Many computer vision applications rely on feature matching, hence the need for computationally efficient and robust 4D light field (LF) feature detectors and descriptors for applications using this imaging modality. In this paper, we propose a novel LF feature extraction method in the scale-disparity space, based on a Fourier disparity layer representation. The proposed feature extraction takes advantage of both the Harris feature detector and SIFT descriptor, and is shown to yield more accurate feature matching, compared with the LiFF light field feature with low computational complexity. In order to evaluate the feature matching performance with the proposed descriptor, we generated synthetic LF datasets with ground truth matching points. Experimental results with synthetic and real datasets show that, our solution outperforms existing methods in terms of both feature detection robustness and feature matching accuracy.