to other molecules to be used in the chemical reactions needed for photosynthesis. Typically, only about 1% of the absorbed sunlight is emitted through fluorescence [2]. Together with another dissipative pathway, non-photochemical quenching (NPQ), fluorescence competes with photosynthesis for the use of absorbed light [3]. Therefore, SIF is strongly related to the photosynthetic process. In earlier studies, the Photochemical Reflectance Index (PRI) [4], which is linked to the xanthophyll cycle, has been used as a proxy for photosynthesis but is strongly affected by the canopy structure, leaf pigments and background [5]. In contrast, SIF seems to be a better indicator of photosynthesis [6]. Numerous studies have shown that making measurements of SIF is a reliable way of obtaining physiological information about plants quickly and in a non-invasive way. For instance, [PERSON] _et al._[7] and [PERSON] _et al._[8] showed that stress in an early phase can be detected by SIF measurements; the studies of [PERSON] _et al._[9] indicated that SIF measurements could be used in the early detection of vegetation disease; and a strong relationship between SIF and Gross Primary Production (GPP) has been demonstrated in several studies at both canopy and global scales [10, 11, 12, 13, 14]. Therefore, it is important to measure the SIF signal in a fast and accurate way. The SIF spectrum covers the approximate spectral range of 650-850 nm. It has a distinct spectral shape with one peak at around 685-690 nm and another at 730-740 nm [15, 16]. There are two photosystems in plants--PS I and PS II--which work in tandem and have different fluorescence emissions. The majority of fluorescence emissions originate from PS II. PS II contributes to the SIF emission in both the red and far-red spectral regions, whereas PS I contributes to the SIF emission only in the far-red region and has a much smaller yield [17, 18]. As a result, the intensity and shape of the SIF spectrum are related to the amount of energy absorbed by PS II and PS I [19, 20]. The left-hand peak in the red region partially overlaps with a peak in the chlorophyll absorption spectrum. This means that light emitted by plants in this spectral region is partially re-absorbed by foliar chloroplast or other biochemical components. The amount of re-absorption is determined mainly by the canopy chlorophyll content [21] and hence the ratio of the two SIF peak-values (SIF\({}_{738}\)/SIF\({}_{685}\)) can also serve as an indicator of foliar chlorophyll content [21, 22]. The use of remote sensing techniques is necessary for the detection of SIF at the canopy level. Compared with the reflected radiance, the SIF signal is quite weak, so the solar Fraunhofer lines or telluric atmospheric absorption bands need to be used to decouple the fluorescence from the reflection based on the Fraunhofer Line Discrimination (FLD) principle [23, 24]. Consequently, most of the commonly used FLD-based methods (comprehensively reviewed by [PERSON] _et al._[3]) can only be used for the retrieval of SIF at certain separate absorption bands--the shape of the SIF spectrum and the peak-values, which are also important, are unavailable. Therefore, a new algorithm for full-spectrum SIF retrieval is needed.