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In this article we examine the use of a curvature wave-front sensor to accurately measure the Laplacian of the line-integrated electron density formed in laser-produced and Z-pinch plasma experiments. Specifically, we propose designs for single shot curvature wave-front sensors capable of quantitatively determining the electron density present in a high density plasma. Wave optics simulations of the proposed designs are presented and are shown to quantitatively reconstruct the phase of a light beam passing through the simulated plasma. A laboratory demonstration of the single shot curvature wave-front sensor is also presented. For this demonstration, a liquid-crystal spatial light modulator is used to introduce a spatially varying phase, thus simulating a phase profile that could occur when a probe passes through a plasma. The phase change measured by the curvature sensor is then computed and shown to accurately reproduce the phase written to the spatial light modulator. Merits associated with the use of a curvature sensor are also discussed. © 2003 American Institute of Physics.