Van Cittert – Zernike – Goodman Theorem
The classical Van Cittert – Zernike theorem describes the degree of mutual coherence of radiation from a completely incoherent source of a limited size at a great distance from the source.
J. Goodman has generalized this theorem for sources of quasihomogeneous partially coherent radiation with a relatively small coherence area.
In the article, the case of arbitrary characteristics of cross-section coherence for a beam of radiation of a limited size is considered.
The concept of integrated coherence function for a beam is introduced -
G( ) = , G(0) = P,
as well as integrated degree of coherence for a beam – g ( ) = G( )/P On the basis of these functions, expressions of the generalized Van Cittert – Zernike – Goodman theorem, connecting the characteristics of radiation in near and far zones are obtained for any size of cross-section coherence.
The obtained generalization of the Van Cittert – Zernike – Goodman theorem is a development of ideas of J.W. Goodman under the theory of distribution of partially coherent radiation. It also allows describing transformation on the large distances of radiation beams of any degree of coherence.
The introduced concepts of integrated degree and integrated indicator of coherence for a radiation beam may appear useful tools for analysis of coherence characteristics of directed beams of radiation with limited aperture – in particular laser beams with random inhomogeneous.