Diffraction of light by volume transparencies

The coupled waves method is used to analyze the diffraction of light by randomly modulated volume transparencies (for example, biological objects). A system of coupled equations is solved by reducing them to integrodifferential equations for the amplitudes of the incident and diffracted waves, which are easily solved in the case of randomly modulated transparencies. It is shown that diffraction attenuates the incident wave exponentially and that the wave vectors of the diffracted waves are concentrated near an Ewald sphere. It is also shown that the Fraunhofer diffraction pattern of a volume transparency is a weighted sum of the diffraction patterns of all cross sections of the transparency.