In stereovision systems, the depth information of objects in the scene can be obtained by estimating the disparity, i.e. the displacement of corresponding pixels in the image pair. In this paper a new FFT-based algorithm for disparity estimation is proposed. The phase difference between the two images is calculated at several frequencies for each pixel. These phase differencies have a linear coherence which can be used to make the approach robust and to avoid local errors. The resulting disparity can then be estimated from the gradient of these phase differencies. In the second part, these disparity maps are used for an efficient stereo image coding approach. Here, the transmission of both left and right image is not necessary. At the receiver, e.g. the right image can be reconstructed having only the left image and the disparity map.