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

Inverse obstacle scattering problems with a single incident wave and the logarithmic differential of the indicator function in the Enclosure Method