## 1 Introduction  
The anisotropic characteristics of forest canopy reflectance from multiple observation directions are greatly affected by the proportions of visible sunlit and shaded components in a forest stand [1; 2; 3]. The shaded/sunlit proportions also affect the estimation accuracy of gross primary production (GPP) using light use efficiency (LUE) models which are sensitive to the shaded/sunlit proportions [4; 5]. A forest stand consists of overstory and forest background matrix, including shrubs, grass, and bare earth in a vertical way. It can be divided into four components as follows: Sunlit overstory, sunlit forest background, shaded overstory, and shaded forest background [6; 7; 8] under the specific observation geometry. The four component proportions directly determine the forest canopy spectral characteristics [9] and further affect the retrieval accuracy of forest leaf area index (LAI) [10, 11] and chlorophyll content [12]. Then characterizing the sunlit and shaded components in a forest stand will be beneficial to the calculation of C assimilation and transpiration using advanced ecosystem models [13]. Most of the methods quantifying four forest components usually fall into three categories: (1) GO models: Various geometric optical (GO) models have been developed to compute the proportions of four forest components and bidirectional reflectance distribution function (BRDF) analytically or empirically [1, 14, 15, 16, 17]. However, there still exist some difficulties and challenges as follows: (i) The assumption that tree crowns have uniform shapes limits their applications in a heterogeneous forest stand with various tree species. Moreover, it is difficult to approximate the actual mutual shadowing effect between tree crowns using a statistical model and determining the unknown parameters of statistical models characterizing tree spatial distribution patterns. (ii) Most of the GO models are only used in relatively flat or slope areas, which prevent their applications in mountain areas [18, 19]. However, the topographic variations affect proportions of the four forest components, further affecting the BRDF of a forest canopy [18, 19, 20]. (2) Ray-tracing algorithm: The ray-tracing based methods have been successfully developed during the past decades, such as deterministic ray-tracing [20], Monte Carlo ray-tracing model [21], and discrete anisotropic radiative transfer model (DART) [22]. Compared to the GO models, DART can simulate complex forest scenes through the importation of 3D trees generated in external modeling software or using turbid layers with defined crown structure parameters [23]. However, it is difficult to reconstruct the same virtual forest scene with the real forest plot used in DART software, which will introduce apparent errors to the estimation and simulation of the four forest components and BRDF [24, 25]. (3) Spectral mixture analysis: The reflectance of a remotely sensed image pixel can be expressed as the weighted linear combinations of reflectance values of the sunlit forest canopy, sunlit forest background, and all shaded components based on the spectral mixture analysis [9, 26, 27, 28]. However, similar spectral characteristics make it challenging to separate the shaded forest components and further obtain the proportions of four forest components in any observation direction using given optical imagery [28, 29]. Thus, a more flexible and generic approach is needed to characterize the spatial variations of the four forest components based on the real forest three-dimensional (3D) scene. The 3D structural information within the aerial laser scanning (ALS) data make it possible to characterize canopy structure [30, 31] and separate overstory and forest background [32] quantitatively. Various structural parameters, such as crown size [33, 34], tree height and location [35, 36], canopy cover [37], and LAI [38], have been successfully obtained from ALS data. [PERSON] [39] found that ALS data outperformed other remotely sensed data in predicting forest structure parameters.