AbstractWe study the interpolation problem for solutions of the two‐dimensional Helmholtz equation, which are sampled along a line. The data are the function values and the normal derivatives at a discrete set of point sensors. Awave transformis used, analogous to the common Fourier transform. Theinversewave transform defines the Hilbert space for oscillatory Helmholtz solutions. We thereby introduce an interpolant that has some advantages over the usual sincxin the Whittaker–Shannon sampling in one dimension; in particular, coefficients of the two‐dimensional solution are invariant under translations and rotations of the sampling line. The analysis is relevant for the optical sampling problem by sensors on a screen. © 1995 John Wiley&Son