  In this paper, we construct and investigate two supersymmetric versions of
the Fokas-Gel'fand formula for the immersion of 2D surfaces associated with a
supersymmetric integrable system. The first version involves an infinitesimal
deformation of the zero-curvature condition and the linear spectral problem
associated with this system. This deformation leads the surfaces to be
represented in terms of a bosonic supermatrix immersed in a Lie superalgebra.
The second supersymmetric version is obtained by using a fermionic parameter
deformation to construct surfaces expressed in terms of a fermionic supermatrix
immersed in a Lie superalgebra. For both extensions, we provide a geometrical
characterization of deformed surfaces using the super Killing form as an inner
product and a super moving frame formalism. The theoretical results are applied
to the supersymmetric sine-Gordon equation in order to construct super soliton
surfaces associated with five different symmetries. We find integrated forms of
these surfaces which represent constant Gaussian curvature surfaces and
nonlinear Weingarten-type surfaces.
