This chapter focuses on the impact of partial coherence on the propagation of optical beams inside a GRIN medium. Section 11.1 introduces the basic coherence-related concepts needed to understand the later material. Section 11.2 uses the evolution of cross-spectral density to study whether periodic self-imaging, an intrinsic property of a GRIN medium, is affected by partial coherence of an incoming beam. Section 11.3 employs the Gaussian-Schell model to discuss how the optical spectrum, the spectral intensity, and the degree of coherence associated with a Gaussian beam change with the beam’s propagation inside a GRIN medium. The focus of Section 11.4 is on Gaussian beams that are only partially polarized. The concept of the polarization matrix is used to study how the degree of polarization evolves when such a partially coherent Gaussian beam is transmitted through a GRIN medium

To have some basic understanding of optical coherence, we discuss temporal coherence and spatial coherence quantitatively in the beginning of the Chapter. We then concentrate on spatial coherent image processing, followed by spatially incoherent image processing. While spatial coherent imaging systems lead to the concept of coherent point spread function and coherent transfer function, spatially incoherent imaging system introduces intensity point spread function and optical transfer function. Scanning image processing is also covered in the chapter, illustrating an important aspect in that a mask in front of the photodetector can change the coherence properties of the optical system. Finally, two-pupil synthesis of optical transfer functions is discussed, illustrating bipolar processing in incoherent imaging systems.