Diffraction pattern representation of images (optical Fourier transform or Wiener spectrum) is very useful for computer image processing. An accurate analysis of spatial frequencies requires very well corrected lenses, and the diffraction pattern must be sampled by means of a moving detector or a stable multiple detector array strictly in the Fourier plane. A theoretical analysis of obtaining and sampling the diffraction pattern is provided. Fourier diffractometry with a directionally changed incident light wave can be realized without the above-mentioned limitations. In this method, a single static detector is placed at the rear focus of a Fourier transform lens while the sampled diffraction pattern is moved over the Fourier plane. Suitable movement of the diffraction pattern can be obtained when the analyzed image is continuously illuminated with a parallel light beam whose inclination is changed with respect to the optical axis of the Fourier transform lens. This idea was tesied experimentally and applied to a new generation of compact diffractometers with unsophisticated transforming lenses.