You can estimate the LAI with the following formula: LAI = A / W * Y
A = added area of all leaves of the subsample [m²]
W = added dry matter weight of all leaves of the subsample [g]
Y = dry matter leaf yield of the plot [g/m²]
(Source: Röver A., Koch H.-J. (1995): Indirect Determination of Leaf Area Index of Sugar Beet Canopies in Comparison to Direct Measurement. J. Agronomy & Crop Science 174:189-195.)
The formula is normally used for field experiments, so you should modify it. For Y you will probably need the surface of the pot and the number of plants per pot to calculate the plant density. If you have only one plant per pot W will be equal to Y.
You can measure the leaf area (A) non-destructively by multiplication of legth * width * factor. The factor can range between 0,65 and 0,8 (KVET et al. 1971, HATFIELD et al. 1976).
I agree with the answer of Jorita Krieger. There is a "rudimentary" method that you can use, it consists in put the leave in a paper a make a copy, there is free programs that calculate the area of the leaves by discrimination between the black and white areas. By aplying different mathematical formulas you can obtain this data also.
SIGMA SAN PRO
http://www.youtube.com/watch?v=BFVkfRFOmSo
Using photoshop : http://www.youtube.com/watch?v=mBFDgkz7yWQ
Some references: (Danson & Curran, 1993; Peterson et al, 1987; Spanner et al, 1990; Chen & Cihlar, 1996; Nemani et al, 1993; Fassnatch et al, 1997)
Leaf area index is applicable to field experimentation. It is suffice to estimate leaf area in pot experiments. The area covered by crop grown in pots would definitely be more than the area of the the pot used. Thus, estimation of leaf area index in such condition would give erroneous value. Since leaf area index is estimation of area of land covered by leaves formed by the crop cultivated. Technically, it is not right to estimate LAI in pot trial but the area of the leaves (LA) formed could be evaluated.
Flag leaf area was calculated in centimetre squares after the anthesis stage by measuring the mean of the flag leaf area from 10 plants randomly taken from the centre lines of each experimental unit as shown below.
Leaf area index = maximum length × maximum width × 0.95