A non-destructive testing technique to obtain information on the electrical structure in semiconductor materials involves traversing the material surface with a laser beam, and measuring induced currents generated by the beam's interaction with the electrical field. A mathematical model has been established, and the inverse problem of reconstructing the electrical structure from the current image has been studied. Here we obtain explicit solutions for simple structures (p-n and p-n-p junctions) in the asymptotic limit of strong doping. Comparison with numerical results shows that the asymptotic solutions are quite accurate. These solutions may provide a quick way to identify the doping profile by matching actual current signals to a class of simple functions.