X-ray spatial frequency heterodyne imaging

We derive an expression for the electric field at the image plane from the Kirchhoff-Fresnel integral for a grating in contact with an object in an x-ray, in-line imaging configuration that shows the grating to give a heterodyning effect. We also show how image contrast in a harmonic of the grating is enhanced depending on the first space derivative of the phase function. Experiments are reported where a Fourier component of the image intensity gives contrast at the edges of objects significantly larger than that found with conventional in-line phase contrast imaging.