Magnetic helicity is a physical quantity that measures the complexity in the field lines. It is given by a volume integral over scalar product of magnetic field and its vector potential. Direct computation of magnetic helicity in the solar atmosphere is not possible in want of observations to compute the volume integral. We have clarified the physical meaning of and its relation with the magnetic helicity. An analytical bipole was generated to study the effect of polarimetric noise on the estimation of various magnetic parameters. We then examined the fine structures of sunspots in terms of...