This is a short reference note on limb darkening by Alberto M. Vasquez (IAFE, alberto.vasquez@conicet.gov.ar). 

It contains simple formulae and reference numbers for limb darkening that we use in our solar rotational tomography codes to treat white-light coronagraph images for determination of the 3D distribution of the low-to-middle corona electron density.

Using the simplest limb-darkening parametric model (Eq. (4) in Minnaert 1930), one finds the ratio of the disk-averaged brightness <I> to the disk center (peak) brightness I0 to be:

<I> / I0 = 1 - u/3   (Eq. 10 in the same paper).

where u is the limb-darkeing coefficient defined as

u = 1 - I_limb / I0.

For various coronagraphs currently included in our tomography codes, the table below indicates their bandpass range D_lambda, center wavelength lambda_0, the Neckel & Labs (1994) value of <I>/I0 at lamba_0, and the derived value of u according to Eq. (10) above.

---------------------------------------------------------
         D_lambda (nm)   lambda_0 (nm)    <I>/I0     u
---------------------------------------------------------
 Metis    540-640           590            0.81     0.57
 C2       580-640           610            0.82     0.54
 KCOR     720-750           735            0.85     0.45
 NFI      450-750           600            0.81     0.57
                            570(*)         0.81     0.57
                            530(+)         0.80     0.60
 ASPIICS  536-566           551       	   0.80	    0.60
---------------------------------------------------------
(*) This is not the bandpass mean, but the lambda of peak transmission.
(+) This is the NFI HEADER.WAVELNTH value.