Weighting for 1D fitting

There are many different ways to put a weight to a datapoint for surface brightness measurement. An error can be determined from its dispersion from the average or one adraddressesweighting depending on the position or strength of the datapoint.
In the case of one dimensional fits, weighting is an absolute necessity, because it has not the constraint of the radial behaviour on the other cuts and is more sensitive to variations in its own profile. Each 1D profile can have its own $z_n$, whereas there is only one $z_n$ for the 2D fit. Because we fit our surface brightness profiles in magnitudes the errors are determined from the variation in the residual background, using the formula

$$\mu_{\pm}\ = -2.5\ \textrm{log} \left(\frac{I_1\pm3\sigma}{\textrm{pixel}^2}\right)\ +\ \textrm{zeropoint}\ ,$$ (15)

where $I_1$ is the intensity of the datapoint, $\sigma$ the variation in the sky background and pixel the size of the pixel in arcseconds. The logarithmic conversion causes the errorbars to be unequal on the lower and higher side, which makes them difficult to use for correct weighting.
So to retrieve a weighting by error according to the intensity we add the square root of the intensity of each datapoint along the profile, divided by the intensity of the first datapoint to the $\chi^2$ calculation. The square root was used because differences in intensity grow larger rapidly due to its logarithmic behaviour.