How to get the luminosity function from a lensed field

I just want to try to recall the discussion in last week. However, there are still things I have lost.

There could be two methods to complete this job in my knowledge.

(1)  The luminosity function can be described as a formula with several parameters, so you just need to estimate the values to solve the problem. By comparing the lensed luminosity function based on the lensing map and  the observed number density of galaxies, you can get the best fit parameters.

(2)  for each point in the lensed field, you have already known the magnification and you can obtain the volume and the magnitude limit. So you can repeat this process for the whole field to get the real volume for a particular magnitude range. You may know what to do next. Just use the simple equation desity = N/V.