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We present a new method for quantitative nondestructive characterization of objects by x-ray phase-contrast imaging. Spatial distributions of the projected values of the complex refractive index in the sample are reconstructed by processing near-field images collected at a fixed sample-to-detector distance using a polychromatic incident beam and an energy-sensitive area detector, such as a CCD used in the photon-counting spectroscopy mode. The method has the potential advantages of decreased radiation dose and increased accuracy compared to conventional techniques of x-ray imaging.