Focusing schlieren with white light extended sources, an optical processing technique used to visualize phase images, is mathematically formalized in terms of Fourier optics and therefore classified as a typical procedure of optical image processing. The visualization is obtained by completely or partially stopping the image of the light source. In these two situations, the relation between the resulting image intensity and the phase that must be visualized is described by different equations. In the first case, the result is similar to that obtainable by the strioscopy (dark-field technique) operated in coherent optics; in the second case, the result resembles that of the coherent schlieren. The mathematical treatment is carried out using an extended white light source codified by a grid: the filter is the negative of the source grid image, centered or shifted with respect to the image itself. Experimental phase images are visualized by means of the codified source and by an incandescent bulb.