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In the 1980s, E. Wolf proposed a new theory of partial coherence formulated in the space-frequency domain. The fundamental result of this theory is the fact that a stationary optical field of any state of coherence may be represented as a superposition of coherent modes, i.e., elementary uncorrelated field oscillations that are spatially completely coherent. The importance of this result can hardly be exaggerated since it opens a new perspective in understanding and interpreting the physics of generation, propagation, and transformation of optical radiation. In this chapter, using primarily the basic book by Mandel and Wolf, we give an outline of the theory of optical coherence in the space-frequency domain and coherent-mode representations of an optical field. We also consider the concept of the effective number of modes needed for the coherent-mode representation of an optical field, and give a brief survey of the known coherent-mode representations of some model sources, namely, the Gaussian Schell-model source, Bessel correlated source, and the Lambertian source.
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