This study presents an improved theoretical formulation of the gap probability (Pgap) model, typically applied to indirectly estimate LAI in woody ecosystems. Specifically, we present the woody element projection function (GW), which characterises the angular contribution of non-leaf facets in woody ecosystems, and explain how it may be used to improve the accuracy of indirect LAI retrieval via the application of the Pgap model. GW enables separate treatment of the leaf and wood projection functions in the theoretical model, important in the typical case when Pgap includes the influence of both leaf and wood canopy elements. This study then validates the improved theoretical model using experimental data. Here, Pgap was calculated from a 3D scattering model, parameterised with highly-detailed 3D explicit tree models reconstructed from empirical data of a sampled forest stand. The experimental data was then used to quantify additional effects of view zenith angle (VZA), leaf angle distribution (LAD), and the influence of woody components on the indirect estimation of LAI and within-crown clumping via application of the Pgap model. Additionally, we quantify within-crown clumping of reconstructed tree models for leaf and woody elements both together and separately for the first time. LAI errors up to 25% at zenith were found when ignoring GW and were shown to be a function of VZA. Conversely, at the approximate 57.3° (1 radian) VZA, results show that there was no effect of GW due to the wood projection function converging with leaf projection functions. Within-crown clumping factors for the modelled dataset were as low as 0.35. Consequently, making a common assumption of a random distribution of canopy elements at the crown scale would lead to an LAI error of up to 65% for the 3D forest stand. We also conclude that when estimating LAI via the Pgap model, separate treatment of canopy material projection '. G' functions are required at VZA's other than 1 radian. The findings of this study and the extended physical formulation presented here impact upon indirect Pgap LAI retrieval methods from sensors of all platforms in clumped canopy environments or canopies with woody (non-leaf) elements contributing to the extinction of light.