This paper presents the theoretical basis of the algorithm designed for the generation of leaf area index and diurnal course of its sunlit portion from NASA's Earth Polychromatic Imaging Camera (EPIC) onboard NOAA's Deep Space Climate Observatory (DSCOVR). The Look-up- Table (LUT) approach implemented in the MODIS operational LAI/FPAR algorithm is adopted. The LUT, which is the heart of the approach, has been significantly modified. First, its parameterization incorporates the canopy hot spot phenomenon and recent advances in the theory of canopy spectral invariants. This allows more accurate decoupling of the structural and radiometric components of the measured Bidirectional Reflectance Factor (BRF), improves scaling properties of the LUT and consequently simplifies adjustments of the algorithm for data spatial resolution and spectral band compositions. Second, the stochastic radiative transfer equations are used to generate the LUT for all biome types. The equations naturally account for radiative effects of the three-dimensional canopy structure on the BRF and allow for an accurate discrimination between sunlit and shaded leaf areas. Third, the LUT entries are measurable, i.e., they can be independently derived from both below canopy measurements of the transmitted and above canopy measurements of reflected radiation fields. This feature makes possible direct validation of the LUT, facilitates identification of its deficiencies and development of refinements. Analyses of field data on canopy structure and leaf optics collected at 18 sites in the Hyytiälä forest in southern boreal zone in Finland and hyperspectral images acquired by the EO-1 Hyperion sensor support the theoretical basis.