This paper describes the Shannon entropy in a partially coherent imaging system with Koehler illumination. Numerical simulation shows that the entropy has a one-to-one relationship with the normalized mutual intensity given by the van Cittert–Zernike theorem. Analytical evaluation shows that the entropy is consistent with the definition of coherence and incoherence, which is also verified by numerical simulations. Additional numerical experiments confirm that the entropy depends on the source intensity distribution, polarization state of the source, object, and pupil. Therefore, the entropy quantitatively measures the degree of coherence of the partially coherent imaging system.
© 2011 Optical Society of America
Coherence and Statistical Optics
Original Manuscript: September 10, 2010
Revised Manuscript: January 5, 2011
Manuscript Accepted: January 9, 2011
Published: February 28, 2011
Kenji Yamazoe and Andrew R. Neureuther, "Numerical experiment of the Shannon entropy in partially coherent imaging by Koehler illumination to show the relationship to degree of coherence," J. Opt. Soc. Am. A 28, 448-454 (2011)