Leaf Area Index (LAI) is the ratio of foliage area to ground area. LAI can be determined directly by taking a statistically significant sample of foliage from a plant canopy, measuring the leaf area per sample plot and dividing it by the plot land surface area. The best indirect method is hemispheric photography and optical sensors :)

In accordance with Andrew Pegman, field experience would suggest to 1) establishing relatively long transects, the elevation gradient may be added along step slopes; 2) selecting dominant and possibly healthy trees at regular distances; 3) taking 2-4 LAI measures per each selected crown (i.e: N-E-S-W); 4) measuring the LAI of all the selected crowns either upward and downward the slope (the two ways being separate); 5) calculating both the average LAI per each crown and the average LAI of the upward and downward measurements; 6) comparing both the types of measurements. For example, the average LAI given by averaging the sum of the individual measurements of trees and the average LAI given by dividing the LAI of each transect by the number of selected trees; 7) comparing the respective distributions, means, and standard deviations; all the rest is about statistics.

Then you may want to use the results to calibrate parameters/values produced by remote sensing (broad sense).

Thank you for your answers. 

Do you think that hemispheric photography could work also for individual trees? The trees are in a forest environment, thus, it is difficult to remove the effect of neighbouring trees. 

... Actually, it is. You may try to set the angle of view of the LAI-meter (there should be 4-5 positions already set in the device) from the open field to the most restricted field - in practice, from the full crown to the portion at the top of the tree. The open-crown view provides the best LAI estimate but comprehends the influence of the surrounding trees. Viceversa, the crown top should be free from the others' crowns shade but provides a result that may not apply to the entire crown ... Part A) One may take measurements of the LAI with different angles and identify in what range the differences in LAI vary the less between different angles. This would provide a practical field value that can be compared and averaged with the other individual LAIs of the transect. Once that the range of angles of view above  or below which the LAI varies little is identified, you may have a handy parameter value that helps to understand what (vertical) portion of the crowns is less or little influenced by sorrounding trees. Part B) You may proceed to set the hemispheric photographs by shooting and/or measuring and/or accepting only the values that fit within the range/ray/section of the crown that corresponds to the portion relatively free from influences as found in Part A)