Calculating Limb Darkening Coefficient

I calculated the Limb Darkening Coefficient from the Linear Limb Darkening law assuming a plane-parallel solar atmosphere.:

As a base, I used a picture from the solar disk taken during the recent solar eclipse with an OIII filter (500nm). Using ImageJ software I was able to plot the intensity (limb darkening) graph by retrieving the gray intensity data per pixel. Using above formule, I calculated the Linear Limb Darkening coefficient (LDC). To calculate the LDC, I took the average LDC's of the radius between 0,9 and 0,3 . This results in a LDC of 0,22 (500nm)

I put this data together in a graph which combines the intensity graph from ImageJ and the theoretical derived graph with a LDC of 0,22.

Discussion:
In the literature I found LDC's  of around 0,8 (eg. Dias-Cordoves see this link)  

Conclusion : my LDC calculation is not really near the ones published in different studies. 

See also interesting LD calculators like the one for the James Webb Telescope. See this link