The problems of developing an optical system to perform image Hadamard transforms are discussed. The method involves parallel-successive calculations of the elements of the matrix of spectral components resulting from the decomposition of an initial image into Walsh functions. The basic unit of the optical system realizing this method is an integrator representing a projecting optical system with defocusing in one of the directions. The procedure of the choice of the parameters of such a unit pulse response is described, and the experimental results are given. The matrix of 8 x 8 spectral components was calculated. The calculation error is equal to 1.5-2%. The possibilities of the suggested method for image coding are noted.