Coherency matrix formulation for partially coherent imaging to evaluate the degree of coherence for image

This paper defines a matrix from which coherence property of imaging by partially coherent Koehler illumination is determined. The matrix termed coherency matrix in imaging system is derived by the space average of a product of a column vector and its transpose conjugate where each row of the column vector represents mutually incoherent light. The coherency matrix in imaging system has similar properties to the polarization matrix that is utilized for calculating the light intensity and degree of polarization of polarized light. The coherency matrix in imaging system enables us to calculate not only image intensity but also degree of coherence for image. Simulation results of the degree of coherence for image given by the coherency matrix in imaging system correspond to the complex degree of coherence obtained by the van Cittert-Zernike theorem.