Terrestrial LiDAR becomes more and more popular to estimate leaf and plant area density.Voxel-based approaches account for this vegetation heterogeneity and significant work has been done in this recent research field, but no general theoretical analysis is available.Although estimators have been proposed and several causes of biases have been identified, their consistency and efficiency have not been evaluated. Also, confidence intervals are almost never provided.In the present paper, we solve the transmittance equation and use the Maximum Likelihood Estimation (MLE), to derive unbiased estimators and confidence intervals for the attenuation coefficient, which is proportional to leaf area density. The new estimators and confidence intervals are defined at voxel scale, and account for the number of beams crossing the voxel, the inequality of path lengths in voxel, the size of vegetation elements, as well as for the variability of element positions between vegetation samples. They are completed by numerous numerical simulations for the evaluation of estimator consistency and efficiency, as well as the assessment of the coverage probabilities of confidence intervals.• Although commonly used when the beam number is low, the usual estimators are strongly biased and the 95% confidence intervals can be ≈ ±100% of the estimate.

Reliable measurements of the 3D distribution of Leaf Area Density (LAD) in forest canopy are crucial for describing and modelling microclimatic and eco-physiological processes involved in forest ecosystems functioning. To overcome the obvious limitations of direct measurements, several indirect methods have been developed, including methods based on Terrestrial LiDAR scanning (TLS). This work focused on various LAD estimators used in voxel-based approaches. LAD estimates were compared to reference measurements at branch scale in laboratory, which offered the opportunity to investigate in controlled conditions the sensitivity of estimations to various factors such as voxel size, distance to scanner, leaf morphology (species), type of scanner and type of estimator. We found that all approaches to retrieve LAD estimates were highly sensitive to voxel size whatever the species or scanner and to distance to the FARO scanner. We provided evidence that these biases were caused by vegetation heterogeneity and variations in the effective footprint of the scanner. We were able to identify calibration functions that could be readily applied when vegetation and scanner are similar to those of the present study. For different vegetation and scanner, we recommend replicating our method, which can be applied at reasonable cost. While acknowledging that the test conditions in the laboratory were very different from those of the measurements taken in the forest (especially in terms of occlusion), this study revealed existence of strong biases, including spatial biases. Because the distance between scanner and vegetation varies in field scanning, these biases should occur in a similar manner in the field and should be accounted for in voxel-based methods but also in gap-fraction methods.

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