The paper examines the phenomenon of scattering of electromagnetic radiation by a random inhomogeneous medium, taking into account the coherence characteristics of the radiation field. In § 2 the case of a finite scattering volume irradiated with light having a high degree of coherence is discussed. The conclusion is that the angular spectrum of intensity is expressed as a sum of two terms: the first corresponds to the ideal case of an indefinitely large volume and the second represents the noise, the ‘speckleness’ which is superimposed, due to the finite size of the irradiated volume. In § 3 the treatment is generalized to sources having a finite extent, and a more general formula, which accounts for the partial coherence of the radiation, is deduced. The last section shows that, as the coherence factor cancels the second term representing the noise, the speckleness does not generally occur. Examining how the Fraunhofer condition is different and more relaxed for partially coherent light, compared with coherent radiation, it is concluded that partially coherent radiation is more convenient for scattering techniques. © 1969 Taylor & Francis Group, LLC.