  This paper gives a remark on the Enclosure Method by considering inverse
obstacle scattering problems with a single incident wave whose governing
equation is given by the Helmholtz equation in two dimensions. It is concerned
with the indicator function in the Enclosure Method. The previous indicator
function is essentially real-valued since only its absolute value is used. In
this paper, another method for the use of the indicator function is introduced.
The method employs the logarithmic differential with respect to the independent
variable of the indicator function and yields directly the coordinates of the
vertices of the convex hull of unknown polygonal sound-hard obstacles or thin
ones. The convergence rate of the formulae is better than that of the previous
indicator function. Some other applications of this method are also given.
